Signatures of nonlinear magnetoelectricity in the second harmonic spectra of SU(2) symmetry-broken quantum many-body systems

Quantum mechanical perturbative expressions for second-order dynamical magnetoelectric (ME) susceptibilities have been derived and calculated for a small molecular system using the Hubbard Hamiltonian with SU(2) symmetry breaking in the form of spin–orbit coupling (SOC) or spin–phonon coupling. These susceptibilities will have signatures in second harmonic generation spectra. We show that SU(2) symmetry breaking is the key to generate these susceptibilities. We have calculated these ME coefficients using the full many-body basis and solved the Hamiltonian matrix for low-lying excited states using Lanczos method. Varying the Hubbard term along with SOC strength, we find spin and charge and both spin–charge dominated spectra of dynamical ME coefficients. We have shown that intensities of the peaks in the spectra are the highest when the magnitudes of Hubbard and SOC strengths are in a similar range.