Phase Transitions in the Anisotropic Ferrimagnetic Ytterbium Iron Garnet

Abstract

The thermal and magnetic properties of YbIG in field-induced canted configurations are discussed with emphasis on phase-transition singularities. By using the (for this case, well-justified) mean-field formalism of Wolf and the $\overrightarrow{\mathrm{G}}$ and $\overrightarrow{\mathrm{g}}$ tensors of Wickersheim, we calculate properties for applied fields of 0 to 300 kOe and for temperatures from 0 to 30 °K. Complete entropy and magnetic-moment predictions are presented for the field along the [111] and [100] directions. Selected results for specific heat and susceptibility are given for [111], [100], and [314] directions. We also discuss torque curves and variation of level splittings with applied field. Although it is clear that the Wickersheim parameters do not provide an over-all "best fit," the agreement for such data as are available is qualitatively good. Unfortunately, there are few data suitable for comparison with the phase-transition predictions. Four kinds of phase transitions are predicted: (I) ordinary first order, (II) liquid-vapor-like second order, (III) symmetry-affected first order, and (IV) symmetry-affected second order. Of particular interest are the following divergence and near divergence of the specific heat $C$ for examples of the second and third types, respectively: (II) ($T$ near $T_c=7.51\mathrm{}$ °K, $H=43.640\mathrm{}$ kOe along [100]) $C\sim {0.36(T-T_c)}^{\frac{-2\mathrm{}}{3}} \frac{R}{\mathrm{mole}}$; (III) ($T<\mathrm{}{T}_t=16.18\mathrm{}$ °K, $H=110\mathrm{}$ kOe along [111]) $C\sim 6.0 \frac{(1+\{\frac{3}{{[1-60(T-T_t\left)\right]}^{\frac{1}{2}}}\left\}\right)R}{\mathrm{mole}}$. A phenomenological theory applicable to all RIG's and perhaps other ferrimagnets describes very well the singularities in thermal-magnetic properties at the phase transitions and also the positions of phase boundaries.