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A problem of moment realizability in quantum statistical physics
Diffusion limit of a generalized matrix Boltzmann equation for spin-polarized transport
1. | Institute of Theoretical and Computational Physics, Graz University of Technology, Petersgasse 16, 8010 Graz |
2. | Laboratoire CMI/LATP, Université de Provence, 39, rue Joliot Curie, 13453 Marseille Cedex 13 |
References:
[1] |
L. E. Ballentine, "Quantum Mechanics. A Modern Development,'' Revised edition, World Scientific Publishing Co., Inc., River Edge, NJ, 1998. |
[2] |
L. Barletti and G. Frosali, Diffusive limit of the two-band k.p model for semiconductors, J. Stat. Phys., 139 (2010), 280-306.
doi: 10.1007/s10955-010-9940-9. |
[3] |
L. Barletti and F. Méhats, Quantum drift-diffusion modeling of spin transport in nanostructures, J. Math. Phys., 51 (2010), 053304, 20 pp. |
[4] |
G. S. D. Beach, M. Tsoi and J. L. Erskine, Current-induced domain wall motion, J. Magn. Magn. Mater., 320 (2008), 1272-1281.
doi: 10.1016/j.jmmm.2007.12.021. |
[5] |
L. Berger, Emission of spin waves by a magnetic multilayer traversed by a current, Phys. Rev. B, 54 (1996), 9353-9358.
doi: 10.1103/PhysRevB.54.9353. |
[6] |
D. V. Berkov and J. Miltat, Spin-torque driven magnetization dynamics: micromagnetic modeling, J. Magn. Magn. Mater., 320 (2008), 1238-1259.
doi: 10.1016/j.jmmm.2007.12.023. |
[7] |
H.-P. Breuer and F. Petruccione, "The Theory of Open Quantum Systems,'' Oxford University Press, New York, 2002. |
[8] |
I. A. Campbell, A. Fert and A. R. Pomeroy, Evidence for two current conduction in iron, Phil. Mag., 15 (1967), 977-981, arXiv:0711.4478. |
[9] |
M. I. Dyakonov, ed., "Spin Physics in Semiconductors,'' Springer-Verlag, Berlin Heidelberg, 2008. |
[10] |
R. El Hajj, Diffusion models for spin transport derived from the spinor Boltzmann equation,, Comm. Math. Sci., ().
|
[11] |
R. El Hajj, "Etude Mathématique et Numérique de Modèles de Transport: Application à la Spintronique," Ph.D. thesis, Institut de Mathámatiques de Toulouse (IMT), Université Paul Sabatier, 2008. |
[12] |
H. A. Engel, E. I. Rashba and B. I. Halperin, Theory of spin Hall effects in semiconductors, Handbook of Magnetism and Advanced Magnetic Materials, John Wiley & Sons, Ltd., 2007, arXiv:cond-mat/0603306v3. |
[13] |
C. Ertler, A. Matos-Abiague, M. Gmitra, M. Turek and J. Fabian, Perspectives in spintronics: Magnetic resonant tunneling, spin-orbit coupling, and GaMnAs, J. Phys. Conf. Ser., 129 (2008), 012021, arXiv:0811.0500. |
[14] |
A. Fert, Nobel lecture: Origin, development, and future of spintronics, Rev. Mod. Phys., 80 (2008), 1517-1530.
doi: 10.1103/RevModPhys.80.1517. |
[15] |
A. Fert and I. A. Campbell, Electrical resistivity of ferromagnetic nickel and iron based alloys, J. Phys. F: Metal Phys., 6 (1976), 849-871.
doi: 10.1088/0305-4608/6/5/025. |
[16] |
O. Gunnarsson, Band model for magnetism of transition metals in the spin-density-functional formalism, J. Phys. F: Metal Phys., 6 (1976), 587.
doi: 10.1088/0305-4608/6/4/018. |
[17] |
R. Q. Hood and R. M. Falicov, Boltzmann-equation approach to the negative magnetoresistance of ferromagnetic-normal-metal multilayers, Phys. Rev. B, 46 (2007), 8287.
doi: 10.1103/PhysRevB.46.8287. |
[18] |
M. Johnson and R. H. Silsbee, Interfacial charge-spin coupling: Injection and detection of spin magnetization in metals, Phys. Rev. Lett., 55 (1985), 1790.
doi: 10.1103/PhysRevLett.55.1790. |
[19] |
J. A. Katine and E. E. Fullerton, Device implications of spin-transfer torques, J. Magn. Magn. Mater., 320 (2008), 1217-1226.
doi: 10.1016/j.jmmm.2007.12.013. |
[20] |
D. Loss and D. P. DiVincenzo, Quantum computation with quantum dots, Phys. Rev. A, 57 (1998), 120-126.
doi: 10.1103/PhysRevA.57.120. |
[21] |
O. Morandi and F. Schürrer, Wigner model for quantum transport in graphene, J. Phys. A, accepted, 2011, arXiv:1102.2416. |
[22] |
W. Nolting and A. Ramakanth, "Quantum Theory of Magnetism,'' Springer-Verlag, Berlin-Heidelberg, 2009.
doi: 10.1007/978-3-540-85416-6. |
[23] |
K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos and A. A. Firsov, Two-dimensional gas of massless Dirac fermions in graphene, Nature, 438 (2005), 197-200.
doi: 10.1038/nature04233. |
[24] |
F. Piéchon and A. Thiaville, Spin transfer torque in continuous textures: semiclassical Boltzmann approach, Phys. Rev. B, 75 (2007), 174414.
doi: 10.1103/PhysRevB.75.174414. |
[25] |
F. Poupaud, Diffusion approximation of the linear semiconductor Boltzmann equation: Analysis of boundary layers, Asympt. Anal., 4 (1991), 293-317. |
[26] |
Y. Qi and S. Zhang, Spin diffusion at finite electric and magnetic fields, Phys. Rev. B, 67 (2003), 052407.
doi: 10.1103/PhysRevB.67.052407. |
[27] |
D. C. Ralph and M. D. Stiles, Spin transfer torques, J. Magn. Magn. Mater., 320 (2008), 1190-1216. |
[28] |
S. Saikin, A drift-diffusion model for spin-polarized transport in a two-dimensional non-degenerate electron gas controlled by spin-orbit interaction, J. Phys.: Condens. Matter, 16 (2010), 5071-5081, arXiv:cond-mat/0311221v3. |
[29] |
E. Simanek, Spin accumulation and resistance due to a domain wall, Phys. Rev. B, 63 (2001), 224412.
doi: 10.1103/PhysRevB.63.224412. |
[30] |
J. C. Slonczewski, Current-driven excitation of magnetic multilayers, J. Magn. Magn. Mater., 159 (1996), L1-L7.
doi: 10.1016/0304-8853(96)00062-5. |
[31] |
M. D. Stiles and J. Miltat, Spin-transfer torque and dynamics, Top. Appl. Phys., 101 (2006), 225.
doi: 10.1007/10938171_7. |
[32] |
M. Tsoi, A. G. M. Jansen, J. Bass, W.-C. Chiang, M. Seck, V. Tsoi and P. Wyder, Excitation of a magnetic multilayer by an electric current, Phys. Rev. Lett., 80 (1998), 4281.
doi: 10.1103/PhysRevLett.80.4281. |
[33] |
T. Valet and A. Fert, Theory of the perpendicular magnetoresistance in magnetic multilayers, Phys. Rev. B, 48 (1993), 7099.
doi: 10.1103/PhysRevB.48.7099. |
[34] |
P. C. van Son, H. van Kempen and P. Wyder, Boundary resistance of the ferromagnetic-nonferromagnetic metal interface, Phys. Rev. Lett., 58 (1987), 2271.
doi: 10.1103/PhysRevLett.58.2271. |
[35] |
L. Villegas-Lelovsky, Hydrodynamic model for spin-polarized electron transport in semiconductors, J. Appl. Phys., 101 (2007), 053707.
doi: 10.1063/1.2437570. |
[36] |
C. Vouille, A. Barthélémy, F. Elokan Mpondo, A. Fert, P. A. Schroeder, S. Y. Hsu, A. Reilly and R. Loloee, Microscopic mechanisms of giant magnetoresistance, Phys. Rev. B, 60 (1999), 6710.
doi: 10.1103/PhysRevB.60.6710. |
[37] |
M. Wenin and W. Pötz, Optimal control of a single qubit by direct inversion, Phys. Rev. A, 74 (2006), 022319.
doi: 10.1103/PhysRevA.74.022319. |
[38] |
J. Xiao, A. Zangwill, and M. D. Stiles, A numerical method to solve the Boltzmann equation for a spin valve, Eur. Phys. J. B, 59 (2007), 415-427.
doi: 10.1140/epjb/e2007-00004-0. |
[39] |
N. Zamponi and L. Barletti, Quantum electronic transport in graphene: A kinetic and fluid-dynamic approach, Mathematical Methods in Applied Sciences, 34 (2011), 807-818.
doi: 10.1002/mma.1403. |
[40] |
J. Zhang, P. M. Levy, S. Zhang and V. Antropov, Identification of transverse spin currents in noncollinear magnetic structures, Phys. Rev. Lett., 93 (2004), 256602, arXiv:cond-mat/0405610v1. |
[41] |
S. Zhang, P. M. Levy and A. Fert, Mechanisms of spin-polarized current-driven magnetization switching, Phys. Rev. Lett., 88 (2002), 236601.
doi: 10.1103/PhysRevLett.88.236601. |
[42] |
I. Zutic, J. Fabian and S. Das Sarma, Spintronics: Fundamentals and applications, Rev. Mod. Phys., 76 (2004), 323-410. |
show all references
References:
[1] |
L. E. Ballentine, "Quantum Mechanics. A Modern Development,'' Revised edition, World Scientific Publishing Co., Inc., River Edge, NJ, 1998. |
[2] |
L. Barletti and G. Frosali, Diffusive limit of the two-band k.p model for semiconductors, J. Stat. Phys., 139 (2010), 280-306.
doi: 10.1007/s10955-010-9940-9. |
[3] |
L. Barletti and F. Méhats, Quantum drift-diffusion modeling of spin transport in nanostructures, J. Math. Phys., 51 (2010), 053304, 20 pp. |
[4] |
G. S. D. Beach, M. Tsoi and J. L. Erskine, Current-induced domain wall motion, J. Magn. Magn. Mater., 320 (2008), 1272-1281.
doi: 10.1016/j.jmmm.2007.12.021. |
[5] |
L. Berger, Emission of spin waves by a magnetic multilayer traversed by a current, Phys. Rev. B, 54 (1996), 9353-9358.
doi: 10.1103/PhysRevB.54.9353. |
[6] |
D. V. Berkov and J. Miltat, Spin-torque driven magnetization dynamics: micromagnetic modeling, J. Magn. Magn. Mater., 320 (2008), 1238-1259.
doi: 10.1016/j.jmmm.2007.12.023. |
[7] |
H.-P. Breuer and F. Petruccione, "The Theory of Open Quantum Systems,'' Oxford University Press, New York, 2002. |
[8] |
I. A. Campbell, A. Fert and A. R. Pomeroy, Evidence for two current conduction in iron, Phil. Mag., 15 (1967), 977-981, arXiv:0711.4478. |
[9] |
M. I. Dyakonov, ed., "Spin Physics in Semiconductors,'' Springer-Verlag, Berlin Heidelberg, 2008. |
[10] |
R. El Hajj, Diffusion models for spin transport derived from the spinor Boltzmann equation,, Comm. Math. Sci., ().
|
[11] |
R. El Hajj, "Etude Mathématique et Numérique de Modèles de Transport: Application à la Spintronique," Ph.D. thesis, Institut de Mathámatiques de Toulouse (IMT), Université Paul Sabatier, 2008. |
[12] |
H. A. Engel, E. I. Rashba and B. I. Halperin, Theory of spin Hall effects in semiconductors, Handbook of Magnetism and Advanced Magnetic Materials, John Wiley & Sons, Ltd., 2007, arXiv:cond-mat/0603306v3. |
[13] |
C. Ertler, A. Matos-Abiague, M. Gmitra, M. Turek and J. Fabian, Perspectives in spintronics: Magnetic resonant tunneling, spin-orbit coupling, and GaMnAs, J. Phys. Conf. Ser., 129 (2008), 012021, arXiv:0811.0500. |
[14] |
A. Fert, Nobel lecture: Origin, development, and future of spintronics, Rev. Mod. Phys., 80 (2008), 1517-1530.
doi: 10.1103/RevModPhys.80.1517. |
[15] |
A. Fert and I. A. Campbell, Electrical resistivity of ferromagnetic nickel and iron based alloys, J. Phys. F: Metal Phys., 6 (1976), 849-871.
doi: 10.1088/0305-4608/6/5/025. |
[16] |
O. Gunnarsson, Band model for magnetism of transition metals in the spin-density-functional formalism, J. Phys. F: Metal Phys., 6 (1976), 587.
doi: 10.1088/0305-4608/6/4/018. |
[17] |
R. Q. Hood and R. M. Falicov, Boltzmann-equation approach to the negative magnetoresistance of ferromagnetic-normal-metal multilayers, Phys. Rev. B, 46 (2007), 8287.
doi: 10.1103/PhysRevB.46.8287. |
[18] |
M. Johnson and R. H. Silsbee, Interfacial charge-spin coupling: Injection and detection of spin magnetization in metals, Phys. Rev. Lett., 55 (1985), 1790.
doi: 10.1103/PhysRevLett.55.1790. |
[19] |
J. A. Katine and E. E. Fullerton, Device implications of spin-transfer torques, J. Magn. Magn. Mater., 320 (2008), 1217-1226.
doi: 10.1016/j.jmmm.2007.12.013. |
[20] |
D. Loss and D. P. DiVincenzo, Quantum computation with quantum dots, Phys. Rev. A, 57 (1998), 120-126.
doi: 10.1103/PhysRevA.57.120. |
[21] |
O. Morandi and F. Schürrer, Wigner model for quantum transport in graphene, J. Phys. A, accepted, 2011, arXiv:1102.2416. |
[22] |
W. Nolting and A. Ramakanth, "Quantum Theory of Magnetism,'' Springer-Verlag, Berlin-Heidelberg, 2009.
doi: 10.1007/978-3-540-85416-6. |
[23] |
K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos and A. A. Firsov, Two-dimensional gas of massless Dirac fermions in graphene, Nature, 438 (2005), 197-200.
doi: 10.1038/nature04233. |
[24] |
F. Piéchon and A. Thiaville, Spin transfer torque in continuous textures: semiclassical Boltzmann approach, Phys. Rev. B, 75 (2007), 174414.
doi: 10.1103/PhysRevB.75.174414. |
[25] |
F. Poupaud, Diffusion approximation of the linear semiconductor Boltzmann equation: Analysis of boundary layers, Asympt. Anal., 4 (1991), 293-317. |
[26] |
Y. Qi and S. Zhang, Spin diffusion at finite electric and magnetic fields, Phys. Rev. B, 67 (2003), 052407.
doi: 10.1103/PhysRevB.67.052407. |
[27] |
D. C. Ralph and M. D. Stiles, Spin transfer torques, J. Magn. Magn. Mater., 320 (2008), 1190-1216. |
[28] |
S. Saikin, A drift-diffusion model for spin-polarized transport in a two-dimensional non-degenerate electron gas controlled by spin-orbit interaction, J. Phys.: Condens. Matter, 16 (2010), 5071-5081, arXiv:cond-mat/0311221v3. |
[29] |
E. Simanek, Spin accumulation and resistance due to a domain wall, Phys. Rev. B, 63 (2001), 224412.
doi: 10.1103/PhysRevB.63.224412. |
[30] |
J. C. Slonczewski, Current-driven excitation of magnetic multilayers, J. Magn. Magn. Mater., 159 (1996), L1-L7.
doi: 10.1016/0304-8853(96)00062-5. |
[31] |
M. D. Stiles and J. Miltat, Spin-transfer torque and dynamics, Top. Appl. Phys., 101 (2006), 225.
doi: 10.1007/10938171_7. |
[32] |
M. Tsoi, A. G. M. Jansen, J. Bass, W.-C. Chiang, M. Seck, V. Tsoi and P. Wyder, Excitation of a magnetic multilayer by an electric current, Phys. Rev. Lett., 80 (1998), 4281.
doi: 10.1103/PhysRevLett.80.4281. |
[33] |
T. Valet and A. Fert, Theory of the perpendicular magnetoresistance in magnetic multilayers, Phys. Rev. B, 48 (1993), 7099.
doi: 10.1103/PhysRevB.48.7099. |
[34] |
P. C. van Son, H. van Kempen and P. Wyder, Boundary resistance of the ferromagnetic-nonferromagnetic metal interface, Phys. Rev. Lett., 58 (1987), 2271.
doi: 10.1103/PhysRevLett.58.2271. |
[35] |
L. Villegas-Lelovsky, Hydrodynamic model for spin-polarized electron transport in semiconductors, J. Appl. Phys., 101 (2007), 053707.
doi: 10.1063/1.2437570. |
[36] |
C. Vouille, A. Barthélémy, F. Elokan Mpondo, A. Fert, P. A. Schroeder, S. Y. Hsu, A. Reilly and R. Loloee, Microscopic mechanisms of giant magnetoresistance, Phys. Rev. B, 60 (1999), 6710.
doi: 10.1103/PhysRevB.60.6710. |
[37] |
M. Wenin and W. Pötz, Optimal control of a single qubit by direct inversion, Phys. Rev. A, 74 (2006), 022319.
doi: 10.1103/PhysRevA.74.022319. |
[38] |
J. Xiao, A. Zangwill, and M. D. Stiles, A numerical method to solve the Boltzmann equation for a spin valve, Eur. Phys. J. B, 59 (2007), 415-427.
doi: 10.1140/epjb/e2007-00004-0. |
[39] |
N. Zamponi and L. Barletti, Quantum electronic transport in graphene: A kinetic and fluid-dynamic approach, Mathematical Methods in Applied Sciences, 34 (2011), 807-818.
doi: 10.1002/mma.1403. |
[40] |
J. Zhang, P. M. Levy, S. Zhang and V. Antropov, Identification of transverse spin currents in noncollinear magnetic structures, Phys. Rev. Lett., 93 (2004), 256602, arXiv:cond-mat/0405610v1. |
[41] |
S. Zhang, P. M. Levy and A. Fert, Mechanisms of spin-polarized current-driven magnetization switching, Phys. Rev. Lett., 88 (2002), 236601.
doi: 10.1103/PhysRevLett.88.236601. |
[42] |
I. Zutic, J. Fabian and S. Das Sarma, Spintronics: Fundamentals and applications, Rev. Mod. Phys., 76 (2004), 323-410. |
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