Ba$_2$CuGe$_2$O$_7$ 中由宇称混合的 $d$-$p$ 杂化态与电多极子引起的场致电极化与弹性软化
Field-induced electric polarization and elastic softening caused by parity-mixed $d$-$p$ hybridized states with electric multipoles in Ba$_2$CuGe$_2$O$_7$
AI总结：
通过高磁场实验和量子态分析，发现 Ba$_2$CuGe$_2$O$_7$ 中电偶极子与电四极子耦合导致场致电极化和弹性软化，表明轨道自由度参与高场多铁性。
摘要：
我们对 Ba$_2$CuGe$_2$O$_7$ 进行了高磁场磁化、极化和超声测量，以研究由电偶极子与电四极子之间的交叉关联以及磁偶极子与电偶极子之间的交叉关联引起的场致多铁性质。对于多个磁场方向，磁化强度 $M$ 在 20 T 以上表现出饱和行为，然而电极化 $P_c$ 呈现增加，弹性常数在 20 T 以上表现出软化。基于 $D_{2d}$ 点群晶体电场和 Cu-$3d$ 与 O-$2p$ 电子之间 $d$-$p$ 杂化的量子态，我们确认了电偶极子 $P_z$ 的矩阵与电四极子 $O_{xy}$ 的矩阵成正比。此外，考虑 $3d$ 电子的自旋轨道耦合和塞曼效应，我们表明 $P_z$ 和 $O_{xy}$ 同时表现出场致响应。这些发现表明，除了自旋自由度外，轨道自由度也贡献于 Ba$_2$CuGe$_2$O$_7$ 的高场多铁性。
英文摘要：
We performed high-magnetic-field magnetization, polarization, and ultrasonic measurements in Ba$_2$CuGe$_2$O$_7$ to investigate field-induced multiferroic properties arising from a cross-correlation between electric dipoles and electric quadrupoles in addition to cross-correlation between magnetic dipoles and electric dipoles. Magnetization $M$ shows saturation behavior above 20 T for several magnetic field directions, however, electric polarization $P_c$ exhibits an increase, and elastic constants show a softening above 20 T. Based on quantum states with a crystalline electric field for the $D_{2d}$ point group and $d$-$p$ hybridization between Cu-$3d$ and O-$2p$ electrons, we confirmed that the matrix of an electric dipole $P_z$ was proportional to that of an electric quadrupole $O_{xy}$. Furthermore, considering the spin-orbit coupling of $3d$ electrons and the Zeeman effect, we showed that $P_z$ and $O_{xy}$ simultaneously exhibited field-induced responses. These findings indicate that the orbital degrees of freedom, in addition to the spin degrees of freedom, contribute to the high-field multiferroicity in Ba$_2$CuGe$_2$O$_7$.
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