Dissipationless spin - current between Heisenberg ferromag - nets with spin - orbit coupling

– A system exhibiting multiple simultaneously broken symmetries offers the opportunity to influence physical phenomena such as tunneling currents by means of external control parameters. Time-reversal symmetry and inversion symmetry are both absent in ferromag-netic metals with substantial spin-orbit coupling. We here study transport of spin in a system consisting of two ferromagnets with spin-orbit coupling separated by an insulating tunneling junction. A persistent spin-current across the junction is found, which can be controlled in a well-defined manner by external magnetic and electric fields. The behavior of the spin-current for important geometries and limits is studied. Due to the increasing interest in the field of spintronics in recent years [1], the idea of utilizing the spin degree of freedom in electronic devices has triggered an extensive response in many scientific communities. The spin-Hall effect is arguably the research area which has received most focus in this context, with substantial effort being put into theoretical considerations [2] as well as experimental observations [3]. As the ambition of spintronics is to make use of the spin degree of freedom rather than electrical charge, investigations of mechanisms that offer ways of controlling spin-currents are of great interest. Ferromagnetism and spin-orbit coupling are physical properties of a system that crucially influence the behavior of spins present in that system. For instance, the presence of spin-orbit coupling is highly important when considering ferromagnetic semiconductors [4]. Such heterostructures have been proposed as devices for obtaining controllable spin injection and manipulating single electron spins by means of external electrical fields, making them a central topic of semiconductor spintronics [5]. In ferromagnetic metals, spin-orbit coupling is ordinarily significantly smaller than for semiconductors due to the bandstructure. However, the presence of a spin-orbit coupling in ferromagnets could lead to new effects in terms of quantum transport. Studies of tunneling between ferromagnets have uncovered interesting physical effects [7, 15]. Nogueira et al. predicted [15] that a dissipationless spin-current should be established across the junction of two Heisenberg ferromagnets, and that the spin-current was maximal in the special case of tunneling between planar ferromagnets. Also, there has been investigations of what kind of impact spin-orbit coupling constitutes on tunneling currents c EDP Sciences