Magnetic Phase Diagram of MnF2from Ultrasonic and Differential Magnetization Measurements

Abstract

The magnetic phase diagram of Mn${\mathrm{F}}_{2}$, in the $H\ensuremath{-}T$ plane, is determined in magnetic fields up to 200 kG directed along the [001] and [100] directions. The magnetic phase transitions appear as anomalies in the ultrasonic attenuation and/or the differential magnetization. Near the various second-order phase transitions, the attenuation of longitudinal sound waves exhibits $\ensuremath{\lambda}$ anomalies, whereas near the spin-flop transition (which is a first-order transition) the ultrasonic attenuation exhibits a sharp spike and/or an abrupt increase, depending on the mode of propagation. The spin-flop transition is accompanied by a spike in the differential magnetic moment. The N\'eel temperature is ${T}_{N}=(67.33\ifmmode\pm\else\textpm\fi{}0.03)\ifmmode^\circ\else\textdegree\fi{}$K, and the triple point for H\ensuremath{\parallel}[001] is at ${T}_{3}=(64.9\ifmmode\pm\else\textpm\fi{}0.1)\ifmmode^\circ\else\textdegree\fi{}$K and ${H}_{3}=119\ifmmode\pm\else\textpm\fi{}2$ kG. The field at the spin-flop transition (for H\ensuremath{\parallel}[001]) increases monotonically with temperature from 92\ifmmode\pm\else\textpm\fi{}1.5 kG at 4.2\ifmmode^\circ\else\textdegree\fi{}K to 119\ifmmode\pm\else\textpm\fi{}2 kG at the triple point. The curvature, at ${T}_{N}$, of the antiferromagnetic-paramagnetic boundary with H\ensuremath{\parallel}[001] is $\frac{{d}^{2}T}{d{H}^{2}}=\ensuremath{-}(3.2\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}\ifmmode^\circ\else\textdegree\fi{}$K/${\mathrm{G}}^{2}$. The curvature, at ${T}_{N}$, for the antiferromagnetic-paramagnetic boundary with H\ensuremath{\parallel}[100] is smaller by about an order of magnitude. The various phase boundaries are compared with the predictions of the molecular-field theory and other theoretical models.