Macroscopic description of spin transfer torque

Barnaś, J.; Fert, A.; Gmitra, Martin; Weymann, Ireneusz; Dugaev, V. K.

doi:10.1016/j.mseb.2005.09.016

Cited by 13 publications

(14 citation statements)

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“…For the simulations of the magnetization dynamics, we have solved a Landau Lifschitz Gilbert equation including a spin transfer term of the form M 1 x(M 1 xM 2 ) with the angular dependence shown in Fig.1a [17], the solid straight lines represent the slopes of the torque variation as the angle tends to 0 and π and have been derived from the small angle expression of Fert et al [16]. The parameters used in the calculations and mainly derived from CPP-GMR data are listed in the Section Methods.…”

Section: Methodsmentioning

confidence: 99%

“…1a. We present the results of calculations in the models of Fert et al [15] and Barnaś et al [16][17] for a Py(8)/Cu(10)/Co(8) pillar. With respect to standard structures like Co/Cu/Co or Py/Cu/Py, the difference we have introduced is a large asymmetry between the spin diffusion lengths (SDL) in the magnetic layers, with a long SDL in Co ≈ 38 nm (at room temperature) and a short SDL in Py ≈ 4 nm [22][23].…”

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confidence: 99%

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Shaped angular dependence of the spin-transfer torque and microwave generation without magnetic field

et al. 2007

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The generation of oscillations in the microwave frequency range is one of the most important applications expected from spintronics devices exploiting the spin transfer phenomenon. We report transport and microwave power measurements on specially designed nanopillars for which a non-standard angular dependence of the spin transfer torque (wavy variation) is predicted by theoretical models. We observe a new kind of current-induced dynamics that is characterized by large angle precessions in the absence of any applied field, as this is also predicted by simulation with such a wavy angular dependence of the torque. This type of non-standard nanopillars can represent an interesting way for the implementation of spin transfer oscillators since they are able to generate microwave oscillations without applied magnetic field. We also emphasize the theoretical implications of our results on the angular dependence of the torque. 2The magnetization of a ferromagnetic body can be manipulated by transfer of spin angular momentum from a spin-polarized current. This is the concept of spin transfer introduced by Slonczewski [1] and Berger [2] in 1996. In most experiments, a spin-polarized current is injected from a spin polarizer into a "free" magnetic element, for example in pillar-shaped magnetic trilayers [3][4][5][6]. The phenomenon of spin transfer has a great potential for applications. It can be used either to switch a magnetic configuration (the configuration of a magnetic memory for example) [3][4][5] or to generate magnetic precessions and voltage oscillations in the microwave frequency range [6][7]. In the most usual situations, such oscillations are observed in the presence of a magnetic field.From a fundamental point of view, spin transfer effects raise two different types of problems [8]. First the spin transfer torque acting on a magnetic element is related to the transverse spin polarisation of the current (transverse meaning perpendicular to the magnetization axis of the element) and can be derived from spin-dependent transport equations [8][9][10][11][12][13][14][15][16][17]. On the other hand, the description of the magnetic excitations generated by the spin transfer torque raises problems of non-linear dynamics [8,[18][19][20]. For example, in the simple limit where the excitation is supposed to be a uniform precession of the magnetization (macrospin approximation), this precession can be determined by introducing the spin transfer torque into a Landau-LifshitzGilbert (LLG) equation for the motion of the magnetic moment. However, the determination of the spin transfer torque and the description of the magnetization dynamics cannot be regarded as independent problems. In standard trilayered structures with in-plane magnetizations and with the usual angular dependence, a switching regime is found at zero and low magnetic field and the precession regime with generation of voltage oscillations is mainly observed above some threshold field [8]. We will show that a new behavior, characterized by large a...

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Section: Methodsmentioning

confidence: 99%

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Shaped angular dependence of the spin-transfer torque and microwave generation without magnetic field

et al. 2007

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“…A recent generalization of the Valet-Fert model to noncollinear spin structures [10][11][12] rests heavily on two additional properties of spin currents. First, the transverse ͑perpendicular to local exchange field͒ component of the spin current inside a ferromagnet becomes rapidly damped over a typical distance of a few interatomic spacings.…”

Section: Introductionmentioning

confidence: 99%

“…18,21 This feature is closely linked to properties of the current-induced steady-state torques in noncollinear spin valves and it results in a very small torque component perpendicular to the plane spanned by magnetization directions of the two FM layers. 12 The assumption of a negligible imaginary part of the spin-mixing conductance has also been employed in theoretical studies of angular magnetoresistance of spin valves 22 as well as of magnetization dynamics of thin FM films; 21 its validity, however, has to be checked in each particular case. As indicated by several authors, this becomes especially important for nonmetallic systems, such as systems containing tunneling barriers 18 or insulating FM parts.…”

Section: Introductionmentioning

confidence: 99%

Spin-mixing conductances of thin magnetic films from first principles

Carva

Turek

2007

Phys. Rev. B

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We present a first-principles theory of the spin-mixing conductance for a thin ferromagnetic film embedded epitaxially between two nonmagnetic metallic electrodes. The complex spin-mixing conductance is formulated as a linear response of the spin torque experienced by the film due to the spin accumulation in one of the electrodes. The derivation is based on nonequilibrium Green's functions; the obtained result for the torque response is in agreement with the response of spin fluxes on both sides of the ferromagnet as well as with expressions derived within the Landauer-Büttiker scattering theory. Numerical implementation of the developed formalism employs the tight-binding linear muffin-tin orbital method and calculations are performed for selected metallic and half-metallic ferromagnetic films relevant for spintronics applications. The spin-mixing conductance of the Cu/ Ni/ Cu͑100͒ system is found to exhibit pronounced oscillations as a function of Ni thickness; their period is explained by spin-resolved Fermi-surface properties of nickel. Investigated halfmetallic films include the full-Heusler Co 2 MnSi compound and the diluted ͑Ga,Mn͒As magnetic semiconductors attached to nonmagnetic Cr͑100͒ leads; the imaginary part of their spin-mixing conductance has a magnitude comparable to the real part. This unusual feature has been qualitatively explained in terms of a freeelectron model.

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“…Above certain threshold current both collinear states of the magnetization are unstable for one current orientation, and the only solution of the Landau-Lifshitz-Gilbert ͑LLG͒ equation ͑within the macrospin model͒ is the steady-state precession or a noncollinear static magnetization state. 24 Note also that the torque calculations are based on a onedimensional transport model, 9 where the lateral diffusion was neglected. The model requirement of sample cylindrical symmetry is approximately fulfilled since in both structures presented in Fig.…”

Section: Spin Torque In An Asymmetric Pillarmentioning

confidence: 99%

Computational study of microwave oscillations in nonstandard spin valves in the diffusive transport limit

et al. 2010

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An anomalous ͑inverse͒ spin accumulation in the nonmagnetic spacer may build up when the spin valve consists of magnetic films having different spin asymmetries and spin-diffusion lengths ͓J. Barnaś, A. Fert, M. Gmitra, I. Weymann, and V. K. Dugaev, Phys. Rev. B 72, 024426 ͑2005͔͒. This leads to wavylike dependence of spin-transfer torque on the angle between magnetizations, as predicted by spin-dependent diffusive transport model, and also confirmed experimentally. Making use of these predictions, we have numerically studied the magnetization dynamics in the presence of such a wavy torque in Co͑8 nm͒/Cu͑10 nm͒/Py͑8 nm͒ nanopillar, considering geometry with extended and etched Co layer. In both cases we specify conditions for the out-ofplane precession to appear in absence of external magnetic field and thermal fluctuations. We prove the assumption of wavylike torque angular dependence to be fully consistent with experimental observations. We also show that some features reported experimentally, such as nonlinear slope of frequency vs current, are beyond the applicability range of the macrospin approximation and can be explained only by full micromagnetic analysis.

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Macroscopic description of spin transfer torque

Cited by 13 publications

References 14 publications

Shaped angular dependence of the spin-transfer torque and microwave generation without magnetic field

Shaped angular dependence of the spin-transfer torque and microwave generation without magnetic field

Spin-mixing conductances of thin magnetic films from first principles

Computational study of microwave oscillations in nonstandard spin valves in the diffusive transport limit

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