Intrinsic spin-dependent thermal transport

Efficient Spin-to-Charge Conversion via Altermagnetic Spin Splitting Effect in Antiferromagnet RuO_{2}

The relativistic spin Hall effect and inverse spin Hall effect enable the efficient generation and detection of spin current. Recently, a nonrelativistic altermagnetic spin splitting effect (ASSE) has been theoretically and experimentally reported to generate time-reversal-odd spin current with controllable spin polarization in antiferromagnet RuO_{2}. The inverse effect, electrical detection of spin current via ASSE, still remains elusive. Here we show the spin-to-charge conversion stemming from ASSE in RuO_{2} by the spin Seebeck effect measurements. Unconventionally, the spin Seebeck voltage can be detected even when the injected spin current is polarized along the directions of either the voltage channel or the thermal gradient, indicating the successful conversion of x- and z-spin polarizations into the charge current. The crystal axes-dependent conversion efficiency further demonstrates that the nontrivial spin-to-charge conversion in RuO_{2} is ascribed to ASSE, which is distinct from the magnetic or antiferromagnetic inverse spin Hall effects. Our finding not only advances the emerging research landscape of altermagnetism, but also provides a promising pathway for the spin detection.

Tunable anomalous Hall and Nernst effects in MM'X compounds

Based on first-principles calculations, the anomalous Hall conductivity (AHC) and anomalous Nernst conductivities (ANCs) of the XMnP (X = Ti, Zr, Hf) compounds are evaluated, and the possibility to tailor such properties in compounds susceptible to changing the magnetization directions is also investigated. We observe large changes in the calculated AHC and ANC for different magnetization directions that are originating from changes in the band structure all over the whole Brillouin zone. Our study gives a promising clue on engineering magnetic intermetallic compounds for tunable transverse thermoelectric applications.

Observation of Vector Spin Seebeck Effect in a Noncollinear Antiferromagnet

Spintronic phenomena to date have been established in magnets with collinear moments, where the spin injection through the spin Seebeck effect (SSE) is always along the out-of-plane direction. Here, we report the observation of a vector SSE in a noncollinear antiferromagnet (AF) LuFeO_{3}, where temperature gradient along the out-of-plane and also the in-plane directions can both inject a pure spin current and generate a voltage in the heavy metal via the inverse spin Hall effect (ISHE). We show that the thermovoltages are due to the magnetization from canted spins in LuFeO_{3}. Furthermore, in contrast to the challenges of generating, manipulating, and detecting spin current in collinear AFs, the vector SSE in LuFeO_{3} is readily viable in zero magnetic field and can be controlled by a small magnetic field of about 150 Oe at room temperature. The noncollinear AFs expand new realms for exploring spin phenomena and provide a new route to low-field antiferromagnetic spin caloritronics and magnonics.

Cationic Ordering and Its Influence on the Magnetic Properties of Co-Rich Cobalt Ferrite Thin Films Prepared by Reactive Solid Phase Epitaxy on Nb-Doped SrTiO3(001)

Here, we present the (element-specific) magnetic properties and cation ordering for ultrathin Co-rich cobalt ferrite films. Two Co-rich CoxFe3-xO4 films with different stoichiometry (x=1.1 and x=1.4) have been formed by reactive solid phase epitaxy due to post-deposition annealing from epitaxial CoO/Fe3O4 bilayers deposited before on Nb-doped SrTiO3(001). The electronic structure, stoichiometry and homogeneity of the cation distribution of the resulting cobalt ferrite films were verified by angle-resolved hard X-ray photoelectron spectroscopy. From X-ray magnetic circular dichroism measurements, the occupancies of the different sublattices were determined using charge-transfer multiplet calculations. For both ferrite films, a partially inverse spinel structure is found with increased amount of Co3+ cations in the low-spin state on octahedral sites for the Co1.4Fe1.6O4 film. These findings concur with the results obtained by superconducting quantum interference device measurements. Further, the latter measurements revealed the presence of an additional soft magnetic phase probably due to cobalt ferrite islands emerging from the surface, as suggested by atomic force microscope measurements.

Quantum Sensing of Thermoelectric Power in Low-Dimensional Materials

Thermoelectric power, has been extensively studied in low-dimensional materials where quantum confinement and spin textures can largely modulate thermopower generation. In addition to classical and macroscopic values, thermopower also varies locally over a wide range of length scales, and is fundamentally linked to electron wave functions and phonon propagation. Various experimental methods for the quantum sensing of localized thermopower have been suggested, particularly based on scanning probe microscopy. Here, critical advances in the quantum sensing of thermopower are introduced, from the atomic to the several-hundred-nanometer scales, including the unique role of low-dimensionality, defects, spins, and relativistic effects for optimized power generation. Investigating the microscopic nature of thermopower in quantum materials can provide insights useful for the design of advanced materials for future thermoelectric applications. Quantum sensing techniques for thermopower can pave the way to practical and novel energy devices for a sustainable society.

Spin-Seebeck effect and thermoelectric properties of one-dimensional graphene-like nanoribbons periodically embedded with four- and eight-membered rings

The spin-Seebeck effect together with a high spin thermoelectric conversion efficiency has been regarded as one of the core topics in spin caloritronics. In this work, we propose a spin caloritronic device constructed on hydrogen-terminated sawtooth graphene-like nanoribbons periodically embedded with four- and eight-membered rings to investigate the thermal spin currents and thermoelectric properties by using density functional theory combined with the non-equilibrium Green's function method. Our theoretical results show that spin-Seebeck currents are induced by the temperature gradient between two leads due to two isolated spin-up and spin-down transport channels above or below the Fermi level. Besides, the embedded four- and eight-membered rings break the mirror symmetry of graphene-like nanoribbons and increase the phonon scattering to lower the lattice conductivity, contributing to the enhancement of the spin figure of merit. Moreover, the increasing width of the nanoribbons can effectively enhance the spin-Seebeck currents and reduce their threshold temperatures to improve the device performances. These systematic investigations not only give us an in-depth understanding into the realistic spin caloritronic device applications of graphene-like nanoribbons, but also help us to choose feasible routes to improve the spin-Seebeck effect with a high spin figure of merit in nanostructures.

The Strain-Tuned Spin Seebeck Effect, Spin Polarization, and Giant Magnetoresistance of a Graphene Nanobubble in Zigzag Graphene Nanoribbons

By using first-principle calculations combined with the non-equilibrium Green's function approach, we studied the spin caloritronic properties of zigzag graphene nanoribbons with a nanobubble at the edge (NB-ZGNRs). The thermal spin-polarized currents can be induced by a temperature difference, and the spin Seebeck effect is found in the nanoribbon. The spin polarization, magnetoresistance, and Seebeck coefficients are discussed, which are strongly affected and can be tuned by the geometrical strain. Moreover, some novel spin caloritronic devices are designed, such as a device that generates bidirectional perfect spin currents and thermally induced giant magnetoresistances. Our results open up the possibility of tuning the spin caloritronic properties of the NB-ZGNR-based devices by changing the elastic strain on the graphene nanobubble.

Electrical-field tuned thermoelectric performance of graphene nanoribbon with sawtooth edges

By using first-principle calculations combined with the non-equilibrium Green's function approach, we report that a vertical electrical field can modulate the thermoelectric performance of a graphene nanoribbon with sawtooth edges. The results show that the sawtooth graphene nanoribbon exhibits the spin-dependent Seebeck effect under the temperature gradients, and is strengthened by increasing the width of the sawtooth graphene nanoribbon. When the vertical electrical field is applied to the device, the spin-dependent Seebeck effect can also be enhanced. The vertical electrical field can modulate the device transferring from hole-conducting to electron-conducting. This opens up the possibility of tuning the thermal transport properties of the device by the electrical field.

Dependence of spin-orbit torque effective fields on magnetization uniformity in Ta/Co/Pt structure

The spin-orbit torque (SOT) effective fields, namely field-like and damping-like terms, depend on the thicknesses of heavy metal (HM) and ferromagnetic metal (FM) layers, in a stack comprising of HM/FM/HM or oxide. In this work, we report on the dependence of the SOT effective fields on the magnetization uniformity in the wires comprising of Ta/Co/Pt layer structure. SOT dependence on magnetization uniformity dependence was investigated by concurrent variation of the magnetization uniformity in Co layer and characterization of the SOT effective fields in each wire which excludes the layer thickness dependence influences. Our experimental results reveal that the field-like term decreases while the damping-like term increases with increasing Co magnetization uniformity. The magnetization uniformity influence on the effective fields is attributed to the spin Hall effect, which contributes to the SOT.

Machine-learning guided discovery of a new thermoelectric material

Thermoelectric technologies are becoming indispensable in the quest for a sustainable future. Recently, an emerging phenomenon, the spin-driven thermoelectric effect (STE), has garnered much attention as a promising path towards low cost and versatile thermoelectric technology with easily scalable manufacturing. However, progress in development of STE devices is hindered by the lack of understanding of the fundamental physics and materials properties responsible for the effect. In such nascent scientific field, data-driven approaches relying on statistics and machine learning, instead of more traditional modeling methods, can exhibit their full potential. Here, we use machine learning modeling to establish the key physical parameters controlling STE. Guided by the models, we have carried out actual material synthesis which led to the identification of a novel STE material with a thermopower an order of magnitude larger than that of the current generation of STE devices.

Generation and Detection of Pure Spin Current in an H-Shaped Structure of a Single Metal

Distinct from all the existing methods for determining the spin Hall angle with bilayers, we have developed a new approach based on the mesoscopic H-shaped structure, which generates and detects pure spin current in a single metal. Using this approach we have unequivocally addressed the long-standing controversy of the magnitude of the spin Hall angle of gold. By exploiting the long spin diffusion length of Cu and the large spin-orbit coupling of Bi, we have realized a very large spin Hall effect in 10 nm Cu films delta doped with 0.15 nm of Bi. This new artificial material can generate a large spin-orbit torque to switch an adjacent Fe layer. We have thus demonstrated new artificial materials with a simultaneously large spin Hall angle and long spin diffusion length.

The spin-dependent Seebeck effect and the charge and spin figure of merit in a hybrid structure of single-walled carbon nanotubes and zigzag-edge graphene nanoribbons

A hybrid structure of carbon nanotubes and graphene nanoribbons was predicted and synthesized (Y. Li et al., Nat. Nanotechnol., 2012, 7, 394-400; P. Lou, J. Phys. Chem. C, 2014, 118, 4475-4482). Herein, using the non-equilibrium Green's function (NEGF) combined with density functional theory (DFT), the thermal spin transport properties and the figure of merit (a material constant proportional to the efficiency of a thermoelectric couple made with the material) of a composite of single-walled carbon nanotubes and zigzag-edge graphene nanoribbons, labeled (6,6)SWCNT/n-ZGNR, are investigated for n = 1, 2, 3, and 8. The results manifest that spin-dependent currents with opposite flow directions were generated when a temperature gradient was applied between two electrodes, indicating the occurrence of the spin-dependent Seebeck effect (SDSE). Remarkably, when n = 3, the charge current is equal to zero, meaning that a perfect SDSE is observed. Moreover, a pure spin-dependent Seebeck diode (SDSD) effect can be observed. Finally, we notice that the device presents an n-type characteristic when n = 1, while the device has a p-type feature when n = 2. In particular, the spin-up thermopower is equal to the spin-down thermopower when n = 3; as a consequence, the charge thermopower is equal to zero, further demonstrating that a perfect SDSE is generated. These discoveries indicate that the (6,6)SWCNT/n-ZGNR is a promising candidate for spin caloritronics devices.

Quantitative Disentanglement of the Spin Seebeck, Proximity-Induced, and Ferromagnetic-Induced Anomalous Nernst Effect in Normal-Metal-Ferromagnet Bilayers

We identify and investigate thermal spin transport phenomena in sputter-deposited Pt/NiFe_{2}O_{x} (4≥x≥0) bilayers. We separate the voltage generated by the spin Seebeck effect from the anomalous Nernst effect (ANE) contributions and even disentangle the ANE in the ferromagnet (FM) from the ANE produced by the Pt that is spin polarized due to its proximity to the FM. Further, we probe the dependence of these effects on the electrical conductivity and the band gap energy of the FM film varying from nearly insulating NiFe_{2}O_{4} to metallic Ni_{33}Fe_{67}. A proximity-induced ANE could only be identified in the metallic Pt/Ni_{33}Fe_{67} bilayer in contrast to Pt/NiFe_{2}O_{x} (x>0) samples. This is verified by the investigation of static magnetic proximity effects via x-ray resonant magnetic reflectivity.

How to realize a spin-dependent Seebeck diode effect in metallic zigzag γ-graphyne nanoribbons?

The spin-dependent Seebeck effect (SDSE) is one of the core topics of spin caloritronics. In the traditional device designs of spin-dependent Seebeck rectifiers and diodes, finite spin-dependent band gaps of materials are required to realize the on-off characteristic in thermal spin currents, and nearly zero charge current should be achieved to reduce energy dissipation. Here, we propose that two ferromagnetic zigzag γ-graphyne nanoribbons (ZγGNRs) without any spin-dependent band gaps around the Fermi level can not only exhibit the SDSE, but also display rectifier and diode effects in thermal spin currents characterized by threshold temperatures, which originates from the compensation effect occurring in spin-dependent transmissions but not from the spin-splitting band gaps in materials. The metallic characteristics of ZγGNRs bring about an advantage that the gate voltage is an effective route to adjust the symmetry of spin-splitting bands to obtain pure thermal spin currents. The results provide a new mechanism to realize spin-Seebeck rectifier and diode effects in 2D materials and expand material candidates towards spin-Seebeck device applications.

The spin Nernst effect in tungsten

The spin Hall effect allows the generation of spin current when charge current is passed along materials with large spin-orbit coupling. It has been recently predicted that heat current in a nonmagnetic metal can be converted into spin current via a process referred to as the spin Nernst effect. We report the observation of the spin Nernst effect in W. In W/CoFeB/MgO heterostructures, we find changes in the longitudinal and transverse voltages with magnetic field when temperature gradient is applied across the film. The field dependence of the voltage resembles that of the spin Hall magnetoresistance. A comparison of the temperature gradient-induced voltage and the spin Hall magnetoresistance allows direct estimation of the spin Nernst angle. We find the spin Nernst angle of W to be similar in magnitude but opposite in sign to its spin Hall angle. Under an open-circuit condition, this sign difference results in the spin current generation larger than otherwise. These results highlight the distinct characteristics of the spin Nernst and spin Hall effects, providing pathways to explore materials with unique band structures that may generate large spin current with high efficiency.

Thickness dependence of anomalous Nernst coefficient and longitudinal spin Seebeck effect in ferromagnetic NixFe100-x films

Spin Seebeck effect (SSE) measured for metallic ferromagnetic thin films in commonly used longitudinal configuration contains the contribution from anomalous Nernst effect (ANE). The ANE is considered to arise from the bulk of the ferromagnet (FM) and the proximity-induced FM boundary layer. We fabricate a FM alloy with zero Nernst coefficient to mitigate the ANE contamination of SSE and insert a thin layer of Cu to separate the heavy metal (HM) from the FM to avoid the proximity contribution. These modifications to the experiment should permit complete isolation of SSE from ANE in the longitudinal configuration. However, further thickness dependence studies and careful analysis of the results revealed, ANE contribution of the isolated FM alloy is twofold, surface and bulk. Both surface and bulk contributions, whose magnitudes are comparable to that of the SSE, can be modified by the neighboring layer. Hence surface contribution to the ANE in FM metals is an important effect that needs to be considered.

Longitudinal spin Seebeck coefficient: heat flux vs. temperature difference method

The determination of the longitudinal spin Seebeck effect (LSSE) coefficient is currently plagued by a large uncertainty due to the poor reproducibility of the experimental conditions used in its measurement. In this work we present a detailed analysis of two different methods used for the determination of the LSSE coefficient. We have performed LSSE experiments in different laboratories, by using different setups and employing both the temperature difference method and the heat flux method. We found that the lack of reproducibility can be mainly attributed to the thermal contact resistance between the sample and the thermal baths which generate the temperature gradient. Due to the variation of the thermal resistance, we found that the scaling of the LSSE voltage to the heat flux through the sample rather than to the temperature difference across the sample greatly reduces the uncertainty. The characteristics of a single YIG/Pt LSSE device obtained with two different setups was (1.143 ± 0.007) 10^-7 Vm/W and (1.101 ± 0.015) 10^-7 Vm/W with the heat flux method and (2.313 ± 0.017) 10^-7 V/K and (4.956 ± 0.005) 10^-7 V/K with the temperature difference method. This shows that systematic errors can be considerably reduced with the heat flux method.

Interface-Induced Phenomena in Magnetism

This article reviews static and dynamic interfacial effects in magnetism, focusing on interfacially-driven magnetic effects and phenomena associated with spin-orbit coupling and intrinsic symmetry breaking at interfaces. It provides a historical background and literature survey, but focuses on recent progress, identifying the most exciting new scientific results and pointing to promising future research directions. It starts with an introduction and overview of how basic magnetic properties are affected by interfaces, then turns to a discussion of charge and spin transport through and near interfaces and how these can be used to control the properties of the magnetic layer. Important concepts include spin accumulation, spin currents, spin transfer torque, and spin pumping. An overview is provided to the current state of knowledge and existing review literature on interfacial effects such as exchange bias, exchange spring magnets, spin Hall effect, oxide heterostructures, and topological insulators. The article highlights recent discoveries of interface-induced magnetism and non-collinear spin textures, non-linear dynamics including spin torque transfer and magnetization reversal induced by interfaces, and interfacial effects in ultrafast magnetization processes.

Temperature-controlled colossal magnetoresistance and perfect spin Seebeck effect in hybrid graphene/boron nitride nanoribbons

Thermal spin transport properties of graphene and hexagonal boron nitride nanoribbon heterojunctions have been investigated using density functional theory calculations combined with the Keldysh nonequilibrium Green's function approach. The results showed that the perfect spin Seebeck effect and analogy negative differential thermoelectric resistance occurred in the device under a temperature difference without a gate or bias voltage. An intriguing thermally induced colossal magnetoresistance without gate regulation was also observed, which can be switched between a positive and negative value with temperature control. It was also found that the unit number of zigzag graphene nanoribbons and boron nitride nanoribbons can tune the electronic band structure and the energy gap of the heterostructure, and then modulate the thermal spin transport properties. The results suggest that graphene and hexagonal boron nitride nanoribbon heterostructures may have potential applications in graphene-based nanodevices.

Unique magnetic and thermoelectric properties of chemically functionalized narrow carbon polymers

We analyze magnetic, transport and thermoelectric properties of narrow carbon polymers, which are chemically functionalized with nitroxide groups. Numerical calculations of the electronic band structure and the corresponding transmission function are based on density functional theory. Transport and thermoelectric parameters are calculated in the linear response regime, with particular interest in charge and spin thermopowers (charge and spin Seebeck effects). Such nanoribbons are shown to have thermoelectric properties described by large thermoelectric efficiency, which makes these materials promising from the application point of view.

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.

Absence of the Thermal Hall Effect in Anomalous Nernst and Spin Seebeck Effects

The anomalous Nernst effect (ANE) and the spin Seebeck effect (SSE) in spin caloritronics are two of the most important mechanisms to manipulate the spin-polarized current and pure spin current by thermal excitation. While the ANE in ferromagnetic metals and the SSE in magnetic insulators have been extensively studied, a recent theoretical work suggests that the signals from the thermal Hall effect (THE) have field dependences indistinguishable from, and may even overwhelm, those of the ANE and SSE. Therefore, it is vital to investigate the contribution of the THE in the ANE and SSE. In this work, we systematically study the THE in a ferromagnetic metal, Permalloy (Py), and magnetic insulator, an yttrium iron garnet (YIG), by using different Seebeck coefficients between electrodes and contact wires. Our results demonstrate that the contribution of the THE by the thermal couple effect in the Py and YIG is negligibly small if one includes the thickness dependence of the Seebeck coefficient. Thus, the spin-polarized current in the ANE and the pure spin current in the SSE remain indispensable for exploring spin caloritronics phenomena.

Magnons and Phonons Optically Driven out of Local Equilibrium in a Magnetic Insulator

The coupling and possible nonequilibrium between magnons and other energy carriers have been used to explain several recently discovered thermally driven spin transport and energy conversion phenomena. Here, we report experiments in which local nonequilibrium between magnons and phonons in a single crystalline bulk magnetic insulator, Y_{3}Fe_{5}O_{12}, has been created optically within a focused laser spot and probed directly via micro-Brillouin light scattering. Through analyzing the deviation in the magnon number density from the local equilibrium value, we obtain the diffusion length of thermal magnons. By explicitly establishing and observing local nonequilibrium between magnons and phonons, our studies represent an important step toward a quantitative understanding of various spin-heat coupling phenomena.

Spectacular enhancement of thermoelectric phenomena in chemically synthesized graphene nanoribbons with substitution atoms

We analyze theoretically the transport and thermoelectric properties of graphene nanoribbons of a specific geometry, which have been synthesized recently from polymers [Cai, et al., Nature, 2011, 466, 470]. When such nanoribbons are modified at one of the two edges by Al or N substitutions, they acquire a ferromagnetic moment localized at the modified edge. We present numerical results on the electronic structure and thermoelectric properties (including also spin thermoelectricity) of the modified nanoribbons. The results show that such nanoribbons can display large thermoelectric efficiency in certain regions of chemical potential, where the corresponding electric and spin figures of merit achieve unusually large values. The enhancement of thermoelectric efficiency follows from a reduced phonon heat conductance of the nanoribbons and from their peculiar electronic band structure. Thus, such nanoribbons are promising for practical applications in nanoelectronic and spintronic devices.

Asymmetric magnetic proximity effect in a Pd/Co/Pd trilayer system

In spintronic devices consisting of ferromagnetic/nonmagnetic systems, the ferromagnet-induced magnetic moment in the adjacent nonmagnetic material significantly influences the spin transport properties. In this study, such magnetic proximity effect in a Pd/Co/Pd trilayer system is investigated by x-ray magnetic circular dichroism and x-ray resonant magnetic reflectivity, which enables magnetic characterizations with element and depth resolution. We observe that the total Pd magnetic moments induced at the top Co/Pd interface are significantly larger than the Pd moments at the bottom Pd/Co interface, whereas transmission electron microscopy and reflectivity analysis indicate the two interfaces are nearly identical structurally. Such asymmetry in magnetic proximity effects could be important for understanding spin transport characteristics in ferromagnetic/nonmagnetic systems and its potential application to spin devices.

Enhanced spin Seebeck effect signal due to spin-momentum locked topological surface states

Spin-momentum locking in protected surface states enables efficient electrical detection of magnon decay at a magnetic-insulator/topological-insulator heterojunction. Here we demonstrate this property using the spin Seebeck effect (SSE), that is, measuring the transverse thermoelectric response to a temperature gradient across a thin film of yttrium iron garnet, an insulating ferrimagnet, and forming a heterojunction with (Bi_xSb_1−x)₂Te₃, a topological insulator. The non-equilibrium magnon population established at the interface can decay in part by interactions of magnons with electrons near the Fermi energy of the topological insulator. When this decay channel is made active by tuning (Bi_xSb_1−x)₂Te₃ into a bulk insulator, a large electromotive force emerges in the direction perpendicular to the in-plane magnetization of yttrium iron garnet. The enhanced, tunable SSE which occurs when the Fermi level lies in the bulk gap offers unique advantages over the usual SSE in metals and therefore opens up exciting possibilities in spintronics.

Future spintronic devices may exploit topological insulators, bulk insulators with unique spin-momentum locked conductive surface states. Here, the authors demonstrate the detection of thermally-generated spin currents in a ferromagnetic-insulator/topological-insulator heterostructure.

Influence of Interface Structure on Magnetic Proximity Effect in Pt/Y3Fe5O12 Heterostructures

The influence of interface structure on the magnetic proximity effect (MPE) in Pt/Y3Fe5O12 (YIG) bilayered heterostructures is studied by first-principles calculations based on the density functional theory (DFT). When Pt atoms are in close proximity with Y or Fe ions at the interface, Pt-Y and Pt-Fe bonds are observed. The crystalline orientations and interface termination layers of the YIG strongly modify both the strength and the length of the Pt-Fe bonding and thereby influence the magnetic properties of the Pt. Point defects including tetrahedral Fe, octahedral Fe, and Y vacancies are introduced at the Pt/YIG interface to quantitatively evaluate the influence on the MPE from individual atoms. For the Pt(100)/YIG(100) structure, the interface tetrahedral Fe vacancies can significantly reduce or even completely diminish the magnetic moments in the Pt. In a stark contrast, the octahedral Fe vacancies slightly enhance the Pt magnetism, and the nonmagnetic Y vacancies cause little influences to the Pt magnetism. These results indicate that the strength of the MPE at the Pt/YIG interface strongly depends on the interface structure. This dependence originated from the direct exchange interaction between the Fe 3d and Pt 5d electrons via electronic state hybridization as well as the electron exchange coupling between the Pt atoms.

Thermally Driven Pure Spin and Valley Currents via the Anomalous Nernst Effect in Monolayer Group-VI Dichalcogenides

The spin and valley-dependent anomalous Nernst effects are analyzed for monolayer MoS_{2} and other group-VI dichalcogenides. We find that pure spin and valley currents can be generated perpendicular to the applied thermal gradient in the plane of these two-dimensional materials. This effect provides a versatile platform for applications of spin caloritronics. A spin current purity factor is introduced to quantify this effect. When time reversal symmetry is violated, e.g., two-dimensional materials on an insulating magnetic substrate, a dip-peak feature appears for the total Nernst coefficient. For the dip state it is found that carriers with only one spin and from one valley are driven by the temperature gradient.

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.

Static Magnetic Proximity Effect in Pt/NiFe2O4 and Pt/Fe Bilayers Investigated by X-Ray Resonant Magnetic Reflectivity

The spin polarization of Pt in Pt/NiFe2O4 and Pt/Fe bilayers is studied by interface-sensitive x-ray resonant magnetic reflectivity to investigate static magnetic proximity effects. The asymmetry ratio of the reflectivity is measured at the Pt L3 absorption edge using circular polarized x-rays for opposite directions of the magnetization at room temperature. The results of the 2% asymmetry ratio for Pt/Fe bilayers are independent of the Pt thickness between 1.8 and 20 nm. By comparison with ab initio calculations, the maximum magnetic moment per spin polarized Pt atom at the interface is determined to be (0.6±0.1)  μB for Pt/Fe. For Pt/NiFe2O4 the asymmetry ratio drops below the sensitivity limit of 0.02  μB per Pt atom. Therefore, we conclude, that the longitudinal spin Seebeck effect recently observed in Pt/NiFe2O4 is not influenced by a proximity induced anomalous Nernst effect.

Thermoelectric Signal Enhancement by Reconciling the Spin Seebeck and Anomalous Nernst Effects in Ferromagnet/Non-magnet Multilayers

The utilization of ferromagnetic (FM) materials in thermoelectric devices allows one to have a simpler structure and/or independent control of electric and thermal conductivities, which may further remove obstacles for this technology to be realized. The thermoelectricity in FM/non-magnet (NM) heterostructures using an optical heating source is studied as a function of NM materials and a number of multilayers. It is observed that the overall thermoelectric signal in those structures which is contributed by spin Seebeck effect and anomalous Nernst effect (ANE) is enhanced by a proper selection of NM materials with a spin Hall angle that matches to the sign of the ANE. Moreover, by an increase of the number of multilayer, the thermoelectric voltage is enlarged further and the device resistance is reduced, simultaneously. The experimental observation of the improvement of thermoelectric properties may pave the way for the realization of magnetic-(or spin-) based thermoelectric devices.

Enhanced thermoelectric efficiency in ferromagnetic silicene nanoribbons terminated with hydrogen atoms

Using ab initio methods we calculate thermoelectric and spin thermoelectric properties of silicene nanoribbons with bare, mono-hydrogenated and di-hydrogenated edges. Asymmetric structures, in which one edge is either bare or di-hydrogenated while the other edge is mono-hydrogenated (0H-1H and 2H-1H nanoribbons), have a ferromagnetic ground state and display remarkable conventional and spin thermoelectric properties. Strong enhancement of the thermoelectric efficiency, both conventional and spin ones, results from a very specific band structure of such nanoribbons, where one spin channel is blocked due to an energy gap while the other spin channel is highly conductive. In turn, 0H-2H and 2H-2H nanoribbons (with one edge being either bare or di-hydrogenated and the other edge being di-hydrogenated) are antiferromagnetic in the ground state. Accordingly, the corresponding spin channels are equivalent, and only conventional thermoelectric effects can occur in these nanoribbons.

A review on the flexural mode of graphene: lattice dynamics, thermal conduction, thermal expansion, elasticity and nanomechanical resonance

Single-layer graphene is so flexible that its flexural mode (also called the ZA mode, bending mode, or out-of-plane transverse acoustic mode) is important for its thermal and mechanical properties. Accordingly, this review focuses on exploring the relationship between the flexural mode and thermal and mechanical properties of graphene. We first survey the lattice dynamic properties of the flexural mode, where the rigid translational and rotational invariances play a crucial role. After that, we outline contributions from the flexural mode in four different physical properties or phenomena of graphene-its thermal conductivity, thermal expansion, Young's modulus and nanomechanical resonance. We explain how graphene's superior thermal conductivity is mainly due to its three acoustic phonon modes at room temperature, including the flexural mode. Its coefficient of thermal expansion is negative in a wide temperature range resulting from the particular vibration morphology of the flexural mode. We then describe how the Young's modulus of graphene can be extracted from its thermal fluctuations, which are dominated by the flexural mode. Finally, we discuss the effects of the flexural mode on graphene nanomechanical resonators, while also discussing how the essential properties of the resonators, including mass sensitivity and quality factor, can be enhanced.

Spin and charge Nernst effect in a four-terminal quantum dot ring

Based on the Keldysh nonequilibrium Green's function technique, we study the spin and charge Nernst effect in a four-terminal quantum dot (QD) ring device, in which the Rashba spin-orbit interaction (RSOI) is taken into the QDs and the magnetic field penetrates the ring. We find that only with the assistance of RSOI, can the pure spin Nernst effect occur by applying a thermal bias without any magnetic field or ferromagnetic materials in the system. Under certain RSOI and magnetic field strengths, spin-down or spin-up currents can be driven from terminal 2 or 4. The sign and the magnitude of the spin currents or voltages can be modulated by adjusting the RSOI-induced phase factor and the magnetic flux. Moreover, the magnitude of the Nernst effect can be remarkably enhanced by the intra-dot Coulomb blockade. The Nernst coefficient is predicted to be more than two times larger than the case of zero Coulomb interaction. Our results indicate that such a four-terminal QD ring may be used as a manipulative thermoelectric generator.

Boron nitride zigzag nanoribbons: optimal thermoelectric systems

Conventional and spin related thermoelectric effects in zigzag boron nitride nanoribbons are studied theoretically within the Density Functional Theory (DFT) approach.

Longitudinal spin Seebeck effect: from fundamentals to applications

The spin Seebeck effect refers to the generation of spin voltage as a result of a temperature gradient in ferromagnetic or ferrimagnetic materials. When a conductor is attached to a magnet under a temperature gradient, the thermally generated spin voltage in the magnet injects a spin current into the conductor, which in turn produces electric voltage owing to the spin-orbit interaction. The spin Seebeck effect is of increasing importance in spintronics, since it enables direct generation of a spin current from heat and appears in a variety of magnets ranging from metals and semiconductors to insulators. Recent studies on the spin Seebeck effect have been conducted mainly in paramagnetic metal/ferrimagnetic insulator junction systems in the longitudinal configuration in which a spin current flowing parallel to the temperature gradient is measured. This 'longitudinal spin Seebeck effect' (LSSE) has been observed in various sample systems and exclusively established by separating the spin-current contribution from extrinsic artefacts, such as conventional thermoelectric and magnetic proximity effects. The LSSE in insulators also provides a novel and versatile pathway to thermoelectric generation in combination of the inverse spin-Hall effects. In this paper, we review basic experiments on the LSSE and discuss its potential thermoelectric applications with several demonstrations.

Spin current generated by thermally driven ultrafast demagnetization

Spin current is the key element for nanoscale spintronic devices. For ultrafast operation of such nano-devices, generation of spin current in picoseconds, a timescale that is difficult to achieve using electrical circuits, is highly desired. Here we show thermally driven ultrafast demagnetization of a perpendicular ferromagnet leads to spin accumulation in a normal metal and spin transfer torque in an in-plane ferromagnet. The data are well described by models of spin generation and transport based on differences and gradients of thermodynamic parameters. The temperature difference between electrons and magnons is the driving force for spin current generation by ultrafast demagnetization. On longer timescales, a few picoseconds following laser excitation, we also observe a small contribution to spin current by a temperature gradient and the spin-dependent Seebeck effect.

Spin seebeck effect and thermal colossal magnetoresistance in graphene nanoribbon heterojunction

Spin caloritronics devices are very important for future development of low-power-consumption technology. We propose a new spin caloritronics device based on zigzag graphene nanoribbon (ZGNR), which is a heterojunction consisting of single-hydrogen-terminated ZGNR (ZGNR-H) and double-hydrogen-terminated ZGNR (ZGNR-H₂). We predict that spin-up and spin-down currents flowing in opposite directions can be induced by temperature difference instead of external electrical bias. The thermal spin-up current is considerably large and greatly improved compared with previous work in graphene. Moreover, the thermal colossal magnetoresistance is obtained in our research, which could be used to fabricate highly-efficient spin caloritronics MR devices.

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.

Experimental test of the spin mixing interface conductivity concept

We perform a quantitative, comparative study of the spin pumping, spin Seebeck, and spin Hall magnetoresistance effects, all detected via the inverse spin Hall effect in a series of over 20 yttrium iron garnet/Pt samples. Our experimental results fully support present, exclusively spin current-based, theoretical models using a single set of plausible parameters for spin mixing conductance, spin Hall angle, and spin diffusion length. Our findings establish the purely spintronic nature of the aforementioned effects and provide a quantitative description, in particular, of the spin Seebeck effect.

Transport equations of energy for ferromagnetic insulators in contact with electrodes

A phenomenological derivation of the transport equations for ferromagnetic moments and associated energy and heat is proposed. The model describes the transfer of energy through an interface composed of a ferromagnetic insulator in contact with normal electrodes. A reduction method applied to the ferromagnetic degrees of freedom allows a two-channel model to be defined for the transport of magnetic moments. It is shown that a heat current flowing into the insulating ferromagnet-produced e.g. by electromagnetic resonance, thermal gradient, magneto-mechanical or magneto-optical excitations-can generate a magneto-voltaic potential and a pure spin-current in the non-ferromagnetic electrode.

Inverse spin Hall effect in a ferromagnetic metal

The inverse spin Hall effect (ISHE) has been observed only in nonmagnetic metals, such as Pt and Au, with a strong spin-orbit coupling. We report the observation of ISHE in a ferromagnetic permalloy (Py) on ferromagnetic insulator yttrium iron garnet (YIG). Through controlling the spin current injection by altering the Py-YIG interface, we have isolated the spin current contribution and demonstrated the ISHE in a ferromagnetic metal, the reciprocal phenomenon of the anomalous Hall effect. A large spin Hall angle in Py, determined from Py thin films of different thicknesses, indicates many other ferromagnetic metals may be exploited as superior pure spin current detectors and for applications in spin current.

Theory of the spin Seebeck effect

The spin Seebeck effect refers to the generation of a spin voltage caused by a temperature gradient in a ferromagnet, which enables the thermal injection of spin currents from the ferromagnet into an attached nonmagnetic metal over a macroscopic scale of several millimeters. The inverse spin Hall effect converts the injected spin current into a transverse charge voltage, thereby producing electromotive force as in the conventional charge Seebeck device. Recent theoretical and experimental efforts have shown that the magnon and phonon degrees of freedom play crucial roles in the spin Seebeck effect. In this paper, we present the theoretical basis for understanding the spin Seebeck effect and briefly discuss other thermal spin effects.

Intrinsic spin Seebeck effect in Au/YIG

The acute magnetic proximity effects in Pt/YIG compromise the suitability of Pt as a spin current detector. We show that Au/YIG, with no anomalous Hall effect and a negligible magnetoresistance, allows the measurements of the intrinsic spin Seebeck effect with a magnitude much smaller than that in Pt/YIG. The experiment results are consistent with the spin polarized density functional calculations for Pt with a sizable and Au with a negligible magnetic moment near the interface with YIG.

Spin-dependent thermoelectric effects in graphene-based spin valves

Using first-principles calculations combined with non-equilibrium Green's function (NEGF), we investigate spin-dependent thermoelectric effects in a spin valve which consists of zigzag graphene nanoribbon (ZGNR) electrodes with different magnetic configurations. We find that electron transport properties in the ZGNR-based spin valve are strongly dependent on the magnetic configurations. As a result, with a temperature bias, thermally-induced currents can be controlled by switching the magnetic configurations, indicating a thermal magnetoresistance (MR) effect. Moreover, based on the linear response assumption, our study shows that the remarkably different Seebeck coefficients in the various magnetic configurations lead to a very large and controllable magneto Seebeck ratio. In addition, we evaluate thermoelectric properties, such as the power factor, electron thermal conductance and figure of merit (ZT), of the ZGNR-based spin valve. Our results indicate that the power factor and the electron thermal conductance are strongly related to the transmission gap and electron-hole symmetry of the transmission spectrum. Moreover, the value of ZT can reach 0.15 at room temperature without considering phonon scattering. In addition, we investigate the thermally-controlled magnetic distributions in the ZGNR-based spin valve and find that the magnetic distribution, especially the local magnetic moment around the Ni atom, is strongly related to the thermal bias. The very large, multi-valued and controllable thermal magnetoresistance and Seebeck effects indicate the strong potential of ZGNR-based spin valves for extremely low-power consuming spin caloritronics applications. The thermally-controlled magnetic moment in the ZGNR-based spin valve indicates its possible applications for information storage.

Thermoelectric detection of spin waves

We report on the thermoelectric detection of spin waves in Permalloy stripes via the anomalous Nernst effect. Spin waves are locally excited by a dynamic magnetic field generated from a microwave current flowing in a coplanar waveguide placed on top of a Permalloy stripe, which acts as a waveguide for spin waves. Electric contacts at the ends of the Permalloy stripe measure a dc voltage generated along the stripe. Magnetic field sweeps for different applied microwave frequencies reveal, with a remarkable signal-to-noise ratio, an electric voltage signature characteristic of spin-wave excitations. The symmetry of the signal with respect to the applied magnetic field direction indicates that the anomalous Nernst effect is responsible; Seebeck effects, anisotropic magnetoresistance, and voltages due to spin-motive forces are excluded. The dissipation of spin waves causes local heating that drains into the substrate, giving rise to a temperature gradient perpendicular to the sample plane, resulting in the anomalous Nernst voltage.

Observation of the planar Nernst effect in permalloy and nickel thin films with in-plane thermal gradients

We present experimental evidence of a transverse thermopower, or planar Nernst effect, in ferromagnetic metal thin films driven by thermal gradients applied in the plane of the films. Samples of 20 nm thick Ni and Ni(80)Fe(20) were deposited on 500 nm thick suspended Si-N thermal isolation platforms with integrated platinum strips designed originally to allow measurement of thermally generated spin currents (the spin Seebeck effect). The low thermal conductivity of the thin supporting Si-N structure results in an essentially 2D geometry that approaches the zero substrate limit, dramatically reducing the contribution of thermal gradients perpendicular to the sample plane typically found in similar experiments on bulk substrates. The voltage on the platinum strips generated transverse to the applied thermal gradient (V(T)) is linear with increasing ΔT and exhibits a sign reversal on hot and cold sides of the sample. However, V(T) is always even in applied magnetic field and shows a sinθ cosθ angular dependence, both key indicators of the planar Nernst effect. Within the 5 nV estimated error of our experiment there is no evidence of a signal from the spin Seebeck effect, which would have cosθ angular dependence, suggesting a reduced spin Seebeck coefficient in a planar, entirely thin-film geometry.

Unidirectional thermal effects in current-induced domain wall motion

We report experimental evidence of thermal effects on the displacement of vortex walls in NiFe nanostrips. With the use of nanosecond current pulses, a unidirectional motion of the magnetic domain walls towards the hotter part of the nanostrips is observed, in addition to current-induced domain wall motion. By tuning the heat dissipation in the samples and modeling the heat diffusion, we conclude that this unidirectional motion can only be explained by the presence of a temperature profile along the nanostrip. A quantitative analysis of the experiments shows that, on top of the classical thermodynamic pressure on the domain wall, another force, probably the magnonic spin Seebeck effect, is displacing the domain walls.

Transport magnetic proximity effects in platinum

Platinum (Pt) metal, being nonmagnetic and with a strong spin-orbit coupling interaction, has been central in detecting the pure spin current and establishing most of the recent spin-based phenomena. Magnetotransport measurements, both electrical and thermal, conclusively show strong ferromagnetic characteristics in thin Pt films on the ferromagnetic insulator due to the magnetic proximity effects. The pure spin current phenomena measured by Pt, including the inverse spin Hall and the spin Seebeck effects, are thus contaminated and not exclusively established.