Estimation of transverse spin penetration length using second-harmonic measurement: Proposal of an experimental method

Abstract

A theoretical description of spin current injection from a nonmagnetic layer into a magnetic one is presented, with the main emphasis on the description and determination of the penetration depth of spin current component transverse to the magnetization. This penetration depth also determines the depth of spin transfer torque generation. Physically, the spin current may be driven by an external electric field or by a temperature gradient. To determine the penetration depth we used ab initio calculations of channel and mixing conductances as well as of mixing transmission. The results are then used to determine the second harmonic voltage response, which in turn can be used to determine the penetration depth experimentally.

Spin transparency for the interface of an ultrathin magnet within the spin dephasing length

“…(8a) implies that G ↑↓ T can even be a negative real number, as also demonstrated in Refs. [11,48,49]. For this case, T ′ 2 /T 2 < 0, thus it is always smaller than T 12 > 0.…”

“…The total inverse spin Hall current in NM2 is given by I ISHE,2 = W t + d2 t θ SH,2 ŷ • j s (z)dz, where W is the width of the wire and θ SH,i = σ SH,i /σ i is the spin Hall angle, and σ SH,2 is the spin Hall conductivity of NM2. Using the solution in Appendix B for j s (z), we obtain (11)]. We use the same parameter as Fig.…”

“…It is typically assumed that the spin dephasing in the ferromagnetic bulk is infinitely fast, thus the spin current right at the interface solely determines the total angular momentum transfer to the ferromagnet [8]. Indeed, the spin dephasing length is on the order of or less than a nanometer [9][10][11], this assumption has provided a very simple but still reasonable way to calculate a spin torque.…”

Transport theory for femtosecond laser-induced spin-transfer torques

“…The typical length scale at which the transverse spin current is absorbed in the magnetic layer is at most few nanometers. [31][32][33][34][35] Clearly, the STT appears only in the case when the magnetizations of the two adjacent magnetic layers are noncollinear. The effect of the STT can be described in a way analogous to the Valet-Fert 36 model using the diffusive spin transport description taking into account bulk resistivities and interface conductances.…”