Universal angular magnetoresistance and spin torque in ferromagnetic/normal metal hybrids

Bauer, G.; Tserkovnyak, Yaroslav; Huertas‐Hernando, Daniel; Brataas, Arne

doi:10.1103/physrevb.67.094421

Cited by 94 publications

(104 citation statements)

References 38 publications

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“…(10)) in term of these new variables. This will be done toward the end of this section, and we will find that j(x) and µ(x) satisfies the well known Valet-Fert diffusive equations 40 for continuous collinear systems and the equations of circuit theory for discrete non-collinear ones 24 . This connection is very interesting from the theoretical point of view as very different routes have been taken to obtain these equations (scattering and Random matrix theory on one side and Keldysh Green function formalism and quasiclassical approximation on the other side).…”

Section: B Random Matrix Theory (Rmt) For Magnetic Multilayersmentioning

confidence: 99%

“…An alternative popular and powerful approach in this case is the so-called circuit theory 24 where the system is discretized into various parts connected by "nodes" where one defines the spin resolved chemical potential. Circuit theory, initially derived for very resistive elements has been further extended into the "generalized" circuit theory to properly take into account the Sharvin resistance.…”

Section: F Correspondence Between Rmt and (Generalized) Circuit Theorymentioning

confidence: 99%

“…(61) are precisely the equations that define generalized circuit theory 24 which proves the equivalence with (C)RMT in this limit. In fact, the renormalization coefficients of generalized circuit theory 24 were chosen such that the calculation of the conductance with RMT and generalized circuit theory fully agree with each other.…”

Section: F Correspondence Between Rmt and (Generalized) Circuit Theorymentioning

confidence: 99%

“…Many different approaches have been developed, ranging from purely quantum 16,17 to semi-classical Boltzmann equation [18][19][20] , (generalized) circuit theory [21][22][23][24][25][26][27] or Random Matrix Theory (RMT) 28,29 or full ab-initio (density functional theory) calculations [30][31][32][33] . A good understanding has now been reached of the respective domains of applicability and links between the various approaches 26,29 .…”

Section: Introductionmentioning

confidence: 99%

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Multiscale approach to spin transport in magnetic multilayers

et al. 2011

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This article discusses two dual approaches to spin transport in magnetic multilayers: a direct, purely quantum, approach based on a Tight-Binding model (TB) and a semiclassical approach (Continuous Random Matrix Theory, CRMT). The combination of both approaches provides a systematic way to perform multi-scales simulations of systems that contain relevant physics at scales larger (spin accumulation, spin diffusion...) and smaller (specular reflexions, tunneling...) than the elastic mean free paths of the layers. We show explicitly that CRMT and TB give consistent results in their common domain of applicability.

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Section: B Random Matrix Theory (Rmt) For Magnetic Multilayersmentioning

confidence: 99%

Section: F Correspondence Between Rmt and (Generalized) Circuit Theorymentioning

confidence: 99%

Section: F Correspondence Between Rmt and (Generalized) Circuit Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Multiscale approach to spin transport in magnetic multilayers

et al. 2011

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“…The dependence of resistance on the angle θ between the magnetizations of the "free" layer F1 and the "polarizer" F2 [ Fig. 1(a)] is RðθÞ ¼ Rð0Þ þ ΔR sin 2 ðθ=2Þ≈ Rð0Þ þ ΔRθ 2 =4, with magnetoresistance ΔR [29]. The current-induced fluctuations discussed below are dominated by the nonuniform dynamical states.…”

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confidence: 99%

Quantum Spin Torque

Zhang

2017

Physics

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We utilize a nanoscale magnetic spin-valve structure to demonstrate that current-induced magnetization fluctuations at cryogenic temperatures result predominantly from the quantum fluctuations enhanced by the spin transfer effect. The demonstrated spin transfer due to quantum magnetization fluctuations is distinguished from the previously established current-induced effects by a nonsmooth piecewise-linear dependence of the fluctuation intensity on current. It can be driven not only by the directional flows of spinpolarized electrons, but also by their thermal motion and by scattering of unpolarized electrons. This effect is expected to remain non-negligible even at room temperature, and entails a ubiquitous inelastic contribution to spin-polarizing properties of magnetic interfaces. DOI: 10.1103/PhysRevLett.119.257201 Spin transfer [1-3]-the transfer of angular momentum from spin-polarized electrical current to magnetic materials-has been extensively researched as an efficient mechanism for the electronic manipulation of nanomagnetic systems, advancing our understanding of nanomagnetism and electronic transport, and enabling the development of magnetoelectronic nanodevices [3][4][5][6][7][8][9][10][11][12][13][14][15]. This effect can be understood based on the argument of angular momentum conservation for spin-polarized electrons, scattered by a ferromagnet whose magnetization ⃗ M is not aligned with their polarization. The component of the electron spin transverse to ⃗ M becomes absorbed, exerting a spin transfer torque (STT) on the magnetization. In nanomagnetic devices such as spin valve nanopillars [ Fig. 1(a)], STT can enhance thermal fluctuations of magnetization [ Fig. 1(b)], resulting in its reversal [5,16] or auto-oscillation [6], which can be utilized in memory, microwave generation, and spin-wave logic [17,18].The approximation for the magnetization as a thermally fluctuating classical vector ⃗ M provides an excellent description for the quasiuniform magnetization dynamics [19]. However, for typical transition-metal ferromagnets, the frequencies f of the dynamical magnetization modes extend to ∼100 THz [19,20]. The modes with f > 6 THz are frozen out at room temperature (f > 70 GHz at T ¼ 3.4 K), and the effect of STT on them cannot be described in terms of the enhancement or suppression of thermal fluctuations. Such high-frequency modes are only now becoming experimentally accessible [21][22][23][24], and their role in spin transfer remains unexplored.Here, we introduce a frequency nonselective, magnetoelectronic approach allowing measurements of the effects of spin transfer on the magnetization fluctuations, not limited to quasiuniform modes. Our central result is that at low temperatures the current-dependent fluctuations arise predominantly from the quantum fluctuations enhanced by spin transfer; the quantum contribution remains non-negligible even at room temperature. The observed effect is analogous to the well-studied spontaneous emission of a photon by a two-level system, also caused by qu...

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Theory of Spin‐transfer Torque

Stiles

2007

Handbook of Magnetism and Advanced Magnetic Materials

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In magnetic multilayers, the spin‐polarized currents flowing between the magnetic layers can exert torques on the magnetizations of the layers when the magnetizations are not collinear. The theory of these spin‐transfer torques is developed in terms of semiclassical transport calculations coupled with quantum‐mechanical calculations of the behavior of spins at interfaces. The result is an expression for the torque in terms of the geometry of the devices and the magnetic configuration.

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Universal angular magnetoresistance and spin torque in ferromagnetic/normal metal hybrids

Cited by 94 publications

References 38 publications

Multiscale approach to spin transport in magnetic multilayers

Multiscale approach to spin transport in magnetic multilayers

Quantum Spin Torque

Theory of Spin‐transfer Torque

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