Magnetic phase boundaries near the bicritical and Néel points ofCr2O3

Abstract

The magnetic phase diagram of the easy-axis uniaxial antiferromagnet ${\mathrm{Cr}}_{2}$${\mathrm{O}}_{3}$ was measured in magnetic fields $\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}$ up to 180 kOe. Phase transitions were determined from anomalies in the attenuation of 30- and 50-MHz longitudinal ultrasonic waves. Temperatures $T$ were measured with a precision of \ensuremath{\sim}10 mK, corresponding to $\frac{\ensuremath{\Delta}T}{T}\ensuremath{\sim}3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$. Attention was focused on the phase boundaries near both the N\'eel point (${T}_{N}=307.3$ K) and the bicritical point [${T}_{b}={T}_{N}\ensuremath{-}(0.505\ifmmode\pm\else\textpm\fi{}0.01)$ K, ${H}_{b}=120.04\ifmmode\pm\else\textpm\fi{}0.6$ kOe]. Data were taken for $\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}$ parallel to the easy axis, perpendicular to the easy axis, and for some intermediate orientations. Near the bicritical point, the phase boundaries in the $T\ensuremath{-}{H}_{\ensuremath{\parallel}}\ensuremath{-}{H}_{\ensuremath{\perp}}$ space (where $\ensuremath{\parallel}$ and $\ensuremath{\perp}$ indicate parallel and perpendicular to the easy axis, respectively) show marked deviations from mean-field theory. In contrast, the recent theory of Fisher, Nelson, and Kosterlitz (FNK) explains all the salient features of the phase boundries near the bicritical point. The crossover exponent $\ensuremath{\varphi}$ was determined from numerical fits of the data near the bicritical point taken (i) with $\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}$ parallel to the easy axis, and (ii) with $\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}$ gradually tipped away from the easy axis, keeping ${H}_{\ensuremath{\parallel}}={H}_{b}=\mathrm{const}$. The values for $\ensuremath{\varphi}$ were consistent with the FNK theory. However, it appears that Fisher's estimate for one of the best scaling axes ($\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{t}=0$, for $\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}$ parallel to the easy axis) is not applicable to ${\mathrm{Cr}}_{2}$${\mathrm{O}}_{3}$. Near ${T}_{N}$ and with $\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}$ parallel to the easy axis, the ordering temperature ${T}_{c}$ decreases linearly with ${H}^{2}$. However, for $\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}$ perpendicular to the easy axis, ${T}_{c}$ increases with increasing $H$ in fields up to 180 kOe. This increase is attributed to the extremely low anisotropy of ${\mathrm{Cr}}_{2}$${\mathrm{O}}_{3}$ which causes the behavior in perpendicular fields to qualitatively resemble the behavior predicted by FNK for the completely isotropic antiferromagnet. Ultrasonic methods for determining phase boundaries of antiferromagnets are reviewed briefly.