Spin-Resolved Thermoelectric Transport

Updated 18 December 2025

Spin-resolved thermoelectric transport is defined by the generation and manipulation of spin- and energy-polarized currents through thermal gradients in systems with strong electronic and magnetic couplings.
It employs advanced modeling techniques such as the Landauer-Büttiker formalism, nonequilibrium Green’s functions, and numerical renormalization group to quantify spin-dependent conductances and Seebeck coefficients.
Optimized device design leverages lattice topology, magnetic anisotropy, and interfacial engineering to achieve high spin thermopower and superior energy conversion efficiencies.

Spin-resolved thermoelectric transport encompasses the generation, manipulation, and detection of simultaneously spin- and energy-polarized currents in materials and devices where electronic, lattice, and magnetic degrees of freedom are strongly coupled. In these systems, temperature gradients drive both charge and spin currents, leading to various phenomena—including the spin Seebeck effect, spin-dependent Seebeck and Peltier effects, spin thermopower, and spin figures of merit. The interplay of lattice topology, magnetic order, quantum interference, correlations, and interfacial engineering determines the spectral separation and asymmetry of spin channels, which is essential for efficient spin caloritronics and for surpassing the performance of conventional charge-based thermoelectrics.

1. Microscopic Theories and Model Frameworks

Spin-resolved thermoelectric transport is formalized by Hamiltonians incorporating the relevant electronic and magnetic structure, lattice geometry, and coupling to external reservoirs. For spin-selective effects, models often feature spatially separated spin channels (ladders or chains), spin-dependent onsite energies, exchange-induced Zeeman fields, and classical or quantum descriptions of local moments. In frustrated or low-dimensional geometries, multiple interfering paths and frustration-induced spin filtering are habitual. For example, in a triangular spin ladder, the Hamiltonian is partitioned as

$H = H_S + H_D + H_{tn} + H_L,$

where $H_{U,\uparrow}$ and $H_{D,\downarrow}$ represent spin-polarized upper and lower arms, $H_\Delta$ encodes diagonal hopping ( $t_{dg}$ ), and the Zeeman terms ( $\pm h$ ) model antiferromagnetic alignment (Bhattacharya et al., 16 Dec 2025).

Correlated quantum dot and molecular junction models include on-site Hubbard interactions, exchange coupling to fixed molecular spins, and magnetic anisotropy. The Hamiltonians feature coupling to spin-polarized leads, resulting in spin-resolved tunnel rates and exchange fields that split dot or molecular levels (Manaparambil et al., 2021, Senapati et al., 16 Jan 2024, Manaparambil et al., 2023). Effects such as Kondo resonance splitting, quantum interference (Fano/Dicke resonances), and coupling to Majorana modes are treated using advanced numerical techniques such as the numerical renormalization group (NRG) (Majek et al., 17 Sep 2025, Majek et al., 2021, Karwacki et al., 2017).

For extended (bulk or device-level) systems, transport models employ the Landauer-Büttiker formalism or nonequilibrium Green’s functions (NEGF), including DFT-extracted band parameters (effective masses, exchange splittings), as in NEGF-DFT-ISHE workflows (Koneru et al., 2017). Magnon and phonon contributions are modeled via master equations, hydrodynamic drag frameworks, or explicit magnon diffusion formalism (Heremans, 2020).

2. Transport Formalism: Conductances, Seebeck Coefficients, and Figures of Merit

Spin-resolved currents are expressed via Landauer-type integrals or kinetic coefficients: $L_n^\sigma = -\frac{1}{h} \int dE\, \tau^\sigma(E)\, (\partial f/\partial E)\, (E-E_F)^n,$ yielding spin-channel conductances ( $G^\sigma = e^2 L_0^\sigma$ ), Seebeck coefficients ( $S^\sigma = -(1/eT)\, (L_1^\sigma / L_0^\sigma)$ ), and spin-resolved electronic thermal conductances ( $\kappa_e^\sigma$ ) (Bhattacharya et al., 16 Dec 2025).

Charge and spin observables are constructed as

$G_C = G^\uparrow + G^\downarrow, \quad G_S = G^\uparrow - G^\downarrow,$

$S_C = (S^\uparrow + S^\downarrow)/2, \quad S_S = S^\uparrow - S^\downarrow,$

with figures of merit

$ZT_C = \frac{S_C^2\,G_C\,T}{\kappa_e}, \quad ZT_S = \frac{S_S^2\,G_S\,T}{\kappa_e}$

(Bhattacharya et al., 16 Dec 2025, Senapati et al., 16 Jan 2024). For molecular and quantum dot systems, spin-resolved Onsager integrals are formulated over the transmission functions derived from calculated spectral densities (Manaparambil et al., 2021, Majek et al., 17 Sep 2025, Manaparambil et al., 2023).

Nonlinear and nonequilibrium extensions (e.g., for far-from-equilibrium or strong bias situations) introduce differential Seebeck coefficients (e.g., $S_d$ , $S_s$ ) and account for spin accumulation by considering independent spin chemical potentials ( $\mu_\uparrow$ , $\mu_\downarrow$ ) (Manaparambil et al., 2023, Muralidharan et al., 2012).

3. Mechanisms for Spin Channel Separation and Spin Thermopower Enhancement

Achieving substantial spin-resolved thermoelectric response requires engineering minimal spectral overlap and sharp asymmetries between spin channels. Key mechanisms include:

Lattice Topology and Frustration: Zig-zag or helical connectivity induces path interference and geometric frustration, which, upon breaking arm-to-arm symmetry via onsite energies or hopping asymmetry, acts as a selective spin filter. In antiferromagnetic spin ladders, a small onsite energy or hopping asymmetry can shift $\tau^\uparrow(E)$ and $\tau^\downarrow(E)$ apart, maximizing $S_S$ and producing $ZT_S \gg ZT_C$ (Bhattacharya et al., 16 Dec 2025, Ganguly et al., 3 Jul 2025).
Magnetic Order: Rigid AF alignment or large internal exchange fields split spin bands in the absence of external magnetic fields or spin-orbit coupling, providing robust and tunable spin splitting (Polash et al., 2021).
Magnetic Anisotropy and Spin-Flips: In tunnel junctions with nanomagnets, transverse and uniaxial anisotropy enable energy- and angular momentum-exchange processes leading to finite spin Seebeck response even when net charge flow is suppressed (Misiorny et al., 2014, Misiorny et al., 2014).
Zeeman and Exchange Fields: Spin-polarized leads or external fields selectively shift or broaden spin channels in molecular, nanostructure, or quantum dot junctions, thereby enabling nearly pure spin currents and high $ZT_S$ (Senapati et al., 16 Jan 2024, Manaparambil et al., 2021).
Quantum Interference: Dicke-like, Fano, or Majorana-induced interference yields sharp antiresonances, doublet resonances, or fractional plateau features in both $G_\sigma$ and $S_\sigma$ , enhancing spin thermoelectric response near antiresonances or in regimes dominated by Majorana-Kondo competition (Majek et al., 17 Sep 2025, Majek et al., 2021, Karwacki et al., 2017).
Interaction and Correlation Effects: Kondo resonance splitting and spin-channel-resolved Kondo physics, under exchange or Majorana coupling, generate temperature- or bias-dependent sign changes and extrema in $S_\sigma$ and $S_S$ (Manaparambil et al., 2021, Majek et al., 17 Sep 2025, Manaparambil et al., 2023).

4. Prototypical Material and Device Platforms

Spin-resolved thermoelectric effects have been demonstrated or predicted in a range of systems:

System/Geometry	Mechanism	Typical Spin FOM ( $ZT_S$ )	Reference
Triangular AF spin ladder	Frustration, AF order	$\sim 4$	(Bhattacharya et al., 16 Dec 2025)
Chiral ferromagnetic helix (irradiated)	Floquet-engineered splitting	$3$–$7$ (light-tuned)	(Ganguly et al., 3 Jul 2025)
Benzene-based single-molecule junction	Electrode polarization/field	$4.1$	(Senapati et al., 16 Jan 2024)
Quantum dot or molecule (Kondo, anisotropy)	Exchange/anisotropy/Kondo	$0.1$–$1$ (molecular)	(Manaparambil et al., 2021, Misiorny et al., 2014)
Double QD with Majorana wire	Interference, Majorana-Kondo	— (unique $S_s$ fingerprints)	(Majek et al., 17 Sep 2025, Majek et al., 2021)
Antiferromagnetic MnTe (bulk)	Magnon/paramagnon drag, entropy	$\gtrsim 1$ (bulk $zT$ )	(Polash et al., 2021, Heremans, 2020)
TmIG/Pt nonlocal devices	Magnon diffusion, Nernst/SSE	Signal decomposition	(Gao et al., 2022)
Skyrmion multilayers (nanoscale)	ANE, PNE, AMTP fingerprinting	Spatially resolved	(Barker et al., 26 Jun 2025)

Optimization strategies include tuning hopping/onsite energies, light-driven Floquet parameters, electrode polarization or field, and exploiting quantum interference at appropriately engineered transmission zeros or antiresonances.

In insulating or weakly conducting magnets and hybrid contacts, spin and magnon degrees of freedom mediate spin-resolved thermoelectric functionality:

Spin Seebeck Effect (SSE): Thermally-driven magnon currents in FMs or AFMs generate spin accumulations at interfaces, which are converted to charge voltages via the inverse spin Hall effect (ISHE) in adjacent nonmagnetic metals. The spin-dependent thermopower is governed by Onsager matrix elements connecting thermal gradients to spin currents (Koneru et al., 2017, Heremans, 2020).
Magnon-drag thermopower: In bulk magnets, magnon or paramagnon drag can boost thermopower by factors of 2–3 over conventional diffusive contributions, resulting in room-temperature $zT > 1$ in antiferromagnetic semiconductors (exemplified by Li-doped MnTe) (Polash et al., 2021, Heremans, 2020).
Nonlocal device scaling: In ultrathin TmIG/Pt systems, nonlocal voltage measurements decompose into first-harmonic (magnon diffusion, exponential in distance) and second-harmonic (thermoelectric, geometric in $1/d$) contributions, each linked to SSE, ordinary, planar, spin, and anomalous Nernst mechanisms, with scaling laws capturing magnetic field and geometry dependencies (Gao et al., 2022).

Scanning thermoelectric microscopy provides sub-100 nm spatial resolution of spin and thermal voltages in topologically protected spin textures (e.g., skyrmions), revealing unique ANE, AMTP, and PNE fingerprints specific to the underlying magnetization configuration (Barker et al., 26 Jun 2025).

6. Optimization Principles, Materials Design, and Future Directions

Core design principles emerging from current research include:

Spectral engineering: Maximal spin thermopower and $ZT_S$ require clear spectral separation and sharp energy-dependent features between spin channels, achievable by symmetry-breaking in hopping, onsite energies, or via quantum interference (Bhattacharya et al., 16 Dec 2025, Ganguly et al., 3 Jul 2025, Karwacki et al., 2017).
Magnetic and structural order: Strong antiferromagnetic or chiral order, high spin multiplicity, and appropriately tailored exchange or magnetic anisotropy enhance spin-entropy and magnon-drag contributions (Polash et al., 2021, Misiorny et al., 2014).
Interfacial engineering: Maximizing spin-mixing conductance, spin Hall angle, and minimizing spin-flip scattering at interfaces are critical for the efficiency of ISHE-based detection and spin transfer (Koneru et al., 2017, Heremans, 2020).
Device and material selection: Promising platforms range from engineered low-dimensional frustrated magnets, molecular junctions, quantum dot arrays, topological insulators, to bulk AFMs and paramagnetic semiconductors.

Future research is expected to expand high-throughput and machine-learning-based screening for materials with favorable spin-resolved band characteristics, development of device architectures for pure spin-thermoelectric circuits, and use of spatially resolved probes (e.g., SThEM) for direct mapping and manipulation of spin caloritronic functionalities at the nanoscale (Barker et al., 26 Jun 2025, Koneru et al., 2017).

Spin-resolved thermoelectric transport now constitutes a foundational paradigm for designing high-efficiency energy converters, logic, and sensor devices, leveraging the interplay of geometry, magnetism, correlation, and topology to realize functionalities unattainable in traditional charge-based thermoelectrics (Bhattacharya et al., 16 Dec 2025, Senapati et al., 16 Jan 2024, Heremans, 2020, Polash et al., 2021, Ganguly et al., 3 Jul 2025).