Theory of the spin Seebeck effect

Gate-Tunable Spin Seebeck Effect and Pure Spin Current Generation in Molecular Junctions Based on Bipolar Magnetic Molecules

Generating pure spin currents is very desirable in spintronics, as it provides a promising way to substantially reduce Joule heating and achieve ultrahigh integration density. However, to date, most spintronic devices exhibit spin currents that are accompanied by charge currents. The generation of pure spin currents on the nanoscale, particularly at the single-molecule level, remains challenging. Here, we propose that by exploiting our recently reported bipolar magnetic molecules (BMMs) as the core component of single-molecule devices, where the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) come from different spin channels, the generation of pure spin currents can be easily realized via the spin Seebeck effect (SSE) with applied temperature gradient. Moreover, the spin Seebeck coefficient can be modulated over a wide range by applying an external gate voltage. The proposal is verified through first-principles calculations on two BMM-based molecular junctions.

Longitudinal Spin Seebeck Effect Thermopiles Based on Flexible Co-Rich Amorphous Ribbons/Pt Thin-Film Heterostructures

Thermoelectric phenomena, such as the Anomalous Nernst and Longitudinal Spin Seebeck Effects, are promising for sensor applications in the area of renewable energy. In the case of flexible electronic materials, the request is even larger because they can be integrated into devices having complex shape surfaces. Here, we reveal that Pt promotes an enhancement of the thermoelectric response in Co-rich ribbon/Pt heterostructures due to the spin-to-charge conversion. Moreover, we demonstrated that the employment of the thermopiles configuration in this system increases the induced thermoelectric current, a fact related to the considerable decrease in the electric resistance of the system. By comparing present findings with the literature, we were able to design a flexible thermopile based on LSSE without the lithography process. Additionally, the thermoelectric voltage found in the studied flexible heterostructures is comparable to the ones verified for rigid systems.

Comparative study between charge and spin thermoelectric figure of merits in an antiferromagnetic ring

Considering the unique and diverse characteristic features of antiferromagnetic (AFM) systems, here in our work, we explore spin-dependent thermoelectric behavior in an AFM ring geometry. A reasonably large (≫1) spin figure of merit, referred to asZST, is obtained under suitable input conditions. Two important prerequisites are (i) breaking the symmetry among up and down spin sub-Hamiltonians and (ii) generating different asymmetric transmission line shapes across a Fermi energy for two opposite spin electrons. Describing the physical system within a tight-binding framework, where spin-dependent scattering occurs due to the interaction of itinerant electrons with local magnetic moments via the usual spin-moment exchange interaction, we compute all the thermoelectric quantities based on Landauer integrals following the Green's function technique. The behavior of charge figure of merit, denoted asZCT, is also discussed along withZST. ThoughZCTreaches above unity, it is much smaller compared toZST. This is the key finding of our investigation. To make the present communication a self-contained one, we compare the results with another arrangement of magnetic moments in a ring-like geometry and in a chain-like one. Our analysis gives a suitable hint that in the presence of spin-dependent scattering, much more favorable energy conversion can be substantiated.

Terahertz Spin Current Dynamics in Antiferromagnetic Hematite

An important vision of modern magnetic research is to use antiferromagnets (AFMs) as controllable and active ultrafast components in spintronic devices. Hematite (α-Fe₂ O₃ ) is a promising model material in this respect because its pronounced Dzyaloshinskii-Moriya interaction leads to the coexistence of antiferromagnetism and weak ferromagnetism. Here, femtosecond laser pulses are used to drive terahertz (THz) spin currents from α-Fe₂ O₃ into an adjacent Pt layer. Two contributions to the generation of the spin current with distinctly different dynamics are found: the impulsive stimulated Raman scatting that relies on the AFM order and the ultrafast spin Seebeck effect that relies on the net magnetization. The total THz spin current dynamics can be manipulated by a medium-strength magnetic field below 1 T. The control of the THz spin current achieved in α-Fe₂ O₃ opens the pathway toward tailoring the exact spin current dynamics from ultrafast AFM spin sources.

Anomalous Nernst Effect in Flexible Co-Based Amorphous Ribbons

Fe3Co67Cr3Si15B12 ribbons with a high degree of flexibility and excellent corrosion stability were produced by rapid quenching technique. Their structural, magnetic, and thermomagnetic (Anomalous Nernst Effect) properties were studied both in an as-quenched (NR) state and after stress annealing during 1 h at the temperature of 350 °C and a specific load of 230 MPa (AR). X-ray diffraction was used to verify the structural characteristics of our ribbons. Static magnetic properties were explored by inductive technique and vibrating sample magnetometry. The thermomagnetic curves investigated through the Anomalous Nernst Effect are consistent with the obtained magnetization results, presenting a linear response in the thermomagnetic signal, an interesting feature for sensor applications. Additionally, Anomalous Nernst Effect coefficient SANE values of 2.66μV/K and 1.93μV/K were estimated for the as-quenched and annealed ribbons, respectively. The interplay of the low magnetostrictive properties, soft magnetic behavior, linearity of the thermomagnetic response, and flexibility of these ribbons place them as promising systems to probe curved surfaces and propose multifunctional devices, including magnetic field-specialized sensors.

Magnetic moment impact on spin-dependent Seebeck coefficient of ferromagnetic thin films

Magnetic materials may be engineered to produce thermoelectric materials using spin-related effects. However, clear understanding of localized magnetic moments (µ_I), free carriers, and Seebeck coefficient (S) interrelations is mandatory for efficient material design. In this work, we investigate µ_I influence on the spin-dependent S of model ferromagnetic thin films, allowing µ_I thermal fluctuations, ordering, and density variation influence to be independently investigated. µ_I influence on free carrier polarization is found to be of highest importance on S: efficient coupling of free carrier spin and localized magnetic moment promotes the increase of S, while spin-dependent relaxation time difference between the two spin-dependent conduction channels leads to S decrease. Our observations support new routes for thermoelectric material design based on spin-related effects in ferromagnetic materials.

All-electrical reading and writing of spin chirality

Spintronics promises potential data encoding and computing technologies. Spin chirality plays a very important role in the properties of many topological and noncollinear magnetic materials. Here, we propose the all-electrical detection and manipulation of spin chirality in insulating chiral antiferromagnets. We demonstrate that the spin chirality in insulating epitaxial films of TbMnO₃ can be read electrically via the spin Seebeck effect and can be switched by electric fields via the multiferroic coupling of the spin chirality to the ferroelectric polarization. Moreover, multivalued states of the spin chirality can be realized by the combined application of electric and magnetic fields. Our results are a path toward next-generation, low-energy consumption memory and logic devices that rely on spin chirality.

Local thermoelectric response from a single Néel domain wall

Spatially resolved thermoelectric detection of magnetic systems provides a unique platform for the investigation of spintronic and spin caloritronic effects. Hitherto, these investigations have been resolution-limited, confining analysis of the thermoelectric response to regions where the magnetization is uniform or collinear at length scales comparable to the domain size. Here, we investigate the thermoelectric response from a single trapped domain wall using a heated scanning probe. Following this approach, we unambiguously resolve the domain wall due to its local thermoelectric response. Combining analytical and thermal micromagnetic modeling, we conclude that the measured thermoelectric signature is unique to that of a domain wall with a Néel-like character. Our approach is highly sensitive to the plane of domain wall rotation, which permits the distinct identification of Bloch or Néel walls at the nanoscale and could pave the way for the identification and characterization of a range of noncollinear spin textures through their thermoelectric signatures.

Spin and polarization: a new direction in relativistic heavy ion physics

Since the first evidence of a global polarization of Λ hyperons in relativistic nuclear collisions in 2017, spin has opened a new window in the field, both at experimental and theoretical level, and an exciting perspective. The current state of the field is reviewed with regard to the theoretical understanding of the data, reporting on the most recent achievements and envisioning possible developments. The intriguing connections of spin physics in relativistic matter with fundamental questions in quantum field theory and applications in the non-relativistic domain are discussed.

Enhanced Magnetism in Heterostructures with Transition-Metal Dichalcogenide Monolayers

Two-dimensional materials and their heterostructures have opened up new possibilities for magnetism at the nanoscale. In this study, we utilize first-principles simulations to investigate the structural, electronic, and magnetic properties of Fe/WSe₂/Pt systems containing pristine, defective, or doped WSe₂ monolayers. The proximity effects of the ferromagnetic Fe layer are studied by considering defective and vanadium-doped WSe₂ monolayers. All heterostructures are found to be ferromagnetic, and the insertion of the transition-metal dichalcogenide results in a redistribution of spin orientation and an increased density of magnetic atoms due to the magnetized WSe₂. There is an increase in the overall total density of states at the Fermi level due to WSe₂; however, the transition-metal dichalcogenide may lose its distinct semiconducting properties due to the stronger than van der Waals coupling. Spin-resolved electronic structure properties are linked to larger spin Seebeck coefficients found in heterostructures with WSe₂ monolayers.

A robust spin-dependent Seebeck effect and remarkable spin thermoelectric performance in graphether nanoribbons

The generation of spin currents is a significant issue in spintronics. A spin current can be induced by a temperature gradient in the spin-dependent Seebeck effect, which has attracted growing interest over recent years. Herein we propose spin caloritronic devices based on magnetic graphether nanoribbons and investigate the spin thermoelectric properties by first-principles calculations. Owing to the symmetrical spin-resolved transmission spectra, our devices exhibit a robust spin-dependent Seebeck effect and could generate a pure spin current. Moreover, they manifest a high spin Seebeck coefficient and a giant spin figure of merit. Our findings demonstrate that graphether-nanoribbon-based devices possess remarkable spin thermoelectric performance, and might be promising candidates for spin caloritronics.

Spin-thermoelectric properties and giant tunneling magnetoresistance of boron-substituted graphene nanoribbon: a first principle study

In this study we have designed a spin caloritronic device based on boron doped armchair graphene nanoribbons (B2-7AGNR). In presence of ferromagnetic (FM) graphitic-carbon nitride (g-C₄N₃) electrodes the spin-thermoelectric features of the device, both for FM and antiferromagnetic (AFM) states, are studied using first principle calculations. The spin polarized transmission peaks and the presence of density of states near the Fermi level indicate that the system have large spin-thermoelectric figure of merit. In addition, it is observed that the system has a large tunneling magnetoresistance due to the difference in total current between FM and AFM configurations. Further studies reveal that the spin component of the Seebeck coefficient of the device is much higher than the other zigzag and armchair nanoribbons. When the spin magnetic moments of the electrodes are aligned in parallel manner, spin-thermoelectric figure of merit of the system becomes significantly high. It has also been found that on decreasing temperature the efficiency of the device increases. As a whole, the numerical results show thatg-C₄N₃-B2-7AGNR-g-C₄N₃system in FM configuration is an efficient low temperature thermoelectric device.

Theory of drift-enabled control in nonlocal magnon transport

Electrically injected and detected nonlocal magnon transport has emerged as a versatile method for transporting spin as well as probing the spin excitations in a magnetic insulator. We examine the role of drift currents in this phenomenon as a method for controlling the magnon propagation length. Formulating a phenomenological description, we identify the essential requirements for existence of magnon drift. Guided by this insight, we examine magnetic field gradient, asymmetric contribution to dispersion, and temperature gradient as three representative mechanisms underlying a finite magnon drift velocity, finding temperature gradient to be particularly effective.

Spin Seebeck Effect in Iron Oxide Thin Films: Effects of Phase Transition, Phase Coexistence, And Surface Magnetism

Understanding the effects of phase transition, phase coexistence, and surface magnetism on the longitudinal spin Seebeck effect (LSSE) in a magnetic system is essential to manipulate the spin to charge current conversion efficiency for spincaloritronic applications. We aim to elucidate these effects by performing a comprehensive study of the temperature dependence of the LSSE in biphase iron oxide (BPIO = α-Fe₂O₃ + Fe₃O₄) thin films grown on Si (100) and Al₂O₃ (111) substrates. A combination of a temperature-dependent anomalous Nernst effect (ANE) and electrical resistivity measurements show that the contribution of the ANE from the BPIO layer is negligible in comparison to the intrinsic LSSE in the Si/BPIO/Pt heterostructure, even at room temperature. Below the Verwey transition of the Fe₃O₄ phase, the total signal across BPIO/Pt is dominated by the LSSE. Noticeable changes in the intrinsic LSSE signal for both Si/BPIO/Pt and Al₂O₃/BPIO/Pt heterostructures around the Verwey transition of the Fe₃O₄ phase and the antiferromagnetic (AFM) Morin transition of the α-Fe₂O₃ phase are observed. The LSSE signal for Si/BPIO/Pt is found to be almost 2 times greater than that for Al₂O₃/BPIO/Pt; however, an opposite trend is observed for the saturation magnetization. Magnetic force microscopy reveals the higher density of surface magnetic moments of the Si/BPIO film in comparison to the Al₂O₃/BPIO film, which underscores the dominant role of interfacial magnetism on the LSSE signal and thereby explains the larger LSSE for Si/BPIO/Pt.

Designing light-element materials with large effective spin-orbit coupling

Spin-orbit coupling (SOC), which is the core of many condensed-matter phenomena such as nontrivial band gap and magnetocrystalline anisotropy, is generally considered appreciable only in heavy elements. This is detrimental to the synthesis and application of functional materials. Therefore, amplifying the SOC effect in light elements is crucial. Herein, focusing on 3d and 4d systems, we demonstrate that the interplay between crystal symmetry and electron correlation can significantly enhance the SOC effect in certain partially occupied orbital multiplets through the self-consistently reinforced orbital polarization as a pivot. Thereafter, we provide design principles and comprehensive databases, where we list all the Wyckoff positions and site symmetries in all two-dimensional (2D) and three-dimensional crystals that could have enhanced SOC effect. Additionally, we predict nine material candidates from our selected 2D material pool as high-temperature quantum anomalous Hall insulators with large nontrivial band gaps of hundreds of meV. Our study provides an efficient and straightforward way for predicting promising SOC-active materials, relieving the use of heavy elements for next-generation spin-orbitronic materials and devices.

Role of Magnon-Magnon Scattering in Magnon Polaron Spin Seebeck Effect

The spin Seebeck effect (SSE) signal of magnon polarons in bulk-Y_{3}Fe_{5}O_{12} (YIG)/Pt heterostructures is found to drastically change as a function of temperature. It appears as a dip in the total SSE signal at low temperatures, but as the temperature increases, the dip gradually decreases before turning to a peak. We attribute the observed dip-to-peak transition to the rapid rise of the four-magnon scattering rate. Our analysis provides important insights into the microscopic origin of the hybridized excitations and the overall temperature dependence of the SSE anomalies.

Reconfigurable single-material Peltier effect using magnetic-phase junctions

Peltier effects, which produce a heat flux at the junction of two different materials, have been an important technology for heating and cooling by electrical means. Whereas Peltier devices have advantages such as cleanliness, silence, compactness, flexibility, reliability, and efficiency, relatively complicated modular structures are unavoidable, leading to a higher cost than that of commonly used refrigeration technology. Here, we provide a concept of a Peltier device composed of a single magnetic material exhibiting a first-order magnetic transition. Our concept is based on a controllable junction structure consisting of two magnetic phases with opposite Peltier coefficients instead of a semiconductor junction. Using \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{Mn}}_{1.96}{\mathrm{Cr}}_{0.04}\mathrm{Sb}$$\end{document}Mn1.96Cr0.04Sb samples with the first-order magnetic transition between ferrimagnetic (FI) and antiferromagnetic (AF) states, we successfully made a stable junction structure of AF/FI/AF by a pulse heating method and achieved a maximum Peltier coefficient of 0.58 mV. Our device concept was further verified by a numerical simulation based on a finite element method. The single-material Peltier effect reported here avoids a complex device design involving material junctions and is importantly reconfigurable.

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.

Pure spin photocurrent in non-centrosymmetric crystals: bulk spin photovoltaic effect

Spin current generators are critical components for spintronics-based information processing. In this work, we theoretically and computationally investigate the bulk spin photovoltaic (BSPV) effect for creating DC spin current under light illumination. The only requirement for BSPV is inversion symmetry breaking, thus it applies to a broad range of materials and can be readily integrated with existing semiconductor technologies. The BSPV effect is a cousin of the bulk photovoltaic (BPV) effect, whereby a DC charge current is generated under light. Thanks to the different selection rules on spin and charge currents, a pure spin current can be realized if the system possesses mirror symmetry or inversion-mirror symmetry. The mechanism of BSPV and the role of the electronic relaxation time [Formula: see text] are also elucidated. We apply our theory to several distinct materials, including monolayer transition metal dichalcogenides, anti-ferromagnetic bilayer MnBi2Te4, and the surface of topological crystalline insulator cubic SnTe.

Strong Crystallographic Influence on Spin Hall Mechanism in PLD-Grown IrO2 Thin Films

Spin-to-charge conversion is a central process in the emerging field of spintronics. One of its main applications is the electrical detection of spin currents, and for this, the inverse spin Hall effect (ISHE) has become one of the preferred methods. We studied the thickness dependence of the ISHE in iridium oxide (IrO2) thin films, producing spin currents by means of the spin Seebeck effect in γ−Fe2O3/IrO2 bilayers prepared by pulsed laser deposition (PLD). The observed ISHE charge current density, which features a maximum as a consequence of the spin diffusion length scale, follows the typical behaviour of spin-Hall-related phenomena. By fitting to the theory developed by Castel et al., we find that the spin Hall angle θSH scales proportionally to the thin film resistivity, θSH∝ρc, and obtains a value for the spin diffusion length λIrO2 of λIrO2=3.3(7) nm. In addition, we observe a negative θSH for every studied thickness and temperature, unlike previously reported works, which brings the possibility of tuning the desired functionality of high-resistance spin-Hall-based devices. We attribute this behaviour to the textured growth of the sample in the context of a highly anisotropic value of the spin Hall conductivity in this material.

The spin-dependent transport properties of defected zigzag graphene nanoribbons with graphene nanobubbles

Zigzag-edged graphene nanoribbons (ZGNRs) have important applications in spintronics and spin caloritronics. While in the preparation of a ZGNR, defects like the graphene nanobubbles often appear, which may affect the physical properties of the ZGNR. In this paper, we studied the transport properties of a defected ZGNR with a graphene nanobubble by performing first-principles quantum transport calculations. The results show that when the nanobubble is intact and locates at the centre, the spin polarization and magnetoresistance tend to drop off in the low bias voltage cases, compared to the ideal ZGNR. While when the nanobubble is split and locates at the edge, all the transport properties are significantly affected and altered, such as the spin polarization, the giant magnetoresistance effect and the spin Seebeck effect. Meanwhile, some new results are obtained from the device, including the negative differential resistance effect and the pure thermal-induced spin-current.

Transport phenomena in spin caloritronics

The interconversion between spin, charge, and heat currents is being actively studied from the viewpoints of both fundamental physics and thermoelectric applications in the field of spin caloritronics. This field is a branch of spintronics, which has developed rapidly since the discovery of the thermo-spin conversion phenomenon called the spin Seebeck effect. In spin caloritronics, various thermo-spin conversion phenomena and principles have subsequently been discovered and magneto-thermoelectric effects, thermoelectric effects unique to magnetic materials, have received renewed attention with the advances in physical understanding and thermal/thermoelectric measurement techniques. However, the existence of various thermo-spin and magneto-thermoelectric conversion phenomena with similar names may confuse non-specialists. Thus, in this Review, the basic behaviors, spin-charge-heat current conversion symmetries, and functionalities of spin-caloritronic phenomena are summarized, which will help new entrants to learn fundamental physics, materials science, and application studies in spin caloritronics.

On the dissipative coherent states of magnons

Research in spintronics has attracted much attention in the last few years due to the technological progress in generating and manipulating spin currents in miniaturized devices. Notwithstanding dissipative effects are inherent to experiments, in many theoretical works the damping of spin waves is included later by phenomenological arguments or even disregarded. Among the many techniques that have been used to treat magnetic models, bosonic representations is one of them. In this work, we chose the Holstein-Primakoff bosonic formalism to treat a ferromagnetic model with a priori inclusion of the damping term. Damping is included through a non-Hermitian term in the Hamiltonian and we showed that the well-known coherent state formalism can be generalized to properly represent the dissipative magnon model. The obtained results are then used to describe the precession magnetization in spintronic experiments, as the spin pumping process.

Spin Seebeck effect in bipolar magnetic semiconductor: A case of magnetic MoS2 nanotube

Bipolar magnetic semiconductors (BMSs) are a new member of spintornic materials. In BMSs, one can obtain 100% spin-polarized currents by means of the gate voltage. However, most of previous studies focused on their applications in spintronics instead of spin caloritronics. Herein, we show that BMS is an intrinsic model for spin Seebeck effect (SSE). Without any gate voltage and electric field, currents with opposite spin orientation are generated and flow in opposite directions with almost equal magnitude when simply applying a temperature bias. This is also due to the special electronic structure of BMS where the conduction and valence bands near the Fermi level belong to opposite spin orientation. Based on density function theory and non-equilibrium Green's function methods, we confirm the thermal-induced SSE in BMS using a case of magnetic MoS₂ nanotube. The magnitude of spin current in zigzag tube is almost four times higher than that in armchair tube. BMS is promising candidates for spin caloritronic applications.

Spin current as a probe of quantum materials

Spin current historically referred to the flow of electrons carrying spin information, in particular since the discovery of giant magnetoresistance in the 1980s. Recently, it has been found that spin current can also be mediated by spin-triplet supercurrent, superconducting quasiparticles, spinons, magnons, spin superfluidity and so on. Here, we review key progress concerning the developing research direction utilizing spin current as a probe of quantum materials. We focus on spin-triplet superconductivity and spin dynamics in the ferromagnet/superconductor heterostructures, quantum spin liquids, magnetic phase transitions, magnon-polarons, magnon-polaritons, magnon Bose-Einstein condensates and spin superfluidity. The unique characteristics of spin current as a probe will be fruitful for future investigation of spin-dependent properties and the identification of new quantum materials.

Distinct Detection of Thermally Induced Spin Voltage in Pt/WS2/Ni81Fe19 by the Inverse Spin Hall Effect

Conversion of heat into a spin current by means of the spin Seebeck effect (SSE) is one of the exciting topics in spin caloritronics. By use of this technique, the excess heat may be transformed into a valuable electric voltage by coupling SSE with the inverse spin Hall effect (ISHE). In this study, a thermal gradient and an in-plane magnetic field are used as the driving power to mobilize the spin electrons to produce SSE. A spin voltage is detected by ISHE in the Ni₈₁Fe₁₉ heterostructure by means of a WS₂/Pt strip. Using WS₂ sheets of different thicknesses, we obtained a large spin Seebeck coefficient of 0.72 μV/K, which is 12 times greater than the conventional spin Seebeck coefficient observed in Pt/Ni₈₁Fe₁₉ bilayer devices. We observe the thickness dependence of tungsten disulfide (WS₂) flakes and the polarity reversal of pure SSE signals that are measured without influence from the other thermoelectric effects in our Pt/WS₂/Ni₈₁Fe₁₉ device-the most intriguing feature of this study. Without the electric charge conduction, the spins are distributed over a longer distance that is greater than the spin diffusion length of the Ni₈₁Fe₁₉ layer. Such features are strongly desired for designing the efficient spin-caloritronics devices that may be used in the thermoelectric spin generators and the temperature sensors such as thermocouples.

Spin Seebeck Effect from Antiferromagnetic Magnons and Critical Spin Fluctuations in Epitaxial FeF_{2} Films

We report a longitudinal spin Seebeck effect (SSE) study in epitaxially grown FeF_{2}(110) antiferromagnetic (AFM) thin films with strong uniaxial anisotropy over the temperature range of 3.8-250 K. Both the magnetic-field and temperature-dependent SSE signals below the Néel temperature (T_{N}=70  K) of the FeF_{2} films are consistent with a theoretical model based on the excitations of AFM magnons without any net induced static magnetic moment. In addition to the characteristic low-temperature SSE peak associated with the AFM magnons, there is another SSE peak at T_{N} which extends well into the paramagnetic phase. All the SSE data taken at different magnetic fields up to 12 T near and above the critical point T_{N} follow the critical scaling law very well with the critical exponents for magnetic susceptibility of 3D Ising systems, which suggests that the AFM spin correlation is responsible for the observed SSE near T_{N}.

Anisotropic and Controllable Gilbert-Bloch Dissipation in Spin Valves

Spin valves form a key building block in a wide range of spintronic concepts and devices from magnetoresistive read heads to spin-transfer-torque oscillators. We elucidate the dependence of the magnetic damping in the free layer on the angle its equilibrium magnetization makes with that in the fixed layer. The spin pumping-mediated damping is anisotropic and tensorial, with Gilbert- and Bloch-like terms. Our investigation reveals a mechanism for tuning the free layer damping in situ from negligible to a large value via the orientation of fixed layer magnetization, especially when the magnets are electrically insulating. Furthermore, we expect the Bloch contribution that emerges from the longitudinal spin accumulation in the nonmagnetic spacer to play an important role in a wide range of other phenomena in spin valves.

CuPt Alloy Thin Films for Application in Spin Thermoelectrics

Spin thermoelectrics represents a new paradigm of thermoelectricity that has a potential to overcome the fundamental limitation posed by the Wiedmann-Franz law on the efficiency of conventional thermoelectric devices. A typical spin thermoelectric device consists of a bilayer of a magnetic insulator and a high spin-orbit coupling (SOC) metal coated over a non-magnetic substrate. Pt is the most commonly used metal in spin thermoelectric devices due to its strong SOC. In this paper, we found that an alloy of Cu and Pt can perform much better than Pt in spin thermoelectric devices. A series of CuPt alloy films with different Pt concentrations were deposited on yttrium iron garnet (YIG) films coated gadolinium gallium garnet (GGG) substrate. Through spin Seebeck measurements, it was found that the Cu0.4Pt0.6/YIG/GGG device shows almost 3 times higher spin Seebeck voltage compared to Pt/YIG/GGG under identical conditions. The improved performance was attributed to the higher resistivity as well as enhanced spin hall angle of the CuPt layer.

Femtosecond formation dynamics of the spin Seebeck effect revealed by terahertz spectroscopy

Understanding the transfer of spin angular momentum is essential in modern magnetism research. A model case is the generation of magnons in magnetic insulators by heating an adjacent metal film. Here, we reveal the initial steps of this spin Seebeck effect with <27 fs time resolution using terahertz spectroscopy on bilayers of ferrimagnetic yttrium iron garnet and platinum. Upon exciting the metal with an infrared laser pulse, a spin Seebeck current j_s arises on the same ~100 fs time scale on which the metal electrons thermalize. This observation highlights that efficient spin transfer critically relies on carrier multiplication and is driven by conduction electrons scattering off the metal–insulator interface. Analytical modeling shows that the electrons’ dynamics are almost instantaneously imprinted onto j_s because their spins have a correlation time of only ~4 fs and deflect the ferrimagnetic moments without inertia. Applications in material characterization, interface probing, spin-noise spectroscopy and terahertz spin pumping emerge.

Probing spin pumping in the terahertz regime allows one to reveal its initial elementary steps. Here, the authors show that the formation of the spin Seebeck current in YIG/Pt critically relies on hot thermalized metal electrons because they impinge on the metal-insulator interface with maximum noise.

Dirac surface state-modulated spin dynamics in a ferrimagnetic insulator at room temperature

This work demonstrates markedly modified spin dynamics of magnetic insulator (MI) by the spin momentum-locked Dirac surface states of the adjacent topological insulator (TI), which can be harnessed for spintronic applications. As the Bi concentration x is systematically tuned in 5-nm-thick (Bi _x Sb_1-x )₂Te₃ TI films, the weight of the surface relative to bulk states peaks at x = 0.32 when the chemical potential approaches the Dirac point. At this concentration, the Gilbert damping constant of the precessing magnetization in 10-nm-thick Y₃Fe₅O₁₂ MI films in the MI/TI heterostructures is enhanced by an order of magnitude, the largest among all concentrations. In addition, the MI acquires additional strong magnetic anisotropy that favors the in-plane orientation with similar Bi concentration dependence. These extraordinary effects of the Dirac surface states distinguish TI from other materials such as heavy metals in modulating spin dynamics of the neighboring magnetic layer.

Complex Terahertz and Direct Current Inverse Spin Hall Effect in YIG/Cu1-xIrx Bilayers Across a Wide Concentration Range

We measure the inverse spin Hall effect of Cu_1-xIr_x thin films on yttrium iron garnet over a wide range of Ir concentrations (0.05 ⩽ x ⩽ 0.7). Spin currents are triggered through the spin Seebeck effect, either by a continuous (dc) temperature gradient or by ultrafast optical heating of the metal layer. The spin Hall current is detected by electrical contacts or measurement of the emitted terahertz radiation. With both approaches, we reveal the same Ir concentration dependence that follows a novel complex, nonmonotonous behavior as compared to previous studies. For small Ir concentrations a signal minimum is observed, whereas a pronounced maximum appears near the equiatomic composition. We identify this behavior as originating from the interplay of different spin Hall mechanisms as well as a concentration-dependent variation of the integrated spin current density in Cu_1-xIr_x. The coinciding results obtained for dc and ultrafast stimuli provide further support that the spin Seebeck effect extends to terahertz frequencies, thus enabling a transfer of established spintronic measurement schemes into the terahertz regime. Our findings also show that the studied material allows for efficient spin-to-charge conversion even on ultrafast time scales.

Spin Pumping and Shot Noise in Ferrimagnets: Bridging Ferro- and Antiferromagnets

A combination of novel technological and fundamental physics prospects has sparked a huge interest in pure spin transport in magnets, starting with ferromagnets and spreading to antiferro- and ferrimagnets. We present a theoretical study of spin transport across a ferrimagnet-nonmagnetic conductor interface, when a magnetic eigenmode is driven into a coherent state. The obtained spin current expression includes intra- as well as cross-sublattice terms, both of which are essential for a quantitative understanding of spin pumping. The dc current is found to be sensitive to the asymmetry in interfacial coupling between the two sublattice magnetizations and the mobile electrons, especially for antiferromagnets. We further find that the concomitant shot noise provides a useful tool for probing the quasiparticle spin and interfacial coupling.

Roles of bulk and surface magnetic anisotropy on the longitudinal spin Seebeck effect of Pt/YIG

A clear understanding of the temperature evolution of the longitudinal spin Seebeck effect (LSSE) in the classic Pt/yttrium iron garnet (YIG) system and its association with magnetic anisotropy is essential towards optimization of its spin-caloric functionality for spintronics applications. We report here for the first time the temperature dependences of LSSE voltage (V_LSSE), magnetocrystalline anisotropy field (H_K) and surface perpendicular magnetic anisotropy field (H_KS) in the same Pt/YIG system. We show that on lowering temperature, the sharp drop in V_LSSE and the sudden increases in H_K and H_KS at ~175 K are associated with the spin reorientation due to single ion anisotropy of Fe²⁺ ions. The V_LSSE peak at ~75 K is attributed to the H_KS and M_S (saturation magnetization) whose peaks also occur at the same temperature. The effects of surface and bulk magnetic anisotropies are corroborated with those of thermally excited magnon number and magnon propagation length to satisfactorily explain the temperature dependence of LSSE in the Pt/YIG system. Our study also emphasizes the important roles of bulk and surface anisotropies in the LSSE in YIG and paves a new pathway for developing novel spin-caloric materials.

Strong Modulation of Spin Currents in Bilayer Graphene by Static and Fluctuating Proximity Exchange Fields

Two-dimensional materials provide a unique platform to explore the full potential of magnetic proximity-driven phenomena, which can be further used for applications in next-generation spintronic devices. Of particular interest is to understand and control spin currents in graphene by the magnetic exchange field of a nearby ferromagnetic material in graphene-ferromagnetic-insulator (FMI) heterostructures. Here, we present the experimental study showing the strong modulation of spin currents in graphene layers by controlling the direction of the exchange field due to FMI magnetization. Owing to clean interfaces, a strong magnetic exchange coupling leads to the experimental observation of complete spin modulation at low externally applied magnetic fields in short graphene channels. Additionally, we discover that the graphene spin current can be fully dephased by randomly fluctuating exchange fields. This is manifested as an unusually strong temperature dependence of the nonlocal spin signals in graphene, which is due to spin relaxation by thermally induced transverse fluctuations of the FMI magnetization.

Picosecond Spin Seebeck Effect

We report time-resolved magneto-optic Kerr effect measurements of the longitudinal spin Seebeck effect in normal metal/Y_{3}Fe_{5}O_{12} bilayers driven by an interfacial temperature difference between electrons and magnons. The measured time evolution of spin accumulation induced by laser excitation indicates transfer of angular momentum across normal metal/Y_{3}Fe_{5}O_{12} interfaces on a picosecond time scale, too short for contributions from a bulk temperature gradient in an yttrium iron garnet. The product of spin-mixing conductance and the interfacial spin Seebeck coefficient determined is of the order of 10^{8}  A m^{-2} K^{-1}.

Thermal imaging of spin Peltier effect

The Peltier effect modulates the temperature of a junction comprising two different conductors in response to charge currents across the junction, which is used in solid-state heat pumps and temperature controllers in electronics. Recently, in spintronics, a spin counterpart of the Peltier effect was observed. The ‘spin Peltier effect' modulates the temperature of a magnetic junction in response to spin currents. Here we report thermal imaging of the spin Peltier effect; using active thermography technique, we visualize the temperature modulation induced by spin currents injected into a magnetic insulator from an adjacent metal. The thermal images reveal characteristic distribution of spin-current-induced heat sources, resulting in the temperature change confined only in the vicinity of the metal/insulator interface. This finding allows us to estimate the actual magnitude of the temperature modulation induced by the spin Peltier effect, which is more than one order of magnitude greater than previously believed.

The spin Peltier effect produces a temperature difference along the direction of a spin current. Here, the authors use an active thermography technique to visualize the temperature modulation induced by a spin current injected into a magnetic insulator from an adjacent metal.

Thermodynamic restrictions on linear reversible and irreversible thermo-electro-magneto-mechanical processes

A unified thermodynamic framework for the characterization of functional materials is developed. This framework encompasses linear reversible and irreversible processes with thermal, electrical, magnetic, and/or mechanical effects coupled. The comprehensive framework combines the principles of classical equilibrium and non-equilibrium thermodynamics with electrodynamics of continua in the infinitesimal strain regime. In the first part of this paper, linear Thermo-Electro-Magneto-Mechanical (TEMM) quasistatic processes are characterized. Thermodynamic stability conditions are further imposed on the linear constitutive model and restrictions on the corresponding material constants are derived. The framework is then extended to irreversible transport phenomena including thermoelectric, thermomagnetic and the state-of-the-art spintronic and spin caloritronic effects. Using Onsager's reciprocity relationships and the dissipation inequality, restrictions on the kinetic coefficients corresponding to charge, heat and spin transport processes are derived. All the constitutive models are accompanied by multiphysics interaction diagrams that highlight the various processes that can be characterized using this framework.

Laser-Driven Multiferroics and Ultrafast Spin Current Generation

We propose an ultrafast way to generate spin chirality and spin current in a class of multiferroic magnets using a terahertz circularly polarized laser. Using the Floquet formalism for periodically driven systems, we show that it is possible to dynamically control the Dzyaloshinskii-Moriya interaction in materials with magnetoelectric coupling. This is supported by numerical calculations, by which additional resonant phenomena are found. Specifically, when a static magnetic field is applied in addition to the circularly polarized laser, a large resonant enhancement of spin chirality is observed resembling the electron spin resonance. Spin current is generated when the laser is spatially modulated by chiral plasmonic structures and could be detected using optospintronic devices.

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.

Nanoscale solid-state cooling: a review

The recent developments in nanoscale solid-state cooling are reviewed. This includes both theoretical and experimental studies of different physical concepts, as well as nanostructured material design and device configurations. We primarily focus on thermoelectric, thermionic and thermo-magnetic coolers. Particular emphasis is given to the concepts based on metal-semiconductor superlattices, graded materials, non-equilibrium thermoelectric devices, Thomson coolers, and photon assisted Peltier coolers as promising methods for efficient solid-state cooling. Thermomagnetic effects such as magneto-Peltier and Nernst-Ettingshausen cooling are briefly described and recent advances and future trends in these areas are reviewed. The ongoing progress in solid-state cooling concepts such as spin-calorimetrics, electrocalorics, non-equilibrium/nonlinear Peltier devices, superconducting junctions and two-dimensional materials are also elucidated and practical achievements are reviewed. We explain the thermoreflectance thermal imaging microscopy and the transient Harman method as two unique techniques developed for characterization of thermoelectric microrefrigerators. The future prospects for solid-state cooling are briefly summarized.

Theory of spin Hall magnetoresistance (SMR) and related phenomena

We review the so-called spin Hall magnetoresistance (SMR) in bilayers of a magnetic insulator and a metal, in which spin currents are generated in the normal metal by the spin Hall effect. The associated angular momentum transfer to the ferromagnetic layer and thereby the electrical resistance is modulated by the angle between the applied current and the magnetization direction. The SMR provides a convenient tool to non-invasively measure the magnetization direction and spin-transfer torque to an insulator. We introduce the minimal theoretical instruments to calculate the SMR, i.e. spin diffusion theory and quantum mechanical boundary conditions. This leads to a small set of parameters that can be fitted to experiments. We discuss the limitations of the theory as well as alternative mechanisms such as the ferromagnetic proximity effect and Rashba spin-orbit torques, and point out new developments.

Flexible heat-flow sensing sheets based on the longitudinal spin Seebeck effect using one-dimensional spin-current conducting films

Heat-flow sensing is expected to be an important technological component of smart thermal management in the future. Conventionally, the thermoelectric (TE) conversion technique, which is based on the Seebeck effect, has been used to measure a heat flow by converting the flow into electric voltage. However, for ubiquitous heat-flow visualization, thin and flexible sensors with extremely low thermal resistance are highly desired. Recently, another type of TE effect, the longitudinal spin Seebeck effect (LSSE), has aroused great interest because the LSSE potentially offers favourable features for TE applications such as simple thin-film device structures. Here we demonstrate an LSSE-based flexible TE sheet that is especially suitable for a heat-flow sensing application. This TE sheet contained a Ni0.2Zn0.3Fe2.5O4 film which was formed on a flexible plastic sheet using a spray-coating method known as "ferrite plating". The experimental results suggest that the ferrite-plated film, which has a columnar crystal structure aligned perpendicular to the film plane, functions as a unique one-dimensional spin-current conductor suitable for bendable LSSE-based sensors. This newly developed thin TE sheet may be attached to differently shaped heat sources without obstructing an innate heat flux, paving the way to versatile heat-flow measurements and management.

Antiferromagnetic Spin Seebeck Effect

We report on the observation of the spin Seebeck effect in antiferromagnetic MnF_{2}. A device scale on-chip heater is deposited on a bilayer of MnF_{2} (110) (30  nm)/Pt (4 nm) grown by molecular beam epitaxy on a MgF_{2} (110) substrate. Using Pt as a spin detector layer, it is possible to measure the thermally generated spin current from MnF_{2} through the inverse spin Hall effect. The low temperature (2-80 K) and high magnetic field (up to 140 kOe) regime is explored. A clear spin-flop transition corresponding to the sudden rotation of antiferromagnetic spins out of the easy axis is observed in the spin Seebeck signal when large magnetic fields (>9  T) are applied parallel to the easy axis of the MnF_{2} thin film. When the magnetic field is applied perpendicular to the easy axis, the spin-flop transition is absent, as expected.

Thermal Generation of Spin Current in an Antiferromagnet

The longitudinal spin Seebeck effect has been investigated for a uniaxial antiferromagnetic insulator Cr(2)O(3), characterized by a spin-flop transition under magnetic field along the c axis. We have found that a temperature gradient applied normal to the Cr(2)O(3)/Pt interface induces inverse spin Hall voltage of spin-current origin in Pt, whose magnitude turns out to be always proportional to magnetization in Cr(2)O(3). The possible contribution of the anomalous Nernst effect is confirmed to be negligibly small. The above results establish that an antiferromagnetic spin wave can be an effective carrier of spin current.

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.

Paramagnetic spin seebeck effect

We report the observation of the longitudinal spin Seebeck effect in paramagnetic insulators. By using a microscale on-chip local heater, we generate a large thermal gradient confined to the chip surface without a large increase in the total sample temperature. Using this technique at low temperatures (<20  K), we resolve the paramagnetic spin Seebeck effect in the insulating paramagnets Gd3Ga5O12 (gadolinium gallium garnet) and DyScO3 (DSO), using either W or Pt as the spin detector layer. By taking advantage of the strong magnetocrystalline anisotropy of DSO, we eliminate contributions from the Nernst effect in W or Pt, which produces a phenomenologically similar signal.

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.

Generalized two-temperature model for coupled phonon-magnon diffusion

We generalize the two-temperature model [Sanders and Walton, Phys. Rev. B 15, 1489 (1977)] for coupled phonon-magnon diffusion to include the effect of the concurrent magnetization flow, with a particular emphasis on the thermal consequence of the magnon flow driven by a nonuniform magnetic field. Working within the framework of the Boltzmann transport equation, we derive the constitutive equations for coupled phonon-magnon transport driven by gradients of both temperature and external magnetic fields, and the corresponding conservation laws. Our equations reduce to the original Sanders-Walton two-temperature model under a uniform external field, but predict a new magnon cooling effect driven by a nonuniform magnetic field in a homogeneous single-domain ferromagnet. We estimate the magnitude of the cooling effect in an yttrium iron garnet, and show it is within current experimental reach. With properly optimized materials, the predicted cooling effect can potentially supplement the conventional magnetocaloric effect in cryogenic applications in the future.