Theory of induced quadrupolar order in tetragonalYbRu2Ge2

Abstract

The tetragonal compound $\mathrm{Yb}{\mathrm{Ru}}_{2}{\mathrm{Ge}}_{2}$ exhibits a nonmagnetic transition at ${T}_{0}=10.2\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ and a magnetic transition at ${T}_{1}=6.5\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ in zero magnetic field. We present a model for this material based on a quasiquartet of ${\mathrm{Yb}}^{3+}$ crystalline electric field (CEF) states and discuss its mean-field solution. Taking into account the broadening of the specific heat jump at ${T}_{0}$ for magnetic field perpendicular to [001] and the decrease of ${T}_{0}$ with magnetic field parallel to [001], it is shown that ferroquadrupole order of either ${\mathrm{O}}_{2}^{2}$- or ${\mathrm{O}}_{xy}$-type are prime candidates for the nonmagnetic transition. Considering the matrix element of these quadrupole moments, we show that the lower CEF states of the level scheme consist of a ${\ensuremath{\Gamma}}_{6}$ and a ${\ensuremath{\Gamma}}_{7}$ doublet. This leads to induced type of ${\mathrm{O}}_{2}^{2}$ and ${\mathrm{O}}_{xy}$ quadrupolar order parameters. The quadrupolar order introduces exchange anisotropy for planar magnetic moments. This causes a spin-flop transition at low fields perpendicular [001] which explains the observed metamagnetism. We also obtain a good explanation for the temperature dependence of magnetic susceptibility and specific heat for fields both parallel and perpendicular to the [001] direction.