Optical control of structure-driven magnetic order offers a platform for magneto-optical terahertz devices. We control the magnetic phases of d1 Mott insulating titanates using nonlinear phononics to transiently perturb the atomic structure based on density functional theory (DFT) simulations and solutions to a lattice Hamiltonian including nonlinear multimode interactions. We show that magnetism is tuned by indirect excitation of a Raman-active phonon mode, which affects the amplitude of the TiO₆ octahedral rotations that couple to static Ti-O Jahn-Teller distortions, through driven infrared-active modes of LaTiO₃ and YTiO₃. The mode excitation reduces the rotational angle, driving a magnetic phase transition from a ferromagnetic (FM) to G-type antiferromagnetic (AFM) state. A novel A-type AFM state hidden in the bulk equilibrium phase diagram emerges as a dynamically accessible optically induced phase under multimode excitations. Our work shows that nonlinear phononics can stabilize phases inaccessible to static chemical substitutions or lattice strains.

The linear and nonlinear phononic interactions between an optically excited infrared (IR) or hyper-Raman mode and a driven Raman mode are computed for the d0 (CaTiO₃) and d1 (LaTiO₃) titanates within a first-principles density functional framework. We calculate the potential energy surface expanded in terms of the A_g or B_1g mode amplitudes coupled to the Au or the B3u mode and determine the coupling coefficients for these multimode interactions. We find that the linear-quadratic coupling dominates the anharmonicities over the quadratic-quadratic interaction in the perovskite titanates. The IR and Raman modes both modify the electronic structure with the former being more significant but occurring on a different time scale; furthermore, the coupled-mode interactions lead to sizable perturbations to the valence bandwidth (∼100 meV) and band gap (∼50 meV). By comparing the coupling coefficients of undoped CaTiO₃ and LaTiO₃ to those for electron-doped (CaTiO₃) and hole-doped (LaTiO₃) titanates, we isolate the role of orbital filling in the nonlinear coupling process. We find that with increasing occupancy of the d manifold, the linear-quadratic interaction decreases by approximately 30% with minor changes induced by the cation chemistry (that mainly affect the phonon mode frequencies) or by electron correlation. We identify the importance of the Ti-O bond stiffness, which depends on the orbital filling, in governing the lattice anharmonicitiy. This microscopic understanding can be used to increase the nonlinear coupling coefficient to facilitate more facile access of nonequilibrium structures and properties through ionic Raman scattering processes.