Direct numerical study on ESR line shape

Abstract

In low dimensional spin systems, the Electron Spin Resonance (ESR) line shape depends on the geometrical situations among the lattice axes, the static field, and the oscillating filed, where the dipole–dipole interaction takes an important role. The famous example is the case of the one dimensional Heisenberg magnet. Models with pure Heisenberg interactions result in only the paramagnetic resonance regardless of the spatial structure of the interaction. Therefore, some perturbations are needed that violate the SU(2) symmetry to have line shift or broadening of the resonance. Usually, the dipole–dipole interaction takes place of this perturbation. Dependence of the line shape of the paramagnetic resonance because of the dipole–dipole interaction is also described. It depends on the angle θH between the chain axis and the static field H0. The angle- and temperature-dependence of the shifts were studied by Nagata and Tazuke with the effective mode method proposed by Kanamori–Tachiki. The shift also depends on the angle φ between the RF field and the chain axis when the static field is applied perpendicular to the chain. The chapter studies temperature dependence of the line shape of ESR for strongly interacting quantum spin systems and characterizes the system by dependence on the relative angles among the axis of the system, static field, and RF field. Direct numerical estimation has been exploited of the dynamical susceptibility with the Kubo formula. This method has been applied to several systems and confirmed validity of the method. Several examples of temperature- and field-dependence of the line shape have been shown.