Nuclear-Magnetic-Resonance Studies of Critical Phenomena in MnF2. I. Time-Average Properties

Abstract

A detailed experimental study is made of the ${\mathrm{F}}^{19}$ nuclear resonance in the antiferromagnet Mn${\mathrm{F}}_2$ near its paramagnetic-antiferromagnetic critical point $T_{\mathrm{N}}=67.34\mathrm{}°$K. The dependence of the time-averaged sublattice magnetizations on temperature and external magnetic field is deduced from the behavior of the NMR frequencies. In zero external field the reduced sublattice magnetization is given by the cube-root law $\frac{M_0\mathrm{}\left(T\right)\mathrm{}}{M_0\mathrm{}\left(0\right)\mathrm{}}=1.20\mathrm{}{(1-\frac{T}{T_{\mathrm{N}}})}^{0.333\pm 0.003}$. It was possible to make measurements up to within about 5 mdeg of $T_{\mathrm{N}}$ and so demonstrate that this law holds with remarkable precision over the reduced temperature range $0.92<\mathrm{}\frac{T}{T_{\mathrm{N}}}<0.99993\mathrm{}$. The corresponding range in reduced magnetization was from 0.50 to 0.05. The influence of an external field on the sublattices was studied in detail. In addition to field-proportional changes in the magnetizations, nonlinear effects occur which can be associated quantitatively with the observed downward shift in the Néel temperature produced by the field. A theoretical discussion of the magnetic critical behavior is made using the molecular-field approximation. It is found that the experimentally observed relation between the nonlinear effects of the applied field and the shift of the Néel point is a property of the molecular-field model near $T_{\mathrm{N}}$. However, the observed shift is about three times the calculated shift. An accurate experimental determination of the effect of hydrostatic pressure on the Néel temperature is made. The result, $\frac{d{T}_{\mathrm{N}}}{\mathrm{dP}}=(3.03\mathrm{}\pm 0.03)\times {10}^{-4\mathrm{}}°$K/kg/${\mathrm{cm}}^2$, is used together with thermal-expansion data to estimate that the magnetic critical behavior of Mn${\mathrm{F}}_2$ corrected to the case of fixed lattice parameters is described by $\frac{M_0\mathrm{}\left(T\right)\mathrm{}}{M_0\mathrm{}\left(0\right)\mathrm{}}=1.19\mathrm{}{(1-\frac{T}{T_{\mathrm{N}}})}^{0.335\pm 0.005}$.