Determination of Penetration Depth of Transverse Spin Current in Ferromagnetic Metals by Spin Pumping

Abstract

Spin pumping in nonmagnetic/ferromagnetic metal multilayers is studied both theoretically and experimentally. We show that the line widths of the ferromagnetic resonance (FMR) spectrum depend on the thickness of the ferromagnetic metal layers, which must not be in resonance with the oscillating magnetic field. We also show that the penetration depths of the transverse spin current in ferromagnetic metals can be determined by analyzing the line widths of their FMR spectra. The obtained penetration depths in NiFe, CoFe and CoFeB were 3.7 [nm], 2.5 [nm] and 12.0 [nm], respectively.PACS numbers: 72.25. Mk, 75.70.Cn, 76.50.+g, 76.60.Es The field of current-driven magnetization dynamics (CDMD) has drawn enormous attention because of its potential applications to non-volatile magnetic random access memory and microwave devices. CDMD is also important from a scientific point of view since it provides much information about non-equilibrium dynamics of the magnetization and physics of spin transport and spin relaxation. The concept of CDMD was first proposed by Slonczewski [1] and independently by Berger [2] in 1996. In the last decade much effort has been devoted to studying the physics and applications of CDMD both theoretically and experimentally [3,4].One of the most important quantities in CDMD is the penetration depth of the transverse spin current λ t , over which spin transfer torque is exerted for the magnetization of the free layer. However, there is a controversial issue regarding the penetration depth of the transverse spin current. One argument is based on the ballistic theory of electron transport, and its λ t = π/|k ↑ F − k ↓ F |, which is on the order of the lattice constant in conventional ferromagnets such as Fe, Co, Ni, and their alloys [5,6]. The other argument is based on the Boltzmann theory of electron transport, and its λ t is on the order of a few nm [7]. Urazhdin et al. analyzed the CPP-GMR of noncollinear magnetic multilayers using the extended twoseries-resistance model and concluded that λ t =0.8 [nm] for permalloy [8]. On the other hand, Chen et al. analyzed the critical current of the CDMD in the Co/Cu/Co trilayer system and concluded that λ t =3.0 [nm] for Co [9].The inverse process of CDMD is spin pumping, where spin current is generated by precession of magnetization in the ferromagnetic layer [10]. Enhancement of the Gilbert damping constant due to spin pumping has been extensively studied, and spin diffusion lengths, i.e., penetration depths of spin current in nonmagnetic metals, have been obtained by analyzing the dependence of the enhancement of the Gilbert damping constant on the thickness of the nonmagnetic metal layer. In spin FIG. 1: Schematic illustration of a nonmagnetic/ferromagnetic metal five-layer system. The magnetization of the F1 layer (m1) precesses around the z-axis with angle θ. The magnetization of the F2 layer (m2) is fixed with the z-axis. The precession of the magnetization in the F1 layer pumps the spin current I pump s . The pumped spin current creates spin a...

Current-Induced Instability of a Perpendicular Ferromagnet in Spin Hall Geometry

“…In other words, the direction of the spin polarization of the electrons becomes parallel to the magnetization direction when it is injected into the ferromagnet. We note that a finite penetration depth of the transverse spin current can be taken into account in the following calculations, as done in the case of spin pumping [26]. It does not however affect the main conclusion significantly, in spite of the fact that it makes the calculations complex.…”

“…The relaxation length of the transverse spin accumulation, called the penetration depth of the transverse spin current, depends on both the spin-flip scattering time and precession period of spin around the local magnetization due to the exchange coupling. Since the penetration depth of the transverse spin current is usually shorter than the spin diffusion length [23][24][25][26][27][28], let us assume that the spin accumulation in the F layer, µ F , has only the longitudinal component, for simplicity. In other words, the direction of the spin polarization of the electrons becomes parallel to the magnetization direction when it is injected into the ferromagnet.…”

“…(15). The values of parameters are taken from typical experiments in CoFeB/TaN heterostructure [16] or similar metallic F/N multilayer [22][23][24][25][26] as λ F = 12 nm, ρ F = 1600 Ωnm, β = 0.56, d F = 1 nm, λ N = 2.5 nm, ρ N = 3750 Ωnm, d N = 4 nm, ϑ = 0.1, r = 0.28 kΩnm 2 , γ = 0.70, g r /S = 15 nm −2 , γ 0 = 1.764 × 10 7 rad/(Oe s), α = 0.005, M 2 = 1250 emu/cm 3 , and H K = 450 Oe, where, we assume that the interface conductances, g and g r , at the F k /N k and F k /N interfaces are the same. We assume that the magnetization of the F 1 layer points to the direction m 1 = (sin θ p cos ϕ p , sin θ p sin ϕ p , cos θ p ) where θ p = 30…”

“…While the first torque τ (1) points to the y-direction, as in the case of the conventional spin Hall system, the directions of τ (2) and τ (3) depend on the magnetization of the F 1 layer. This is because the longitudinal and transverse spin currents [22][23][24][25][26][27][28] have different relaxation length scales; here the longitudinal and transverse correspond to parallel and perpendicular to the local magnetization, respectively. Deterministic switching of the F 2 layer is possible when the F 1 layer tilts from the zaxis.…”

Magnetoresistance generated from charge-spin conversion by anomalous Hall effect in metallic ferromagnetic/nonmagnetic bilayers

“…(4) indicate that the anomalous Hall effect generates an electric current perpendicular to both the external current and magnetization. We assume that the penetration depth of the transverse spin current in the ferromagnet is sufficiently short due to the large exchange interaction between the conduction electrons and the magnetization, for simplicity [28][29][30][31][32][33]. The spin polarizations of the spin current and accumulation in the ferromagnet then become parallel to the magnetization m. Using the conservation law of the electric current, ∂ i J ci,F = 0, and applying the open-circuit boundary condition along the z direction, J cz,F = 0, we find that the electrochemical potential and spin accumulation in the ferromagnet are related as…”