No abstract

Many proposed and realized spintronic devices involve spin injection and accumulation at an interface between a ferromagnet and a non-magnetic material. We examine the electric field, voltage profile, charge distribution, spin fluxes, and spin accumulation at such an interface. We include the effects of both screening and spin scattering. We also include both the spin-dependent chemical potentials µ ↑,↓ and the effective magnetic field H * that is zero in equilibrium. For a Co/Cu interface, we find that the spin accumulation in the copper is an order of magnitude larger when both chemical potential and effective magnetic field are included. We also show that screening contributes to the spin accumulation in the ferromagnet; this contribution can be significant.

We have applied the Andreev-Lifshitz hydrodynamic theory of supersolids to an ordinary solid. This theory includes an internal pressure P , distinct from the applied pressure Pa and the stress tensor λ ik . Under uniform static Pa, we have λ ik = (P −Pa)δ ik . For Pa = 0, Maxwell relations imply that P ∼ P 2 a . The theory also permits vacancy diffusion but treats vacancies as conserved. It gives three sets of propagating elastic modes; it also gives two diffusive modes, one largely of entropy density and one largely of vacancy density (or, more generally, defect density). For the vacancy diffusion mode (or, equivalently, the lattice diffusion mode) the vacancies behave like a fluid within the solid, with the deviations of internal pressure associated with density changes nearly canceling the deviations of stress associated with strain. We briefly consider pressurization experiments in solid 4 He at low temperatures in light of this lattice diffusion mode, which for small Pa has diffusion constant DL ∼ P 2 a . The general principles of the theory -that both volume and strain should be included as thermodynamic variables, with the result that both P and λ ik appear -should apply to all solids under pressure, especially near the solid-liquid transition. The lattice diffusion mode provides an additional degree of freedom that may permit surfaces with different surface treatments to generate different responses in the bulk.

With spintronics applications in mind, we use irreversible thermodynamics to derive the rates of entropy production and heating near an interface when heat current, electric current, and spin current cross it. Associated with these currents are apparent discontinuities in temperature (∆T ), electrochemical potential (∆μ), and spin-dependent "magnetoelectrochemical potential" (∆μ ↑,↓ ). This work applies to magnetic semiconductors and insulators as well as metals, due to the inclusion of the chemical potential µ, which usually is neglected in works on interfacial thermodynamic transport. We also discuss the (non-obvious) distinction between entropy production and heat production. Heat current and electric current are conserved, but spin current is not, so it necessitates a somewhat different treatment. At low temperatures or for large differences in material properties, the surface heating rate dominates the bulk heating rate near the surface. We also consider the case, noted by Rashba, where bulk spin currents occur in equilibrium. Although a surface spin current (in A/m 2 ) should yield about the same rate of heating as an equal surface electric current, production of such a spin current requires a relatively large "magnetization potential" difference across the interface.Résumé : Avec applications dans l'esprit de spintronics, nous employons la thermodynamique irréversibleà obtenir les taux de production d'entropie et de chauffageà proximité d'une interface lorsque la chaleur actuelle, le courant electrique, et courant de spin la traverser. Associésà ces courants sont discontinuités apparentes de la température (∆T ), potentielélectrochimique (∆μ), et dépendant du spin potentiel "magnetoélectrochimique" (∆μ ↑,↓ ). Ce travail s'appliquè a semi-conducteurs magnétiques et isolants ainsi que des métaux, dueà l'inclusion de la potentiel chimique µ, ce qui est généralement négligée dans les travaux sur les transports thermodynamique interfaciale. Nous discutonségalement de la distinction (nonévidente) entre la production d'entropie et la production de chaleur. Chaleur actuelle et le courant electrique sont conservés, mais n'est pas courant de spin, il nécessite un traitement quelque peu différent. A basse température, ou pour de grandes différences dans les propriétés du matériau, la vitesse de chauffage de surface domine la vitesse de chauffage en vrac prés de la surface. Nous considéronségalement le cas, a noté par Rashba, oú les courants de spin en vrac se produireà l'équilibre. Même si un courant de spin de surface (en A/m 2 ) devrait donner environ le même taux de chauffage d'une surfaceégale de courantélectrique, la production d'un tel courant de spin nécessite un potentiel relativement important "aimantation différence" entre l'interface. ). details of the non-conservation of the spin current due to spinflip processes, and did not study the rate of heating near the surface. The present work considers these non-conservation phenomena, which require more refined considerations than when they are not present. (Th...

Using Andreev and Lifshitz's supersolid hydrodynamics, we obtain the propagating longitudinal modes at nonzero applied pressure P a ͑necessary for solid 4 He͒, and their generation efficiencies by heaters and transducers. For small P a , a solid develops an internal pressure P ϳ P a 2 . This theory has stress contributions both from the lattice and an internal pressure P. Because both types of stress are included, the normal-mode analysis differs from previous works. Not surprisingly, transducers are significantly more efficient at producing elastic waves and heaters are significantly more efficient at producing fourth sound waves. We take the system to be isotropic, which should apply to systems that are glassy or consist of many crystallites; the results should also apply, at least qualitatively, to single-crystal hcp 4 He.scribe a supersolid related to the NCRI effect proposed by Leggett than to vacancy superflow. Most of the present work assumes that the system is isotropic. One effect this has is that the superfluid density, which properly is a second-rank tensor s J , is proportional to the unit matrix so we take s J Ϸ 1 J s . 23,24 We then write the superfluid fraction as

We have re-examined the Andreev-Lifshitz theory of supersolids. This theory implicitly neglects uniform bulk processes that change the vacancy number, and assumes an internal pressure P in addition to lattice stress λ ik . Each of P and λ ik takes up a part of an external, or applied, pressure Pa (necessary for solid 4 He). The theory gives four pairs of propagating elastic modes, of which one corresponds to a fourth-sound mode, and a single diffusive mode, which has not been analyzed previously. The diffusive mode has three distinct velocities, with the superfluid velocity much larger than the normal fluid velocity, which in turn is much larger than the lattice velocity. The mode structure depends on the relative values of certain kinetic coefficients and thermodynamic derivatives. We consider pressurization experiments in solid 4 He at low temperatures in light of this diffusion mode and a previous analysis of modes in a normal solid with no superfluid component.

Recent spin-Seebeck experiments on thin ferromagnetic films apply a temperature difference ∆Tx along the length x and measure a (transverse) voltage difference ∆Vy along the width y. The connection between these involves: (1) thermal equilibration between sample and substrate; (2) spin currents along the height (or thickness) z; and (3) the measured voltage difference ∆Vy. The present work models in detail the first of these steps, and outlines how to obtain the other two. In 1D, thermal equilibration between the magnons and phonons in the sample, as well as additonal equilibration between the sample and the substrate, leads to two surface modes, with lengths λ, to provide thermal equilibration. Increasing the coupling between the two modes increases the longer mode length and decreases the shorter mode length. In 2D, the applied thermal gradient along x leads to a thermal gradient along z that varies as sinh (x/λ), which produce fluxes along z of the up-and down-spin carriers, and gradients of their associated magnetoelectrochemical potentials µ ↑,↓ , which vary as sinh (x/λ). There is also an infinite spectrum of shorter lengths λ that are geometrically determined. By the inverse spin Hall effect, the spin current along z can produce a transverse voltage difference ∆Vy that also varies as sinh (x/λ). This is consistent with experiments if the longest λ is comparable to or larger than the sample length L, and the shorter λ's are smaller than the separation between the input or output lead and the nearest voltage probe. In this model even seemingly linear voltage profiles are due to a surface mode.

Many relatively thick metal oxide films grow according to what is called the parabolic law L = √ 2At + . . . . Mott explained this for monovalent carriers by assuming that monovalent ions and electrons are the bulk charge carriers, and that their number fluxes vary as t −1/2 at sufficiently long t. In this theory no charge is present in the bulk, and surface charges were not discussed. However, it can be analyzed in terms of a discharging capacitor, with the oxide surfaces as the plates. The theory is inconsistent because the field decreases, corresponding to discharge, but there is no net current to cause discharge. The present work, which also includes non-monovalent carriers, systematically extends the theory and obtains the discharge current. Because the Planck-Nernst equations are nonlinear (although Gauss's Law and the continuity equations are linear) this leads to a systematic order-by-order expansion in powers of t −1/2 for the number currents, concentrations, and electric field during oxide growth. At higher order the bulk develops a non-zero charge density, with a corresponding non-uniform net current, and there are corrections to the electric field and the ion currents. The second order correction to ion current implies a logarithmic term in the thickness of the oxide layer: L = √ 2At + B ln t + . . . . It would be of interest to verify this result with high-precision measurements.arXiv:1006.3819v1 [cond-mat.mtrl-sci]