Laboratoire de Physique Théorique
Toulouse - UMR 5152

Generation of electric current loops by local injection of pure spin current :

Spin injection has been a key element of many prototypical spintronic (spin electronic) setups, and understanding its fundamentals would be vital for building real devices. With Yaroslaw Bazaliy, we studied spin injection in ferromagnetic-normal sandwiches. Curiously enough, we found that, if pure spin injection is local, it inevitably produces electric current vortices, centered at the interface between the ferromagnet and the normal metal. Remarkably, the effect takes place in the absence of any electric current entering or leaving the device :

Yaroslaw Bazaliy and RR, Appl. Phys. Lett. 110, 092405 (2017)

The work above was done for a perfectly transparent interface between the normal (N) and ferromagnetic (F) parts. Recently, we followed up this work by studying the case of a tunnel barrier, separating N from F :

Ya. B. Bazaliy and RR, arXiv:1911.01034 (2019)

Curiously enough, the effect survives even in the limit of a low-transparency tunnel barrier, and circulating electric currents significantly alter the voltage distribution in the device.

The image below shows a device, made of a normal (N) layer and a ferromagnetic (F) overlayer, with an insulating tunnel barrier between them. No electric current is entering or leaving the device, while pure spin current j^s is injected from the left. Closed loops show circulating electric currents, induced by pure spin injection :

Reciprocity in diffusive spintronic devices :

In DC electric circuits, a textbook resistor is characterized by a single parameter, the resistance R that encapsulates the element’s material properties, shape, size, and contact positions. In spintronics, where spin and charge currents are interconnected, an element is characterized by a conductance matrix rather than by a single number. Even for a simplest two-terminal diffusive device, this is an 8 x 8 matrix, and one may wonder about the number of its independent entries. With Ya. Bazaliy, we showed, that that in diffusive devices of a certain class, the entries of the spintronic conductance matrix obey a special kind of general relations that are independent of shape, size and material constants of the actual physical elements, and are similar to classic reciprocity relations for electric circuits. Generally, these relations are different from the Onsager reciprocity relations. As a result, the 8 x 8 conductance matrix of a two-terminal diffusive device reduces to only 28 independent entries :

Ya. B. Bazaliy and RR, Phys. Rev. B 99, 184443 (2019)