  We report cooperative magnetic orderings in a 6H-perovskite multiferroic
system, Ba3HoRu2O9, via comprehensive neutron powder diffraction measurements.
This system undergoes long-range antiferromagnetic ordering at TN1 ~ 50 K with
a propagation wave vector of K1 = (0.5 0 0), a transition temperature much
higher than the previously reported one at ~10 K (TN2). Both Ru and Ho-moments
order simultaneously below TN1, followed by spin-reorientations at lower
temperatures, demonstrating strong Ru(4d)-Ho(4f) magnetic correlation. Below
TN1 another magnetic phase with a propagation wave vector K2 = (0.25 0.25 0)
emerges and coexists with the one associated with K1, which is rarely observed
and suggests complex magnetism due to phase competition in the magnetic ground
state. We argue that the exchange-striction arising from the up-up-down-down
spin structure associated with K2-wave vector below TN2 may be responsible for
the small ferroelectric polarization reported previously in this compound.
