Spintronic Memristor
1. INTRODUCTION
Generally when most people think about electronics, they may initially think of products such as cell phones, radios, laptop computers, etc. others, having some engineering background, may think of resistors, capacitors, etc. which are the basic components necessary for electronics to function. Such basic components are fairly limited in number and each having their own characteristic function. Memristor theory was formulated and named by Leon Chua in a 1971 paper. Chua strongly believed that a fourth device existed to provide conceptual symmetry with the resistor, inductor, and capacitor. A device linking charge and flux (themselves defined as time integrals of current and voltage), which would be the memristor, was still hypothetical at the time. However, thirty-seven years later, on April 30, 2008, a team at HP Labs led by the scientist R. Stanley Williams announced the discovery of a switching memristor. Based on a thin film of titanium dioxide, it has been presented as an approximately ideal device. The reason that the memristor is radically different from the other fundamental circuit elements is that, unlike them, it carries a memory of its past. When you turn off the voltage to the circuit, the memristor still remembers how much was applied before and for how long. That 's an effect that can 't be duplicated by any circuit combination of resistors, capacitors, and inductors, which is why the memristor qualifies as a fundamental circuit element. Memristor has very broad applications that include non-volatile memory, signal processing, control and learning system etc. Shortly after the demonstration of memristance, researchers began looking for this property in spintronics—a relatively new branch of electronics itself. In this ever changing world of technology, products of technology have evolved at an extremely quick rate. Computers have been doubling in speed in no time flat, audio recording has evolved, though more slowly, from albums now to mpeg players that can store around 700 minutes worth of music, and the gaming console business, not to mention all the other areas of advancement. But, getting back to computer speed and storage, the advancement in this category is starting to slow down (there can only be so many “switches/transistors” placed on a chip). So to deal with storage and speed advancements some new research is being done. One of these areas is that of spintronics.
Spintronics is at the heart of recent advances in hard-drive data density and the niche nonvolatile memory known as MRAM. The formal definition of spintronics is “the study of the role played by electron (and more generally nuclear) spin in solid state physics, and possible devices that specifically exploit spin properties instead of or in addition to charge degrees of freedom”. A simpler definition is that spintronics is a “new branch of electronics in which electron spin, in addition to charge, is manipulated to yield a desired outcome”.
Nano-scale spintronic memristor has been proposed based upon spin torque induced magnetization motion and spin transport at semiconductor/ferromagnet junction . Realizing memristive effects in spintronic device not only provides understanding of a wide range of current-voltage behaviours observed in nanoscale spintronic system, but also sheds light on how we should look at existing/proposed magnetic devices and herald new applications.
Fig. 1
2. HISTORY
The transistor was invented in 1925 but lay dormant until finding a corporate champion in Bell Labs during the 1950s.Then in 2008,Hewlett-Packard Labs demonstrated a practical memristor, the fourth passive circuit element after the resistor, and the capacitor the inductor into the electronics mainstream. Postulated in 1971, the “memory resistor” represents a potential revolution in electronic circuit theory similar to the invention of transistor.Now, researchers have come up with a new type of memristor called spintronic memristor that exploits the spin property of electron. The history of the memristor can be traced back to nearly four decades ago when in 1971, Leon Chua, a University of California, Berkeley, engineer predicted that there should be a fourth passive circuit element in addition to the other three known passive elements namely the resistor, the capacitor and the inductor. He called this fourth element a “memory resistor” or a memristor. Examining the relationship between charge, current, voltage and flux in resistors, capacitors, and inductors in a 1971 paper, Chua postulated the existence of memristor. Such a device, he figured, would provide a similar relationship between magnetic flux and charge that a resistor gives between voltage and current. In practice, that would mean it acted like a resistor whose value could vary according to the current passing through it and which would remember that value even after the current disappeared. But the hypothetical device was mostly written off as a mathematical dalliance. However, it took more than three decades for the memristor to be discovered and come to life. Thirty years after Chua’s Proposal of this mysterious device, HP senior fellow Stanley Williams and his group were working on molecular electronics when they started to notice strange behavior in their devices. One of his HP collaborators, Greg Snider, then rediscovered Chua 's work from 1971. Williams spent several years reading and rereading Chua 's papers. It was then that Williams realized that their molecular devices were really memristors.
Fig.2. 17 memristors in a row
Moore’s law on how the speed of computers will keep on doubling is slowing down, and it has been estimated that in the next 10 years or so we will have reached the limit on speed of traditional microprocessors. So back in the early 90’s research was being done on how to make microprocessors better and faster. Research into areas like nanotubes was done, but not until 1998 did researchers set their sights onto a different property of electrons i.e., spin. Researches in the field of spintronics could lead to “quantum computers”.
As we build transistors and other components with nanoscale dimensions, processors and memories are becoming so dense that even their infinitesimal individual currents are combining to produce scorching heat. Furthermore, quantum effects that were negligible before are now so pronounced that they 're threatening to render circuits inoperable. The upshot is that we 're fast approaching the point when moving charge is not going to be enough to keep Moore 's Law chugging along.
Spin is a fundamental yet elusive quantum attribute of electrons and other subatomic particles. It is often regarded as a bizarre form of nanoworld angular momentum, and it underlies permanent magnetism. What makes spin interesting for electronics is that it can assume one of two states relative to a magnetic field, typically referred to as up and down, and you can use these two states to represent the two values of binary logic—to store a bit, in other words.
The development of spin-based electronics, or spintronics, promises to open up remarkable possibilities. In principle, manipulating spin is faster and requires far less energy than pushing charge around, and it can take place at smaller scales. The holy grail in the field is a spin transistor. Chips built out of spin transistors would be faster and more powerful than traditional ones and, farther down the road, may feature such new and remarkable properties as the ability to change their logic functions on the fly.
3. DEVICE THEORY
The original definition of memristor is
dϕ = Mdq
where q is the electric charge, ϕ is the magnetic flux, and M is the memristance. Because magnetic flux is the integration of voltage and charge is the integration of current, it is easy to show that memristance can be defined as
M(q) = (dϕ/dt)/(dq/dt) = VI
What makes memristance different from an ordinary constant resistance or a current- or voltage-dependent nonlinear resistance is that memristance is a function of charge, which depends on the hysteretic behavior of current/voltage profile. The aforementioned definition of memristor can be generalized to
V = M(w)I dw/dt = f(i,w)
where w is an implicit state variable (e.g., charge) that depends on the integral of current profile over time. V and i are the voltage and current, respectively. Again, the key point in the definition (3) of memristor is its dependence on the historic behavior of current (or, for example, the integral of current profile over time).
This circuit element shares many of the properties of resistors and shares the same unit of measurement (ohms). However, in contrast to ordinary resistors, in which the resistance is permanently fixed, memristance may be programmed or switched to different resistance states based on the history of the voltage applied to the memristance material. This phenomena can be understood graphically in terms of the relationship between the current flowing through a memristor and the voltage applied across the memristor. In ordinary resistors there is a linear relationship between current and voltage so that a graph comparing current and voltage results in a straight line. However, for memristors a similar graph is a little more complicated as shown in Fig. 3 illustrates the current vs. voltage behavior of memristance. In contrast to the straight line expected from most resistors the behavior of a memristor appear closer to that found in hysteresis curves associated with magnetic materials. It is notable from Fig. 3 that two straight line segments are formed within the curve. These two straight line curves may be interpreted as two distinct resistance states with the remainder of the curve as transition regions between these two states.
Fig. 3.. Current vs. Voltage curve demonstrating hysteretic effects of memristance. Fig. 3 illustrates an idealized resistance behavior demonstrated in accordance with Fig.4 wherein the linear regions correspond to a relatively high resistance (RH) and lowresistance (RL) and the transition regions are represented by straight lines. Fig . 4. Resistance vs. Voltage
Thus for voltages within a threshold region (-VL2<V<VL1 in Fig. 4) either a high or low resistance exists for the memristor. For a voltage above threshold VL1 the resistance switches from a high to a low level and for a voltage of opposite polarity above threshold VL2 the resistance switches back to a high resistance.
Spin is the property that is responsible for magnetism—materials are magnetized when a majority of their electrons have their spins pointing in the same direction. Melding memristors and spintronics yields devices whose resistance changes according to the spin of electrons passing through it, and those devices will remember that resistance.
Spintronics (short for spin-based electronics), sometimes called magnetoelectronics, is the term given to microelectronic devices that function by exploiting the spin of electrons. The most common use of spintronics today is in computer hard drives. Here memory storage is based on giant magnetoresistance (GMR) a spintronic effect. There is current research focusing on bringing magnetic random-access memory (MRAM) to market. Spintronic based MRAMs should rival the speed and rewritability of conventional RAM and retain their state (and thus memory) even when the power is turned off. Motorola has recently developed a 256-kb MRAM) based on a single magnetic tunnel junction and a single transistor. This MRAM has read/write cycles of less than 50 nanoseconds. |
Fig 5. A 256-kb MRAM based on modern spintronics technology. (Image courtesy of Motorola Corp.)
Spintronics focuses on two types of materials. Ferromagnetic metallic alloys are currently used for magnetoelectronic devices. Ferromagnetic semiconductors, however, are attracting greater attention. If the manufacture of ferromagnetic semiconductors becomes practical, the current microchip industry could switch over to these types of spintronic devices with relatively little change in their infrastructure. The primary barrier to the synthesis of ferromagnetic semiconductors is finding a way to inject spin-polarized currents (spin currents) into a semiconductor.
Most of the work in making semiconductors ferromagnetic has focused on II-VI semiconductors such as CdTe (Aldrich product 25,654-4) or ZnSe (Aldrich products 24,461-9 and 55,301-8).29 Here the semiconductors are doped with magnetic ions (such as manganese) to create small pockets of magnetic character resulting in a diluted magnetic semiconductor (DMS). More recent work has focused on doping III-V semiconductors such as GaAs (Aldrich product 32,901-0) into a DMS state. With III-V semiconductors, however, the magnetic elements are much less soluble than in II-VI semiconductors making them much more difficult to inject into a material like GaAs. Molecular beam epitaxy (MBE) has proven to be an excellent technique in overcoming the difficulty in making DMS III-V materials.
As new and better techniques for synthesizing ferromagnetics are developed, their prospects for revolutionizing the microelectronic industry increases, spintronics will sure play a major role in the next generation of information storage devices.
Let us consider a spintronic device where the current electron spin changes the magnetization state of the device.. The resistance is caused by the spin of electrons in one section of the device pointing in a different direction than those in another section, creating a “domain wall,” a boundary between the two states. Electrons flowing into the device have a certain spin, which alters the magnetization state of the device. Changing the magnetization, in turn, moves the domain wall and changes the device’s resistance. The magnetization state of the device is thus dependent upon the cumulative effects of electron spin excitations.
The different designs can be flipped between high- and low-resistance states at different rates, from picoseconds to microseconds, each preferable in different applications. For reading a hard drive, for instance, you’d want to sense changes in a magnetic field in a few picoseconds, whereas for something like a radiation sensor, you’d want a response time measured in microseconds.
In the next figure, three examples of spintronic memristors based upon spin-torque-induced magnetization switching and magnetic domain wall motion are being shown.
Fig.6. Spintronic memristors. (a) MTJ with spin-torque-induced magnetization switching. (b) Thin-film element with spin-torque-induced domain-wall motion. (c) Spin valve with spin-torque-induced domain-wall motion in the free layer. 3.1 Current Induced Domain Wall Motion
In magnetism, a domain wall is an interface separating magnetic domains. It is a transition between different magnetic moments and usually undergoes an angular displacement of 90° or 180°. Domain wall is a gradual reorientation of individual moments across a finite distance. The domain wall thickness depends on the anisotropy of the material, but on average spans across around 100-150 atoms.
The energy of a domain wall is simply the difference between the magnetic moments before and after the domain wall was created. This value is usually expressed as energy per unit wall area.
Non-magnetic inclusions in the volume of a ferromagnetic material, or dislocations in crystallographic structure, can cause "pinning" of the domain walls (see animation). Such pinning sites cause the domain wall to seat in a local energy minimum and external field is required to "unpin" the domain wall from its pinned position. The act of unpinning will cause sudden movement of the domain wall and sudden change of the volume of both neighbouring domains. This causes Barkhausen noise and in effect it is most likely to be the source of magnetic hysteresis.
When a current is passed to a ferromagnetic wire that contains domain walls, the flowing electrons exert a pressure on the domain wall that tends to drive the domain wall in the direction of the electron flow. This current control of domain wall motion is proposed as a basis for a memory device in which the information is stored in magnetic domains. The domain walls between the domains can be moved past a read out device by a current flowing through the wire. Such a device could potentially have a high storage density, fast read out, and non-volatility. Such current induced domain wall motion is currently studied in the Electron Physics Group using Scanning Electron Microscopy with Polarization Analysis (SEMPA).
Experimentally, current induced domain wall motion is typically studied in lithographically defined, narrow magnetic wires. The wires are frequently curved or the ends are designed to make it possible to controllably introduce a domain wall into the wire using an applied field. The position of the domain walls can be imaged using techniques such as Magnetic Force Microscopy (MFM) or Scanning Electron Microscopy with Polarization Analysis (SEMPA). Measuring the position before and after a current pulse with a technique like Scanning Electron Microscopy allows an estimate of the wall velocity. Alternatively, the location of the wall could be determined in real time using the Magneto-Optic Kerr Effect (MOKE) or electrically using GMR sandwich structures or through the extra resistance due to anisotropic magnetoresistance (AMR) in a domain wall. Using these various techniques, experimentalists typically determine the wall velocity as a function of current and applied magnetic field and compare with theoretical predictions.
To a first approximation, current induced domain wall motion is quite simple. The flowing electron spins adiabatically follow the magnetization direction because the magnetization exerts a torque on them. There is a reaction torque on the magnetization that is proportional to the current. If the current is uniform, this torque density simply translates the domain wall in the direction of electron flow with a speed that is proportional to the current. There are several factors that complicate this simple description, including damping, non-adiabatic torques, and extrinsic effects like pinning.
We have computed the degree to which the spin adiabatically follow the magnetization. The deviations are small except for rather narrow domain walls. When they are non-negligible, the adiabatic torque becomes non-local and there is a additional non-local torque perpendicular to the adiabatic torque. This torque is referred to as a non-adiabatic torque because it derives from the inability of the electron spins to adiabatically follow the magnetization direction. For realistic walls, this correction is not important.
Fig.7 .A schematic view of the magnetization direction in a domain wall in a narrow wire. As electrons flow through the domain wall, their spins(remain aligned with the magnetization due to a torque exerted by the magnetization. The reaction torque on the magnetization tends to translate it.
The theoretical description of current induced domain wall motion has lead to significant debate associated with how to describe the damping and whether there is an additional torque in the direction of the non-adiabatic torque that arises from the same processes that lead to damping. Even though this torque is physically distinct from the non-adiabatic torque discussed above, it is in the same direction and is frequently called a non-adiabatic torque and less frequently the beta term. It is closely tied to the description of the magnetization damping. The two most commonly used descriptions of the damping are due to Landau and Lifshitz and to Gilbert. In the absence of current induced torques, these can be shown to be equivalent. They remain equivalent in the presence of spin transfer torques, but with different values of this non-adiabatic torque. We argue that the Landau-Lifshitz form of the damping gives a more physical description of current induced domain wall motion. This description emphasizes the importance of the adiabatic torque, which is much larger than its non-adiabatic counterpart.
3.2 Spin Torque Induced Magnetization Switching
Magnetization switching refers to magnetization motion from one equilibrium state to another equilibrium state. The magnetization equilibrium state is determined by magnetic energy minimization with respect to the magnetization vector:
The derivative of magnetic energy to magnetization vector gives a restoring force called effective field:
For magnetization motion under a constant magnetic field H, the effective field is the magnetic field and magnetic energy is Zeeman energy:
Additional energy terms in a magnetic system include exchange energy and anisotropy energy. Exchange energy brings magnetization order in ferromagnetic material. For a spatially distributed magnetization system (where i denotes spatial position), exchange energy prefers to order neighboring magnetization to the same direction: , where < i, j> denotes nearest neighboring positions. Magnetization magnitude at individual spatial location is conserved (=constant). As nano-scale magnetic device scales down, magnetization reversal can be well approximated by the coherent switching mode, where due to exchange ordering effects. In this manuscript, we study coherent magnetization switching with element magnetization described by a magnetization vector with constant magnitude:
.
Exchange energy does not explicitly enter coherent magnetization switching formalism. When the physical property of a device has a spatial direction preference, that property is called anisotropy. The preference for the magnetization to point in a particular direction is the result of magnetic anisotropy energy. There are two types of anisotropy energy. The first one is the crystal anisotropy energy from magnetic material crystal structure. The second one is the shape anisotropy energy. The origin of shape anisotropy comes from magnetic dipole interaction (or magnetostatic interaction). The basic property of magnetostatic interaction is the avoidance of surface magnetic charge accumulation. Figure 1 illustrates shape anisotropy (or demagnetization anisotropy). Starting with a cubic element with magnetization orientation in the vertical direction, two cuts change the element shape to a thin film and an elongated needle. The magnetization direction changes in the process as a result of minimizing shape anisotropy energy. The minimization of shape anisotropy is the same as avoiding surface magnetic charge accumulation. Here we assume the material crystal anisotropy is much smaller than the shape anisotropy and the magnetization direction is determined by shape anisotropy. For magnetic material with much stronger crystal anisotropy, the magnetization direction follows the direction of the crystal anisotropy. For example, in the thin film structure Figure 5(b), if there is huge perpendicular crystal anisotropy, the equilibrium magnetization points in the vertical direction against the thin film plane demagnetization factor. This structure is called perpendicular thin film structure.
The magnetic anisotropy energy can be written in a general form: (1) where is the magnetization saturation, V is the magnetic element volume and is the normalized magnetization are element anisotropy factors (or demagnetization factors) including both shape anisotropy and crystal anisotropy.
Figure 8. Shape anisotropy (or demagnetization factor) effects on magnetization equilibrium states. Starting with a cubic element with magnetization orientation in the vertical direction, two cuts change the element shape to a thin film and an elongated needle. The magnetization direction changes in the process as a result of minimizing shape anisotropy energy. The minimization of shape anisotropy is the same as avoiding surface magnetic charge accumulation.
Spin torque induced magnetization switching involves a structure of two ferromagnetic layers sandwiching an insulating barrier. The magnetization direction of one ferromagnetic layer (reference layer) is fixed by coupling to a pinned magnetization layer, while the magnetization direction of the other ferromagnetic layer (free layer) can be changed. To switch the free layer magnetization to the same direction as the reference layer magnetization, an electric current is passed from the reference layer to the free layer. The injected current electrons have spins pointing to the same and the opposite directions of the reference layer magnetization. After passing through the reference layer, the electrons have a preferred spin orientation direction pointing to the same direction as the reference layer magnetization. This is because most of the electrons with spin pointing to the opposite direction of the reference layer magnetization are reflected back due to interaction between itinerant electron spin and reference layer local magnetization. The polarized current electrons, with a net spin moment in the same direction as the reference layer magnetization, will switch the free layer magnetization to the same direction as the reference layer magnetization. In order to switch the free layer magnetization to the opposite direction of the reference layer magnetization, electron current passes from the free layer to the reference layer. Based upon the same physics argument as before, the electrons reflected from the reference layer have a preferred spin direction opposite to the direction of the reference layer magnetization. These will switch the free layer magnetization to the opposite direction of the reference layer magnetization.
The magnetization dynamics at finite temperature is described by the stochastic Landau-Lifshitz-Gilbert equation with spin torque terms: (2) where is the normalized magnetization vector, time t is normalized by with being the gyromagnetic ratio. is the normalized effective field with normalized energy density , and is the damping parameter. is the thermal fluctuation field, whose magnitude is determined by the fluctuation-dissipation condition at room temperature is the normalized spin torque term with units of magnetic field. The net spin torque T can be obtained through a microscopic quantum electronic spin transport model .
At the level of macroscopic magnetization dynamics, spin torque can be approximated through an adiabatic term proportional to and non-adiabatic term proportional to where is a unit vector pointing to the spin polarization direction.
We consider the dynamic thermal reversal of a magnetic element under combined magnetic field and spin torque excitation. For the case of magnetic field lying in the plane X–Z, the energy of the magnetic system is: (3)
The spin polarization direction is . Here we neglect the non-adiabatic term (which is usually much smaller) and study the case of spin torque with β proportional to the spin torque current magnitude.
Fig. 9. Configuration of the manuscript: magnetic element under combined magnetic field and spin torque current excitations.
4. EXAMPLES OF SPINTRONIC MEMRISTORS
4.1 MAGNETIC TUNNEL JUNCTION A magnetic tunnel junction (MTJ) consists of two layers of magnetic metal, such as cobalt-iron, separated by an ultrathin layer of insulator, typically aluminum oxide with a thickness of about 1 nm. The insulating layer is so thin that electrons can tunnel through the barrier if a bias voltage is applied between the two metal electrodes. In MTJs the tunneling current depends on the relative orientation of magnetizations of the two ferromagnetic layers, which can be changed by an applied magnetic field. This phenomenon is called tunneling magnetoresistance (TMR) which is a consequence of spin-dependent tunneling.
MTJ resistance can be written as a function of angle between the free-layer magnetization direction and the pinned layer magnetization direction
where G˳ is the MTJ conductance when the free-layer magnetization direction is perpendicular to the reference-layer magnetization direction and tunneling magnetoresistance (TMR) is defined as the ratio of the difference between high and low conductance to low conductance. High conductance corresponds to the case of free-layer magnetization parallel to pinned-layer magnetization, and low conductance corresponds to the case of free-layer magnetization anti parallel to pinned layer magnetization.
Nowadays MTJs that are based on transition-metal ferromagnets and Al2O3 barriers can be fabricated with reproducible characteristics and with TMR values up to 50% at room temperature. Recently large values of TMR observed in crystalline MTJs with MgO barriers further boosted interest in spin dependent tunneling. MTJs are nowadays used in magnetic random access memories.
Fig. 10
5.2 SPIN-VALVE STRUCTURE A spin valve consists of two or more conducting magnetic materials, that alternates its electrical resistance (from low to high or high to low) depending on the alignment of the magnetic layers, in order to exploit the Giant Magnetoresistive effect . The magnetic layers of the device align "up" or "down" depending on an external magnetic field. Layers are made of two materials with different magnetic coercivity, which can be seen in the layers ' hysteresis curves. Due to the different coercivities one layer ("soft" layer) changes polarity at small magnetic fields while the other ("hard" layer) changes polarity at a higher magnetic field. As the magnetic field across the sample is swept two distinct states can exist, one with the magnetisations of the layers parallel, and one with the magnetisations of the layers antiparallel.
In the figures below, the top layer is soft and the bottom layer is hard.
Fig. 11
Spin valves work because of a quantum property of electrons (and other particles) called spin. When a magnetic layer is polarized, the unpaired carrier electrons align their spins to the external magnetic field. When a potential exists across a spin valve, the spin-polarized electrons keep their spin alignment as they move through the device. If these electrons encounter a material with a magnetic field pointing in the opposite direction, they have to flip spins to find an empty energy state in the new material. This flip requires extra energy which causes the device to have a higher resistance than when the magnetic materials are polarized in the same direction.
The resistance of this structure depends on domain-wall position x:
R = [(RLx/D) + (RH(D − x)/D)], where D is the free-layer length, RL is the low resistance when magnetizations of the free and reference layers are parallel, and RH is the high resistance when magnetizations of the free and reference layers are antiparallel.
Spin valves are used in magnetic sensors and hard disk read heads. They are also used in magnetic random access memories (MRAM).
5.3 THIN FILM ELEMENT
Thin-film element has varying width and constant thickness . Here, we consider the current induced domain-wall motion in the film-length direction x, as shown.
Fig. 12
The domain-wall velocity in a thin-film element is, in general, a function of driving current density
Where is the current density. The driving force exerted by electrons on the domain wall corresponds to a reaction force applied to electrons by the domain wall, which manifests itself as a wall resistance where μ0 is the vacuum permeability, R0 is the ordinary Hall coefficient, β is a correction factor ≈2, and μ is the domain-wall mobility in the thin-film element, which scales with the thin-film aspect ratio the resistance of the element is a function of domain-wall position x:
5. APPLICATIONS * Multi-bit Data Storage and Logic
Magnetic tunneling junction (MTJ) has been used in commercial recording heads to sense magnetic flux. It is the core device cell for spin torque magnetic random access memory and has also been proposed for logic devices . MTJ in these applications are generally viewed as a two resistance states device. The resistance states are non-volatile and the switching is achieved when reversal current/voltage magnitude passes a critical threshold. Based upon this view, MTJ is characterized as a nonlinear resistance through R-I or R-V curve. * Novel Sensing Scheme
For multi-bit MTJ cells, if the domain wall can be controlled to move and stop continuously across the free layer and/or many stable MTJ layers can be stacked vertically, the memory device can theoretically store continuous information through continuous resistance change.
* Temperature Sensor
The device structure for temperature sensor consists of a long spin-valve strip which includes two ferromagnetic layers: reference layer and free layer. The magnetization direction of reference layer is fixed by coupling to a pinned magnetic reference layer. The free layer is divided by a domain-wall into two segments that have opposite magnetization directions to each other. Domain wall velocity at finite temperature depends upon both spin torque excitation strength and thermal fluctuation magnitude.Domain wall velocity increases as temperature increases.
For temperature sensing, a biasing voltage pulse with constant magnitude is applied to the device. Resistance difference before and after voltage pulse is measured. This resistance difference is calibrated to sense temperature. Higher temperature results a bigger resistance dropping . Spintronic memristor has remarkable characters to sense nano-scale temperature. * Power Management
The ability to accumulate current/voltage through constant current and/or voltage driving strength makes memristor suitable for power monitor. Figure 9 shows connecting a memristor to a circuit either in series or in parallel.
Fig. 13
For connecting memristor in series with circuit (Fig. 10 a), the whole system is owered by a constant voltage V. The energy consumed by the whole system, including both memristor and circuit, is calculated as: E = ∫VIdt = V ∫Idt . For connecting memristor in parallel with circuit (Fig. 10 b), the whole system is powered by a constant current I. The energy consumed by the whole system, including both memristor and circuit, is calculated as: E = ∫VIdt = I ∫Vdt .
* Information Security
Spintronic memristor can also serve the following purpose: when a user reads the data information stored in the device, the administrator who wrote the data knows immediately if he/she checks the device. The advantage of spintronic memristor in information security is due to its resistance dependence upon historic current/voltage profile behavior. In order to access the data stored in a spintronic memristor, the user must excite the device electrically. This excitation activity can be memorized in a memristor and later be revealed for security check . 6. ADVANTAGES
Conventional microelectronics exploits only the charge degree of freedom of the electron. Though electrons have both charge and a spin, until recently these were considered separately. In classical electronics, charges are moved by electric fields to transmit information and are stored in a capacitor to save it. Bringing the spin degree of freedom to bear on sensing, radio frequency, memory and logic applications opens up new possibilities for ‘more than Moore’ devices incorporating magnetic components that can couple to an external field, store a bit of data or represent a Boolean state. Moreover, the electron spin is an archetypal two-state quantum system that is an excellent candidate for a solid-state realization of a qubit.
The first practical memristor that HP demonstrated was based on the movement of ions in the material. HP fabricated them using conventional lithography techniques: laying down a series of parallel metal nanowires, coating the wires with a layer of titanium dioxide a few nanometers thick, and then laying down a second array of wires perpendicular to the first. The points where the wires crossed were the memristors, and each as small as about three nanometers. This cross-bar structure made it possible to pack memristors in very dense arrays. Memristor memory could withstand up to about a million read-write cycles in lab tests.
Memristor memory technology based on spintronics can be scaled better than flash and hopes to offer a product with a storage density of about 20 gigabytes per square centimeter in 2013--double the storage that flash is expected to offer at that time Also the devices are all relatively easy to construct. We can easily integrate a magnetic device on top of a CMOS device.
A spin memristor can be more finely tuned and is more flexible than the device HP described,. That’s because of the variable switching rates, but it’s also because spin is not a binary condition—neither up nor down but rather existing along a continuum. So a device doesn’t need to make a complete change from magnetized to nonmagnetized to register a change in the resistance.
7. LIMITATIONS
Unlike conventional electronics, which uses an electron’s charge-carrying property to create circuits, spintronics exploits the quantum mechanical property of electrons known as electron spin to create useful devices. However,electron spins typically have short lifetimes (microseconds), which make it challenging to create registers and other devices necessary to perform calculations, since those actions require that the information be stored for a relatively long period of time. But it is found that the spin lifetime and diffusion length of electrons are many orders of magnitude larger in semiconductors than in metals and hence, semiconductors could be the most suitable for spintronics. Now, a team of physicists led by Dane McCamey of the University of Sydney, in Australia, has succeeded in using the magnetic spins of phosphorus nuclei in phosphorus-doped silicon to store information for 112 seconds. For this property, called spin, 2 minutes is an eternity. The breakthrough could lead to new kinds of silicon-based memories that might even work at the level of a single atom. Basically, it is a clever technique that allows the researchers to map and store the electronic spin information onto the nuclei of the phosphorus donors. The nuclear spins can be read out electronically repeatedly, and the information lasts much longer than the lifetimes of electron spin.
Another drawback of this technology is that storage for this length of time can only be done at low temperatures (around 3.5 Kelvin) as at high temperatures (temperatures above Curie temperature), ferromagnetic materials will lose their magnetic property and become paramagnetic.But one needs to remember that giant magnetoresistance (GMR) started out as only a low-temperature phenomenon, and now it is in all of our disk drives. Indeed, the researcher’s next goal is to find a way to make the memory work at warmer temperatures and with weaker magnetic fields.
8. CONCLUSION
Spintronic memristors have open up remarkable possibilities in the field of electronic circuit technology. Just as the last century belonged to transistors, the new century could belong to memristors. By redesigning certain types of circuits to include memristors, it is possible to obtain the same function with fewer components, making the circuit itself less expensive and significantly decreasing its power consumption. In fact, it can be hoped to combine memristors with traditional circuit-design elements to produce a device that does computation.
Melding memristors and spintronics yields devices whose resistance changes according to the spin of electrons passing through it, and those devices will remember that resistance., making it a natural for nonvolatile memory. The memristor promises the introduction of much tinier circuits, instant-on computers, and the ability to mimic the function of neurons in the human brain. As rightly said by Leon Chua and R.Stanley Williams (originators of memristor), memrisrors are so significant that it would be mandatory to re-write the existing electronics engineering textbooks. Linking memristance and other phenomena such as spin transport is a very excellent path forward to putting a lot of functionality into a small package.
REFERENCES
* X. Wang, Y. Chen, H. Xi, H.Li and D. Dimitrov, Spintronic memristor through spin torque induced magnetization motion’ IEEE Device Letters, vol. 30,n o. 3, pp. 294-297,2009. * L. O. Chua, “Memristor”, The missing circuit element, IEEE Tran.Circuit Theory, vol. CT-18, no. 5, pp. 507 - 519, Sep. 1971. * Neil Savage , Spintronic Memristors , IEEE Spectrum, March 2009 . * X. Wang, Y. Chen, Y. Gu, H.Li, Spintronic memristor temperature sensor, IEEE Electron Device Letters, Vol . 31, No . 1,January 2010. * Xiaobin Wang, Yiran Chen -‘Spintronic Memristor Devices and Application’, Design, Automation & Test in Europe Conference & Exhibition (DATE), 2010 , v.50, no .1, p.5-23,January 2010. * R. Stanley Williams, How we found the missing memristor, IEEE Spectrum , December 2008, pp 25-31.
References: * X. Wang, Y. Chen, H. Xi, H.Li and D. Dimitrov, Spintronic memristor through spin torque induced magnetization motion’ IEEE Device Letters, vol. 30,n o. 3, pp. 294-297,2009. ‡ * L. O. Chua, “Memristor”, The missing circuit element, IEEE Tran.Circuit Theory, vol. CT-18, no. 5, pp. 507 - 519, Sep. 1971. * Neil Savage , Spintronic Memristors , IEEE Spectrum, March 2009 . * X. Wang, Y. Chen, Y. Gu, H.Li, Spintronic memristor temperature sensor, IEEE Electron Device Letters, Vol . 31, No . 1,January 2010. ‡ * Xiaobin Wang, Yiran Chen -‘Spintronic Memristor Devices and Application’, Design, Automation & Test in Europe Conference & Exhibition (DATE), 2010 , v.50, no .1, p.5-23,January 2010. ‡ * R. Stanley Williams, How we found the missing memristor, IEEE Spectrum , December 2008, pp 25-31.
Generally when most people think about electronics, they may initially think of products such as cell phones, radios, laptop computers, etc. others, having some engineering background, may think of resistors, capacitors, etc. which are the basic components necessary for electronics to function. Such basic components are fairly limited in number and each having their own characteristic function. Memristor theory was formulated and named by Leon Chua in a 1971 paper. Chua strongly believed that a fourth device existed to provide conceptual symmetry with the resistor, inductor, and capacitor. A device linking charge and flux (themselves defined as time integrals of current and voltage), which would be the memristor, was still hypothetical at the time. However, thirty-seven years later, on April 30, 2008, a team at HP Labs led by the scientist R. Stanley Williams announced the discovery of a switching memristor. Based on a thin film of titanium dioxide, it has been presented as an approximately ideal device. The reason that the memristor is radically different from the other fundamental circuit elements is that, unlike them, it carries a memory of its past. When you turn off the voltage to the circuit, the memristor still remembers how much was applied before and for how long. That 's an effect that can 't be duplicated by any circuit combination of resistors, capacitors, and inductors, which is why the memristor qualifies as a fundamental circuit element. Memristor has very broad applications that include non-volatile memory, signal processing, control and learning system etc. Shortly after the demonstration of memristance, researchers began looking for this property in spintronics—a relatively new branch of electronics itself. In this ever changing world of technology, products of technology have evolved at an extremely quick rate. Computers have been doubling in speed in no time flat, audio recording has evolved, though more slowly, from albums now to mpeg players that can store around 700 minutes worth of music, and the gaming console business, not to mention all the other areas of advancement. But, getting back to computer speed and storage, the advancement in this category is starting to slow down (there can only be so many “switches/transistors” placed on a chip). So to deal with storage and speed advancements some new research is being done. One of these areas is that of spintronics.
Spintronics is at the heart of recent advances in hard-drive data density and the niche nonvolatile memory known as MRAM. The formal definition of spintronics is “the study of the role played by electron (and more generally nuclear) spin in solid state physics, and possible devices that specifically exploit spin properties instead of or in addition to charge degrees of freedom”. A simpler definition is that spintronics is a “new branch of electronics in which electron spin, in addition to charge, is manipulated to yield a desired outcome”.
Nano-scale spintronic memristor has been proposed based upon spin torque induced magnetization motion and spin transport at semiconductor/ferromagnet junction . Realizing memristive effects in spintronic device not only provides understanding of a wide range of current-voltage behaviours observed in nanoscale spintronic system, but also sheds light on how we should look at existing/proposed magnetic devices and herald new applications.
Fig. 1
2. HISTORY
The transistor was invented in 1925 but lay dormant until finding a corporate champion in Bell Labs during the 1950s.Then in 2008,Hewlett-Packard Labs demonstrated a practical memristor, the fourth passive circuit element after the resistor, and the capacitor the inductor into the electronics mainstream. Postulated in 1971, the “memory resistor” represents a potential revolution in electronic circuit theory similar to the invention of transistor.Now, researchers have come up with a new type of memristor called spintronic memristor that exploits the spin property of electron. The history of the memristor can be traced back to nearly four decades ago when in 1971, Leon Chua, a University of California, Berkeley, engineer predicted that there should be a fourth passive circuit element in addition to the other three known passive elements namely the resistor, the capacitor and the inductor. He called this fourth element a “memory resistor” or a memristor. Examining the relationship between charge, current, voltage and flux in resistors, capacitors, and inductors in a 1971 paper, Chua postulated the existence of memristor. Such a device, he figured, would provide a similar relationship between magnetic flux and charge that a resistor gives between voltage and current. In practice, that would mean it acted like a resistor whose value could vary according to the current passing through it and which would remember that value even after the current disappeared. But the hypothetical device was mostly written off as a mathematical dalliance. However, it took more than three decades for the memristor to be discovered and come to life. Thirty years after Chua’s Proposal of this mysterious device, HP senior fellow Stanley Williams and his group were working on molecular electronics when they started to notice strange behavior in their devices. One of his HP collaborators, Greg Snider, then rediscovered Chua 's work from 1971. Williams spent several years reading and rereading Chua 's papers. It was then that Williams realized that their molecular devices were really memristors.
Fig.2. 17 memristors in a row
Moore’s law on how the speed of computers will keep on doubling is slowing down, and it has been estimated that in the next 10 years or so we will have reached the limit on speed of traditional microprocessors. So back in the early 90’s research was being done on how to make microprocessors better and faster. Research into areas like nanotubes was done, but not until 1998 did researchers set their sights onto a different property of electrons i.e., spin. Researches in the field of spintronics could lead to “quantum computers”.
As we build transistors and other components with nanoscale dimensions, processors and memories are becoming so dense that even their infinitesimal individual currents are combining to produce scorching heat. Furthermore, quantum effects that were negligible before are now so pronounced that they 're threatening to render circuits inoperable. The upshot is that we 're fast approaching the point when moving charge is not going to be enough to keep Moore 's Law chugging along.
Spin is a fundamental yet elusive quantum attribute of electrons and other subatomic particles. It is often regarded as a bizarre form of nanoworld angular momentum, and it underlies permanent magnetism. What makes spin interesting for electronics is that it can assume one of two states relative to a magnetic field, typically referred to as up and down, and you can use these two states to represent the two values of binary logic—to store a bit, in other words.
The development of spin-based electronics, or spintronics, promises to open up remarkable possibilities. In principle, manipulating spin is faster and requires far less energy than pushing charge around, and it can take place at smaller scales. The holy grail in the field is a spin transistor. Chips built out of spin transistors would be faster and more powerful than traditional ones and, farther down the road, may feature such new and remarkable properties as the ability to change their logic functions on the fly.
3. DEVICE THEORY
The original definition of memristor is
dϕ = Mdq
where q is the electric charge, ϕ is the magnetic flux, and M is the memristance. Because magnetic flux is the integration of voltage and charge is the integration of current, it is easy to show that memristance can be defined as
M(q) = (dϕ/dt)/(dq/dt) = VI
What makes memristance different from an ordinary constant resistance or a current- or voltage-dependent nonlinear resistance is that memristance is a function of charge, which depends on the hysteretic behavior of current/voltage profile. The aforementioned definition of memristor can be generalized to
V = M(w)I dw/dt = f(i,w)
where w is an implicit state variable (e.g., charge) that depends on the integral of current profile over time. V and i are the voltage and current, respectively. Again, the key point in the definition (3) of memristor is its dependence on the historic behavior of current (or, for example, the integral of current profile over time).
This circuit element shares many of the properties of resistors and shares the same unit of measurement (ohms). However, in contrast to ordinary resistors, in which the resistance is permanently fixed, memristance may be programmed or switched to different resistance states based on the history of the voltage applied to the memristance material. This phenomena can be understood graphically in terms of the relationship between the current flowing through a memristor and the voltage applied across the memristor. In ordinary resistors there is a linear relationship between current and voltage so that a graph comparing current and voltage results in a straight line. However, for memristors a similar graph is a little more complicated as shown in Fig. 3 illustrates the current vs. voltage behavior of memristance. In contrast to the straight line expected from most resistors the behavior of a memristor appear closer to that found in hysteresis curves associated with magnetic materials. It is notable from Fig. 3 that two straight line segments are formed within the curve. These two straight line curves may be interpreted as two distinct resistance states with the remainder of the curve as transition regions between these two states.
Fig. 3.. Current vs. Voltage curve demonstrating hysteretic effects of memristance. Fig. 3 illustrates an idealized resistance behavior demonstrated in accordance with Fig.4 wherein the linear regions correspond to a relatively high resistance (RH) and lowresistance (RL) and the transition regions are represented by straight lines. Fig . 4. Resistance vs. Voltage
Thus for voltages within a threshold region (-VL2<V<VL1 in Fig. 4) either a high or low resistance exists for the memristor. For a voltage above threshold VL1 the resistance switches from a high to a low level and for a voltage of opposite polarity above threshold VL2 the resistance switches back to a high resistance.
Spin is the property that is responsible for magnetism—materials are magnetized when a majority of their electrons have their spins pointing in the same direction. Melding memristors and spintronics yields devices whose resistance changes according to the spin of electrons passing through it, and those devices will remember that resistance.
Spintronics (short for spin-based electronics), sometimes called magnetoelectronics, is the term given to microelectronic devices that function by exploiting the spin of electrons. The most common use of spintronics today is in computer hard drives. Here memory storage is based on giant magnetoresistance (GMR) a spintronic effect. There is current research focusing on bringing magnetic random-access memory (MRAM) to market. Spintronic based MRAMs should rival the speed and rewritability of conventional RAM and retain their state (and thus memory) even when the power is turned off. Motorola has recently developed a 256-kb MRAM) based on a single magnetic tunnel junction and a single transistor. This MRAM has read/write cycles of less than 50 nanoseconds. |
Fig 5. A 256-kb MRAM based on modern spintronics technology. (Image courtesy of Motorola Corp.)
Spintronics focuses on two types of materials. Ferromagnetic metallic alloys are currently used for magnetoelectronic devices. Ferromagnetic semiconductors, however, are attracting greater attention. If the manufacture of ferromagnetic semiconductors becomes practical, the current microchip industry could switch over to these types of spintronic devices with relatively little change in their infrastructure. The primary barrier to the synthesis of ferromagnetic semiconductors is finding a way to inject spin-polarized currents (spin currents) into a semiconductor.
Most of the work in making semiconductors ferromagnetic has focused on II-VI semiconductors such as CdTe (Aldrich product 25,654-4) or ZnSe (Aldrich products 24,461-9 and 55,301-8).29 Here the semiconductors are doped with magnetic ions (such as manganese) to create small pockets of magnetic character resulting in a diluted magnetic semiconductor (DMS). More recent work has focused on doping III-V semiconductors such as GaAs (Aldrich product 32,901-0) into a DMS state. With III-V semiconductors, however, the magnetic elements are much less soluble than in II-VI semiconductors making them much more difficult to inject into a material like GaAs. Molecular beam epitaxy (MBE) has proven to be an excellent technique in overcoming the difficulty in making DMS III-V materials.
As new and better techniques for synthesizing ferromagnetics are developed, their prospects for revolutionizing the microelectronic industry increases, spintronics will sure play a major role in the next generation of information storage devices.
Let us consider a spintronic device where the current electron spin changes the magnetization state of the device.. The resistance is caused by the spin of electrons in one section of the device pointing in a different direction than those in another section, creating a “domain wall,” a boundary between the two states. Electrons flowing into the device have a certain spin, which alters the magnetization state of the device. Changing the magnetization, in turn, moves the domain wall and changes the device’s resistance. The magnetization state of the device is thus dependent upon the cumulative effects of electron spin excitations.
The different designs can be flipped between high- and low-resistance states at different rates, from picoseconds to microseconds, each preferable in different applications. For reading a hard drive, for instance, you’d want to sense changes in a magnetic field in a few picoseconds, whereas for something like a radiation sensor, you’d want a response time measured in microseconds.
In the next figure, three examples of spintronic memristors based upon spin-torque-induced magnetization switching and magnetic domain wall motion are being shown.
Fig.6. Spintronic memristors. (a) MTJ with spin-torque-induced magnetization switching. (b) Thin-film element with spin-torque-induced domain-wall motion. (c) Spin valve with spin-torque-induced domain-wall motion in the free layer. 3.1 Current Induced Domain Wall Motion
In magnetism, a domain wall is an interface separating magnetic domains. It is a transition between different magnetic moments and usually undergoes an angular displacement of 90° or 180°. Domain wall is a gradual reorientation of individual moments across a finite distance. The domain wall thickness depends on the anisotropy of the material, but on average spans across around 100-150 atoms.
The energy of a domain wall is simply the difference between the magnetic moments before and after the domain wall was created. This value is usually expressed as energy per unit wall area.
Non-magnetic inclusions in the volume of a ferromagnetic material, or dislocations in crystallographic structure, can cause "pinning" of the domain walls (see animation). Such pinning sites cause the domain wall to seat in a local energy minimum and external field is required to "unpin" the domain wall from its pinned position. The act of unpinning will cause sudden movement of the domain wall and sudden change of the volume of both neighbouring domains. This causes Barkhausen noise and in effect it is most likely to be the source of magnetic hysteresis.
When a current is passed to a ferromagnetic wire that contains domain walls, the flowing electrons exert a pressure on the domain wall that tends to drive the domain wall in the direction of the electron flow. This current control of domain wall motion is proposed as a basis for a memory device in which the information is stored in magnetic domains. The domain walls between the domains can be moved past a read out device by a current flowing through the wire. Such a device could potentially have a high storage density, fast read out, and non-volatility. Such current induced domain wall motion is currently studied in the Electron Physics Group using Scanning Electron Microscopy with Polarization Analysis (SEMPA).
Experimentally, current induced domain wall motion is typically studied in lithographically defined, narrow magnetic wires. The wires are frequently curved or the ends are designed to make it possible to controllably introduce a domain wall into the wire using an applied field. The position of the domain walls can be imaged using techniques such as Magnetic Force Microscopy (MFM) or Scanning Electron Microscopy with Polarization Analysis (SEMPA). Measuring the position before and after a current pulse with a technique like Scanning Electron Microscopy allows an estimate of the wall velocity. Alternatively, the location of the wall could be determined in real time using the Magneto-Optic Kerr Effect (MOKE) or electrically using GMR sandwich structures or through the extra resistance due to anisotropic magnetoresistance (AMR) in a domain wall. Using these various techniques, experimentalists typically determine the wall velocity as a function of current and applied magnetic field and compare with theoretical predictions.
To a first approximation, current induced domain wall motion is quite simple. The flowing electron spins adiabatically follow the magnetization direction because the magnetization exerts a torque on them. There is a reaction torque on the magnetization that is proportional to the current. If the current is uniform, this torque density simply translates the domain wall in the direction of electron flow with a speed that is proportional to the current. There are several factors that complicate this simple description, including damping, non-adiabatic torques, and extrinsic effects like pinning.
We have computed the degree to which the spin adiabatically follow the magnetization. The deviations are small except for rather narrow domain walls. When they are non-negligible, the adiabatic torque becomes non-local and there is a additional non-local torque perpendicular to the adiabatic torque. This torque is referred to as a non-adiabatic torque because it derives from the inability of the electron spins to adiabatically follow the magnetization direction. For realistic walls, this correction is not important.
Fig.7 .A schematic view of the magnetization direction in a domain wall in a narrow wire. As electrons flow through the domain wall, their spins(remain aligned with the magnetization due to a torque exerted by the magnetization. The reaction torque on the magnetization tends to translate it.
The theoretical description of current induced domain wall motion has lead to significant debate associated with how to describe the damping and whether there is an additional torque in the direction of the non-adiabatic torque that arises from the same processes that lead to damping. Even though this torque is physically distinct from the non-adiabatic torque discussed above, it is in the same direction and is frequently called a non-adiabatic torque and less frequently the beta term. It is closely tied to the description of the magnetization damping. The two most commonly used descriptions of the damping are due to Landau and Lifshitz and to Gilbert. In the absence of current induced torques, these can be shown to be equivalent. They remain equivalent in the presence of spin transfer torques, but with different values of this non-adiabatic torque. We argue that the Landau-Lifshitz form of the damping gives a more physical description of current induced domain wall motion. This description emphasizes the importance of the adiabatic torque, which is much larger than its non-adiabatic counterpart.
3.2 Spin Torque Induced Magnetization Switching
Magnetization switching refers to magnetization motion from one equilibrium state to another equilibrium state. The magnetization equilibrium state is determined by magnetic energy minimization with respect to the magnetization vector:
The derivative of magnetic energy to magnetization vector gives a restoring force called effective field:
For magnetization motion under a constant magnetic field H, the effective field is the magnetic field and magnetic energy is Zeeman energy:
Additional energy terms in a magnetic system include exchange energy and anisotropy energy. Exchange energy brings magnetization order in ferromagnetic material. For a spatially distributed magnetization system (where i denotes spatial position), exchange energy prefers to order neighboring magnetization to the same direction: , where < i, j> denotes nearest neighboring positions. Magnetization magnitude at individual spatial location is conserved (=constant). As nano-scale magnetic device scales down, magnetization reversal can be well approximated by the coherent switching mode, where due to exchange ordering effects. In this manuscript, we study coherent magnetization switching with element magnetization described by a magnetization vector with constant magnitude:
.
Exchange energy does not explicitly enter coherent magnetization switching formalism. When the physical property of a device has a spatial direction preference, that property is called anisotropy. The preference for the magnetization to point in a particular direction is the result of magnetic anisotropy energy. There are two types of anisotropy energy. The first one is the crystal anisotropy energy from magnetic material crystal structure. The second one is the shape anisotropy energy. The origin of shape anisotropy comes from magnetic dipole interaction (or magnetostatic interaction). The basic property of magnetostatic interaction is the avoidance of surface magnetic charge accumulation. Figure 1 illustrates shape anisotropy (or demagnetization anisotropy). Starting with a cubic element with magnetization orientation in the vertical direction, two cuts change the element shape to a thin film and an elongated needle. The magnetization direction changes in the process as a result of minimizing shape anisotropy energy. The minimization of shape anisotropy is the same as avoiding surface magnetic charge accumulation. Here we assume the material crystal anisotropy is much smaller than the shape anisotropy and the magnetization direction is determined by shape anisotropy. For magnetic material with much stronger crystal anisotropy, the magnetization direction follows the direction of the crystal anisotropy. For example, in the thin film structure Figure 5(b), if there is huge perpendicular crystal anisotropy, the equilibrium magnetization points in the vertical direction against the thin film plane demagnetization factor. This structure is called perpendicular thin film structure.
The magnetic anisotropy energy can be written in a general form: (1) where is the magnetization saturation, V is the magnetic element volume and is the normalized magnetization are element anisotropy factors (or demagnetization factors) including both shape anisotropy and crystal anisotropy.
Figure 8. Shape anisotropy (or demagnetization factor) effects on magnetization equilibrium states. Starting with a cubic element with magnetization orientation in the vertical direction, two cuts change the element shape to a thin film and an elongated needle. The magnetization direction changes in the process as a result of minimizing shape anisotropy energy. The minimization of shape anisotropy is the same as avoiding surface magnetic charge accumulation.
Spin torque induced magnetization switching involves a structure of two ferromagnetic layers sandwiching an insulating barrier. The magnetization direction of one ferromagnetic layer (reference layer) is fixed by coupling to a pinned magnetization layer, while the magnetization direction of the other ferromagnetic layer (free layer) can be changed. To switch the free layer magnetization to the same direction as the reference layer magnetization, an electric current is passed from the reference layer to the free layer. The injected current electrons have spins pointing to the same and the opposite directions of the reference layer magnetization. After passing through the reference layer, the electrons have a preferred spin orientation direction pointing to the same direction as the reference layer magnetization. This is because most of the electrons with spin pointing to the opposite direction of the reference layer magnetization are reflected back due to interaction between itinerant electron spin and reference layer local magnetization. The polarized current electrons, with a net spin moment in the same direction as the reference layer magnetization, will switch the free layer magnetization to the same direction as the reference layer magnetization. In order to switch the free layer magnetization to the opposite direction of the reference layer magnetization, electron current passes from the free layer to the reference layer. Based upon the same physics argument as before, the electrons reflected from the reference layer have a preferred spin direction opposite to the direction of the reference layer magnetization. These will switch the free layer magnetization to the opposite direction of the reference layer magnetization.
The magnetization dynamics at finite temperature is described by the stochastic Landau-Lifshitz-Gilbert equation with spin torque terms: (2) where is the normalized magnetization vector, time t is normalized by with being the gyromagnetic ratio. is the normalized effective field with normalized energy density , and is the damping parameter. is the thermal fluctuation field, whose magnitude is determined by the fluctuation-dissipation condition at room temperature is the normalized spin torque term with units of magnetic field. The net spin torque T can be obtained through a microscopic quantum electronic spin transport model .
At the level of macroscopic magnetization dynamics, spin torque can be approximated through an adiabatic term proportional to and non-adiabatic term proportional to where is a unit vector pointing to the spin polarization direction.
We consider the dynamic thermal reversal of a magnetic element under combined magnetic field and spin torque excitation. For the case of magnetic field lying in the plane X–Z, the energy of the magnetic system is: (3)
The spin polarization direction is . Here we neglect the non-adiabatic term (which is usually much smaller) and study the case of spin torque with β proportional to the spin torque current magnitude.
Fig. 9. Configuration of the manuscript: magnetic element under combined magnetic field and spin torque current excitations.
4. EXAMPLES OF SPINTRONIC MEMRISTORS
4.1 MAGNETIC TUNNEL JUNCTION A magnetic tunnel junction (MTJ) consists of two layers of magnetic metal, such as cobalt-iron, separated by an ultrathin layer of insulator, typically aluminum oxide with a thickness of about 1 nm. The insulating layer is so thin that electrons can tunnel through the barrier if a bias voltage is applied between the two metal electrodes. In MTJs the tunneling current depends on the relative orientation of magnetizations of the two ferromagnetic layers, which can be changed by an applied magnetic field. This phenomenon is called tunneling magnetoresistance (TMR) which is a consequence of spin-dependent tunneling.
MTJ resistance can be written as a function of angle between the free-layer magnetization direction and the pinned layer magnetization direction
where G˳ is the MTJ conductance when the free-layer magnetization direction is perpendicular to the reference-layer magnetization direction and tunneling magnetoresistance (TMR) is defined as the ratio of the difference between high and low conductance to low conductance. High conductance corresponds to the case of free-layer magnetization parallel to pinned-layer magnetization, and low conductance corresponds to the case of free-layer magnetization anti parallel to pinned layer magnetization.
Nowadays MTJs that are based on transition-metal ferromagnets and Al2O3 barriers can be fabricated with reproducible characteristics and with TMR values up to 50% at room temperature. Recently large values of TMR observed in crystalline MTJs with MgO barriers further boosted interest in spin dependent tunneling. MTJs are nowadays used in magnetic random access memories.
Fig. 10
5.2 SPIN-VALVE STRUCTURE A spin valve consists of two or more conducting magnetic materials, that alternates its electrical resistance (from low to high or high to low) depending on the alignment of the magnetic layers, in order to exploit the Giant Magnetoresistive effect . The magnetic layers of the device align "up" or "down" depending on an external magnetic field. Layers are made of two materials with different magnetic coercivity, which can be seen in the layers ' hysteresis curves. Due to the different coercivities one layer ("soft" layer) changes polarity at small magnetic fields while the other ("hard" layer) changes polarity at a higher magnetic field. As the magnetic field across the sample is swept two distinct states can exist, one with the magnetisations of the layers parallel, and one with the magnetisations of the layers antiparallel.
In the figures below, the top layer is soft and the bottom layer is hard.
Fig. 11
Spin valves work because of a quantum property of electrons (and other particles) called spin. When a magnetic layer is polarized, the unpaired carrier electrons align their spins to the external magnetic field. When a potential exists across a spin valve, the spin-polarized electrons keep their spin alignment as they move through the device. If these electrons encounter a material with a magnetic field pointing in the opposite direction, they have to flip spins to find an empty energy state in the new material. This flip requires extra energy which causes the device to have a higher resistance than when the magnetic materials are polarized in the same direction.
The resistance of this structure depends on domain-wall position x:
R = [(RLx/D) + (RH(D − x)/D)], where D is the free-layer length, RL is the low resistance when magnetizations of the free and reference layers are parallel, and RH is the high resistance when magnetizations of the free and reference layers are antiparallel.
Spin valves are used in magnetic sensors and hard disk read heads. They are also used in magnetic random access memories (MRAM).
5.3 THIN FILM ELEMENT
Thin-film element has varying width and constant thickness . Here, we consider the current induced domain-wall motion in the film-length direction x, as shown.
Fig. 12
The domain-wall velocity in a thin-film element is, in general, a function of driving current density
Where is the current density. The driving force exerted by electrons on the domain wall corresponds to a reaction force applied to electrons by the domain wall, which manifests itself as a wall resistance where μ0 is the vacuum permeability, R0 is the ordinary Hall coefficient, β is a correction factor ≈2, and μ is the domain-wall mobility in the thin-film element, which scales with the thin-film aspect ratio the resistance of the element is a function of domain-wall position x:
5. APPLICATIONS * Multi-bit Data Storage and Logic
Magnetic tunneling junction (MTJ) has been used in commercial recording heads to sense magnetic flux. It is the core device cell for spin torque magnetic random access memory and has also been proposed for logic devices . MTJ in these applications are generally viewed as a two resistance states device. The resistance states are non-volatile and the switching is achieved when reversal current/voltage magnitude passes a critical threshold. Based upon this view, MTJ is characterized as a nonlinear resistance through R-I or R-V curve. * Novel Sensing Scheme
For multi-bit MTJ cells, if the domain wall can be controlled to move and stop continuously across the free layer and/or many stable MTJ layers can be stacked vertically, the memory device can theoretically store continuous information through continuous resistance change.
* Temperature Sensor
The device structure for temperature sensor consists of a long spin-valve strip which includes two ferromagnetic layers: reference layer and free layer. The magnetization direction of reference layer is fixed by coupling to a pinned magnetic reference layer. The free layer is divided by a domain-wall into two segments that have opposite magnetization directions to each other. Domain wall velocity at finite temperature depends upon both spin torque excitation strength and thermal fluctuation magnitude.Domain wall velocity increases as temperature increases.
For temperature sensing, a biasing voltage pulse with constant magnitude is applied to the device. Resistance difference before and after voltage pulse is measured. This resistance difference is calibrated to sense temperature. Higher temperature results a bigger resistance dropping . Spintronic memristor has remarkable characters to sense nano-scale temperature. * Power Management
The ability to accumulate current/voltage through constant current and/or voltage driving strength makes memristor suitable for power monitor. Figure 9 shows connecting a memristor to a circuit either in series or in parallel.
Fig. 13
For connecting memristor in series with circuit (Fig. 10 a), the whole system is owered by a constant voltage V. The energy consumed by the whole system, including both memristor and circuit, is calculated as: E = ∫VIdt = V ∫Idt . For connecting memristor in parallel with circuit (Fig. 10 b), the whole system is powered by a constant current I. The energy consumed by the whole system, including both memristor and circuit, is calculated as: E = ∫VIdt = I ∫Vdt .
* Information Security
Spintronic memristor can also serve the following purpose: when a user reads the data information stored in the device, the administrator who wrote the data knows immediately if he/she checks the device. The advantage of spintronic memristor in information security is due to its resistance dependence upon historic current/voltage profile behavior. In order to access the data stored in a spintronic memristor, the user must excite the device electrically. This excitation activity can be memorized in a memristor and later be revealed for security check . 6. ADVANTAGES
Conventional microelectronics exploits only the charge degree of freedom of the electron. Though electrons have both charge and a spin, until recently these were considered separately. In classical electronics, charges are moved by electric fields to transmit information and are stored in a capacitor to save it. Bringing the spin degree of freedom to bear on sensing, radio frequency, memory and logic applications opens up new possibilities for ‘more than Moore’ devices incorporating magnetic components that can couple to an external field, store a bit of data or represent a Boolean state. Moreover, the electron spin is an archetypal two-state quantum system that is an excellent candidate for a solid-state realization of a qubit.
The first practical memristor that HP demonstrated was based on the movement of ions in the material. HP fabricated them using conventional lithography techniques: laying down a series of parallel metal nanowires, coating the wires with a layer of titanium dioxide a few nanometers thick, and then laying down a second array of wires perpendicular to the first. The points where the wires crossed were the memristors, and each as small as about three nanometers. This cross-bar structure made it possible to pack memristors in very dense arrays. Memristor memory could withstand up to about a million read-write cycles in lab tests.
Memristor memory technology based on spintronics can be scaled better than flash and hopes to offer a product with a storage density of about 20 gigabytes per square centimeter in 2013--double the storage that flash is expected to offer at that time Also the devices are all relatively easy to construct. We can easily integrate a magnetic device on top of a CMOS device.
A spin memristor can be more finely tuned and is more flexible than the device HP described,. That’s because of the variable switching rates, but it’s also because spin is not a binary condition—neither up nor down but rather existing along a continuum. So a device doesn’t need to make a complete change from magnetized to nonmagnetized to register a change in the resistance.
7. LIMITATIONS
Unlike conventional electronics, which uses an electron’s charge-carrying property to create circuits, spintronics exploits the quantum mechanical property of electrons known as electron spin to create useful devices. However,electron spins typically have short lifetimes (microseconds), which make it challenging to create registers and other devices necessary to perform calculations, since those actions require that the information be stored for a relatively long period of time. But it is found that the spin lifetime and diffusion length of electrons are many orders of magnitude larger in semiconductors than in metals and hence, semiconductors could be the most suitable for spintronics. Now, a team of physicists led by Dane McCamey of the University of Sydney, in Australia, has succeeded in using the magnetic spins of phosphorus nuclei in phosphorus-doped silicon to store information for 112 seconds. For this property, called spin, 2 minutes is an eternity. The breakthrough could lead to new kinds of silicon-based memories that might even work at the level of a single atom. Basically, it is a clever technique that allows the researchers to map and store the electronic spin information onto the nuclei of the phosphorus donors. The nuclear spins can be read out electronically repeatedly, and the information lasts much longer than the lifetimes of electron spin.
Another drawback of this technology is that storage for this length of time can only be done at low temperatures (around 3.5 Kelvin) as at high temperatures (temperatures above Curie temperature), ferromagnetic materials will lose their magnetic property and become paramagnetic.But one needs to remember that giant magnetoresistance (GMR) started out as only a low-temperature phenomenon, and now it is in all of our disk drives. Indeed, the researcher’s next goal is to find a way to make the memory work at warmer temperatures and with weaker magnetic fields.
8. CONCLUSION
Spintronic memristors have open up remarkable possibilities in the field of electronic circuit technology. Just as the last century belonged to transistors, the new century could belong to memristors. By redesigning certain types of circuits to include memristors, it is possible to obtain the same function with fewer components, making the circuit itself less expensive and significantly decreasing its power consumption. In fact, it can be hoped to combine memristors with traditional circuit-design elements to produce a device that does computation.
Melding memristors and spintronics yields devices whose resistance changes according to the spin of electrons passing through it, and those devices will remember that resistance., making it a natural for nonvolatile memory. The memristor promises the introduction of much tinier circuits, instant-on computers, and the ability to mimic the function of neurons in the human brain. As rightly said by Leon Chua and R.Stanley Williams (originators of memristor), memrisrors are so significant that it would be mandatory to re-write the existing electronics engineering textbooks. Linking memristance and other phenomena such as spin transport is a very excellent path forward to putting a lot of functionality into a small package.
REFERENCES
* X. Wang, Y. Chen, H. Xi, H.Li and D. Dimitrov, Spintronic memristor through spin torque induced magnetization motion’ IEEE Device Letters, vol. 30,n o. 3, pp. 294-297,2009. * L. O. Chua, “Memristor”, The missing circuit element, IEEE Tran.Circuit Theory, vol. CT-18, no. 5, pp. 507 - 519, Sep. 1971. * Neil Savage , Spintronic Memristors , IEEE Spectrum, March 2009 . * X. Wang, Y. Chen, Y. Gu, H.Li, Spintronic memristor temperature sensor, IEEE Electron Device Letters, Vol . 31, No . 1,January 2010. * Xiaobin Wang, Yiran Chen -‘Spintronic Memristor Devices and Application’, Design, Automation & Test in Europe Conference & Exhibition (DATE), 2010 , v.50, no .1, p.5-23,January 2010. * R. Stanley Williams, How we found the missing memristor, IEEE Spectrum , December 2008, pp 25-31.
References: * X. Wang, Y. Chen, H. Xi, H.Li and D. Dimitrov, Spintronic memristor through spin torque induced magnetization motion’ IEEE Device Letters, vol. 30,n o. 3, pp. 294-297,2009. ‡ * L. O. Chua, “Memristor”, The missing circuit element, IEEE Tran.Circuit Theory, vol. CT-18, no. 5, pp. 507 - 519, Sep. 1971. * Neil Savage , Spintronic Memristors , IEEE Spectrum, March 2009 . * X. Wang, Y. Chen, Y. Gu, H.Li, Spintronic memristor temperature sensor, IEEE Electron Device Letters, Vol . 31, No . 1,January 2010. ‡ * Xiaobin Wang, Yiran Chen -‘Spintronic Memristor Devices and Application’, Design, Automation & Test in Europe Conference & Exhibition (DATE), 2010 , v.50, no .1, p.5-23,January 2010. ‡ * R. Stanley Williams, How we found the missing memristor, IEEE Spectrum , December 2008, pp 25-31.
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