Manipulation of electromagnetic wave propagation in quantum-spin-chain medium

We consider a simple model of one-dimensional magnetic crystal and examine the propagation of an electromagnetic wave through such a medium. Calculating the dispersion relation $\mathbf{k}(\omega )$ allows us to illustrate how the spread of the electromagnetic wave can be controlled by an external magnetic field. Our rigorous calculations should be useful for more realistic (and less tractable mathematically) models of magnetic media.