  Epitaxial strain and chemical substitution have been the workhorses of
functional materials design. These static techniques have shown immense success
in controlling properties in complex oxides through the tuning of subtle
structural distortions. Recently, an approach based on the excitation of an
infrared active phonon with intense mid-infrared light has created an
opportunity for dynamical control of structure through special nonlinear
coupling to Raman phonons. We use first-principles techniques to show that this
approach can dynamically induce a magnetic phase transition from the
ferromagnetic ground state to a hidden antiferromagnetic phase in the rare
earth titanate GdTiO$_3$ for realistic experimental parameters. We show that a
combination of a Jahn-Teller distortion, Gd displacement, and infrared phonon
motion dominate this phase transition with little effect from the octahedral
rotations, contrary to conventional wisdom.
