Effects of the Dzyaloshinskii-Moriya Interaction on Low-Energy Magnetic Excitations in Copper Benzoate

Abstract

We have investigated the physical effects of the Dzyaloshinskii-Moriya (DM) interaction in copper benzoate. In the low field limit, the spin gap is found to vary as H 2/3 ln 1/6 (J/µBHs) (Hs: an effective staggered field induced by the external field H) in agreement with the prediction of conformal field theory, while the staggered magnetization varies as H 1/3 and the ln 1/3 (J/µBHs) correction predicted by conformal field theory is not confirmed. The linear scaling behavior between the momentum shift and the magnetization is broken. We have determined the coupling constant of the DM interaction and have given a complete quantitative account for the field dependence of the spin gaps along all three principal axes, without resorting to additional interactions like interchain coupling. A crossover to strong applied field behavior is predicted for further experimental verification. . In these materials, the Dzyaloshinskii-Moriya (DM) interaction [7,8,9] plays an important role, especially in an applied magnetic field. This has stimulated extensive investigation on the physical properties of the DM interaction. However, this interaction is rather difficult to handle analytically, which has brought much uncertainty in the interpretation of experimental data and has limited our understanding of many interesting quantum phenomena of low-dimensional magnetic materials.For copper benzoate, Dender et al [1,2] found that the spin excitation gap shows a peculiar field dependence, ∆ ∼ H 0.65 , in low fields. On the contrary, excitations remain gapless in the S=1/2 Heisenberg model below a critical field. Oshikawa and Affleck (OA) suggested that this field dependence of the gap is due to a staggered magnetic field induced by the DM interaction in addition to the staggered g-factor in a uniform field [9,10]. However, a satisfactory explanation for the field-dependence of the energy gaps in all three directions is still lacking [11,12]. It was argued that the inconsistency between the experimental data and theoretical results might be due to the neglect of the interchain coupling and/or anisotropic interaction terms in the low-field effective model used by Oshikawa and Affleck [9,11]. We believe this issue can be clarified by a thorough study of the DM interaction and a direct comparison with experiments.Copper benzoate is a quasi-1D spin-1/2 antiferromagnetic Heisenberg system. The chain direction is the caxis. It contains two types of alternating and slightly tilted CuO 8 octahedra. This leads to two inequivalent Cu ++ ions and an alternating DM coupling [13]. In an applied field, copper benzoate can be modeled by the following Hamiltonian,( 1) where the three terms in the summation are the antiferromagnetic Heisenberg, DM and Zeeman splitting interactions, respectively. The exchange coupling constant J, determined from the neutron scattering measurements, is about 1.57meV. The DM interaction is much weaker than the Heisenberg term. The D-vector, primarily aligned along the a ′′ axis, will be determined numerically. g u and ...

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