Spin torques in ferromagnetic/normal-metal structures

K. Xia; P. J. Kelly; G. E. W. Bauer; A. Brataas; I. Turek

doi:10.1103/PhysRevB.65.220401

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Spin torques in ferromagnetic/normal-metal structures

K. Xia¹, P. J. Kelly¹, G. E. W. Bauer², A. Brataas³, and I. Turek⁴

¹Faculty of Applied Physics and MESA+ Research Institute, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
²Department of Applied Physics and DIMES, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, The Netherlands
³Harvard University, Lyman Laboratory of Physics, Cambridge, Massachusetts 02138
⁴Institute of Physics of Materials, Academy of Sciences of the Czech Republic, CZ-616 62 Brno, Czech Republic

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Phys. Rev. B 65, 220401(R) – Published 23 May, 2002

DOI: https://doi.org/10.1103/PhysRevB.65.220401

Abstract

Recent theories of spin-current-induced magnetization reversal are formulated in terms of a spin-mixing conductance $G^{mix} .$ We evaluate $G^{mix}$ from first principles for a number of (dis)ordered interfaces between magnetic and nonmagnetic materials. We predict that the magnetization direction of a ferromagnetic insulator or of one side of a tunnel junction in a multiterminal device can be switched even though a negligible charge current is passed.

References (22)

For recent reviews, see M.A.M. Gijs and G.E.W. Bauer, Adv. Phys. 46, 285 (1997); J.-P. Ansermet, J. Phys.: Condens. Matter 10, 6027 (1998); A. Barthélémy, A. Fert, and F. Petroff, in Handbook of Magnetic Materials, edited by K. H. J. Buschow (Elsevier, Amsterdam, 1999), Vol. 12; E.Y. Tsymbal and D.G. Pettifor, Solid State Phys. 56, 113 (2001).
J.C. Slonczewski, J. Magn. Magn. Mater. 159, L1 (1996).
L. Berger, Phys. Rev. B 54, 9353 (1996).
K. Inomata, IEICE Trans. Electron. E84-C, 740 (2001).
M. Tsoi et al., Phys. Rev. Lett. 80, 4281 (1998); J.-E. Wegrowe et al., Europhys. Lett. 45, 626 (1999); J.Z. Sun, J. Magn. Magn. Mater. 202, 157 (1999); E.B. Myers et al., Science 285, 867 (1999); J.A. Katine et al., Phys. Rev. Lett. 84, 3149 (2000); J. Grollier et al., Appl. Phys. Lett. 78, 3663 (2001).
K.M. Schep, P.J. Kelly, and G.E.W. Bauer, Phys. Rev. Lett. 74, 586 (1995).
P. Zahn, I. Mertig, M. Richter, and H. Eschrig, Phys. Rev. Lett. 75, 2996 (1995).
X. Waintal et al., Phys. Rev. B 62, 12 317 (2000).
A. Brataas, Yu.V. Nazarov, and G.E.W. Bauer, Phys. Rev. Lett. 84, 2481 (2000); Eur. Phys. J. B 22, 99 (2001).
K.M. Schep et al., Phys. Rev. B 56, 10 805 (1997)
M.D. Stiles and D.R. Penn, Phys. Rev. B 61, 3200 (2000).
K. Xia et al., Phys. Rev. B 63, 064407 (2001).
S. Datta, Electronic Transport in Mesoscopic Systems (Cambridge University Press, Cambridge, England, 1995).
J.S. Moodera et al., Phys. Rev. Lett. 74, 3273 (1995).
G.E.W. Bauer et al., Mater. Sci. Eng., B 84, 31 (2001).
The elements of the transmission matrix t which enter the conductances are the scattering theory transmission amplitudes used in the Landauer-Büttiker formalism to describe electrical transport (Ref. ). In Refs. and where we reported the development of methods for calculating these matrices from first principles, they were used in an application where only the matrix of transmission probabilities T, obtained by squaring the complex amplitudes, ${T = t t}^{†}$ , were needed. In the present work we need t, as discussed in Refs. and .
I. Turek et al., Electronic Structure of Disordered Alloys, Surfaces and Interfaces (Kluwer, Boston, 1997).
O. K. Andersen, O. Jepsen, and D. Glötzel, in Highlights in Condensed Matter Theory, edited by F. Bassani, F. Fumi, and M. P. Tosi (North-Holland, Amsterdam, 1985), p. 59. In our calculations we use the atomic spheres approximation (ASA) in which the atomic Wigner-Seitz cells are replaced by atomic spheres. These fill all space so there is no interstitial region. The ASA is superior to the muffin-tin approximation for close-packed metals.
To determine charge and spin densities one needs a configuration-averaged single Green’s function, a standard procedure using the CPA. Calculation of the conductance requires obtaining a configuration-averaged product of Green’s functions which is much more difficult. By using supercells we obtain virtually exact results without having to compute “vertex” corrections. It has the additional advantage that we can model short-range order, steps, stacking faults, etc.
D. Huertas-Hernando, Yu.V. Nazarov, A. Brataas, and G.E.W. Bauer, Phys. Rev. B 62, 5700 (2000).
D. Huertas-Hernando, Yu.V. Nazarov, and W. Belzig, Phys. Rev. Lett. 88, 047003 (2002).
In the barrier calculations reported here, six layers of empty atomic spheres were used to model the barrier.

[c1] For recent reviews, see M.A.M. Gijs and G.E.W. Bauer, Adv. Phys. 46, 285 (1997); J.-P. Ansermet, J. Phys.: Condens. Matter 10, 6027 (1998); A. Barthélémy, A. Fert, and F. Petroff, in Handbook of Magnetic Materials, edited by K. H. J. Buschow (Elsevier, Amsterdam, 1999), Vol. 12; E.Y. Tsymbal and D.G. Pettifor, Solid State Phys. 56, 113 (2001).

[c2] J.C. Slonczewski, J. Magn. Magn. Mater. 159, L1 (1996).

[c3] L. Berger, Phys. Rev. B 54, 9353 (1996).

[c4] K. Inomata, IEICE Trans. Electron. E84-C, 740 (2001).

[c5] M. Tsoi et al., Phys. Rev. Lett. 80, 4281 (1998); J.-E. Wegrowe et al., Europhys. Lett. 45, 626 (1999); J.Z. Sun, J. Magn. Magn. Mater. 202, 157 (1999); E.B. Myers et al., Science 285, 867 (1999); J.A. Katine et al., Phys. Rev. Lett. 84, 3149 (2000); J. Grollier et al., Appl. Phys. Lett. 78, 3663 (2001).

[c6] K.M. Schep, P.J. Kelly, and G.E.W. Bauer, Phys. Rev. Lett. 74, 586 (1995).

[c7] P. Zahn, I. Mertig, M. Richter, and H. Eschrig, Phys. Rev. Lett. 75, 2996 (1995).

[c8] X. Waintal et al., Phys. Rev. B 62, 12 317 (2000).

[c9] A. Brataas, Yu.V. Nazarov, and G.E.W. Bauer, Phys. Rev. Lett. 84, 2481 (2000); Eur. Phys. J. B 22, 99 (2001).

[c10] K.M. Schep et al., Phys. Rev. B 56, 10 805 (1997)

[c11] M.D. Stiles and D.R. Penn, Phys. Rev. B 61, 3200 (2000).

[c12] K. Xia et al., Phys. Rev. B 63, 064407 (2001).

[c13] S. Datta, Electronic Transport in Mesoscopic Systems (Cambridge University Press, Cambridge, England, 1995).

[c14] J.S. Moodera et al., Phys. Rev. Lett. 74, 3273 (1995).

[c15] G.E.W. Bauer et al., Mater. Sci. Eng., B 84, 31 (2001).

[c16] The elements of the transmission matrix t which enter the conductances are the scattering theory transmission amplitudes used in the Landauer-Büttiker formalism to describe electrical transport (Ref. ). In Refs. and where we reported the development of methods for calculating these matrices from first principles, they were used in an application where only the matrix of transmission probabilities T, obtained by squaring the complex amplitudes, ${T = t t}^{†}$ , were needed. In the present work we need t, as discussed in Refs. and .

[c17] I. Turek et al., Electronic Structure of Disordered Alloys, Surfaces and Interfaces (Kluwer, Boston, 1997).

[c18] O. K. Andersen, O. Jepsen, and D. Glötzel, in Highlights in Condensed Matter Theory, edited by F. Bassani, F. Fumi, and M. P. Tosi (North-Holland, Amsterdam, 1985), p. 59. In our calculations we use the atomic spheres approximation (ASA) in which the atomic Wigner-Seitz cells are replaced by atomic spheres. These fill all space so there is no interstitial region. The ASA is superior to the muffin-tin approximation for close-packed metals.

[c19] To determine charge and spin densities one needs a configuration-averaged single Green’s function, a standard procedure using the CPA. Calculation of the conductance requires obtaining a configuration-averaged product of Green’s functions which is much more difficult. By using supercells we obtain virtually exact results without having to compute “vertex” corrections. It has the additional advantage that we can model short-range order, steps, stacking faults, etc.

[c20] D. Huertas-Hernando, Yu.V. Nazarov, A. Brataas, and G.E.W. Bauer, Phys. Rev. B 62, 5700 (2000).

[c21] D. Huertas-Hernando, Yu.V. Nazarov, and W. Belzig, Phys. Rev. Lett. 88, 047003 (2002).

[c22] In the barrier calculations reported here, six layers of empty atomic spheres were used to model the barrier.

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Spin torques in ferromagnetic/normal-metal structures

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