Critical phenomena at the antiferromagnetic phase transition of azurite

Abstract

We report on high-resolution acoustic, specific-heat and thermal expansion measurements in the vicinity of the antiferromagnetic phase transition at T N = 1.88 K on a high-quality single crystal of the natural mineral azurite. A detailed investigation of the critical contribution to the various quantities at T N is presented. The set of critical exponents and amplitude ratios of the singular contributions above and below the transition indicate that the system can be reasonably well described by a three-dimensional Heisenberg antiferromagnet.

Magnetoelastic couplings in the distorted diamond-chain compound azurite

“…In addition, the elastic data highlight a sharp minimum around 1.9 K, reflecting the transition into long-range antiferromagnetic ordering at T N = 1.88 K, and a steplike softening of comparable size to that at T N around T 0 = 0.37 K. The latter feature is likely to be of magnetic origin as well [24]. In contrast to the distinct softening observed in the c 22 (T ) elastic constant, we note that no accompanying feature is revealed in the ultrasonic attenuation (not shown) for temperatures above 20 K. However, pronounced anomalies in the attenuation were observed at T N [25] and around 10 K, the latter corresponding to the energy scale of the Heisenberg chain not discussed here. This anomaly is similar to the one observed in the quasi-one-dimensional compound CsNiCl 3 [26].…”

“…Elastic anomalies and pressure/strain dependence of the relevant magnetic energy scales [25]. Upon cooling, the c 22 mode initially increases (hardening) as expected for materials where anharmonic phonon interactions dominate.…”