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arXiv:1108.3686 · Physical Review B

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

Frédéric Michaud, F. Vernay, Frédéric Mila

Published Nov 16, 2011• 32 citations
arXivHTMLPDF

Abstract

Motivated by the lack of an obvious spectroscopic probe to investigate nonconventional order such as quadrupolar orders in spin $S>\frac{1}{2}$ 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 $S=\frac{1}{2}$ 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 $\ensuremath{\hbar}{\ensuremath{\omega}}_{\text{in}}\ensuremath{\lesssim}U$, the standard Loudon-Fleury operator remains the leading term of the expansion as in the spin-$\frac{1}{2}$ case. For $\ensuremath{\hbar}{\ensuremath{\omega}}_{\text{in}}\ensuremath{\lesssim}4U$, a second resonant regime is found with a leading term that takes the form of a biquadratic coupling $\ensuremath{\sim}{({\mathbf{S}}_{i}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathbf{S}}_{j})}^{2}$. 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.

DOI
10.1103/physrevb.84.184424

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We study Raman scattering from 1D antiferromagnets within the Fleury-Loudon scheme by applying a finite temperature Lanczos method to a 1D spin-half Heisenberg model with nearest-neighbor ( J1{J}_{1}J1​) and second-neighbor ( J2{J}_{2}J2​) interactions. The low-temperature spectra are analyzed in terms of the known elementary excitations of the system for J2=0{J}_{2}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0J2​=0 and J2=1/2{J}_{2}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2J2​=1/2. We find that the low- TTT Raman spectra are very broad for $|{J}_{2}/{J}_{1}|\ensuremath{\le}0.3$. This broad peak gradually diminishes and shifts with temperature, so that at T>J1T>{J}_{1}T>J1​ the spectra are narrower and peaked at low frequencies. The experimental spectra for CuGeO3{\mathrm{CuGeO}}_{3}CuGeO3​ are discussed in light of our calculations.
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