  The compound Ba3HoRu2O9 magnetically orders at 50 K (TN1) followed by another
complex magnetic ordering at 10.2 K (TN2). The 2nd magnetic phase transition
was characterized by the co-existence of two competing magnetic ground states
associated with two different magnetic wave vectors (K1=1/2 0 0 and K2=1/4 1/4
0). Here, we have discussed the origin of spin-driven ferroelectricity, which
is not known yet. We demonstrate through time-of-flight Neutron diffraction and
theoretical calculation that the non-collinear structure involving two
different magnetic ions, Ru(4d) and Ho(4f), break the spatial inversion
symmetry via inverse Dzyaloshinskii-Moriya (D-M) interaction through strong
4d-4f magnetic correlation, which shifts the oxygen atoms and results in
non-zero polarization. Such an observation of inverse D-M interaction from two
different magnetic ions which caused ferroelectricity is rarely observed. We
have systematically studied the spin and dipolar dynamics, which exhibit
intriguing behavior with shorter coherence lengths of 2nd 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 synchrotron XRD analysis predicts a non-centrosymmetric space group P-62c.
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 2nd magnetic phase.
Our study shows an unconventional mechanism of spin-driven ferroelectricity.
