  We report electric polarization and magnetization measurements in single
crystals of double perovskite Lu2MnCoO6 using pulsed magnetic fields and
optical second harmonic generation (SHG) in DC magnetic fields. we observe
well-resolved magnetic field-induced changes in the electric polarization in
single crystals and thereby resolve the question about whether multiferroic
behavior is intrinsic to these materials or an extrinsic feature of
polycrystals. We find electric polarization along the crystalline b-axis, that
is suppressed by applying a magnetic fields along c-axis and advance a model
for the origin of magnetoelectric coupling. We furthermore map the phase
diagram using both capacitance and electric polarization to identify regions of
ordering and regions of magnetoelectric hysteresis. This compound is a rare
example of coupled hysteretic behavior in the magnetic and electric properties.
The ferromagnetic-like magnetic hysteresis loop that couples to hysteretic
polarization can be attributed not to ordinary ferromagnetic domains, but to
the rich physics of magnetic frustration of Ising-like spins in the axial
next-nearest neighbor interaction model.
