Crossover behavior of the magnetic phase boundary of the isotropic antiferromagnet RbMnF3from ultrasonic measurements

The ordering temperature $T_c\mathrm{}\left(H\right)\mathrm{}$ of the very nearly isotropic antiferromagnet RbMn${\mathrm{F}}_3$ was measured as a function of magnetic field $H$, up to 180 kOe. The order-disorder transition was determined from the $\lambda$ peak in the attenuation of 26- to 82-MHz longitudinal waves. At all fields, $T_c$ was measured with a precision of better than 2 mK. Results for the $H$ dependence of $T_c$ in two different samples (with Néel temperatures $T_N=83.13\mathrm{}\pm 0.03$ K and 83.03 ± 0.03 K) were in very good agreement with each other. With increasing $H$, $T_c\mathrm{}\left(H\right)\mathrm{}$ first increases, then reaches a maximum, and finally decreases. The maximum in $T_c\mathrm{}\left(H\right)\mathrm{}$ is a mere 0.18 K above $T_N$. The phase boundary, $T_c$ vs $H$, is bow-shaped and confirms the theoretical predictions of Fisher, Nelson, and Kosterlitz. Least-squares fits of the data for the two samples, supplemented by error analysis, give the values $\phi =1.278\mathrm{}\pm 0.026$ and 1.274 ± 0.045 for the crossover exponent, in good agreement with the predicted value $\phi =1.250\mathrm{}\pm 0.015$. The present data are in good agreement with, but are more precise than, the recent determination of the phase boundary of RbMn${\mathrm{F}}_3$ from thermal-expansion measurements. The experimental techniques employed to achieve high-precision thermometry in the presence of intense magnetic fields are discussed.