Tricritical scaling and logarithmic corrections for the metamagnet FeCl2

Abstract

The uniform (nonordering) magnetization and heat capacity of Fe${\mathrm{Cl}}_{2}$ have been measured simultaneously in the vicinity of the tricritical point. Using the peak in the heat capacity in the second-order region and the light scattering in the first-order region, we have determined the phase diagram for this metamagnetic tricritical point. A technique is described which permits simultaneous measurement of these properties using the ac calorimetric and Faraday rotation techniques. Data were collected along isotherms as functions of external field and were then corrected to internal field using the measured magnetization and demagnetizing factors. We demonstrate that the data for the magnetization and heat capacity do not satisfy scaling relations with classical exponents, $\ensuremath{\varphi}=2$ and ${\ensuremath{\alpha}}_{t}=\frac{1}{2}$, but may be made to "collapse" in the predicted manner only when ${\ensuremath{\alpha}}_{t}$ is permitted to take an effective value ${\ensuremath{\alpha}}_{t}^{\mathrm{eff}}=0.65$. When logarithmic correction factors of the form $L(r)=1\ensuremath{-}{a}_{6}\mathrm{ln}(r)$ are included, however, the data collapse with classical exponents. The constant ${a}_{6}$ is a nonuniversal amplitude which we find to be ${a}_{6}=0.5\ifmmode\pm\else\textpm\fi{}0.2$ and the field $r$ is defined to vanish along the logarithmically corrected---and experimentally observed---second-order line. Along the first-order line, the behavior of the step change in magnetization is improved by logarithmic corrections, but the classical exponents are not fully recovered. The logarithmic factors occur in the scaled free energy such that, over any limited range of experimental data, they may be represented by power laws with effective exponents. The logarithmic factors appear to be more important for metamagnets such as Fe${\mathrm{Cl}}_{2}$ and CsCo${\mathrm{Cl}}_{3}$. 2${\mathrm{H}}_{2}$O (which behaves similarly) than for $^{3}\mathrm{He}$-$^{4}\mathrm{He}$ mixtures.