Transverse Spin Seebeck Effect Research Articles

Study of magnon–phonon non-equilibrium in a magnetic insulator—Thulium iron garnet

The non-equilibrium state between magnons and phonons is the key to understand the spin-caloric phenomena. We developed a unique optical reflectometry technique to spatially resolve Kerr angle (θK) and optical reflectance (R) in a magnetic insulator—thulium iron garnet (TmIG). The TmIG was subjected to a thermal gradient to estimate populations of thermally excited magnons and phonons through the variation of θK and R. The results showed that the spatial gradient of θK is different from that of R, indicating the non-equilibrium state between magnons and phonons. Particularly, the characteristic decay length of θK was significantly influenced by the heating power and the magnetic field, suggesting non-linear magnon scattering in a high magnon density regime. Our work not only provides a scheme to investigate the spatial profiles of magnons and phonons but also reveals the magnon–phonon non-equilibrium in TmIG. Hence, this report will stimulate further studies based on magnon–phonon non-equilibrium such as a transverse spin Seebeck effect and Bose–Einstein condensation.

Cryogenic spin Seebeck effect

We present a theory of the non-linearities of the spin Seebeck effect (SSE) in a ferromagnetic nanowire at cryogenic temperatures. We adopt a microscopic quantum noise model based on a collection of two-level systems. At certain positions of Pt detectors to the wire, the transverse SSE changes sign as a function of temperature and/or temperature gradient. On the other hand, the longitudinal SSE does not show significant non-linearities even far outside the regime of validity of linear response theory.

Reply to “Comment on ‘Optical detection of transverse spin-Seebeck effect in permalloy film using Sagnac interferometer microscopy’ ”

In their Comment, Kimling and Kuschel (hereafter the commenters) challenge our original interpretation of the magneto-optical Kerr effect (MOKE) measurements using ultrasensitive Sagnac interferometer, claiming that the transverse spin-Seebeck effect (TSSE) is not the only contribution to the measured change in the Kerr rotation angle from a Ni80Fe20 (NiFe) ferromagnetic (FM) slab subjected to a lateral temperature gradient in the presence of a magnetic field. The authors assert that: (1) the TSSE, in general, has not been completely proven so far, and that the existing theories, in particular the phonon magnon drag model that we have used in our publication, in fact cannot explain the original work of Uchida et al. (2) The commenters based their critique on an estimate of the magnitude of the measured effect, arguing that to observe the TSSE that we originally claimed, the temperature gradient in our measurements should have been much larger than the value we measured. In this Reply, firstly, we summarize previous literature reports on the TSSE response in FM metallic systems. Secondly, we dispute the estimate of the necessary large temperature gradient made by the commenters. Importantly, the Kerr effect sensitivity to spin accumulation (via the TSSE response) has not been recognized by the commenters, in fact it was mistakenly assumed that the Kerr effect sensitivity to the spin accumulation by the TSSE is the same as the Kerr sensitivity to the bulk magnetization change due to the temperature change. In conclusion, we show that the TSSE is the only viable interpretation of our original measurements, and that the phonon-magnon drag model is indeed capable of explaining our results.

Comment on “Optical detection of transverse spin-Seebeck effect in permalloy film using Sagnac interferometer microscopy”

Measuring spin currents and spin accumulations is challenging. This is mainly because of their small size and the lack of a standard spin detector comparable to conventional ampere meters or voltage detectors. It is all the more pleasing to hear about new methods for detecting spin currents and spin accumulations. A recent example is the paper of McLaughlin et al. [Phys. Rev. B 95, 180401 (2017)], who report novel measurements of the transverse spin-Seebeck effect (TSSE) in metals by optical means using a Sagnac interferometer microscope. However, because no standard procedures or reference measurements are available for verification, critical discussions are crucial for evaluation of such novel experimental approaches. In our comment, we estimate the size of the effect observed by McLaughlin et al. To illustrate that the estimated size is exceptionally large, we use a comparison with another spin-caloritronic effect: the spin-dependent Seebeck effect. Such a large TSSE is in contradiction with previous experiments that could not resolve a TSSE signal. Therefore, we suggest that signal measured by McLaughlin et al. is not or not only caused by the TSSE.

Interplay of wave localization and turbulence in spin Seebeck effect

One of the most important discoveries in spintronics is the spin Seebeck effect (SSE) recently observed in both insulating and (semi-)conducting magnets. However, the very existence of the effect in transverse configuration is still a subject of current debates, due to conflicting results reported in different experiments. Present understanding of the SSE is mainly based on a particle-like picture with the local equilibrium approximation (LEA), i.e., spatially resolved temperature-field assumed to describe the system. In this work, we abandon the LEA to some extent and develop a wave theory to explain the SSE, by highlighting the interplay between wave localization and turbulence. We show that the emerging SSE with a sign change in the high/low-temperature regions is closely related to the extendedness of the spin wave that senses an average temperature of the system. On the one hand, ubiquitous disorders (or magnetic field gradients) can strongly suppress the transverse spin Seebeck effect (TSSE) due to Anderson (or Wannier-Zeeman) spin-wave localization. On the other hand, the competing wave turbulence of interacting magnons tends to delocalize the wave, and thus remarkably revives the TSSE before the magnon self-trapping. Our theory provides a promising route to resolve the heated debate on TSSE with a clear experiment scheme to test it in future spin caloritronic devices.

Long-range transverse spin Seebeck effect in permalloy stripes using Sagnac interferometer microscopy

Coupling of spins and phonons in ferromagnets (FM) may persist up to mm length scale, thus generating macroscopic spatially distributed spin accumulation along the direction of an applied thermal gradient to an FM slab. This typical feature of transverse spin Seebeck effect (TSSE) has been demonstrated so far using electrical detection methods in FM films, in particular in a patterned structure, in which FM stripes grown onto a substrate perpendicular to the applied thermal gradient direction are electrically and magnetically isolated. Here we report optically detected TSSE response in isolated FM stripes based on permalloy deposited on SiN substrate, upon the application of a thermal gradient. For these measurements we used the magneto-optic Kerr effect measured by an ultrasensitive Sagnac interferometer microscope that is immune to thermo-electrics artefacts. We found that the optical TSSE coefficient in the NiFe stripes geometry is about one order of magnitude smaller than that in the continuous NiFe film, which is due to the limited phonons path in the FM stripes along the thermal gradient direction. Our results further confirm the existence of TSSE response in conducting FM compounds.

Spin-Seebeck Temperature Sensors

The conceptual designs of two nanoscale spin-Seebeck temperature sensors are proposed based on the longitudinal spin-Seebeck effect (LSSE) in bilayers made of a ferromagnetic insulator Y3Fe5O12 and a Pt, and the transverse spin-Seebeck effect) in Ni81Fe19/Pt structure. The working principles of two sensors are presented. The direct conversion of the temperature information into the electric voltage is described in detail. Moreover, the effect of the spin Hall angle on the performance of sensors is discussed. The results obtained here reveal that the LSSE and TSSE have the potential to realize practical temperature sensors.

Quantitative separation of the anisotropic magnetothermopower and planar Nernst effect by the rotation of an in-plane thermal gradient

A thermal gradient as the driving force for spin currents plays a key role in spin caloritronics. In this field the spin Seebeck effect (SSE) is of major interest and was investigated in terms of in-plane thermal gradients inducing perpendicular spin currents (transverse SSE) and out-of-plane thermal gradients generating parallel spin currents (longitudinal SSE). Up to now all spincaloric experiments employ a spatially fixed thermal gradient. Thus, anisotropic measurements with respect to well defined crystallographic directions were not possible. Here we introduce a new experiment that allows not only the in-plane rotation of the external magnetic field, but also the rotation of an in-plane thermal gradient controlled by optical temperature detection. As a consequence, the anisotropic magnetothermopower and the planar Nernst effect in a permalloy thin film can be measured simultaneously. Thus, the angular dependence of the magnetothermopower with respect to the magnetization direction reveals a phase shift, that allows the quantitative separation of the thermopower, the anisotropic magnetothermopower and the planar Nernst effect.

Dependence of transverse magnetothermoelectric effects on inhomogeneous magnetic fields

Transverse magneto-thermoelectric effects are studied in permalloy thin films grown on MgO substrates. We find that small parasitic magnetic fields below 1 Oe can produce artifacts of the order of 1 % of the amplitude of the anisotropic magneto-thermopower which is also detected in the experiments. The measured artifacts reveal a new source of uncertainties for the detection of the transverse spin Seebeck effect. Taking these results into account we conclude that the contribution of the transverse spin Seebeck effect to the detected voltages is below the noise level of 20 nV.

Longitudinal spin Seebeck effect contribution in transverse spin Seebeck effect experiments in Pt/YIG and Pt/NFO.

The spin Seebeck effect, the generation of a spin current by a temperature gradient, has attracted great attention, but the interplay over a millimetre range along a thin ferromagnetic film as well as unintended side effects which hinder an unambiguous detection have evoked controversial discussions. Here, we investigate the inverse spin Hall voltage of a 10 nm thin Pt strip deposited on the magnetic insulators Y3Fe5O12 and NiFe2O4 with a temperature gradient in the film plane. We show characteristics typical of the spin Seebeck effect, although we do not observe the most striking features of the transverse spin Seebeck effect. Instead, we attribute the observed voltages to the longitudinal spin Seebeck effect generated by a contact tip induced parasitic out-of-plane temperature gradient, which depends on material, diameter and temperature of the tip.

Erratum: Skyrmionic spin Seebeck effect via dissipative thermomagnonic torques [Phys. Rev. B89, 241101(R) (2014)

We derive thermomagnonic torque and its “β-type” dissipative correction from the stochastic Landau-Lifshitz-Gilbert equation. The “β-type” dissipative correction describes viscous coupling between magnetic dynamics and magnonic current and it stems from spin mistracking of the magnetic order. We show that thermomagnonic torque is important for describing temperature gradient induced motion of skyrmions in helical magnets while dissipative correction plays an essential role in generating transverse Magnus force. We propose to detect such skyrmionic motion by employing the transverse spin Seebeck effect geometry.

Thermoelectric effects and magnetic anisotropy ofGa1−xMnxAsthin films

The transverse voltages generated in a ${\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}\mathrm{As}$ ferromagnetic semiconductor in planar Hall effect and transverse spin Seebeck effect configurations are systematically analyzed. The observed field dependences consist of symmetric and asymmetric contributions. The former is attributed to the planar Nernst effect in the magnetic film in the presence of an in-plane temperature gradient, while the latter is caused by the anomalous Nernst effect due to spurious out-of-plane temperature gradients with a coefficient as high as 500 $\ensuremath{\mu}V/K$. We also report on the experimental observation of the planar Hall effect measured at different temperatures. Using a Stoner-Wohlfarth model for data analysis, the anisotropy constants ${K}_{u}$ and ${K}_{c}$ of superimposed uniaxial and cubic anisotropies in the magnetic film are determined. The temperature dependence of the ${K}_{u}/{K}_{c}$ ratio reveals a gradual substitution of the cubic anisotropy dominating at low temperatures with the uniaxial anisotropy as the temperature rises. This behavior is confirmed by the simultaneous domain observation using Kerr microscopy, demonstrating different field evolutions of the domain structure at different temperatures.

Skyrmionic spin Seebeck effect via dissipative thermomagnonic torques

We derive thermomagnonic torque and its "$\beta$-type" dissipative correction from the stochastic Landau-Lifshitz-Gilbert equation. The "$\beta$-type" dissipative correction describes viscous coupling between magnetic dynamics and magnonic current and it stems from spin mistracking of the magnetic order. We show that thermomagnonic torque is important for describing temperature gradient induced motion of skyrmions in helical magnets while dissipative correction plays an essential role in generating transverse Magnus force. We propose to detect such skyrmionic motion by employing the transverse spin Seebeck effect geometry.

Spin-Seebeck effect on the surface of a topological insulator due to nonequilibrium spin-polarization parallel to the direction of thermally driven electronic transport

We study the transverse spin-Seebeck effect (SSE) on the surface of a three-dimensional topological insulator (TI) thin film, such as Bi${}_{2}$Se${}_{3}$, which is sandwiched between two normal metal leads. The temperature bias $\ensuremath{\Delta}T$ applied between the leads generates surface charge current which becomes spin polarized due to strong spin-orbit coupling on the TI surface, with polarization vector acquiring a component ${P}_{x}\ensuremath{\simeq}60%$ parallel to the direction of transport. When the third nonmagnetic voltage probe is attached to the portion of the TI surface across its width ${L}_{y}$, pure spin current will be injected into the probe where the inverse spin Hall effect (ISHE) converts it into a voltage signal $|{V}_{\mathrm{ISHE}}{|}^{\mathrm{max}}/\ensuremath{\Delta}T\ensuremath{\simeq}2.5\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}$V/K (assuming the SH angle of the Pt voltage probe and ${L}_{y}=1$ mm). The existence of predicted nonequilibrium spin polarization parallel to the direction of electronic transport and the corresponding electron-driven SSE crucially relies on orienting quintuple layers (QLs) of Bi${}_{2}$Se${}_{3}$ orthogonal to the TI surface and tilted by ${45}^{\ensuremath{\circ}}$ with respect to the direction of transport. Our analysis is based on the Landauer--B\"uttiker-type formula for spin currents in the leads of a multiterminal quantum-coherent junction, which is constructed by using nonequilibrium Green function formalism within which we show how to take into account arbitrary orientation of QLs via the self-energy describing coupling between semi-infinite normal metal leads and the TI sample.

Influence of heat flow directions on Nernst effects in Py/Pt bilayers

We investigated the voltages obtained in a thin Pt strip on a Permalloy film which was subject to in-plane temperature gradients and magnetic fields. The voltages detected by thin W-tips or bond wires showed a purely symmetric effect with respect to the external magnetic field which can be fully explained by the planar Nernst effect (PNE). To verify the influence of the contacts measurements in vacuum and atmosphere were compared and gave similar results. We explain that a slightly in-plane tilted temperature gradient only shifts the field direction dependence but does not cancel out the observed effects. Additionally, the anomalous Nernst effect (ANE) could be induced by using thick Au-tips which generated a heat current perpendicular to the sample plane. The effect can be manipulated by varying the temperature of the Au-tips. These measurements are discussed concerning their relevance in transverse spin Seebeck effect measurements.

Transverse Spin Seebeck Effect versus Anomalous and Planar Nernst Effects in Permalloy Thin Films

Transverse magnetothermoelectric effects are studied in Permalloy thin films grown on MgO and GaAs substrates and compared to those grown on suspended SiN(x) membranes. The transverse voltage along platinum strips patterned on top of the Permalloy films is measured versus the external magnetic field as a function of the angle and temperature gradients. After the identification of the contribution of the planar and anomalous Nernst effects, we find an upper limit for the transverse spin Seebeck effect, which is several orders of magnitude smaller than previously reported.

Magnon, phonon, and electron temperature profiles and the spin Seebeck effect in magnetic insulator/normal metal hybrid structures

We calculate the phonon, electron and magnon temperature profiles in yttrium iron garnet/platinum bilayers by diffusive theory with appropriate boundary conditions, in particular taking into account interfacial thermal resistances. Our calculations show that in thin film hybrids, the interface magnetic heat conductance qualitatively affects the magnon temperature. Based on published material parameters we assess the degree of non-equilibrium at the yttrium iron garnet/platinum interface. The magnitude of the spin Seebeck effect derived from this approach compares well with experimental results for the longitudinal spin Seebeck effect. Additionally we address the temperature profiles in the transverse spin Seebeck effect.

Linear-response theory of the longitudinal spin Seebeck effect

We theoretically investigate the longitudinal spin Seebeck effect, in which the spin current is injected from a ferromagnet into an attached nonmagnetic metal in a direction parallel to the temperature gradient. Using the fact that the phonon heat current flows intensely into the attached nonmagnetic metal in this particular configuration, we show that the sign of the spin injection signal in the longitudinal spin Seebeck effect can be opposite to that in the conventional transverse spin Seebeck effect when the electron-phonon interaction in the nonmagnetic metal is sufficiently large. Our linear-response approach can explain the sign reversal of the spin injection signal recently observed in the longitudinal spin Seebeck effect.