Theory of induced quadrupolar order in tetragonal YbRu_{2}Ge_{2}

Abstract

The tetragonal compound YbRu${}_2$Ge${}_2$ exhibits a non-magnetic transition at $T_0$=10.2K and a magnetic transition at $T_1$=6.5K in zero magnetic field. We present a model for this material based on a quasi-quartet of 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 ferro-quadrupole order of either O${}_2^2$ or O${}_{\mathrm{xy}}$ - type are prime candidates for the non-magnetic transition. Considering the matrix element of these quadrupole moments, we show that the lower CEF states of the level scheme consist of a ${\Gamma }_6$ and a ${\Gamma }_7$ doublet. This leads to induced type of O${}_2^2$ and O${}_{\mathrm{xy}}$ 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.

13 pages, 6 figures, and 5 tables. published in PRB

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