Neutron-scattering study of bicritical behavior in CsMnBr3· 2D2O

Abstract

The behavior of the orthorhombic, weakly anisotropic antiferromagnet CsMn${\mathrm{Br}}_{3}$ \ifmmode\cdot\else\textperiodcentered\fi{} 2${\mathrm{D}}_{2}$O in a magnetic field applied along the easy axis, was investigated by means of neutron scattering. By observing the intensities of several magnetic Bragg reflections a rather complete picture of the field and temperature dependence of the staggered magnetization ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{M}}}_{\mathrm{st}}$ was obtained. The data on ${M}_{\mathrm{st}}^{\ensuremath{\parallel}}(H, T)$ and ${M}_{\mathrm{st}}^{\ensuremath{\perp}}(H, T)$, the order parameters of the antiferromagnetic and the spin-flop phase, respectively, allow several direct experimental tests of the extended-scaling theory for bicritical behavior. From the vanishing of the order parameters the paramagnetic phase boundaries ${T}_{c}^{\ensuremath{\parallel}}(H)$ and ${T}_{c}^{\ensuremath{\perp}}(H)$ were determined. The location of the first-order spin-flop line ${H}_{\mathrm{SF}}(T)$ in the ($H, T$) diagram could be derived from the reorientation of ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{M}}}_{\mathrm{st}}$ at this transition. Although the present compound is known as a pseudo-one-dimensional Heisenberg system, the shape of the phase boundaries is well described by the extended-scaling theory. The observed crossover exponent $\ensuremath{\varphi}$ is in fair agreement with the theoretical prediction for an orthorhombic spin-flop system. However, the fitted slope $q$ of the optimum $t=0$ scaling axis strongly deviates from Fisher's estimate, which probably is not valid for a low-dimensional system. The data also provide a more direct confirmation of the central postulate of the extended-scaling theory. In order to test the validity of this scaling hypothesis, two different procedures for the scaling of the data are employed, and plots are constructed in which all scaled data points accumulate onto the two alternative bicritical scaling functions $\mathcal{W}$ or $\mathcal{m}$. In these plots the anticipated symmetry between the ${M}_{\mathrm{st}}^{\ensuremath{\parallel}}$ and ${M}_{\mathrm{st}}^{\ensuremath{\perp}}$ data is striking. In $\mathcal{m}$ the crossover from bicritical to critical behavior can be observed clearly. As a result of the different data analyses, the following best values for the various parameters might be indicated: ${T}_{b}=5.255(5)$ K, ${H}_{b}=26.55(2)$ kOe, $q=5.5(2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ kOe, $w=6.3(4)\ifmmode\times\else\texttimes\fi{}{10}^{3}$ k${\mathrm{Oe}}^{2}$, $\ensuremath{\varphi}=1.18(3)$, ${\ensuremath{\beta}}_{b}=0.33(2)$, ${\ensuremath{\beta}}_{\ensuremath{\parallel}}=0.321(4)$, and ${\ensuremath{\beta}}_{\ensuremath{\perp}}=0.326(6)$. The critical exponents ${\ensuremath{\beta}}_{\ensuremath{\parallel}}$ and ${\ensuremath{\beta}}_{\ensuremath{\perp}}$ are in good agreement with the theoretical $d=3$ Ising value. Also the observed bicritical exponents ${\ensuremath{\beta}}_{b}$ and $\ensuremath{\varphi}$ agree with the theoretical $d=3$ $\mathrm{XY}$ values.