Phase diagram, susceptibility, and magnetostriction of MnP: Evidence for a Lifshitz point

Abstract

The phase diagram of MnP was determined from magnetostriction and differential susceptibility measurements. Data were taken from 4.2 K up to the Curie temperature ${T}_{C}=290.9$ K. The applied magnetic field ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}}_{0}$ was parallel to the $b$ axis. The focus of the measurements was on the upper triple point ($T=121\ifmmode\pm\else\textpm\fi{}1$ K, ${H}_{0}\ensuremath{\cong}16.5$ kOe) where the paramagnetic (para), ferromagnetic (ferro), and fan phases meet. The transitions on the para-ferro boundary ${H}_{0\ensuremath{\lambda}}(T)$ and on the para-fan boundary ${H}_{0\ensuremath{\lambda}}^{*}(T)$ were of second order. The ferro-fan transitions on the boundary ${H}_{01}(T)$ were of first order. At the upper triple point, all three phase boundaries were tangent to each other, and the $\ensuremath{\lambda}$ line [composed of the boundaries ${H}_{0\ensuremath{\lambda}}(T)$ and ${H}_{0\ensuremath{\lambda}}^{*}(T)$] had an inflection point. These qualitative features agree with those expected at a Lifshitz point (LP). A quantitative analysis of the difference ${H}_{0\ensuremath{\lambda}}^{*}\ensuremath{-}{H}_{01}$ as a function of $T$ gave a crossover exponent $\ensuremath{\varphi}=0.63\ifmmode\pm\else\textpm\fi{}0.04$. This value agrees with the calculated value for the LP. The correspondence between the scaling axes near the upper triple point and those in the theory of the LP is discussed. The phase diagram near the upper triple point was also measured as a function of the angle $\ensuremath{\theta}$ between ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}}_{0}$ and the $b$ axis. The field ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}}_{0}$ was in the $\mathrm{bc}$ plane, and its $c$ component ${H}_{0c}$ played the role of the ordering field for the ferro phase. The results were interpreted in terms of predictions for a LP, supplemented by considerations of demagnetization effects. In addition to the usual parallel differential susceptibility, $\frac{\ensuremath{\partial}M}{\ensuremath{\partial}{H}_{0}}$, the transverse differential susceptibility was also measured near the upper triple point. Here, the applied dc field ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}}_{0}$ was parallel to $b$, the applied modulation field ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{h}}}_{0}$ was parallel to $c$, and the measured quantity was $\frac{\ensuremath{\partial}{M}_{c}}{\ensuremath{\partial}{h}_{0}}$. The transverse susceptibility showed the features expected near a LP. Additional evidence, from two recent neutron studies, that the upper triple point is a LP is summarized. The global phase diagram of MnP, the para-ferro boundary near ${T}_{C}$, and the screw-ferro transition at ${T}_{\ensuremath{\alpha}}=46$ K, are also discussed.