Landau-Lifshitz theory of the longitudinal spin Seebeck effect

Hoffman, Silas; Sato, Kōji; Tserkovnyak, Yaroslav

doi:10.1103/physrevb.88.064408

Cited by 156 publications

(192 citation statements)

References 44 publications

(38 reference statements)

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“…Instead, we present a model that attributes this characteristic behavior to a finite propagation length of thermally excited magnons, created in the bulk of the ferromagnetic material. An increase and saturation of the SSC with increasing YIG film thickness has also been predicted by the theory of S. Hoffman et al [36], who attribute a saturation of the SSE signal for large thicknesses also to the finite propagation length of thermally excited magnons. From the evaluation of our data at RT, measured in samples grown by PLD, we obtain a mean propagation length of the order of 100 nm for thermally excited magnons, in agreement with other studies predicting a finite propagation length of thermally excited magnons of the order of 100 nm [37].…”

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confidence: 63%

Length Scale of the Spin Seebeck Effect

et al. 2015

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We investigate the origin of the spin Seebeck effect in yttrium iron garnet (YIG) samples for film thicknesses from 20 nm to 50 μm at room temperature and 50 K. Our results reveal a characteristic increase of the longitudinal spin Seebeck effect amplitude with the thickness of the insulating ferrimagnetic YIG, which levels off at a critical thickness that increases with decreasing temperature. The observed behavior cannot be explained as an interface effect or by variations of the material parameters. Comparison to numerical simulations of thermal magnonic spin currents yields qualitative agreement for the thickness dependence resulting from the finite magnon propagation length. This allows us to trace the origin of the observed signals to genuine bulk magnonic spin currents due to the spin Seebeck effect ruling out an interface origin and allowing us to gauge the reach of thermally excited magnons in this system for different temperatures. At low temperature, even quantitative agreement with the simulations is found. The thermal excitation of a spin current by a temperature gradient is commonly called the spin Seebeck effect (SSE) which is detected by the inverse spin Hall effect (ISHE) [1,2], leading to a thermovoltage similar to the charge analogue, the Seebeck effect. Experimental evidence of the SSE, first in ferromagnetic metals [3], and later, both in semiconductors [4] and in insulators [5][6][7][8], has brought up the question about the origin of the SSE. Of particular interest for spin caloritronics is the observation of the SSE in insulators, which allows us to generate pure spin currents in insulating systems.However, the underlying mechanism, properties, and the origin of the observed signals have been highly controversial. Thermally induced magnonic spin currents have been suggested as the origin [9,10], based on the presence of the effect in magnetic insulators, which excludes charge currents as the source. Despite this explanation of the origin of the effect, direct experimental evidence has not been reported. While parasitic interface effects [11] were suggested as an alternative source of the SSE due to a polarization of the paramagnetic detector layer [12], generally, the observed effects are now primarily attributed to magnonic spin currents [13,14].Time resolved experiments trying to address the problem by probing the temporal evolution of the SSE have obtained contradictory results: For film thickness up to 61 nm, no cut-off frequency due to an intrinsic limitation by the SSE was observed [15]. In contrast, for μm thick films, a characteristic rise time was found, and a finite magnon propagation length of the order of several 100 nm was put forward as a possible explanation [16,17]. This clearly calls for study to reveal the origin of this discrepancy as it underlies the fundamental mechanism of the SSE and to determine the intrinsic length scale.To clarify the origin of the measured SSE signals, we present a detailed study of the relevant length scales of the longitudinal SSE (LSSE) coveri...

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confidence: 63%

Length Scale of the Spin Seebeck Effect

et al. 2015

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“…4(a)] a linear gradient of the local magnon density. This result is in agreement with the previous studies [18,35,36]. The local magnon density is quantified here via the squared transversal magnetization components averaged over time, ρ = M 2 y + M 2 z .…”

Section: Exchange and Dmi Spin Currentssupporting

confidence: 92%

Thermally induced magnonic spin current, thermomagnonic torques, and domain-wall dynamics in the presence of Dzyaloshinskii-Moriya interaction

et al. 2016

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Thermally activated domain-wall (DW) motion in magnetic insulators has been considered theoretically, with a particular focus on the role of Dzyaloshinskii-Moriya interaction (DMI) and thermomagnonic torques. The thermally assisted DW motion is a consequence of the magnonic spin current due to the applied thermal bias. In addition to the exchange magnonic spin current and the exchange adiabatic and the entropic spin transfer torques, we also consider the DMI-induced magnonic spin current, thermomagnonic DMI fieldlike torque, and the DMI entropic torque. Analytical estimations are supported by numerical calculations. We found that the DMI has a substantial influence on the size and the geometry of DWs, and that the DWs become oriented parallel to the long axis of the nanostrip. Increasing the temperature smoothes the DWs. Moreover, the thermally induced magnonic current generates a torque on the DWs, which is responsible for their motion. From our analysis it follows that for a large enough DMI the influence of DMI-induced fieldlike torque is much stronger than that of the DMI and the exchange entropic torques. By manipulating the strength of the DMI constant, one can control the speed of the DW motion, and the direction of the DW motion can be switched, as well. We also found that DMI not only contributes to the total magnonic current, but also it modifies the exchange magnonic spin current, and this modification depends on the orientation of the steady-state magnetization. The observed phenomenon can be utilized in spin caloritronics devices, for example in the DMI based thermal diodes. By switching the magnetization direction, one can rectify the total magnonic spin current.

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“…These discoveries enabled unprecedented degree of control in magnetic informationstorage devices in which the magnetization can be flipped at will [12] or the domain wall can be moved in order to change the magnetization configuration [13]. Sizable coupling of spin to thermal flows [14] leads to yet another knob by which we can control magnetization and magnetic textures such as domain walls [15][16][17][18] [25], where the magnetization dynamics have low dissipation as coupling to electron continuum is absent [18,26]. At the same time, even at relatively low temperatures, thermal magnons have very small wavelength and thus can be treated as particles on the scale of magnetic texture [18,27].…”

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confidence: 99%

Skyrmionic spin Seebeck effect via dissipative thermomagnonic torques

Kovalev

2014

Phys. Rev. B

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We derive thermomagnonic torque and its "β-type" dissipative correction from the stochastic Landau-LifshitzGilbert 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. Introduction. Out-of-equilibrium effects involving spin are essential to understanding many spintronic discoveries, such as spin-transfer torque [1][2][3][4], spin pumping [5,6], and the spin Seebeck effect [7][8][9][10][11]. These discoveries enabled unprecedented degree of control in magnetic informationstorage devices in which the magnetization can be flipped at will [12] or the domain wall can be moved in order to change the magnetization configuration [13]. Sizable coupling of spin to thermal flows [14] leads to yet another knob by which we can control magnetization and magnetic textures such as domain walls [15][16][17][18] [25], where the magnetization dynamics have low dissipation as coupling to electron continuum is absent [18,26]. At the same time, even at relatively low temperatures, thermal magnons have very small wavelength and thus can be treated as particles on the scale of magnetic texture [18,27]. This brings a lot of analogies to magnetization dynamics in metallic systems where the dynamics can be controlled by flows of electrons [28][29][30][31]. In conducting materials, on the other hand, thermoelectric spin torque can also couple magnetization to heat flows even in the absence of charge flows [15,22,32].A skyrmion is an example of a magnetic texture that can arise in helical magnets due to inversion asymmetry induced Dzyaloshinsky-Moriya (DM) interaction [33] as observed in bulk samples of MnSi by neutron scattering techniques [34]. Skyrmion crystal (SkX) is particularly stable in twodimensional (2D) systems or thin films as was predicted theoretically [35,36] and later confirmed experimentally [37,38]. Just like other textures, such as domain walls, skyrmions can be manipulated by temperature gradients [39,40]. However, many aspects related to interaction of magnon spin currents to magnetic textures are still unclear [41,42].In this Rapid Communication we address the dissipative β-type corrections to magnonic spin torques. Such corrections play an important role in domain wall dynamics [28][29][30][31]; however, they were introduced only phenomenologically in relation to magnonic torques [18,42]. Here we derive

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Landau-Lifshitz theory of the longitudinal spin Seebeck effect

Cited by 156 publications

References 44 publications

Length Scale of the Spin Seebeck Effect

Length Scale of the Spin Seebeck Effect

Thermally induced magnonic spin current, thermomagnonic torques, and domain-wall dynamics in the presence of Dzyaloshinskii-Moriya interaction

Skyrmionic spin Seebeck effect via dissipative thermomagnonic torques

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