Theory of inelastic light scattering in spin-1 systems: Resonant regimes and detection of quadrupolar order

Motivated by the lack of an obvious spectroscopic probe to investigate nonconventional order such as quadrupolar orders in spin S > 1/2 systems, we present a theoretical approach to inelastic light scattering for spin-1 quantum magnets in the context of a two-band Hubbard model. In contrast to the S = 1/2 case, where the only type of local excited state is a doubly occupied state of energy U, several local excited states with occupation up to four electrons are present. As a consequence, we show that two distinct resonating scattering regimes can be accessed depending on the incident photon energy. For (h) over bar omega(in) less than or similar to U, the standard Loudon-Fleury operator remains the leading term of the expansion as in the spin-1/2 case. For (h) over bar omega(in) less than or similar to 4U, a second resonant regime is found with a leading term that takes the form of a biquadratic coupling similar to(S-i . S-j)(2). Consequences for the Raman spectra of S = 1 magnets with magnetic or quadrupolar order are discussed. Raman scattering appears to be a powerful probe of quadrupolar order.