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.
We have studied spin excitation spectra in the Shastry-Sutherland model compound
SrCu2(BO3)2 in magnetic fields using far-infrared Fourier spectroscopy. The transitions from the ground singlet state to the triplet state at $24\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ and to several bound triplet states are induced by the electric field component of the far-infrared light. To explain the light absorption in the spin system we invoke a dynamic Dzyaloshinskii-Moriya (DM) mechanism where light couples to a phonon mode, allowing the DM interaction. Two optical phonons couple light to the singlet to triplet transition in
SrCu2(BO3)2. One is
a-polarized and creates an intradimer dynamic DM along the
c axis. The other is
c-polarized and creates an intradimer dynamic DM interaction, it is in the
(ab) plane and perpendicular to the dimer axis. Singlet levels at 21.5 and $28.6\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ anticross with the first triplet as is seen in far-infrared spectra. We used a cluster of two dimers with a periodic boundary condition to perform a model calculation with scaled intra- and interdimer exchange interactions. Two static DM interactions are sufficient to describe the observed triplet state spectra. The static interdimer DM in the
c-direction ${d}_{1}=0.7\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ splits the triplet state sublevels in zero field [C\'epas et al., Phys. Rev. Lett. 87, 167205 (2001)]. The static intradimer DM in the
(ab) plane (perpendicular to the dimer axis) ${d}_{2}=1.8\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$, allowed by the buckling of
CuBO3 planes, couples the triplet state to the $28.6\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ singlet as is seen from the avoided crossing.
We calculate the electron spin resonance (ESR) spectra of the quasi-two-dimensional dimer spin liquid
SrCu2(BO3)2 as a function of magnetic field
B. Using the standard Lanczos method, we solve a Shastry-Sutherland Hamiltonian with additional Dzyaloshinsky-Moriya (DM) terms which are crucial to explain different qualitative aspects of the ESR spectra. In particular, a nearest-neighbor DM interaction with a nonzero
Dz component is required to explain the low frequency ESR lines for $B\ensuremath{\Vert}c$. This suggests that crystal symmetry is lowered at low temperatures due to a structural phase transition.
The field and temperature dependence of the line shape of ESR for strongly interacting quantum spin systems would provide various important informations for the magnetic interaction. We have introduced a method of direct numerical estimation of the dynamical susceptibility with the Kubo formula and applied it to spin systems of various lattice structures. There the ESR line shape shows significant dependence on the strength of the field, and also on the geometrical situation among the directions of the fields and lattice axes.