We performed high-magnetic-field magnetization, polarization, and ultrasonic measurements in Ba₂CuGe₂O₇ 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 Pc exhibits an increase, and elastic constants show a softening above 20 T. Based on quantum states with a crystalline electric field for the D2d point group and d-p hybridization between Cu-$3d$ and O-$2p$ electrons, we confirmed that the matrix of an electric dipole Pz was proportional to that of an electric quadrupole Oxy. Furthermore, considering the spin-orbit coupling of $3d$ electrons and the Zeeman effect, we showed that Pz and Oxy 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 Ba₂CuGe₂O₇.
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Kurihara et al. (2024) studied this question.
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