Theory of Microwave Absorption by the Spin-$1/2$ Heisenberg-Ising Magnet

We analyze the problem of microwave absorption by the Heisenberg-Ising magnet in terms of shifted moments of the imaginary part of the dynamical susceptibility. When both the Zeeman field and the wave vector of the incident microwave are parallel to the anisotropy axis, the first four moments determine the shift of the resonance frequency and the linewidth in a situation where the frequency is varied for fixed Zeeman field. For the one-dimensional model we can calculate the moments exactly. This provides exact data for the resonance shift and the linewidth at arbitrary temperatures and magnetic fields. In current ESR experiments the Zeeman field is varied for fixed frequency. We show how in this situation the moments give perturbative results for the resonance shift and for the integrated intensity at small anisotropy as well as an explicit formula connecting the linewidth with the anisotropy parameter in the high-temperature limit.

Figure 1

Resonance shift $\delta \omega /J$ for the 1D model in the critical regime at $\delta =-0.1$ as function of the magnetic field. Crosses from fully numerical calculation for a finite chain Hamiltonian of 16 sites.

Figure 2

Linewidth $\Delta \omega /J$ for the 1D model in the critical regime at $\delta =-0.1$ as function of temperature. Crosses from fully numerical calculation for finite chain Hamiltonians of 16 and 24 sites.