This is a brief overview of the state of the art of spin caloritronics, the science and technology of controlling heat currents by the electron spin degree of freedom (and vice versa)

Spin Caloritronics

Two complementary effects modify the GHz magnetization dynamics of nanoscale heterostructures of ferromagnetic and normal materials relative to those of the isolated magnetic constituents. On the one hand, a time-dependent ferromagnetic magnetization pumps a spin angular-momentum flow into adjacent materials and, on the other hand, spin angular momentum is transferred between ferromagnets by an applied bias, causing mutual torques on the magnetizations. These phenomena are manifestly nonlocal: they are governed by the entire spin-coherent region that is limited in size by spin-flip relaxation processes. This review presents recent progress in understanding the magnetization dynamics in ferromagnetic heterostructures from first principles, focusing on the role of spin pumping in layered structures. The main body of the theory is semiclassical and based on a mean-field Stoner or spin-density-functional picture, but quantum-size effects and the role of electron-electron correlations are also discussed. A growing number of experiments support the theoretical predictions. The formalism should be useful for understanding the physics and for engineering the characteristics of small devices such as magnetic random-access memory elements.

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Nonlocal magnetization dynamics in ferromagnetic heterostructures

Thermoelectric generation is an essential function in future energy-saving technologies. However, it has so far been an exclusive feature of electric conductors, a situation which limits its application; conduction electrons are often problematic in the thermal design of devices. Here we report electric voltage generation from heat flowing in an insulator. We reveal that, despite the absence of conduction electrons, the magnetic insulator LaY(2)Fe(5)O(12) can convert a heat flow into a spin voltage. Attached Pt films can then transform this spin voltage into an electric voltage as a result of the inverse spin Hall effect. The experimental results require us to introduce a thermally activated interface spin exchange between LaY(2)Fe(5)O(12) and Pt. Our findings extend the range of potential materials for thermoelectric applications and provide a crucial piece of information for understanding the physics of the spin Seebeck effect.

Spin Seebeck insulator.

The spin Seebeck effect refers to the generation of a spin voltage caused by a temperature gradient in a ferromagnet, which enables the thermal injection of spin currents from the ferromagnet into an attached nonmagnetic metal over a macroscopic scale of several millimeters. The inverse spin Hall effect converts the injected spin current into a transverse charge voltage, thereby producing electromotive force as in the conventional charge Seebeck device. Recent theoretical and experimental efforts have shown that the magnon and phonon degrees of freedom play crucial roles in the spin Seebeck effect. In this article, we present the theoretical basis for understanding the spin Seebeck effect and briefly discuss other thermal spin effects.

Theory of the Spin Seebeck Effect

The spin Seebeck effect refers to the generation of a spin voltage caused by a temperature gradient in a ferromagnet, which enables the thermal injection of spin currents from the ferromagnet into an attached nonmagnetic metal over a macroscopic scale of several millimeters. The inverse spin Hall effect converts the injected spin current into a transverse charge voltage, thereby producing electromotive force as in the conventional charge Seebeck device. Recent theoretical and experimental efforts have shown that the magnon and phonon degrees of freedom play crucial roles in the spin Seebeck effect. In this paper, we present the theoretical basis for understanding the spin Seebeck effect and briefly discuss other thermal spin effects.

https://iopscience.iop.org/article/10.1088/0034-4885/76/3/036501/pdf

Theory of the spin Seebeck effect.

By scattering theory we show that spin current noise in normal electric conductors in contact with nanoscale ferromagnets increases the magnetization noise by means of a fluctuating spin-transfer torque. Johnson-Nyquist noise in the spin current is related to the increased Gilbert damping due to spin pumping, in accordance with the fluctuation-dissipation theorem. Spin current shot noise in the presence of an applied bias is the dominant contribution to the magnetization noise at low temperatures.

/pdf/magnetization-noise-in-magnetoelectronic-nanostructures-136sv7sgz3.pdf

Magnetization noise in magnetoelectronic nanostructures

In the presence of spatial variation in the magnetization direction, electric current noise causes a fluctuating spin-transfer torque that increases the fluctuations of the ferromagnetic order parameter. By the fluctuationdissipation theorem, the fluctuations at thermal equilibrium are related to the viscous magnetization damping, which in nonuniform ferromagnets acquires a nonlocal tensor structure. At the hand of spin spirals, we demonstrate that the current-induced noise and damping increase with the gradient of the magnetization texture and becomes significant for narrow domain walls.

/pdf/current-induced-noise-and-damping-in-nonuniform-ferromagnets-2m1o450l17.pdf

Current-induced noise and damping in nonuniform ferromagnets

The interplay between current and magnetization fluctuations and dissipation in layered-ferromagnetic-normal-metal nanostructures is investigated. We use scattering theory and magnetoelectronic circuit theory to calculate charge and spin-current fluctuations. Via the spin-transfer torque, spin-current noise causes a significant enhancement of magnetization fluctuations. A special focus is on spin valves in which one of the ferromagnets is pinned. We find that the magnetization noise and damping are tensors that depend on the magnetic configuration. For symmetric spin valves in which both layers fluctuate, dynamic cross-talk between the layers becomes important, causing a possibly large difference in noise level between the parallel and antiparallel magnetic configurations. Due to giant magnetoresistance (GMR), the magnetization fluctuations in spin valves induce resistance noise, which is identified as a prominent source of electric noise at relatively high current densities. The resistance noise is shown to vary considerably with the magnetic configuration, partly due to the dependence of the angular GMR. The contribution from spin-current fluctuations to the resistance noise is shown to be significant. Resistance noise is an experimentally accessible quantity that can be measured to verify our results.

/pdf/noise-and-dissipation-in-magnetoelectronic-nanostructures-lf87jbn38j.pdf

Noise and dissipation in magnetoelectronic nanostructures

This thesis adresses electric and magnetic noise and dissipation in magnetoelectronic nanostructures. Charge and spin current fluctuations are studied in various nanosized metallic structures consisting of both ferromagnetic and non-magnetic elements. The interplay between current and magnetization fluctuations, and the relation of these fluctuations to the electric and magnetic dissipation of energy, are considered. Special focus is on the enhancement of magnetization damping due to so-called spin pumping, which is shown to be directly connected to thermal spin current fluctuations.Two fundamental sources of current noise are considered: Thermal noise and shot noise. Since a spin current polarized transverse to the magnetization is absorbed in a ferromagnet, transverse spin current fluctuations exert a fluctuating torque on the magnetization. This spin-transfer torque causes significant magnetization fluctuations in nanoscale ferromagnets. In single-domain ferromagnets in contact with normal electric conductors, the spin-current induced magnetization noise is directly connected to the magnetization damping caused by spin pumping. In non-uniformly magnetized ferromagnets, the spin-current induced magnetization noise is related to a nonlocal tensor damping that reflects the spatial variation of the magnetization. At low temperatures, spin current shot noise in the presence of an applied bias is the dominant contribution to the magnetization noise.In spin valves, two ferromagnets are separated by a thin normal metal spacer. The interaction of the ferromagnets affects their magnetization noise and damping, which are shown to vary with the relative magnetic orientation of the ferromagnets. Due to giant magnetoresistance, the magnetization fluctuations cause resistance noise. The resistance noise is identified as a prominent source of electric noise at relatively high current densities. The noise level can vary substantially with the relative magnetic orientation.

/pdf/resistance-noise-in-spin-valves-2nhplphee9.pdf

Resistance noise in spin valves

Deteriorated power system components have a higher probability of failure than new components. Still, the reliability of supply analyses traditionally models all components of the same type with the same probability of failure, and thus neglects the effect of deteriorated components. This paper presents a methodology to integrate a condition-dependent component probability of failure model into a power system reliability analysis. The component state is described by a semi-Markov process, and the paper shows how this, under reasonable assumptions, can be approximated by a Markov process. The Markov assumption simplifies the analysis and allows the model to include preventive retirement and be calibrated to statistical data. A case study using statistical data for Norwegian power transformers shows that, in the Norwegian power system, the proportion of failures that are due to the poor condition is small, partly due to the common strategy of preventive retirement. However, if the condition of the transformers were worse, the impact of poor conditions can be considerable. The methodology further enables the identification of the transformers that contribute most to the risk to the reliability of supply. The paper thus highlights the importance of accounting for the component condition in strategic decisions such as long-term renewal planning 

https://onlinelibrary.wiley.com/doi/pdfdirect/10.1049/gtd2.12761

Jørn Foros

Papers

Magnetization noise in magnetoelectronic nanostructures

Current-induced noise and damping in nonuniform ferromagnets

Noise and dissipation in magnetoelectronic nanostructures

Resistance noise in spin valves

Accounting for component condition and preventive retirement in power system reliability analyses