Berezinskii-Kosterlitz-Thouless transition effects on spin current: The normal-metal–insulating-ferromagnet junction case

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We investigate the temperature effects on the spin current through an interface between a normal metal and a quasi-two-dimensional ferromagnetic insulator. Conductive electrons are reflected at the interface absorbing or emitting magnons. The interaction process depends on the temperature, and we are interested in finding out how the transport of spin current is affected close to the Berezinskii-Kosterlitz-Thouless (BKT) transition. That is an important open question. While the thermodynamics of spin currents in the usual normal-metal--insulating-ferromagnet interfaces are known, the results of a BKT transition are still unknown. As it is well documented, the BKT transition is associated with the unbinding of vortex-antivortex pairs in two-dimensional models with an O(2) symmetry. In our work, the ferromagnet is a layered quasi-two-dimensional material, and in the limit of weak interplane coupling, a BKT transition is expected. Using the self-consistent harmonic approximation), we have obtained the BKT transition temperature (${T}_{\text{BKT}}$) and the spin current as a function of the temperature. The spin current behavior at low temperatures is similar to those obtained from theoretical and experimental systems. At ${T}_{\text{BKT}}$, the spin current shows a discontinuous jump associated with vortex dissociation.