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arXiv:cond-mat/0009385 · Journal of the Physical Society of Japan

An Electron Spin Resonance Selection Rule for Spin-Gapped Systems

Tôru Sakai, O. Cépas, Timothy A. L. Ziman

Published Nov 15, 2000• 31 citations
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Abstract

The direct electron spin resonance (ESR) absorption between a singlet ground state and the triplet excited states of spin gap systems is investigated. Such an absorption, which is forbidden by the conservation of the total spin quantum number in isotropic Hamiltonians, is allowed by the Dzyaloshinskii-Moriya interaction. We show a selection rule in the presence of this interaction, using the exact numerical diagonalization of the finite cluster of the quasi-one-dimensional bond-alternating spin system. The selection rule is also modified into a suitable form in order to interpret recent experimental results on CuGeO$_3$ and NaV$_2$O$_5$.

DOI
10.1143/jpsj.69.3521

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The direct electron spin resonance (ESR) absorption between a singlet ground state and the triplet excited states of spin gap systems is investigated. Such an absorption, which is forbidden by the conservation of the total spin quantum number in isotropic Hamiltonians, is allowed by the Dzyaloshinskii-Moriya interaction. We show a selection rule in the presence of this interaction, using the exact numerical diagonalization of the finite cluster of the quasi-one-dimensional bond-alternating spin system. The selection rule is also modified into a suitable form in order to interpret recent experimental results on CuGeO3_33​ and NaV2_22​O5_55​.
We study magnetic excitations for anisotropic spin dimer systems. We present a theory that describes not only the lowest-lying excitation mode but also higher-lying modes of the spin dimers, where the latter modes are important for quantum phase transitions driven by magnetic field and pressure in spin-gapped systems. As the most intriguing application, we calculate electron spin resonance (ESR) intensity in the presence of Dzyaloshinskii–Moriya (DM) interaction, which couples the local triplet with the singlet states of the dimer. The ESR intensities under various configurations of the DM interactions are reported in both disordered and field-induced ordered phases, which are very useful for the analysis of high-field ESR data.
In this review, the importance of the Dzyaloshinskii-Moriya Interaction (DMI) to the magnetic properties of quantum spin systems is discussed mainly focusing on the determination of or understanding the role of DMI extracted from highfrequency high-field electron spin resonance (ESR) measurements.This review includes the ESR theories of the S = 1=2 one-dimensional (1D) antiferromagnet with the staggered field (Oshikawa-Affleck theory) and with the uniform DMI, and several related experimental results are shown.Then, the proposed mechanisms of the singlet-triplet transition in quantum spin systems together with the ESR selection rules are introduced in connection with various experimental results.Finally, the role of DMI in the ground state of kagome lattice antiferromagnets and the honeycomb lattice antiferromagnet is discussed with some experimental results.
The recent ESR measurement on the Shastry-Sutherland compound SrCu 2 (BO 3 ) 2 detected the pressure-induced phase transition that is expected to correspond to the quantum phase transition from the orthogonal dimer to the plaquette singlet phases.In this experiment the pressure dependence of the spin gap was observed by ESR.The ESR transition of the spin gap is forbidden due to the spin conservation law, but the Dzyaloshinsky-Moriya interaction of this compound enables the observation.Then the selection rule of the ESR transition of the spin gap in the presence ot the Dzyaloshinsky-Moriya interaction is investigated using the numerical diagonalization of the Shastry-Sutherland model.As a result, it is found that the selection rule changes at the quantum phase transition between the dimer and the plaquette singlet phases.
The dynamical mean-field-like theory of the electron spin resonance (ESR) in spin-1/2 chains with nearest and next-nearest neighbor interactions (or zigzag spin ladders) and alternation is developed. It is explained that either the magnetic anisotropy of spin-spin couplings or the Dzyaloshinskii-Moriya interaction causes shifts of the resonance position in spin chains, comparing to only magnetically isotropic interactions. The power of the ac ESR field, absorbed by the spin chain, is calculated. It is shown that the temperature dependence of the shift of the resonance position is related to the temperature dependence of the ESR absorption. Depending on the strength of next-nearest neighbor interactions, the shift of the ESR position can become either exponentially small or can be increased near quantum critical points. The absorbed by the alternating spin chain power of the ac magnetic field is calculated, manifesting two resonances. The influence of mentioned spin-spin interactions on the linewidth of the ESR is analyzed.
The field- and frequency-dependence of Electron Spin Resonance (ESR) in the Shastry–Sutherland lattice with small Dzyaloshinsky–Moriya (DM) interaction is studied by the direct numerical estimation of the Kubo formula. Beside the strong paramagnetic resonance, we find the resonance due to the transitions between the triplet and singlet levels which are prohibited in the case without the DM interaction. Furthermore, we find the resonance which is distributed in a wide range of the field for a specific frequency, which corresponds to the transition between the states with the same magnetization.
We report experimental verification of the recently predicted collective modes of spinons, stabilized by backscattering interaction, in a model quantum spin chain material. We exploit the unique geometry of uniform Dzyaloshinskii-Moriya interactions in K_{2}CuSO_{4}Br_{2} to measure the interaction-induced splitting between the two components of the electron spin resonance (ESR) response doublet. From that we directly determine the magnitude of the "marginally irrelevant" backscattering interaction between spinons for the first time.