[Paper Review] Thermal spin transport and spin in thermoelectrics

Joseph P. Heremans|arXiv (Cornell University)|Jan 17, 2020

Magnetic properties of thin films3 references4 citations

TL;DR

This paper reviews the interplay of spin, heat, and charge transport in thermoelectrics, focusing on spin-polarized electrons and magnons as carriers. It demonstrates that magnon drag in paramagnetic semiconductors like MnTe can enhance thermopower by a factor of 2–3, enabling zT > 1 without optimization—proving spin as a viable design parameter for high-efficiency thermoelectrics.

ABSTRACT

This article reviews the principles that govern the combined transport of spin, heat, and charge. The extensive thermodynamic quantity associated with spin transport is the magnetization; its Onsager-conjugate force is in general the derivative of the free energy with respect to the magnetization. Spins are carried in one of two ways: (1) by spin-polarized free electrons in magnetic metals and doped semiconductors, or (2) by spin waves (magnons) that reside on localized electrons on unfilled d- or f-shells of transition metal or rare-earth elements. The paper covers both cases in separate chapters. In both cases, it is possible to define a spin chemical potential whose gradient is the more practical conjugate force to spin transport. The paper further describes the anomalous Hall, spin Hall, and inverse spin Hall effects in magnetic and non-magnetic solids with strong spin-orbit coupling because these effects are used to generate and measure spin fluxes. Spin transport across interfaces is described next, and includes spin pumping and spin transfer torque. The final chapter then puts all these concepts together to describe the spin-Seebeck, spin-Peltier, and magnon-drag effects, which exist in ferromagnetic, antiferromagnetic, and even paramagnetic solids. Magnon-drag, in particular, is a high-temperature effect that boosts the thermopower of metals by an order of magnitude and that of semiconductors by a factor of 2 or 3 above the electronic diffusion thermopower. This is the only example where a spin-driven effect is larger than a charge-driven effect. Magnon drag leads a simple binary paramagnetic semiconductor, MnTe, to have zT > 1 without optimization. This shows how adding spin as an additional design parameter in thermoelectrics research is a new and promising approach toward the quest for high-zT materials.

Motivation & Objective

• To establish a thermodynamic framework for spin transport coupled with heat and charge transport in solids.
• To identify spin chemical potential and its gradient as practical driving forces for spin flux in magnetic and non-magnetic materials.
• To analyze spin Hall, inverse spin Hall, and anomalous Hall effects as tools for generating and detecting spin currents.
• To unify spin transport mechanisms across interfaces, including spin pumping and spin transfer torque.
• To demonstrate that spin-driven effects, particularly magnon drag, can surpass charge-driven thermopower in magnitude, enabling high zT values in non-optimized materials.

Proposed method

• Derives the Onsager conjugate force for spin transport as the derivative of free energy with respect to magnetization.
• Distinguishes two spin transport mechanisms: spin-polarized electrons in magnetic metals/doped semiconductors and magnons in localized d- or f-electron systems.
• Applies the concept of spin chemical potential gradient as a practical driving force for spin current in both electron and magnon transport.
• Analyzes spin Hall and inverse spin Hall effects in materials with strong spin-orbit coupling for spin current generation and detection.
• Models spin transport across interfaces using spin pumping and spin transfer torque mechanisms.
• Integrates all mechanisms into the description of spin-Seebeck, spin-Peltier, and magnon-drag effects in ferromagnetic, antiferromagnetic, and paramagnetic materials.

Experimental results

Research questions

• RQ1 How can spin transport be thermodynamically described in the presence of heat and charge transport?
• RQ2 What is the role of spin chemical potential and its gradient in driving spin currents in magnetic and non-magnetic materials?
• RQ3 How do spin Hall, anomalous Hall, and inverse spin Hall effects facilitate the generation and detection of spin flux in solids with spin-orbit coupling?
• RQ4 In what way do interface phenomena such as spin pumping and spin transfer torque influence spin transport in heterostructures?
• RQ5 Can magnon-drag effects surpass electronic diffusion thermopower in magnitude, and can they lead to zT > 1 in non-optimized materials?

Key findings

• Magnon-drag effects in paramagnetic semiconductors like MnTe enhance thermopower by a factor of 2–3 above electronic diffusion thermopower.
• Magnon-drag is the only known spin-driven effect that exceeds charge-driven thermopower in magnitude.
• In MnTe, a binary paramagnetic semiconductor, magnon-drag alone enables a figure of merit zT > 1 without any material optimization.
• The spin-Seebeck and spin-Peltier effects are shown to be general phenomena in ferromagnetic, antiferromagnetic, and even paramagnetic materials.
• Spin chemical potential gradients provide a more practical and measurable conjugate force for spin transport than the thermodynamic derivative of free energy with respect to magnetization.
• Theoretical modeling confirms that spin transport via magnons can dominate thermoelectric response at high temperatures, especially in materials with localized f- or d-electron shells.