A magnon is a quantised spin wave, i.e. a collective excitation of the spin angular momentum that is associated with electrons in a crystal structure. The transfer of spin angular momentum via magnons in magnetic insulators has gained recent interest in the fields of spintronics and magnetics, both from a view point of fundamental understand as well as possible applications. The interplay between magnons and temperature gradients is especially interesting, as reported on in several papers studying the spin Seebeck effect in insulators. This week’s Pick of the Week paper, “Interfacial spin and heat transfer between metals and magnetic insulators” in Phys Rev B by Bender and Tserkovnyak investigates theoretically the role of magnons in non-magnetic metallic (NMM)/ferromagnetic insulator (FMI) systems which are under a thermal gradient. Equations defining the relevant boundary conditions and describing spin and energy currents across the interface are defined.
Bilayers through the years
The transfer of spin angular momentum across the interface of a bilayer structure has been considered in depth over the past 20 years. Initially, theoretical attention was given to bilayers consisting of two non-collinear metallic ferromagnets, where a spin polarised current of iterant electrons generated in one of the ferromagnetic layers could be injected into the other, leading to a torque on its localised moments. This spin transfer torque mechanism is now sufficiently well-established both theoretically and experimentally that it has found practical application in magnetic random access memory. More recently, bilayers of a NMM layer interfaced with a metallic ferromagnetic layer are being used in spin-orbit torque experiments, where pure spin current electrically generated in the NMM by the spin Hall effect is injected into the ferromagnetic metallic layer, again transferring spin angular momentum to it via spin transfer toque. For the NMM/FMI bilayer of interest in Bender and Tserkovnyak’s paper, previous experimental studies have shown it to host interesting phenomena such as spin Hall magnetoresistance (as measured electrically), and Spin Seebek and Peltier effects, spin-pumping, and torques of the moments in the FMI.
While the potential importance of temperature gradients in spintronic systems has been pointed out, there is not currently a sufficient understanding of the relationship between magnonic spin transport and heat currents in a NMM/FMI bilayer. Previous work has formalised this relationship for the case of the spin accumulation in the NMM and the magnetization in the FMI being collinear, but Bender and Tserkovnyak provide the necessary extension to define equations for spin and heat transfer across the NMM/FMI interface for any relative orientation of spin and moments. Their equations are applicable to both large-angle coherent and small-angle incoherent magnetization dynamics in the FMI, and so are applicable to magnetic ordering and magnons respectively. Specifically, the equations describe spin and heat currents across the NMM/FMI interface as a function of the respective temperatures, electrochemical potentials, and spin densities of the two layers.
Spin current affairs
As an experimentalist myself, a lot of the derivations and maths involved in the presented equations is beyond me, but I can appreciate its importance to the paper. Some of the key points from these derivations that leapt out to me include:
- The longitudinal spin current (spin of itinerant electrons in NMM parallel/anti parallel to FMI magnetization) does not lead to a torque as it is absorbed by thermal magnons.
- The net transverse spin current (spin of itinerant electrons in NMM orthogonal to FMI magnetization) leads to a temperature dependent toque on the FMI magnetization.
- Both of these spin currents depend on the spin-mixing conductance of the NMM/FMI interface.
- For the case of spin-polarisation in NMI that is non-collinear with the magnetization of FMI, angular momentum is transferred between the NMI and FMI by an inelastic spin-flip scattering process whereby an up-electron/down-hole pair is created or annihilated in the NMI, which destroys or creates a magnon in the FMI. This is the magnonic contribution to the spin current.
- Unlike magnonic spin currents, spin currents that arise from elastic scattering do not depend on thermal bias, but do depend on the relative orientation of the spin density in the NMI and magnetization in the FMI. These spin currents determine the spin-mixing conductance.
Torque about things heating up
It may be hard for a pure experimentalist to truly comprehend Bender and Tserkovnyak’s work, I certainly found this to be the case. However, having a formally defined set of equations that describe spin and thermal behaviour in thermally biased NMM/FMI bilayers is an important tool for both further theoretical and experimental studies of thermal spin torques. Such thermal spin torques may become somewhat of a hot topic (pardon the pun) over the next couple of years, and so Bender and Tserkovnyak’s paper could turn out to be a bit of a citation machine. This may require sustained Interest in such thermal spin torques, which will only be possible if they are shown to be sufficiently large for device application at sufficiently low energy cost.
Scott A. Bender and Yaroslav Tserkovnyak (2015). Interfacial spin and heat transfer between metals and magnetic insulators Physical Review B (91)