Spin-orbit and spin-lattice dynamics in magnetic nanostructures

Timothy Ziman1, Gerrit Bauer2,3, Yaroslav Blanter3, Michiyasu Mori 4
1Institut Laue Langevin, and LPMMC, University Grenoble-Alpes, France
2Institute of Materials Research, Tohoku University
3Kavli Institute of Nanotechnology, Delft University of Technology
4ASRC, JAEA

Abstract
We studied the influence of the interplay of spin-orbit interactions and spin-lattice couplingson the dynamics and transport of magnetic structures, such as domain walls and spin currents
in alloys. We related these to observations of Spin Seebeck effects and spin pumping.
1. Research Objectives
Spin-orbit interactions constitute the microscopic mechanism for many key effects in bothpure and applied magnetism, involving coupling of orbital and spin degrees of freedom. Spinorbit effects are also basic to the effects of crystalline anisotropy in magnetic systems and thecoupling between magnetism and lattice effects. The interplay between lattice vibrations,quantized as phonons and magnetic degrees of freedom leads to couplings between heat andspin currents which can lead to a new generation of devices, for example spin-current injectors.
Our aim is to relate the more microscopic measurements, for example of neutron scattering tonano-magnetic transport as is exploited in novel devices.
2. Research Contents
We extended our previous calculations, with particular emphasis on frustrated systems,
guided by choices of experimental colleagues at the ASRC and elsewhere in order to makedirect comparisons between theory and experiment [1,2].
Magnon-phonon and magnon-polaron couplings were studied both from the point of view of
microscopic analysis of bulk materials, as can be compared in great detail to experimental
results by neutron scattering, taking advantage of close contacts at the ASRC and ILL, but
increasingly also by delicate measurements in nano-scale devices by measurements such as
spin-current injection and spin Seebeck effects at the ASRC, IMR, Delft. From a theoreticalpoint of view the spin dynamics can be treated more classically starting with coupled Landau
Lifshitz Gilbert equations or, as appropriate at low temperatures, by explicit quantum
mechanical methods such as Density Matrix Renormalization Group or high order
perturbation theory.

3. Research results
Brillouin light scattering is an established technique to study magnons. Its efficiency can beenhanced by cavities that concentrate the light intensity. In Ref. [3], we considered theinelastic scattering of photons by a magnetic sphere that supports optical whispering gallery
modes in a plane normal to the magnetization (see Fig. 1). Magnons with low angular momenta
scatter the light in the forward direction with a pronounced asymmetry in the Stokes and theanti-Stokes scattering strength while magnons with large angular momenta constitute Damon
Eshbach modes and were shown to reflect light inelastically. We calculated the reflection
spectrum and derived selection rules based on the chirality of the Damon Eshbach magnons.
This gives a means of controlling energy transfer to the magnet by light.

Fig 1：Interaction of incoming light with the whispering gallery modes of a sphericalcavityTerbium gallium garnet (TGG) is well known for its high Verdet constant and is theprototypical system for the thermal Hall effect. The theoretical explanation for this effect wasproposed to stem from resonant phonon scattering from crystal field levels at
superstoichiometric Tb3+ ions. Using recent inelastic neutron scattering results which havedemonstrated that these excess ions are at sites of tetragonal symmetry, we have constructeda detailed description of the crystal field levels for the orthorhombic stoichiometric ions andsuperstoichiometric sites [4]. In particular, the tetragonal sites are predicted to have low-lying
doublet states. This should enable a more quantitative comparison for the measured thermal
Hall effects, starting from the theory of Mori et al. [5].

Fig 2：Crystal field levels analysed in TGG: theprototypical system of the thermal Hall effect
The spin Hall effect is affected by the Coulomb interaction as well as spin–spin correlations
in metals. In Ref. 6, we summarized effects of the enhancement in by resonant skew scattering
induced by electron correlations (See Figs.3 and 4). For example local Coulomb correlations
may significantly change the observed spin Hall angle. Additional effects because of the special
atomic environment close to a surface — extra degeneracies compared to the bulk, enhanced
correlations that move the local atomic levels, and interference effects coming from the local

geometry. We also reconsidered impacts on the spin Hall effect of cooperative effects, mostrecently in metallic spin glasses, where exchange via slowly fluctuating magnetic moments
may lead to the precession of an injected spin current.

k’kspin current

charge current
Fig 3 ： Schematic figure of skew scattering of electron from momentum k to k’ . Its
scattering amplitude depends on the electron spin shown by blue arrows. This converts
charge current (blue broken line) into spin current (red broken line).

Fig 4：Schematic behavior of the anomalous Hall effect, (left), and spin Hall effect, (right).
Figures from Ref. [6].
4. Conclusion
The experimental advances in spintronics devices continue to pose many challenging questions
to the theoretical community, and pressing new questions, are raised especially concerningmodes that are hybrids of phonons, magnons and, most recently light. Skew effects are small
but significant and occur for both electron and phonon scattering. Understanding from a
microscopic point of view is a source of novel theory and may suggest novel control mechanisms.

5. References[1] M. Mori, ‘Broad line-width of antiferromagnetic spinwave due to electrons correlation’, J.
Phys. Soc. Jpn. 86, 124705 (2017).
[2] M. Matsuda, H. Onishi, A. Okutani, J. Ma, H. Agrawal, T. Hong, D. M. Pajerowski, J. R. D.
Copley, K. Okunishi, M. Mori, S. Kimura, and M. Hagiwara, ‘Magnetic structure anddispersion relation of the S=1/2 quasi-one-dimensional Ising-like antiferromagnet BaCo2V2O8
in a transverse magnetic field’, Phys. Rev. B 96, 024439 (2017).
[3] Sharma, Ya. M. Blanter, and G. E. W. Bauer, 'Light scattering by magnons in whispering
gallery mode cavities', Phys. Rev. B 96, 094412 (2017)[4] R. Wawrzynczak et. al., ‘Magnetic order and single-ion anisotropy in the frustrated magnet- Tb3Ga5O12’, in preparation.

[5] M. Mori, A. Spencer-smith, O. P. Sushkov, S. Maekawa, ‘ Origin of the Phonon Hall Effectin Rare-Earth Garnets’, Phys. Rev. Lett. 113, 265901 (2014)[6] T. Ziman, Bo Gu, and S. Maekawa, 'Skew Scattering from Correlated Systems: Impurities
and Collective Excitations in the Spin Hall Effect', J. Phys. Soc. Jpn. 86, 011005 (2017).