Magnetic phase boundaries of CsMnF_{3}: XY-to-Ising crossover and the virtual bicritical point

Abstract

The ordering temperature ${T}_{c}$ of the easy-plane hexagonal antiferromagnet CsMn${\mathrm{F}}_{3}$ was measured as a function of magnetic field $H$, up to 120 kOe. ${T}_{c}$ was determined from the thermal expansion anomaly at constant $H$. At $H=0$, ${T}_{N}\ensuremath{\equiv}{T}_{c}(0)=51.4$ K. When $\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}$ is in the hexagonal plane, the boundary ${T}_{c}(H)$ is bow shaped: with increasing $H$, ${T}_{c}$ first increases, then passes through a maximum, and later decreases. The maximum ${T}_{c}$ is \ensuremath{\sim}37 mK above ${T}_{N}$, and it occurs at $H\ensuremath{\cong}29.5$ kOe. The bow-shaped phase boundary is attributed to the $\mathrm{XY}$-to-Ising crossover which is induced by the magnetic field, as discussed by Fisher, Nelson, and Kosterlitz. Fits to the phase boundary ${T}_{c}(H)$ give a crossover exponent $\ensuremath{\varphi}=1.185\ifmmode\pm\else\textpm\fi{}0.03$ for one sample and $\ensuremath{\varphi}=1.184\ifmmode\pm\else\textpm\fi{}0.025$ for another, compared to the theoretical value $\ensuremath{\varphi}(n=2)=1.175\ifmmode\pm\else\textpm\fi{}0.015$. When $\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}$ is perpendicular to the hexagonal plane, ${T}_{c}$ decreases monotonically with increasing $H$, but the decrease is not in accordance with mean-field theory, which predicts a decrease proportional to ${H}^{2}$. The deviation from mean-field behavior is attributed to a virtual bicritical point (VBP) with Heisenberg symmetry, which exists mathematically at a negative value of ${H}^{2}$. Although the VBP cannot be observed directly, it affects the behavior in the observable region of ${H}^{2}>~0$. Physically, a magnetic field applied perpendicular to the easy plane enhances the Heisenberg-to-$\mathrm{XY}$ symmetry breaking, which at $H=0$ is solely due to the weak easy-plane uniaxial anisotropy. The enhanced symmetry breaking causes a non-mean-field dependence of ${T}_{c}$ on $H$. An equation derived on this basis gives a good description of the phase boundary ${T}_{c}(H)$. This equation contains three adjustable parameters, two of which can also be estimated without recourse to the phase boundary ${T}_{c}(H)$. The values for these two parameters obtained from a best fit to ${T}_{c}(H)$ agree with the independent estimates.