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Handbook of Materials Modeling pp 1–35Cite as

First-Principles Quantum Transport Modeling of Spin-Transfer and Spin-Orbit Torques in Magnetic Multilayers

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Abstract

A unified approach for computing (i) spin-transfer torque in magnetic trilayers like spin valve and magnetic tunnel junction, where injected charge current flows perpendicularly to interfaces, and (ii) spin-orbit torque in magnetic bilayers of the type ferromagnet/spin-orbit-coupled material, where injected charge current flows parallel to the interface, was reviewed. The experimentally explored and technologically relevant spin-orbit-coupled materials include 5d heavy metals, topological insulators, Weyl semimetals, and transition metal dichalcogenides. This approach requires to construct the torque operator for a given Hamiltonian of the device and the steady-state nonequilibrium density matrix, where the latter is expressed in terms of the nonequilibrium Green’s functions and split into three contributions. Tracing these contributions with the torque operator automatically yields field-like and damping-like components of spin-transfer torque or spin-orbit torque vector, which is particularly advantageous for spin-orbit torque where the direction of these components depends on the unknown-in-advance orientation of the current-driven nonequilibrium spin density in the presence of spin-orbit coupling. Illustrative examples are provided by computing spin-transfer torque in a one-dimensional toy model of a magnetic tunnel junction and realistic Co/Cu/Co spin valve, both of which are described by first-principles Hamiltonians obtained from noncollinear density functional theory calculations, as well as by computing spin-orbit torque in a ferromagnetic layer described by a tight-binding Hamiltonian which includes spin-orbit proximity effect within ferromagnetic monolayers assumed to be generated by the adjacent monolayer transition metal dichalcogenide. In addition, it is shown here how spin-orbit proximity effect, quantified by computing (via first-principles retarded Green’s function) spectral functions and spin textures on monolayers of realistic ferromagnetic material like Co in contact with heavy metal or monolayer transition metal dichalcogenide, can be tailored to enhance the magnitude of spin-orbit torque. Errors made in the calculation of spin-transfer torque are quantified when using Hamiltonian from collinear density functional theory, with rigidly rotated magnetic moments to create noncollinear magnetization configurations, instead of proper (but computationally more expensive) self-consistent Hamiltonian obtained from noncollinear density functional theory.

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References

  • Ado IA, Tretiakov OA, Titov M (2017) Microscopic theory of spin-orbit torques in two dimensions. Phys Rev B 95:094401

    Article  ADS  Google Scholar 

  • Areshkin DA, Nikolić BK (2010) Electron density and transport in top-gated graphene nanoribbon devices: first-principles Green function algorithms for systems containing a large number of atoms. Phys Rev B 81:155450

    Article  ADS  Google Scholar 

  • Aronov AG, Lyanda-Geller YB (1989) Nuclear electric resonance and orientation of carrier spins by an electric field. JETP Lett 50:431

    ADS  Google Scholar 

  • Atomistix Toolkit (ATK) 2017.2. http://www.quantumwise.com

  • Bahramy M, King PDC, de la Torre A, Chang J, Shi M, Patthey L, Balakrishnan G, Hofmann P, Arita R, Nagaosa N, Baumberger F (2012) Emergent quantum confinement at topological insulator surfaces. Nat Commun 3:1159

    Article  Google Scholar 

  • Bansil A, Lin H, Das T (2016) Colloquium: topological band theory. Rev Mod Phys 88:021004

    Article  ADS  Google Scholar 

  • Bastin A, Lewiner C, Betbeder-Matibet O, Noziéres P (1971) Quantum oscillations of the Hall effect of a fermion gas with random impurity scattering. J Phys Chem Solids 32:1811

    Article  ADS  Google Scholar 

  • Baumgartner M, Garello K, Mendil J, Avci CO, Grimaldi E, Murer C, Feng J, Gabureac M, Stamm C, Acremann Y, Finizio S, Wintz S, Raabe J, Gambardella P (2017) Spatially and time-resolved magnetization dynamics driven by spin-orbit torques. Nat Nanotech 12:980

    Article  ADS  Google Scholar 

  • Belashchenko KD, Kovalev AA, van Schilfgaarde M (2016) Theory of spin loss at metallic interfaces. Phys Rev Lett 117:207204

    Article  ADS  Google Scholar 

  • Berger L (1996) Emission of spin waves by a magnetic multilayer traversed by a current. Phys Rev B 54:9353

    Article  ADS  Google Scholar 

  • Berkov DV, Miltat J (2008) Spin-torque driven magnetization dynamics: micromagnetic modeling. J Magn Magn Mater 320:1238

    Article  ADS  Google Scholar 

  • Blöchl PE (1994) Projector augmented-wave method. Phys Rev B 50:17953

    Article  ADS  Google Scholar 

  • Borders WA, Akima H, Fukami S, Moriya S, Kurihara S, Horio Y, Sato S, Ohno H (2017) Analogue spin-orbit torque device for artificial-neural-network-based associative memory operation. Appl Phys Expr 10:013007

    Article  ADS  Google Scholar 

  • Brandbyge M, Mozos JL, Ordejón P, Taylor J, Stokbro K (2002) Density-functional method for nonequilibrium electron transport. Phys Rev B 65:165401

    Article  ADS  Google Scholar 

  • Brataas A, Bauer GEW, Kelly PJ (2006) Non-collinear magnetoelectronics. Phys Rep 427:157

    Article  ADS  Google Scholar 

  • Bulik IW, Scalmani G, Frisch MJ, Scuseria GE (2013) Oncollinear density functional theory having proper invariance and local torque properties. Phys Rev B 87:035117

    Article  ADS  Google Scholar 

  • Capelle K, Vignale G, Györffy BL (2001) Spin currents and spin dynamics in time-dependent density-functional theory. Phys Rev Lett 87:206403

    Article  ADS  Google Scholar 

  • Carva K, Turek I (2009) Landauer theory of ballistic torkances in noncollinear spin-valves. Phys Rev B 80:104432

    Article  ADS  Google Scholar 

  • Ceperley DM, Alder BJ (1980) Ground state of the electron gas by a stochastic method. Phys Rev Lett 45:566

    Article  ADS  Google Scholar 

  • Chang P-H, Markussen T, Smidstrup S, Stokbro K, Nikolić BK (2015) Nonequilibrium spin texture within a thin layer below the surface of current-carrying topological insulator Bi2Se3: a first-principles quantum transport study. Phys Rev B 92:201406(R)

    Google Scholar 

  • Chantis AN, Belashchenko KD, Tsymbal EY, van Schilfgaarde M (2007) Tunneling anisotropic magnetoresistance driven by resonant surface states: first-principles calculations on an Fe(001) surface. Phys Rev Lett 98:046601

    Article  ADS  Google Scholar 

  • Christen T, Büttiker M (1996) Gauge-invariant nonlinear electric transport in mesoscopic conductors. Europhys Lett 35:523

    Article  ADS  Google Scholar 

  • Dolui K, Nikolić BK (2017) Spin-memory loss due to spin-orbit coupling at ferromagnet/heavy-metal interfaces: ab initio spin-density matrix approach. Phys Rev B 96:220403(R)

    Google Scholar 

  • Edelstein VM (1990) Spin polarization of conduction electrons induced by electric current in two-dimensional asymmetric electron systems. Solid State Commun 73:233

    Article  ADS  Google Scholar 

  • Eich FG, Gross EKU (2013) Transverse spin-gradient functional for noncollinear spin-density-functional theory. Phys Rev Lett 111:156401

    Article  ADS  Google Scholar 

  • Eich FG, Pittalis S, Vignale G (2013) Transverse and longitudinal gradients of the spin magnetization in spin-density-functional theory. Phys Rev B 88:245102

    Article  ADS  Google Scholar 

  • Ellis MOA, Stamenova M, Sanvito S (2017) Multiscale modeling of current-induced switching in magnetic tunnel junctions using ab initio spin-transfer torques. Phys Rev B 96:224410

    Article  ADS  Google Scholar 

  • Evans RFL, Fan WJ, Chureemart P, Ostler TA, Ellis MOA, Chantrell RW (2014) Atomistic spin model simulations of magnetic nanomaterials. J Phys Condens Matter 26:103202

    Article  ADS  Google Scholar 

  • Fan Y, Upadhyaya P, Kou X, Lang M, Takei S, Wang Z, Tang J, He L, Chang L-T, Montazeri M, Jiang GY, Nie T, Schwartz RN, Tserkovnyak Y, Wang KL (2014) Magnetization switching through giant spin-orbit torque in a magnetically doped topological insulator heterostructure. Nat Mater 13:699

    Article  ADS  Google Scholar 

  • Freimuth F, Blügel S, Mokrousov Y (2014) Spin-orbit torques in Co/Pt(111) and Mn/W(001) magnetic bilayers from first principles. Phys Rev B 90:174423

    Article  ADS  Google Scholar 

  • Garello K, Miron IM, Avci CO, Freimuth F, Mokrousov Y, Blügel S, Auffret S, Boulle O, Gaudin G, Gambardella P (2013) Symmetry and magnitude of spin-orbit torques in ferromagnetic heterostructures. Nat Nanotech 8:587

    Article  ADS  Google Scholar 

  • Ghosh S, Manchon A (2018) Spin-orbit torque in a three-dimensional topological insulator-ferromagnet heterostructure: crossover between bulk and surface transport. Phys Rev B 97:134402

    Article  ADS  Google Scholar 

  • Guimarães MHD, Stiehl GM, MacNeill D, Reynolds ND, Ralph DC (2018) Spin-orbit torques in NbSe2/Permalloy bilayers. Nano Lett 18:1311

    Article  ADS  Google Scholar 

  • Han J, Richardella A, Siddiqui SA, Finley J, Samarth N, Liu L (2017) Room-temperature spin-orbit torque switching induced by a topological insulator. Phys Rev Lett 119:077702

    Article  ADS  Google Scholar 

  • Haney PM, Stiles MD (2010) Current-induced torques in the presence of spin-orbit coupling. Phys Rev Lett 105:126602

    Article  ADS  Google Scholar 

  • Haney PM, Waldron D, Duine RA, Núñez AS, Guo H, MacDonald AH (2007) Current-induced order parameter dynamics: microscopic theory applied to Co/Cu/Co spin-valves. Phys Rev B 76:024404

    Article  ADS  Google Scholar 

  • Haney PM, Lee H-W, Lee K-J, Manchon A, Stiles MD (2013) Current induced torques and interfacial spin-orbit coupling: semiclassical modeling. Phys Rev B 87:174411

    Article  ADS  Google Scholar 

  • Heiliger C, Stiles MD (2008) Ab Initio studies of the spin-transfer torque in magnetic tunnel junctions. Phys Rev Lett 100:186805

    Article  ADS  Google Scholar 

  • Heiliger C, Czerner M, Yavorsky BY, Mertig I, Stiles MD (2008) Implementation of a nonequilibrium Green’s function method to calculate spin-transfer torque. J Appl Phys 103:07A709

    Google Scholar 

  • Hernández AR, Lewenkopf CH (2013) Nonlinear electronic transport in nanoscopic devices: nonequilibrium Green’s functions versus scattering approach. Eur Phys J B 86:131

    Article  ADS  MathSciNet  Google Scholar 

  • Jia X, Xia K, Ke Y, Guo H (2011) Nonlinear bias dependence of spin-transfer torque from atomic first principles. Phys Rev B 84:014401

    Article  ADS  Google Scholar 

  • Johansson A, Henk J, Mertig I (2018) Edelstein effect in Weyl semimetals. Phys Rev B 97:085417

    Article  ADS  Google Scholar 

  • Junquera J, Paz O, Sánchez-Portal D, Artacho E (2001) Numerical atomic orbitals for linear-scaling calculations. Phys Rev B 64:235111

    Article  ADS  Google Scholar 

  • Kalitsov A, Nikolaev SA, Velev J, Chshiev M, Mryasov O (2017) Intrinsic spin-orbit torque in a single-domain nanomagnet. Phys Rev B 96:214430

    Article  ADS  Google Scholar 

  • Karrasch C, Meden V, Schönhammer K (2010) Finite-temperature linear conductance from the Matsubara Green’s function without analytic continuation to the real axis. Phys Rev B 82:125114

    Article  ADS  Google Scholar 

  • Katine JA, Albert FJ, Buhrman RA, Myers EB, Ralph DC (2000) Current-driven magnetization reversal and spin-wave excitations in Co∕Cu∕Co pillars. Phys Rev Lett 84:3149

    Article  ADS  Google Scholar 

  • Kent AD, Worledge DC (2015) A new spin on magnetic memories. Nat Nanotech 10:187

    Article  ADS  Google Scholar 

  • Kim J, Sinha J, Hayashi M, Yamanouchi M, Fukami S, Suzuki T, Mitani S, Ohno H (2013) Layer thickness dependence of the current-induced effective field vector in Ta|CoFeB|MgO. Nat Mater 12:240

    Article  ADS  Google Scholar 

  • Kim K-W, Lee K-J, Sinova J, Lee H-W, Stiles MD (2017) Spin-orbit torques from interfacial spin-orbit coupling for various interfaces. Phys Rev B 96:104438

    Article  ADS  Google Scholar 

  • Kresse G, Furthmüller J (1996) Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput Mater Sci 6:15

    Article  Google Scholar 

  • Kresse G, Hafner J (1993) Ab initio molecular dynamics for liquid metals. Phys Rev B 47:558

    Article  ADS  Google Scholar 

  • Kresse G, Joubert D (1999) From ultrasoft pseudopotentials to the projector augmented-wave method. Phys Rev B 59:1758

    Article  ADS  Google Scholar 

  • Kubota H, Fukushima A, Yakushiji K, Nagahama T, Yuasa S, Ando K, Maehara H, Nagamine Y, Tsunekawa K, Djayaprawira DD, Watanabe N, Suzuki Y (2008) Quantitative measurement of voltage dependence of spin-transfer torque in MgO-based magnetic tunnel junctions. Nat Phys 4:37

    Article  Google Scholar 

  • Kurebayashi H, Fang JSD, Irvine AC, Skinner TD, Wunderlich J, Novák V, Campion RP, Gallagher BL, Vehstedt EK, Zârbo LP, Výborný K, Ferguson AJ, Jungwirth T (2014) An antidamping spin-orbit torque originating from the Berry curvature. Nat Nanotech 9:211

    Article  ADS  Google Scholar 

  • Lee K-S, Go D, Manchon A, Haney PM, Stiles MD, Lee H-W, Lee K-J (2015) Angular dependence of spin-orbit spin-transfer torques. Phys Rev B 91:144401

    Article  ADS  Google Scholar 

  • Levy PM, Fert A (2006) Spin transfer in magnetic tunnel junctions with hot electrons. Phys Rev Lett 97:097205

    Article  ADS  Google Scholar 

  • Li H, Gao H, Zârbo LP, Výborný K, Wang X, Garate I, Doǧan F, Čejchan A, Sinova J, Jungwirth T, Manchon A (2015) Intraband and interband spin-orbit torques in noncentrosymmetric ferromagnets. Phys Rev B 91:134402

    Google Scholar 

  • Liu L, Pai C-F, Li Y, Tseng HW, Ralph DC, Buhrman RA (2012) Spin-torque switching with the giant spin Hall effect of tantalum. Science 336:555

    Article  ADS  Google Scholar 

  • Locatelli N, Cros V, Grollier J (2014) Spin-torque building blocks. Nat Mater 13:11

    Article  ADS  Google Scholar 

  • Lv W, Jia Z, Wang B, Lu Y, Luo X, Zhang B, Zeng Z, Liu Z (2018) Electric-field control of spin-orbit torques in WS2/permalloy bilayers. ACS Appl Mater Interfaces 10:2843

    Article  Google Scholar 

  • MacNeill D, Stiehl GM, Guimaraes MHD, Buhrman RA, Park J, Ralph DC (2017a) Control of spin-orbit torques through crystal symmetry in WTe2/ferromagnet bilayers. Nat Phys 13:300

    Article  Google Scholar 

  • MacNeill D, Stiehl GM, Guimarães MHD, Reynolds ND, Buhrman RA, Ralph DC (2017b) Thickness dependence of spin-orbit torques generated by WTe2. Phys Rev B 96:054450

    Article  ADS  Google Scholar 

  • Mahfouzi F, Kioussis N (2017) Current-induced damping of nanosized quantum moments in the presence of spin-orbit interaction. Phys Rev B 95:184417

    Article  ADS  Google Scholar 

  • Mahfouzi F, Kioussis N (2018) First-principles study of angular dependence of spin-orbit torque in Pt/Co and Pd/Co bilayers. Phys Rev B 97: 224426

    Article  ADS  Google Scholar 

  • Mahfouzi F, Nikolić BK (2013) How to construct the proper gauge-invariant density matrix in steady-state nonequilibrium: applications to spin-transfer and spin-orbit torques. SPIN 3:1330002

    Article  ADS  Google Scholar 

  • Mahfouzi F, Nikolić BK (2014) Signatures of electron-magnon interaction in charge and spin currents through magnetic tunnel junctions: a nonequilibrium many-body perturbation theory approach. Phys Rev B 90:045115

    Article  ADS  Google Scholar 

  • Mahfouzi F, Nikolić BK, Kioussis N (2016) Antidamping spin-orbit torque driven by spin-flip reflection mechanism on the surface of a topological insulator: a time-dependent nonequilibrium Green function approach. Phys Rev B 93:115419

    Article  ADS  Google Scholar 

  • Mahfouzi F, Kim J, Kioussis N (2017) Intrinsic damping phenomena from quantum to classical magnets: an ab initio study of Gilbert damping in a Pt/Co bilayer. Phys Rev B 96:214421

    Article  ADS  Google Scholar 

  • Manchon A, Zhang S (2008) Theory of nonequilibrium intrinsic spin torque in a single nanomagnet. Phys Rev B 78:212405

    Article  ADS  Google Scholar 

  • Manchon A, Miron IM, Jungwirth T, Sinova J, Zelezný J, Thiaville A, Garello K, Gambardella P (2018) Current-induced spin-orbit torques in ferromagnetic and antiferromagnetic systems. https://arxiv.org/abs/1801.09636

  • Manchon A, Ryzhanova N, Vedyayev A, Chschiev M, Dieny B (2008) Description of current-driven torques in magnetic tunnel junctions. J Phys Condens Matter 20:145208

    Article  ADS  Google Scholar 

  • Manchon A, Zhang S, Lee K-J (2010) Signatures of asymmetric and inelastic tunneling on the spin torque bias dependence. Phys Rev B 82:174420

    Article  ADS  Google Scholar 

  • Marmolejo-Tejada JM, Chang P-H, Lazić P, Smidstrup S, Stradi D, Stokbro K, Nikolić BK (2017) Proximity band structure and spin textures on both sides of topological-insulator/ferromagnetic-metal interface and their charge transport probes. Nano Lett 17:5626

    Article  ADS  Google Scholar 

  • Marzari N, Mostofi AA, Yates JR, Souza I, Vanderbilt D (2012) Maximally localized Wannier functions: theory and applications. Rev Mod Phys 84:1419

    Article  ADS  Google Scholar 

  • Mellnik AR, Lee JS, Richardella A, Grab JL, Mintun PJ, Fischer MH, Vaezi A, Manchon A, Kim E-A, Samarth N, Ralph DC (2014) Spin-transfer torque generated by a topological insulator. Nature 511:449

    Article  ADS  Google Scholar 

  • Mikuszeit N, Boulle O, Miron IM, Garello K, Gambardella P, Gaudin G, Buda-Prejbeanu LD (2015) Spin-orbit torque driven chiral magnetization reversal in ultrathin nanostructures. Phys Rev B 92:144424

    Article  ADS  Google Scholar 

  • Miron IM, Garello K, Gaudin G, Zermatten P-J, Costache MV, Auffret S, Bandiera S, Rodmacq B, Schuhl A, Gambardella P (2011) Perpendicular switching of a single ferromagnetic layer induced by in-plane current injection. Nature 476:189

    Article  ADS  Google Scholar 

  • Myers EB, Ralph DC, Katine JA, Louie RN, Buhrman RA (1999) Current-induced switching of domains in magnetic multilayer devices. Science 285:867

    Article  Google Scholar 

  • Ndiaye PB, Akosa CA, Fischer MH, Vaezi A, Kim E-A, Manchon A (2017) Dirac spin-orbit torques and charge pumping at the surface of topological insulators. Phys Rev B 96:014408

    Article  ADS  Google Scholar 

  • Nikolić BK, Zârbo LP, Souma S (2006) Imaging mesoscopic spin Hall flow: spatial distribution of local spin currents and spin densities in and out of multiterminal spin-orbit coupled semiconductor nanostructures. Phys Rev B 73:075303

    Article  ADS  Google Scholar 

  • Nordström L, Singh DJ (1996) Noncollinear intra-atomic magnetism. Phys Rev Lett 76:4420

    Article  ADS  Google Scholar 

  • Oh S-C, Manchon S-YPA, Chshiev M, Han J-H, Lee H-W, Lee J-E, Nam K-T, Jo Y, Kong Y-C, Dieny B, Lee K-J (2009) Bias-voltage dependence of perpendicular spin-transfer torque in asymmetric MgO-based magnetic tunnel junctions. Nat Phys 5:898

    Article  Google Scholar 

  • Okuma N, Nomura K (2017) Microscopic derivation of magnon spin current in a topological insulator/ferromagnet heterostructure. Phys Rev B 95:115403

    Article  ADS  Google Scholar 

  • Openmx 3.8. http://www.openmx-square.org/

  • Ozaki T (2003) Variationally optimized atomic orbitals for large-scale electronic structures. Phys Rev B 67:155108

    Article  ADS  Google Scholar 

  • Ozaki T (2007) Continued fraction representation of the Fermi-Dirac function for large-scale electronic structure calculations. Phys Rev B 75:035123

    Article  ADS  Google Scholar 

  • Perdew JP, Burke K, Ernzerhof M (1996) Generalized gradient approximation made simple. Phys Rev Lett 77:3865

    Article  ADS  Google Scholar 

  • Perez N, Martinez E, Torres L, Woo S-H, Emori S, Beach GSD (2014) Chiral magnetization textures stabilized by the Dzyaloshinskii-Moriya interaction during spin-orbit torque switching. Appl Phys Lett 104:213909

    Article  Google Scholar 

  • Pesin DA, MacDonald AH (2012a) Quantum kinetic theory of current-induced torques in Rashba ferromagnets. Phys Rev B 86:014416

    Article  ADS  Google Scholar 

  • Pesin D, MacDonald AH (2012b) Spintronics and pseudospintronics in graphene and topological insulators. Nat Mater 11:409

    Article  ADS  Google Scholar 

  • Petrović M, Popescu BS, Plecháč P, Nikolić BK (2018) Spin and charge pumping by steady or pulse current driven magnetic domain wall: a self-consistent multiscale time-dependent-quantum/time-dependent-classical approach. https://arxiv.org/abs/1802.05682

  • Ralph D, Stiles M (2008) Spin transfer torques. J Magn Magn Mater 320:1190

    Article  ADS  Google Scholar 

  • Rungger I, Sanvito S (2008) Algorithm for the construction of self-energies for electronic transport calculations based on singularity elimination and singular value decomposition. Phys Rev B 78:035407

    Article  ADS  Google Scholar 

  • Sankey JC, Cui Y-T, Sun JZ, Slonczewski JC, Buhrman RA, Ralph DC (2008) Measurement of the spin-transfer-torque vector in magnetic tunnel junctions. Nat Phys 4:67

    Article  Google Scholar 

  • Sanvito S (2011) Electron transport theory for large systems. In: Bichoutskaia E (ed) Computational nanoscience. RSC Publishing, Cambridge

    Google Scholar 

  • Schlipf M, Gygi F (2015) Optimization algorithm for the generation of ONCV pseudopotentials. Comput Phys Commun 196:36

    Article  ADS  MATH  Google Scholar 

  • Shao Q, Yu G, Lan Y-W, Shi Y, Li M-Y, Zheng C, Zhu X, Li L-J, Khalili Amiri P, Wang KL (2016) Strong Rashba-Edelstein effect-induced spin-orbit torques in monolayer transition metal dichalcogenide/ferromagnet bilayers. Nano Lett 16:7514

    Article  ADS  Google Scholar 

  • Shelley M, Poilvert N, Mostofi AA, Marzari N (2011) Automated quantum conductance calculations using maximally-localised Wannier functions. Comput Phys Commun 182:2174

    Article  ADS  Google Scholar 

  • Sinova J, Valenzuela SO, Wunderlich J, Back CH, Jungwirth T (2015) Spin Hall effects. Rev Mod Phys 87:1260

    Article  Google Scholar 

  • Sklenar J, Zhang W, Jungfleisch MB, Jiang W, Saglam H, Pearson JE, Ketterson JB, Hoffmann A (2016) Perspective: Interface generation of spin-orbit torques. J Appl Phys 120:180901

    Article  ADS  Google Scholar 

  • Slonczewski JC (1996) Current-driven excitation of magnetic multilayers. J Magn Magn Mater 159:L1

    Article  ADS  Google Scholar 

  • Soumyanarayanan A, Reyren N, Fert A, Panagopoulos C (2016) Emergent phenomena induced by spin-orbit coupling at surfaces and interfaces. Nature 539:509

    Article  Google Scholar 

  • Stamenova M, Mohebbi R, Seyed-Yazdi J, Rungger I, Sanvito S (2017) First-principles spin-transfer torque in CuMnAs|GaP|CuMnAs junctions. Phys Rev B 95:060403

    Article  ADS  Google Scholar 

  • Stefanucci G, van Leeuwen R (2013) Nonequilibrium many-body theory of quantum systems: a modern introduction. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  • Stiles MD, Zangwill A (2002) Anatomy of spin-transfer torque. Phys Rev B 66:014407

    Article  ADS  Google Scholar 

  • Theodonis I, Kioussis N, Kalitsov A, Chshiev M, Butler WH (2006) Anomalous bias dependence of spin torque in magnetic tunnel junctions. Phys Rev Lett 97:237205

    Article  ADS  Google Scholar 

  • Theurich G, Hill NA (2001) Self-consistent treatment of spin-orbit coupling in solids using relativistic fully separable ab initio pseudopotentials. Phys Rev B 64:073106

    Article  ADS  Google Scholar 

  • Thygesen K, Jacobsen K (2005) Molecular transport calculations with Wannier functions. Chem Phys 319:111

    Article  Google Scholar 

  • Timopheev AA, Sousa R, Chshiev M, Buda-Prejbeanu LD, Dieny B (2015) Respective influence of in-plane and out-of-plane spin-transfer torques in magnetization switching of perpendicular magnetic tunnel junctions. Phys Rev B 92:104430

    Article  ADS  Google Scholar 

  • Tsoi M, Jansen AGM, Bass J, Chiang W-C, Seck M, Tsoi V, Wyder P (1998) Excitation of a magnetic multilayer by an electric current. Phys Rev Lett 80:4281

    Article  ADS  Google Scholar 

  • Velev J, Butler W (2004) On the equivalence of different techniques for evaluating the green function for a semi-infinite system using a localized basis. J Phys Condens Matter 16:R637

    Article  ADS  Google Scholar 

  • Vienna Ab initio Simulation Package (VASP) 5.4. http://www.vasp.at/

  • Vignale G (2010) Ten years of spin Hall effect. J Supercond Nov Magn 23:3

    Article  Google Scholar 

  • Virtual Nanolab (VNL) 2017.2. http://www.quantumwise.com

  • Wang S, Xu Y, Xia K (2008) First-principles study of spin-transfer torques in layered systems with noncollinear magnetization. Phys Rev B 77:184430

    Article  ADS  Google Scholar 

  • Wang C, Cui Y-T, Katine JA, Buhrman RA, Ralph DC (2011) Time-resolved measurement of spin-transfer-driven ferromagnetic resonance and spin torque in magnetic tunnel junctions. Nat Phys 7:496

    Article  Google Scholar 

  • Wang L, Wesselink RJH, Liu Y, Yuan Z, Xia K, Kelly PJ (2016) Giant room temperature interface spin Hall and inverse spin Hall effects. Phys Rev Lett 116:196602

    Article  ADS  Google Scholar 

  • Wang Y, Zhu D, Wu Y, Yang Y, Yu J, Ramaswamy R, Mishra R, Shi S, Elyasi M, Teo K-L, Wu Y, Yang H (2017) Room temperature magnetization switching in topological insulator-ferromagnet heterostructures by spin-orbit torques. Nat Commun 8:1364

    Article  ADS  Google Scholar 

  • Winkler R (2003) Spin-Orbit coupling effects in two-dimensional electron and Hole systems. Springer, Berlin

    Book  Google Scholar 

  • Xiao J, Bauer GEW, Brataas A (2008) Spin-transfer torque in magnetic tunnel junctions: scattering theory. Phys Rev B 77:224419

    Article  ADS  Google Scholar 

  • Xie Y, Rungger I, Munira K, Stamenova M, Sanvito S, Ghosh AW (2016) Spin transfer torque: a multiscale picture. In: Atulasimha J, Bandyopadhyay S (eds) Nanomagnetic and spintronic devices for energy-efficient memory and computing. Wiley, Hoboken

    Google Scholar 

  • Yang HX, Chshiev M, Kalitsov A, Schuhl A, Butler WH (2010) Effect of structural relaxation and oxidation conditions on interlayer exchange coupling in Fe/MgO/Fe tunnel junctions. Appl Phys Lett 96:262509

    Article  ADS  Google Scholar 

  • Yasuda K, Tsukazaki A, Yoshimi R, Kondou K, Takahashi KS, Otani Y, Kawasaki M, Tokura Y (2017) Current-nonlinear Hall effect and spin-orbit torque magnetization switching in a magnetic topological insulator. Phys Rev Lett 119:137204

    Article  ADS  Google Scholar 

  • Yoon J, Lee S-W, Kwon JH, Lee JM, Son J, Qiu X, Lee K-J, Yang H (2017) Anomalous spin-orbit torque switching due to field-like torque-assisted domain wall reflection. Sci Adv 3:e1603099

    Article  ADS  Google Scholar 

  • Zhang SS-L, Vignale G, Zhang S (2015) Anisotropic magnetoresistance driven by surface spin-orbit scattering. Phys Rev B 92:024412

    Article  ADS  Google Scholar 

  • Zholud A, Freeman R, Cao R, Srivastava A, Urazhdin S (2017) Spin transfer due to quantum magnetization fluctuations. Phys Rev Lett 119:257201

    Article  ADS  Google Scholar 

  • Zhu ZY, Cheng YC, Schwingenschlögl U (2011) Giant spin-orbit-induced spin splitting in two-dimensional transition-metal dichalcogenide semiconductors. Phys Rev B 84:153402

    Article  ADS  Google Scholar 

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Acknowledgements

We are grateful to K. D. Belashchenko, K. Xia, and Z. Yuan for illuminating discussions and P.-H. Chang, F. Mahfouzi, and J.-M. Marmolejo-Tejada for the collaboration. B. K. N. and K. D. were supported by DOE Grant No. DE-SC0016380 and NSF Grant No. ECCS 1509094. M. P. and P. P. were supported by ARO MURI Award No. W911NF-14-0247. K. S. and T. M. acknowledge support from the European Commission Seventh Framework Programme Grant Agreement IIIV-MOS, Project No. 61932, and Horizon 2020 research and innovation program under grant agreement SPICE, Project No. 713481. The supercomputing time was provided by XSEDE, which is supported by NSF Grant No. ACI-1548562.

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Authors and Affiliations

  1. Department of Physics and Astronomy, University of Delaware, Newark, DE, USA

    Branislav K. Nikolić & Kapildeb Dolui

  2. Department of Mathematical Sciences, University of Delaware, Newark, DE, USA

    Marko D. Petrović & Petr Plecháč

  3. Synopsys QuantumWise, Copenhagen, Denmark

    Troels Markussen & Kurt Stokbro

Authors
  1. Branislav K. Nikolić
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  2. Kapildeb Dolui
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  3. Marko D. Petrović
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  4. Petr Plecháč
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  5. Troels Markussen
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  6. Kurt Stokbro
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Correspondence to Branislav K. Nikolić .

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Editors and Affiliations

  1. Institute of Physics, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Wanda Andreoni

  2. Department of Nuclear Science & Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA

    Sidney Yip

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  1. Department of Physics, Trinity College, Dublin, Ireland

    Stefano Sanvito

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Nikolić, B.K., Dolui, K., Petrović, M.D., Plecháč, P., Markussen, T., Stokbro, K. (2018). First-Principles Quantum Transport Modeling of Spin-Transfer and Spin-Orbit Torques in Magnetic Multilayers. In: Andreoni, W., Yip, S. (eds) Handbook of Materials Modeling. Springer, Cham. https://doi.org/10.1007/978-3-319-50257-1_112-1

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  • DOI: https://doi.org/10.1007/978-3-319-50257-1_112-1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-50257-1

  • Online ISBN: 978-3-319-50257-1

  • eBook Packages: Springer Reference Physics and AstronomyReference Module Physical and Materials ScienceReference Module Chemistry, Materials and Physics

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