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.
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