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Thermoelectric generation based on spin Seebeck effects

Ken-ichi Uchida, Hiroto Adachi, Takashi Kikkawa, Akihiro Kirihara, Masahiko Ishida, Shinichi Yorozu, Sadamichi Maekawa, Eiji Saitoh

arXiv:1604.00477v2cond-mat.mtrl-scicond-mat.mes-hall

TL;DR

The paper examines how spin Seebeck effects can support thermoelectric generation and reviews their device physics, efficiency, and application prospects. It finds that insulator-based LSSE devices separate heat and charge transport, offering flexible optimization and scaling, while current thermopower remains small and efficiency is bounded by thermodynamic constraints.

  • Problem

    Conventional thermoelectric optimization is constrained by coupled heat and charge transport, motivating evaluation of spin-Seebeck devices using magnetic insulators and conductive films.

  • Method

    The review synthesizes LSSE experiments, measurement configurations, efficiency theory, material combinations, and emerging device structures for thermoelectric applications.

  • Results

    Insulator-based LSSE devices are free from the Wiedemann–Franz limitation, with efficiency characterized by ZSSET and performance improving through multilayer systems.

  • Takeaways & Limitations

    LSSE devices offer simple bilayer structures, flexible material selection, area-based scaling, and possible applications including energy harvesters, thermometers, and sensors.

  • Takeaways & Limitations

    Present LSSE devices still have very low efficiency, and their thermodynamic upper limit requires (lz/Lz)(1/ξ) ≤1 to remain consistent with the Carnot limit.

Abstract

from arXiv · show

The spin Seebeck effect (SSE) refers to the generation of a spin current as a result of a temperature gradient in magnetic materials including insulators. The SSE is applicable to thermoelectric generation because the thermally generated spin current can be converted into a charge current via spin-orbit interaction in conductive materials adjacent to the magnets. The insulator-based SSE device exhibits unconventional characteristics potentially useful for thermoelectric applications, such as simple structure, device-design flexibility, and convenient scaling capability. In this article, we review recent studies on the SSE from the viewpoint of thermoelectric applications. Firstly, we introduce the thermoelectric generation process and measurement configuration of the SSE, followed by showing fundamental characteristics of the SSE device. Secondly, a theory of the thermoelectric conversion efficiency of the SSE device is presented, which clarifies the difference between the SSE and conventional thermoelectric effects and the efficiency limit of the SSE device. Finally, we show preliminary demonstrations of the SSE in various device structures for future thermoelectric applications and discuss prospects of the SSE-based thermoelectric technologies.

I. INTRODUCTION

Thermoelectric generation converts heat directly into electricity, while the spin Seebeck effect enables a distinct route in which temperature gradients generate spin currents that adjacent conductive films convert into charge currents. Insulator-based LSSE devices separate heat and charge transport, enabling flexible material selection and straightforward scaling, while the review addresses their efficiency and performance limits.

  • Thermoelectric generation directly converts abundant heat into electrical power using solid-state devices that are silent, reliable, and scalable.
  • The conventional Seebeck effect uses serially connected thermocouples, whereas LSSE devices use a magnetic-insulator/conductive-film junction with separated heat and charge currents.This separation removes the Wiedemann–Franz constraint from the product of thermal conductivity and electrical resistivity.
  • The spin Seebeck effect generates a spin current from a temperature gradient, which adjacent conductive films convert into charge current through the inverse spin Hall effect.In LSSE devices, the induced electric field is perpendicular to the temperature gradient.
  • The review formulates LSSE figure-of-merit and conversion-efficiency expressions to clarify their difference from conventional thermoelectric effects and determine an efficiency upper limit.
  • LSSE output power scales with device area because the generated voltage and metallic-layer resistance combine to give Pmax ∝ lxly.Coating and plating methods support simple-structure, large-area, and flexible devices.
  • LSSE thermoelectric generation depends on heat-current/spin-current conversion, interfacial spin-angular-momentum transfer, and spin-current/charge-current conversion.These factors are associated with LSSE efficiency, spin mixing conductance, and spin Hall angle, respectively.

II. THERMOELECTRIC GENERATION PROCESS AND MEASUREMENT CONFIGURATION

The longitudinal spin Seebeck effect is measured in a metallic-film/magnetic-insulator junction with a temperature gradient normal to the interface and spin current parallel to that gradient. Magnon dynamics transfer spin angular momentum into the metal, where the inverse spin Hall effect produces a measurable voltage.

  • The standard LSSE device is a metallic film formed on a magnetic insulator, with the temperature gradient and induced spin current perpendicular to their interface.The magnetization is usually aligned along the x direction with an external magnetic field, although hard magnets do not require one.
  • Two heat baths at different temperatures apply a reversible out-of-plane temperature gradient across the metal/insulator interface.The device surfaces are directly connected to the heat baths, providing temperature control.
  • Nonequilibrium magnon dynamics in the magnetic insulator transfer spin angular momentum across the interface to conduction-electron spins in the attached metal.The interfacial transfer is described by the spin mixing conductance.
  • The inverse spin Hall effect converts the injected spin current into an electric field, so the voltage between the metallic-film ends records the LSSE.The voltage sign is determined by the spin Hall angle.
  • The metallic layer thickness must be comparable to its spin diffusion length because spin current and the inverse-spin-Hall electric field are confined near the interface by spin relaxation.Typical thicknesses range from a few to several hundred nanometers.

III. BASIC CHARACTERISTICS OF SPIN SEEBECK DEVICES

The Pt/YIG slab experiments establish the voltage’s dependence on temperature difference, magnetic field, geometry, and magnetization configuration, while separating LSSE from anomalous-Nernst contributions.

  • Device configuration: The LSSE measurement applies a temperature gradient perpendicular to the metal/insulator interface in a metallic-film/magnetic-insulator junction.The reviewed experiments use Pt/YIG model systems with a YIG slab and sputtered Pt film.
  • Fundamental voltage characteristics: The Pt/YIG-slab voltage increases proportionally with temperature difference and reverses sign when the magnetic field reverses.At fields above 0.5 kOe, the YIG magnetization follows the field direction.
  • Signal identification: Separating LSSE from ANE is necessary because proximity-induced ferromagnetism in very thin Pt can generate an additional anomalous-Nernst voltage.Weak ferromagnetic signals were observed in Pt layers thinner than 3 nm near the Pt/YIG interface.
  • Signal identification: Comparing in-plane and perpendicular magnetization configurations distinguishes LSSE from ANE by changing which voltage contributions can appear.The in-plane configuration permits both LSSE and ANE, whereas the perpendicular configuration permits ANE but suppresses the LSSE geometry.
  • Signal identification: The Pt/YIG voltage is much larger in the in-plane configuration than in the perpendicular configuration, supporting an LSSE origin.The perpendicular-configuration normal Nernst component is comparable to reference nonmagnetic samples.
  • Thermoelectric interpretation: The experiments attribute the Pt/YIG thermoelectric voltage entirely to the inverse spin Hall effect induced by the LSSE.The review also notes that proximity-induced ANE could potentially enhance thermoelectric output if intentionally superposed.

B. High magnetic field dependence

High-field measurements probe how magnetic fields and YIG thickness affect LSSE thermopower. Suppression strengthens at low temperature, while thinner YIG reduces thermopower and motivates thicknesses beyond characteristic magnon lengths.

  • Magnon mechanism: Magnetic-field response is used as a probe of thermo-spin conversion because the field modifies magnon excitation through the Zeeman gap.The microscopic relation between magnon excitation and thermally generated spin current remains incompletely established.
  • Field dependence: The LSSE voltage decreases with increasing magnetic field after reaching a maximum, even though the YIG magnetization remains nearly saturated.This behavior is observed across measurements at 300 K, 10 K, and 5 K.
  • Field dependence: High magnetic fields suppress LSSE voltage increasingly as temperature decreases, reaching approximately 70% suppression at 5 K.The suppression is nearly constant above 30 K and strongly enhanced below 30 K.
  • Model comparison: Above 30 K, the observed field-induced LSSE suppression is not explained by conventional SSE models, whereas below 30 K it seemingly agrees with thermal-spin-pumping calculations.The conventional explanation invokes Zeeman energy being overcome by thermal fluctuations when gµBH ≪ kBT.
  • Thickness dependence: Maximizing LSSE output requires magnetic-insulator thickness greater than the characteristic lengths of low-frequency magnons.Boundary conditions can limit contributions from long-range magnons in thin magnetic insulators.
  • Thickness dependence: The LSSE thermopower decreases monotonically as YIG thickness decreases in slab and film systems.The compared YIG thicknesses include 1 mm, 10.42 µm, 1.09 µm, and 0.31 µm.

C. Current-voltage-power characteristics and scaling law

The LSSE device reaches maximum output power under impedance matching, while its voltage and extractable output increase with metallic-layer area through a distinct scaling law.

  • Current-voltage-power characteristics: Maximum output power occurs when the load resistance matches the Pt layer’s internal resistance, Rload = RPt = 33 Ω.The Pt/Bi:YIG-film measurement used ∆T = 11.2 K.
  • Scaling law: The LSSE voltage in a Pt-Au spin Hall thermopile increases proportionally with total Pt length.The thermopile integrates LSSE voltages from serially connected Pt and Au wires.
  • Scaling law: In the width-dependence measurements, V/∆T and Pt-film resistance were plotted against the metallic-layer width while film length and thickness remained fixed.The supplied passage introduces the measurement configuration but does not state the resulting width trend.
  • Scaling law: A larger film area enables greater thermoelectric output power because the total thermally generated spin current increases with device size.The LSSE scaling differs from conventional Seebeck devices, whose output is enhanced by serially connected thermocouples.
  • Efficiency analysis: The review formulates LSSE efficiency by adapting transverse-device analysis from anomalous Nernst generators.The LSSE and ANE share the characteristic that the induced electric field is orthogonal to the applied temperature gradient.
  • Efficiency analysis: The efficiency analysis uses transport and energy-conservation equations, including Domenicali’s equation for the temperature distribution.Joule heating and thermal conduction are retained, while Thompson-related terms are neglected.
  • Efficiency analysis: For transverse devices, the optimized efficiency has a functional form distinct from conventional Seebeck devices, while maximum power still follows impedance matching.The ANE discussion provides the comparison used in the LSSE efficiency treatment.
  • Efficiency analysis: The transverse-device efficiency bound reaches the Carnot efficiency when Z′ANET = 1, corresponding to r∗ = 0.Here ηC = ∆T/Th.

B. Efficiency of thermoelectric generators based on spin Seebeck effects

The paper derives LSSE thermoelectric efficiency for a paramagnetic-metal/ferrimagnetic-insulator bilayer using coupled spin, charge, and heat transport. The analysis yields an optimized efficiency expression while relying on simplifying assumptions about thermal conductivity and temperature continuity.

  • Model and assumptions: The LSSE model considers a paramagnetic metal and ferrimagnetic insulator bilayer between hot and cold reservoirs.The assumed thermal conductivity of the metal is much greater than that of the ferrimagnetic insulator.
  • Model and assumptions: The calculation assumes κP ≫ κF so the temperature gradient develops primarily inside the ferrimagnetic insulator.This assumption is used to keep the analytical treatment manageable and obtain a simple expression.
  • Model and assumptions: The analytical treatment assumes no discontinuous temperature jump at the paramagnetic-metal/ferrimagnetic-insulator interface.Under this assumption, temperature is treated as smooth across the interface; a more involved numerical approach would otherwise be required.
  • Transport formulation: The transport description uses spin voltage, electrical conductivity, magnon density gradients, magnon conductivity, and magnon Seebeck and Peltier coefficients.Onsager reciprocity imposes Πm = ζmT/σm.
  • Spin-charge conversion: A temperature bias drives a magnon spin current in the ferrimagnetic insulator, which injects spin into the metal and produces an electric response through the inverse spin Hall effect.The injected-spin fraction is represented by c1, which is proportional to the spin mixing conductance.
  • Spin-heat coupling: The reciprocal charge-driven spin current can inject spin back into the ferrimagnetic insulator and contribute an accompanying heat current.The injected-back fraction is represented by c2, with 0 < c2 < 1.
  • Efficiency calculation: The hot-reservoir heat input includes thermal conduction, the spin-associated heat-current term, and Joule heating, while output power is calculated from the driven current.The efficiency is then defined as ηSSE = Pout/Qh.
  • Efficiency result: Maximizing ηSSE with respect to the load-resistance ratio yields an optimized efficiency expression in the limit ∆T ≪ Th.The resulting functional form has a characteristic of transverse devices.

C. Discussion

The LSSE figure of merit separates thermal and electrical transport across different materials, avoiding the Wiedemann–Franz limitation. Its efficiency depends on material, spin-conversion, and geometrical factors, but current devices remain far from practical efficiency.

  • Device figure of merit: The LSSE figure of merit uses κF and ρP from different materials because charge flows through P while thermal resistance is mainly set by F.This separation makes the LSSE figure of merit free from the Wiedemann–Franz-law limitation.
  • Efficiency factors: The LSSE efficiency is determined by the figure of merit ZSSE, spin-converting parameter ξ, and geometrical factor lz/Lz.Estimating ξ requires phenomenological assumptions about spin injection and conductivity ratios, including c2/c1 ≈ 1 for a rough estimate.
  • Efficiency limit: The maximum allowed LSSE efficiency occurs at r∗ = 0, corresponding to ξZSSETh = 1, under the stated efficiency model.The model expects the isothermal LSSE figure of merit to satisfy 0 ≤ ZSSET ≤ 1.
  • Efficiency limit: The maximum-efficiency condition requires 0 ≤ 1/ξ ≤ 1, while the second-law constraint requires (lz/Lz)(1/ξ) ≤ 1 for a Carnot upper limit.The microscopic derivation of this constraint is left for future studies.
  • Practical constraints: ξ has little effect when ξZSSET ≪ 1, so improving LSSE thermopower and reducing F’s thermal conductivity are necessary for realistic applications.Optimizing lz/Lz may conflict with thickness-dependent reductions in LSSE thermopower.

V. DEMONSTRATIONS FOR THERMOELECTRIC APPLICATIONS

The review presents coating films, flexible devices, all-ferromagnetic devices, and multilayer films as approaches for future LSSE thermoelectric applications. Coating and flexible structures target versatility and scalability, whereas all-ferromagnetic and multilayer structures target improved performance.

  • V. DEMONSTRATIONS FOR THERMOELECTRIC APPLICATIONS: Future LSSE thermoelectric applications include coating films, flexible devices, all-ferromagnetic devices, and multilayer films.The first two structures are under development for versatility and scalability; the latter two target thermoelectric performance.

A. Spin thermoelectric coating

The spin thermoelectric coating applies a metal/magnetic-insulator bilayer directly to a heat source. Its simple structure and scaling law are intended to support large-area thermoelectric devices on various-shaped surfaces.

  • A. Spin thermoelectric coating: The STE-coating device consists of a metal/magnetic-insulator bilayer directly coated on a heat source.The proposed structure is intended for large-area devices on surfaces such as electronic instruments and automobiles.
  • A. Spin thermoelectric coating: Spin coating was used to form Pt/Bi:YIG STE-coating films through simple fabrication steps.Bi:YIG served as the magnetic insulator and Pt as the metallic layer.
  • A. Spin thermoelectric coating: A clear LSSE voltage appeared in the thin Pt/Bi:YIG film, whereas no signal appeared in plain Pt on SGGG.The result indicates that the thin Bi:YIG film functions as the thermoelectric generator.

B. Flexible spin Seebeck devices

LSSE devices are suited to flexible thermoelectric generation because their simple structure avoids the bending vulnerability of cascaded conventional thermocouples. Ferrite plating enables low-temperature fabrication of bendable sheets with clear LSSE signals and low thermal resistance.

  • B. Flexible spin Seebeck devices: Conventional thermoelectric devices are rigid and vulnerable to bending stresses because they use electrically series-connected Π-structured thermocouples.This limits their application to curved or uneven heat sources.
  • B. Flexible spin Seebeck devices: Ferrite plating fabricates ferrimagnetic ferrite thin films by spraying an aqueous reaction solution and oxidizer onto a rotating heated substrate.The process can be performed below 100 °C and is applicable to heat-labile plastic substrates.
  • B. Flexible spin Seebeck devices: The flexible LSSE sheet combines a Ni0.2Zn0.3Fe2.5O4 film on polyimide with a sputtered Pt film and remains highly flexible and bendable.Clear LSSE signals were observed with magnitude comparable to that in the conventional device.
  • B. Flexible spin Seebeck devices: Columnar ferrite grains support flexibility because spin currents travel along the columns and grain boundaries relieve bending stress.The columnar structure also reduces the effect of grain scattering on spin-current generation.
  • B. Flexible spin Seebeck devices: The LSSE flexible sheet has remarkably low thermal resistance because it lacks a thick substrate, supporting potential heat-flow sensing applications.Ferrite plating may also enable large-area direct coating of thermoelectric functions onto various surfaces.

C. Hybrid thermoelectric generation based on spin Seebeck and anomalous Nernst effects

Hybrid LSSE–ANE generation combines spin-current-induced ISHE with conventional ANE in ferromagnetic metal/ferrimagnetic insulator junctions, with Ni/Bi:YIG outperforming Pt/Bi:YIG in the reported comparison.

  • Hybrid mechanism: Ferromagnetic metals can replace Pt while combining ANE and LSSE-induced ISHE in a ferromagnetic metal/ferrimagnetic insulator junction.The two voltage contributions have the same direction in various ferromagnetic materials.
  • Experimental comparison: Ni/Bi:YIG-film produces a voltage more than twice the ANE voltage of a plain Ni film on the substrate.This indicates superposition of ANE in Ni and ISHE from spin current injected from Bi:YIG.
  • Experimental comparison: Ni/Bi:YIG-film shows greater voltage than conventional Pt/Bi:YIG-film under the reported temperature-gradient measurements.The figure caption compares H and ΔT dependences for Ni/Bi:YIG, Pt/Bi:YIG, and single-metal films at room temperature.
  • Thermoelectric performance: Because Ni resistivity is comparable to or smaller than Pt resistivity, the Ni/Bi:YIG device also has better reported current and power performance.The comparison concerns the hybrid Ni/Bi:YIG-film and conventional Pt/Bi:YIG-film systems.

D. Spin Seebeck effect in multilayer devices

Alternately stacked P/F multilayers enhance LSSE voltage and output power as the bilayer count increases, through spin-current boundary conditions and layer-dependent length scales.

  • Voltage enhancement: LSSE voltage in [P/F] × n multilayers increases significantly and monotonically with the number n of P/F bilayers.The [Pt/Fe3O4] × 6 system is identified as holding the current room-temperature LSSE thermopower record.
  • Power enhancement: Output power also increases with n because voltage enhancement occurs without increasing internal resistance.This differs from spin Hall thermopile voltage enhancement, where the multilayer comparison is described separately.
  • Voltage enhancement: The multilayer voltage enhancement exceeds the upper limit expected from independent bilayers or spin injection from both adjacent ferromagnetic layers.The independent-bilayer model predicts voltage nonenhancement, while the two-sided injection upper limit is twice the single-bilayer voltage.
  • Mechanism: The proposed mechanism uses vanishing spin currents at the outer surfaces and continuous spin currents across P/F interfaces.These boundary conditions alter spin-current magnitude and spatial profile near interfaces.
  • Optimization: Further improvement requires optimizing layer thicknesses and P/F material combinations according to spin and magnon diffusion lengths.The multilayer enhancement strongly depends on the diffusion lengths of the P and F layers.

VI. CONCLUSIONS AND PROSPECTS

The review identifies LSSE devices as structurally simple, scalable, and distinct from conventional thermoelectrics, while emphasizing that their present thermopower and performance remain inadequate for realistic applications.

  • Conclusions: LSSE devices use a magnetic-insulator/conductor bilayer in which an out-of-plane thermal gradient induces an in-plane electric field through interfacial spin-current generation.The review presents this as the basic insulator-based LSSE structure.
  • Efficiency and comparison: LSSE thermoelectric performance cannot be directly compared with conventional Seebeck devices because their configurations and driving principles differ.The LSSE figure of merit is defined over 0 ≤ ZSSET ≤ 1, characteristic of transverse thermoelectric devices.
  • Limitations: Current LSSE thermopower remains very small, despite reported improvement and scope for further enhancement.The review identifies thermal spin-current generation, spin Hall angle, and spin mixing conductance as improvement targets.
  • Prospects: Multilayer systems improve LSSE output power through combined voltage enhancement and internal-resistance reduction.Time-series trends show improved LSSE thermopower and power factor, while the power factor is normalized by temperature gradient and device area.
  • Limitations: Realistic applications additionally require lower insulator thermal conductivity, lower metal electrical resistivity, and thermal designs enabling stable continuous operation.The review states that the current record remains inadequate and continued development is necessary.
  • Prospects: The simple structure and scaling law support thermoelectric functions on varied heat sources using versatile, low-cost fabrication processes.The review lists potential applications including energy harvesters, thermometers, infrared sensors, position detectors, and user-interface devices.

Profiles:

The supplied profile passages provide biographical and career information for the paper’s authors, including affiliations, research areas, and selected honors.

  • Profiles: The profiles identify the authors’ education, appointments, research interests, and selected professional honors.These passages are biographical rather than scientific findings.
  • Profiles: Saitoh’s profile states that he has worked on spintronics and spin caloritronics and realized thermoelectric generation using insulators.It also lists his academic appointments and awards.
  • Profiles: Several profiles describe research spanning spintronics, spin caloritronics, thermo-spin effects, nanotechnology, quantum technology, and thermoelectric conversion devices.The research areas are stated across the listed author biographies.
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