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Spintronics: the non-equilibrium thermodynamic approach

J.-E. Wegrowe, H.-J. Drouhin

We are investigating experimentally and theoretically Spintronics effects from the point of view of non-equilibrium thermodynamic processes [1-7]. In parallel, we investigate the conditions for a formal definition of spin-polarized density currents in the presence of spin-orbit coupling [8-10].

Spintronics designates the study of spin-dependent transport processes. It is a generalization of electronics (i.e. the study of transport of electric charges) that takes into account the spin degrees of freedom. Magnetoresistance effects, spin accumulation, spin-transfer effects and spin-dependent relaxation phenomena are investigated on single-contacted magnetic nanostructures.

Fig. 1 Left : the sphere of radius Ms is the configuration space of the magnetization. The profile of the energy of a uniform ferromagnet with uniaxial anisotropy is represented by a double well potential in the configuration space. Right : Description of spin accumulation in a metallic ferromagnet (from reference [6]). The spin-transfer effect accounts for the dynamical coupling between the two sub-systems.

The non-equilibrium thermodynamic approach (or "spin-caloritronics") takes into account the associated transport of heat or entropy. The conservation equation for the magnetization and spins - i.e. of the angular momentum of the system - can then be written with taking into accounts all dissipative mechanisms (coupling to the lattice, coupling to the electromagnetic field, coupling to the heat sinks, etc).

Fig. 2. Left : schematic of a contacted single ferromagnetic nanowire with a heater. Right : Measure of the ferromagnetic entropy produced by spin transfer as a function of the injected current density (from reference [3]).

[1] Spin-currents and spin-pumping forces for spintronics, J.-E. Wegrowe, H.-J. Drouhin, Entropy, Special issue « Advances in thermodynamics» 13, 316 (2011)
[2] Spin-transfer from the point of view of the ferromagnetic degree of freedom, J.-E. Wegrowe, Solid State Com. Special issue on “Spin-Caloritronics”, 150 (2010) 519
[3] Measuring entropy production generated by spin-transfer, J.-E. Wegrowe, Q. Anh Nguyen, T. Wade, IEEE Trans.-Mag. 46 (2010) 866
[4] Magnetization reversal driven by spin injection : a diffusive spin transfer effect, J.-E. Wegrowe, S. M. Santos, M.-C. Ciornei, H.-J. Drouhin, M. Rubi., Phys. Rev. B 77, 174408 (2008)
[5] Thermokinetics od Spin-Dependent Transport and Ferromagnetism in Magnetic Nanostructures, chap 15, p 553, Ed. by H. S. Nalwa (American Scientific Publishers), 2008.
[6] Spin transfer in an open ferromagnetic layer: from negative damping to effective temperature. J.-E Wegrowe, M. C. Ciornei, H.-J. Drouhin, J. Phys:Cond-Matter 19, 165213 (2007)
[7] Anisotropic Magneto-thermopower: the contribution of the Interband Relaxation, J.-E. Wegrowe, Q. Anh Nguyen, M. Al-Barki, J.F. Dayen, T. L. Wade, and H.-J. Drouhin, Phys. Rev. B 73, 134422 (2006)
[8] Spin currents in semiconductors: redefinition and counterexemple  H.-J. Drouhin, G. Fishmann, J.-E. Wegrowe, Phys. Rev B 83, 113307 (2011)
[9] Spin-orbit engineering of semiconductor heterostructures: A spin-sensitive quantum-phase shifter, T..L. Hoai Nguyen, H.-J. Drouhin, J.-E. Wegrowe and G. Fishman, Appl. Phys. Lett, 95, 082108 (2009).
[10] Spin rotation, spin filtering, and spin transfer in directional tunnelling through barriers in noncentrosymmetric semiconductors, T. L Hoai Ngyen, H_J. Drouhin, J.-E. Wegrowe, and Guy, Fishman Phys. Rev. B 79, 1652004 (2009)