Origin of spin-driven ferroelectricity and effect of external pressure on the complex magnetism of the 6H perovskite Ba3Ho Ru2 O9

The compound Ba3HoRu2O9 magnetically orders at 50 K (TN1), followed by another complex magnetic ordering at 10.2 K (TN2). The second magnetic phase transition was characterized by the coexistence of two competing magnetic ground states associated with two different magnetic wave vectors (K1=0.500 and K2=0.250.250). The multiferroicity and magnetoelectric coupling were predicted below TN2 in these 4d-based materials. Here, we have discussed the origin of spin-driven ferroelectricity, which is not known yet, and the nature of magnetoelectric domains. We have investigated the compound through time-of-flight neutron diffraction, synchrotron x-ray diffraction (XRD), ac susceptibility, frequency-dependent complex dielectric spectroscopy, and dc magnetization under external pressure. We have demonstrated that the noncollinear structure involving two different magnetic ions, Ru (4d) and Ho (4f), breaks the spatial inversion symmetry via inverse Dzyaloshinskii-Moriya (DM) interaction through strong 4d-4f magnetic correlation, which shifts the oxygen atoms and results in nonzero polarization. Such an observation of inverse DM interaction from two different magnetic ions which cause ferroelectricity is rarely observed. The stronger spin-orbit coupling of 4d orbital might play a major role in creating DM interaction of noncollinear spins. We have systematically studied the spin and dipolar dynamics, which exhibit intriguing behavior with shorter coherence lengths of second magnetic phase associated with the k2 wave vector. The results manifest the development of finite-size magnetoelectric domains instead of true long-range ordering, which justifies the experimentally obtained low value of ferroelectric polarization. The lattice parameters and volume show a sharp anomaly at TN2 obtained by analyzing the temperature-dependence XRD, which is consistent with the ferroelectric transition, predicting a noncentrosymmetric space group, P6¯2c, for this compound. Furthermore, we have investigated the effect of external pressure on this complex magnetism. The result reveals an enhancement of ordering temperature by the application of external pressure (∼1.6 K/GPa). The external pressure might favor stabilizing the magnetic ground state associated with second magnetic phase. Our study shows an unconventional mechanism of spin-driven ferroelectricity involving inverse DM interaction between Ru (4d) and Ho (4f) magnetic ions due to strong 4d-4f cross coupling.