'Pseudo-acoustic' magnon dispersion in yttrium iron garnet

Abstract

The spin Seebeck effect (SSE) is observed in magnetic insulator|heavy metal bilayers as an inverse spin Hall effect voltage under a temperature gradient. The SSE can be detected nonlocally as well, viz. in terms of the voltage in a second metallic contact (detector) on the magnetic film, spatially separated from the first contact that is used to apply the temperature bias (injector). Magnon-polarons are hybridized lattice and spin waves in magnetic materials, generated by the magnetoelastic interaction. Kikkawa et al. [Phys. Rev. Lett. 117, 207203 (2016)] interpreted a resonant enhancement of the local SSE in yttrium iron garnet (YIG) as a function of the magnetic field in terms of magnon-polaron formation. Here we report the observation of magnon-polarons in nonlocal magnon spin injection/detection devices for various injector-detector spacings and sample temperatures. Unexpectedly, we find that the magnon-polaron resonances can suppress rather than enhance the nonlocal SSE. Using finite element modelling we explain our observations as a competition between the SSE and spin diffusion in YIG. These results give unprecedented insights into the magnon-phonon interaction in a key magnetic material. When sound travels through a magnet the local distortions of the lattice exert torques on the magnetic order due to the magnetoelastic coupling 1. By reciprocity , spin waves in a magnet affect the lattice dynamics. The coupling between spin and lattice waves (magnons and phonons) has been intensively researched in the last half century 2,3. Yttrium iron garnet (YIG) has been a singularly useful material here, because it can be grown with exceptional magnetic and acoustic quality 2. Magnons and phonons hybridize at the (anti)crossing of their dispersion relations, a regime that has attracted recent attention 4-10. When the quasiparticle lifetime-broadening is smaller than the interaction strength, the strong coupling regime is reached; the resulting fully mixed quasiparticles have been referred to as magnon-polarons 6,7. In spite of the long history and ubiquity of the magnon-phonon interaction, it still leads to surprises. Evidence of a sizeable magnetoelastic coupling in YIG was recently found in experiments on spin caloritronic effects, i.e. the spin Peltier 11 and spin Seebeck effect 12,13 (SPE and SSE respectively). Recently, Kikkawa et al. showed that the hybridization of magnons and phonons can lead to a resonant enhancement of the local SSE in YIG 9. Bozhko et al. found that this hybridization can play a role in the thermalization of parametrically excited magnons using Brillouin light scattering. They observed an accumulation of magnon-polarons in the spectral region near the anticrossing between the magnon and transverse acoustic phonon modes 14. However, these previous experiments did not address the transport properties of magnon-polarons. Nonlocal spin injection and detection experiments are of great importance in probing the transport of spin in metals 15 , semiconductors 16 and graphene 17. Varying the dis...

The full magnon spectrum of yttrium iron garnet

“…The inclusion of interactions up to the 6th nearest neighbour is guided by previous experimental results and ab initio calculations which indicate that the magnitudes of J 4 -J 6 could be as much as 5-10% that of the dominant exchange interaction J 1 . 21,23 Due to the extremely large number (20) of magnetic atoms within the primitive cell, and the consideration of so many exchange pathways, this analysis would be impossible without the use of sophisticated software such as SpinW as the construction of an analytic model would be prohibitively time consuming. During the fitting process, features in the spectrum were weighted so that weak but meaningful features in the data were considered as significant as strong features.…”

“…Despite this, surprisingly little data exists relating to the detail of its magnon mode structure. The previous key work in this area is due to Plant et al, 20,21 35-45 years ago. Using a triple-axis spectrometer, these early neutron scattering measurements were able to record a few of the spin wave modes up to approximately 55 meV (14 THz), but crucially there are a total of 20 distinct modes for a given wave vector and they are predicted to extend up to approximately 90 meV (22 THz).…”

Effect of the magnon dispersion on the longitudinal spin Seebeck effect in yttrium iron garnets

“…In terms of group velocity, it increases with energy when the dispersion is quadratic, but saturates at a maximum value v GS when the dispersion becomes linear. These features can be captured by fitting the measured "pseudo-acoustic" magnon dispersion curves in YIG 27 (and ignoring the pseudo-optical modes) with a phenomenological model for the magnon dispersion written by analogy with the electron dispersion in narrow gap semiconductors such as PbTe 39 as:…”

“…In addition, we propose here an empirical model for the temperature dependence of the LSSE at low temperature and in thin films wherein magnon transport is ballistic. The model takes into account the change of the magnon dispersion, from quadratic at the zone centerto linear ("pseudo-acoustic" as defined by Plant 27 ) at higher energies;…”

Finite temperature magnon spectra in yttrium iron garnet from a mean field approach in a tight-binding model

“…The full magnon band structure of YIG was modeled by Harris [24] with nearest-neighbor exchange interaction and measured from neutron scattering by Plant [22], from which the values of the exchange interaction coefficients were obtained [2]. The next nearest-neighbor exchange interactions were recently also taken into account with the exchange integrals obtained from the first principle calculation [25] or fitting to the neutron scattering data [26,27]. An atomistic dynamic simulation shows that the nearest-neighbor exchange model with stochastic thermal fluctuation is sufficient to quantitatively reproduce the decrease of the spin wave gap, i.e., the minimal frequency of the antiferromagnetic-like mode, with increasing temperature [23].…”