Abstract. The natural mineral Azurite [Cu3(CO3)2(OH)2] has been considered as a model substance for the 1D distorted antiferromagnetic diamond chain, the microscopic couplings of which, however, are still under discussion. Here we present results of the longitudinal elastic constant c22 down to 80 mK and magnetic fields up to 12 T. c22 reveals clear signatures of the magnetic energy scales involved and discloses distinct anomalies at the Néel ordering TN = 1.88 K. Based on measurement as a function of temperature and magnetic field, a detailed B-T phase diagram is mapped out which includes an additional phase boundary of unknown origin at low temperature (T < 0.5 K). Entering the new phase is accompanied by a pronounced softening of the c22 elastic constant. These observations, together with results obtained by spectroscopic investigations reported in the literature, reflect an unusual long-range magnetically ordered state at very low temperatures.
Low-dimensional (low-D) quantum spin systems are of great interest in solid state physics due to the wealth of exciting phenomena originating from the interplay of reduced dimensionality, competing interactions and strong quantum fluctuations. Recently, great interest and controversy has surrounded the proposal that the spin S = 1/2 moments of the Cu2+ ions in azurite [Cu3(CO3)2(OH)2] form a frustrated 1D distorted diamond chain [1-3]. The magnetic structure of azurite and the relevant microscopic couplings, however, have been disputed both in experimental and theoretical studies [4-6]. In addition, the detailed phase diagram at low temperature and high magnetic fields is still unknown and some recent experiments suggest that there exists a more complicated micromagnetic structure than has previously been thought [7, 8].
Results and Discussion
Using a phase-sensitive detection technique, we have measured the relative change of the velocity of a longitudinal ultrasonic wave propagating along the spin-chain direction (b axis) of a high-quality single crystal of azurite. This geometry corresponds to the c22 acoustic mode. The elastic constant can be calculated from the sound velocity ν and the crystal’s mass density ρ by c22 = ρν2. |[pic] | |Figure 1. a) Temperature dependence of the longitudinal c22 acoustic mode for B = 0 T (left scale) and the magnetic susceptibility | |χmol(T) (right scale) plotted on the same temperature axis. |
Measurements have been performed both as a function of temperature and magnetic field. The external field was applied either perpendicular or parallel to the b axis.
Figure 1 shows the temperature dependence of c22 together with the molar magnetic susceptibility χmol. The latter has been determined by utilizing a homemade SQUID magnetometer. At TN = 1.88 K we observed in both curves a pronounced anomaly - a minimum in c22(T) coinciding with a sharp kink in χ(T) - reflecting long-range antiferromagnetic ordering. The size of the elastic anomaly (of the order of 0.1%) is typical for an antiferromagnetic (AFM) transition. A surprising result obtained from the ultrasonic measurements is the observation of another pronounced softening of c22. The onset of this softening coincides with an abrupt increase of χmol(T) for T < 0.45 K. Note that...