  In order to clarify the mechanism associated with
pressure/magnetic-field-induced giant ferroelectric polarization in TbMnO3,
this work investigated changes in magnetic ordering brought about by variations
in temperature, magnetic field, and pressure. This was accomplished by means of
neutron diffraction analyses under high pressures and high magnetic fields,
employing a single crystal. The incommensurate magnetic ordering of a cycloid
structure was found to be stable below the reported critical pressure of 4.5
GPa. In contrast, a commensurate E-type spin ordering of Mn spins and a
noncollinear configuration of Tb spins with k=(0,1/2,0) appeared above 4.5 GPa.
The application of a magnetic field along the a axis (H_{||a}) under pressure
induces a k=(0,0,0)antiferromagnetic structure in the case of Tb spins above
H_{||a}, enhancing the ferroelectric polarization, while the E-type ordering of
Mn spins is stable even above the critical field. From the present experimental
findings, we conclude that the E-type ordering of Mn spins induces giant
ferroelectric polarization through an exchange striction mechanism. The
H_{||a}-induced polarization enhancement can be understood by considering that
the polarization, reduced by the polar ordering of Tb moments in a zero field,
can be recovered through a field-induced change to nonpolar k=(0,0,0) ordering
at H_{||a} ~ 2T.
