Fig. 10: Magnon-magnon couplings in rare-earth ferrites.

a Schematic of two magnon modes in canted antiferromagnet YFeO₃ and ErFeO₃: quasi-ferromagnetic (qFM) mode, which corresponds to a precession of the magnetization orientation, and the quasi-antiferromagnetic (qAFM) mode, which corresponds to an oscillation of the magnetization amplitude. Microscopically, spin dynamics in the qFM (or qAFM) mode correspond to the out-of-phase (or in-phase) precession of the sublattice spins S₁ and S₂. b Terahertz field-induced free-induction decay signals of ErFeO₃, corresponding to excitation of either the a-axis qFM mode or the c-axis qAFM mode for both \({{\bf{H}}}_{\det }\parallel {{\bf{H}}}_{{\rm{THz}}}\) and \({{\bf{H}}}_{\det }\perp {{\bf{H}}}_{{\rm{THz}}}\) detection configurations. Here, H_THz is the magnetic field in the terahertz pulse and \({{\bf{H}}}_{\det }\) is the detected free-induction decay signals. c Room-temperature nonlinear 2D THz spectrum of ErFeO₃ collected in the \({{\bf{H}}}_{\det }\perp {{\bf{H}}}_{{\rm{THz}}}\) detection geometry, with H_THz∥c showing the strong off-diagonal qFM-to-qAFM magnon up-conversion peak. d Nonlinear 2D THz spectrum of YFeO₃ for the geometry where H_THz∥ac is the bisector direction. Labeled peaks correspond to pump-probe (PP), rephasing or photon echo (R), non-rephasing (NR), second-harmonic-generation (SHG), sum-frequency-generation (SFG), and difference-frequency-generation (DFG) signals; I and II refer to the qFM and qAFM modes, respectively. For the sum and difference frequency signals, the assignment refers to the excitation frequency and indicates which magnon mode was excited by the first THz field. Panels a and d adapted from ref. ²²⁵, and Panels b and c adapted from ref. ²²⁴, Springer Nature Ltd.