Magnetic phase boundaries near the bicritical and Néel points ofCr2O3

The magnetic phase diagram of the easy-axis uniaxial antiferromagnet ${\mathrm{Cr}}_2$ ${\mathrm{O}}_3$ was measured in magnetic fields $\overrightarrow{\mathrm{H}}$ 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 ∼10 mK, corresponding to $\frac{\Delta T}{T}\sim 3\times {10}^{-5\mathrm{}}$. Attention was focused on the phase boundaries near both the Néel point ($T_N=307.3\mathrm{}$ K) and the bicritical point [$T_b=T_N-(0.505\mathrm{}\pm 0.01)$ K, $H_b=120.04\mathrm{}\pm 0.6$ kOe]. Data were taken for $\overrightarrow{\mathrm{H}}$ parallel to the easy axis, perpendicular to the easy axis, and for some intermediate orientations. Near the bicritical point, the phase boundaries in the $T-H_{\parallel }-H_{\perp }$ space (where $\parallel$ and $\perp$ 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 $\phi$ was determined from numerical fits of the data near the bicritical point taken (i) with $\overrightarrow{\mathrm{H}}$ parallel to the easy axis, and (ii) with $\overrightarrow{\mathrm{H}}$ gradually tipped away from the easy axis, keeping $H_{\parallel }=H_b=\mathrm{const}$. The values for $\phi$ were consistent with the FNK theory. However, it appears that Fisher's estimate for one of the "best" scaling axes ($\tilde{t}=0\mathrm{}$, for $\overrightarrow{\mathrm{H}}$ parallel to the easy axis) is not applicable to ${\mathrm{Cr}}_2$ ${\mathrm{O}}_3$. Near $T_N$ and with $\overrightarrow{\mathrm{H}}$ parallel to the easy axis, the ordering temperature $T_c$ decreases linearly with $H^2$. However, for $\overrightarrow{\mathrm{H}}$ perpendicular to the easy axis,