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

Electrically Induced Angular Momentum Flow between Separated Ferromagnets

Converting angular momentum between different degrees of freedom within a magnetic material results from a dynamic interplay between electrons, magnons, and phonons. This interplay is pivotal to implementing spintronic device concepts that rely on spin angular momentum transport. We establish a new concept for long-range angular momentum transport that further allows us to address and isolate the magnonic contribution to angular momentum transport in a nanostructured metallic ferromagnet. To this end, we electrically excite and detect spin transport between two parallel and electrically insulated ferromagnetic metal strips on top of a diamagnetic substrate. Charge-to-spin current conversion within the ferromagnetic strip generates electronic spin angular momentum that is transferred to magnons via electron-magnon coupling. We observe a finite angular momentum flow to the second ferromagnetic strip across a diamagnetic substrate over micron distances, which is electrically detected in the second strip by the inverse charge-to-spin current conversion process. We discuss phononic and dipolar interactions as the likely cause to transfer angular momentum between the two strips. Moreover, our Letter provides the experimental basis to separate the electronic and magnonic spin transport and thereby paves the way towards magnonic device concepts that do not rely on magnetic insulators.

Observation of the Anisotropic Magneto-Thomson Effect

We report the observation of the anisotropic magneto-Thomson effect (AMTE), which is one of the higher-order thermoelectric effects in a ferromagnet. Using lock-in thermography, we demonstrated that in a ferromagnetic NiPt alloy, the cooling or heating induced by the Thomson effect depends on the angle between the magnetization direction and the temperature gradient or charge current applied to the alloy. AMTE observed here is the missing ferromagnetic analog of the magneto-Thomson effect in a nonmagnetic conductor, providing the basis for nonlinear spin caloritronics and thermoelectrics.

Absence of Spin-Orbit Torque and Discovery of Anisotropic Planar Nernst Effect in CoFe Single Crystal

Exploration of exotic spin polarizations in single crystals is of increasing interest. A current of longitudinal spins, the so-called "Dresselhaus-like" spin current, which is forbidden in materials lacking certain inversion asymmetries, is implied to be generated by a charge current at the interface of single-crystal CoFe. This work reports unambiguous evidence that there is no indication of spin current of any spin polarizations from the interface or bulk of single-crystalline CoFe and that the sin2φ second harmonic Hall voltage, which is previously assumed to signify Dresselhaus-like spin current, is not related to any spin currents but rather a planar Nernst voltage induced by a longitudinal temperature gradient within the sample. Such sin2φ signal is independent of large applied magnetic fields and interfacial spin-orbit coupling, inversely correlated to the heat capacity of the substrates and overlayers, quadratic in charge current, and appears also in polycrystalline ferromagnets. Strikingly, the planar Nernst effect (PNE) in the CoFe single crystal has a strong fourfold anisotropy and varies with the crystalline orientation. Such strong, anisotropic PNE has widespread impacts on the analyses of a variety of spintronic experiments and opens a new avenue for the development of PNE-based thermoelectric battery and sensor applications.

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.

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.

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.

Magneto-transport phenomena of type-I multi-Weyl semimetals in co-planar setups

Having the chiral anomaly (CA) induced magneto-transport phenomena extensively studied in single Weyl semimetal as characterized by topological charge n = 1, we here address the transport properties in the context of multi-Weyl semimetals (m-WSMs) where n > 1. Using semiclassical Boltzmann transport formalism with the relaxation time approximation, we investigate several intriguing transport properties such as longitudinal magneto-conductivity (LMC), planar Hall conductivity (PHC), thermo-electric coefficients (TECs) and planar Nernst coefficient (PNC) for m-WSMs in the co-planar setups with external magnetic field, electric field and temperature gradient. Starting from the low-energy model, we show analytically that at zero temperature both LMC and PHC vary cubically with topological charge as n ³ while the finite temperature (T ≠ 0) correction is proportional to (n + n ²)T ². Interestingly, we find that both the longitudinal and transverse TECs vary quadratically with topological charge as n ² and the PNC is found to vary non-monotonically as a function of n. Our study hence clearly suggests that the inherent properties of m-WSMs indeed show up distinctly through the CA and the chiral magnetic effect induced transport coefficients in two different setups. Moreover, in order to obtain an experimentally realizable picture, we simultaneously verify our analytical findings through the numerical calculations using the lattice model of m-WSMs.

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.

Observation of the Magneto-Thomson Effect

We report the observation of the higher-order thermoelectric conversion based on a magneto-Thomson effect. By means of thermoelectric imaging techniques, we directly observed the temperature change induced by the Thomson effect in a polycrystalline Bi_{88}Sb_{12} alloy under a magnetic field and found that the magnetically enhanced Thomson coefficient can be comparable to or even larger than the Seebeck coefficient. Our experiments reveal the significant contribution of the higher-order magnetothermoelectric conversion, opening the door to "nonlinear spin caloritronics."

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.

Observation of spin-orbit effects with spin rotation symmetry

The spin-orbit interaction enables interconversion between a charge current and a spin current. It is usually believed that in a nonmagnetic metal (NM) or at a NM/ferromagnetic metal (FM) bilayer interface, the symmetry of spin-orbit effects requires that the spin current, charge current, and spin orientation are all orthogonal to each other. Here we demonstrate the presence of spin-orbit effects near the NM/FM interface that exhibit a very different symmetry, hereafter referred to as spin-rotation symmetry, from the conventional spin Hall effect while the spin polarization is rotating about the magnetization. These results imply that a perpendicularly polarized spin current can be generated with an in-plane charge current simply by use of a FM/NM bilayer with magnetization collinear to the charge current. The ability to generate a spin current with arbitrary polarization using typical magnetic materials will benefit the development of magnetic memories.Converting charge to spin currents using spin-orbit interactions has useful applications in spintronics but symmetry constraints can limit the control over spin polarization. Here the authors demonstrate spin-orbit effects with a different symmetry, which could help generate arbitrary spin polarizations.

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.

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.

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.

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.

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.

Peltier cooling and onsager reciprocity in ferromagnetic thin films

We present direct measurements of the Peltier effect as a function of temperature from 77 to 325 K in Ni, Ni(80)Fe(20), and Fe thin films made using a suspended Si-N membrane structure. Measurement of the Seebeck effect in the same films allows us to directly test predictions of Onsager reciprocity between the Peltier and Seebeck effects. The Peltier coefficient Π is negative for both Ni and Ni(80)Fe(20) films and positive for the Fe film. The Fe film also exhibits a peak associated with the magnon drag Peltier effect. The observation of magnon drag in the Fe film verifies that the coupling between the phonon, magnon, and electron systems in the film is the same whether driven by heat current or charge current. The excellent agreement between Π values predicted using the experimentally determined Seebeck coefficient for these films and measured values offers direct experimental confirmation of the Onsager reciprocity between these thermoelectric effects in ferromagnetic thin films near room temperature.

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.

Time-resolved measurement of the tunnel magneto-Seebeck effect in a single magnetic tunnel junction

Recently, several groups have reported spin-dependent thermoelectric effects in magnetic tunnel junctions. In this paper, we present a setup for time-resolved measurements of thermovoltages and thermocurrents of a single micro- to nanometer-scaled tunnel junction. An electrically modulated diode laser is used to create a temperature gradient across the tunnel junction layer stack. This laser modulation technique enables the recording of time-dependent thermovoltage signals with a temporal resolution only limited by the preamplifier for the thermovoltage. So far, time-dependent thermovoltage could not be interpreted. Now, with the setup presented in this paper, it is possible to distinguish different Seebeck voltage contributions to the overall measured voltage signal in the μs time regime. A model circuit is developed that explains those voltage contributions on different sample types. Further, it will be shown that a voltage signal arising from the magnetic tunnel junction can only be observed when the laser spot is directly centered on top of the magnetic tunnel junction, which allows a lateral separation of the effects.