Spin-spin interaction of spatially separated electron spins in the field of electromagnetic radiation

Background. At present, researchers are paying considerable attention to the search for new magnetic metamaterials. In this regard, this article solves the urgent problem of deriving nonlocal equations for the propagation of electromagnetic waves in magnetic media, where spin transitions are carried out under the action of radio frequency, microwave and terahertz fields. Based on these equations, it is proposed to solve various problems similar to those already being solved in optics.
Materials and methods. The solution to the problem posed is based on the effects of the 2$^{nd}$ and 3$^{rd}$ orders of quantum electrodynamics, highlighting the spin-spin interactions of spatially separated electrons of two hydrogen atoms. In this case, the expansion of the retarded potentials takes into account two smallness parameters $(v/c)$ and $(\Delta\xi/R_{12})$, where $v$ is the speed of motion of electrons, $c$ is the speed of light in vacuum, $\Delta\xi$ is the displacement of electrons relative to immobile nuclei, $R_{12}$ is the distance between the nuclei of atoms. Сonclusions. It is shown that the operator of the spin-spin interaction of two spatially separated electrons belonging to two hydrogen-like atoms contains terms proportional to $1/R_{12}^{3}$, $1/R_{12}^{2}$, $1/R_{12}$, in contrast to the Breit operator, where the interaction of two electrons is determined only by the terms $1/R_{12}^{3}$. On the basis of the obtained operator of spin-spin interaction of two spatially separated electrons, passing to the effects of the third order of quantum electrodynamics, an equation for the propagation of electromagnetic waves in a system of electron spins is obtained.