Anomalous domain wall velocity and Walker breakdown in hybrid systems with anisotropic exchange

Abstract

It has recently been proposed that spin-transfer torques in magnetic systems with anisotropic exchange can be strongly enhanced, reducing the characteristic current density with up to four orders of magnitude compared to conventional setups. Motivated by this, we analytically solve the equations of motion in a collective-coordinate framework for this type of anisotropic exchange system, to investigate the domain wall dynamics in detail. In particular, we obtain analytical expressions for the maximum attainable domain wall velocity of such a setup and also for the occurrence of Walker breakdown. Surprisingly, we find that, in contrast to the standard case with domain wall motion driven by the non-adiabatic torque, the maximum velocity obtained via the anisotropic exchange torque is completely independent of the non-adiabaticity parameter β, in spite of the torque itself being very large for small β. Moreover, the Walker breakdown threshold has an opposite dependence on β in these two cases, i.e. for the anisotropic exchange torque scenario, the threshold value decreases monotonically with β. These findings are of importance to any practical application of the proposed giant spin-transfer torque in anisotropic exchange systems.

Andreev reflection and 0- π transition in graphene-based antiferromagnetic superconducting junctions

“…However, a ferromagnetic metal can be perturbed by the external magnetic field. So someone investigated the Josephson current in the antiferromagnetic Josephson junction and proposed some possible schemes for realizing the 0-π transition [7][8][9][10][11][12][13]. The neighboring magnetic moments in the antiferromagnetic materials point in the opposite directions, which results in zero net magnetization.…”

Equal-spin Andreev reflection in ferromagnet/superconductor junctions with the interfacial Rashba spin-orbit coupling

“…The triplet proximity effect requires a formation of equal-spin AR (ESAR) that includes a spin flip [3]. A number of mechanisms that give rise to the ESAR, such as magnetic domain walls [3], spin-orbit interaction in noncentrosymmetric superconductors [8], and a rotating magnetization in the F close to the interface [9,28], have been investigated in F/S systems. Motivated by the advantages of the Rashba spin-orbit coupling (RSOC) in spintronics [29], the influences of the RSOC on the AR have been studied in refs.…”

“…Here θ s is the angle between the F/S interface normal and the wave vector of the quasiparticle in the S. For s-wave pairing we use g(θ s ) = 1. For d-wave pairing we use g(θ s ) = cos (2θ s − 2β) where β = 0 and π/4 correspond to d x 2 −y 2 and d xy pairing, respectively [28]. h = h(0, sin α, cos α) is the magnetization vector in the F with h the exchange energy and α the angle between h and the z-axis.…”

“…In eq. ( 3) we take [28]. The wave vector in the S is given by k = k F R cos θ s and those in the F are given by k e(h)↑ = (1…”

Quantized Josephson phase battery

“…We take the superconducting gap of the form Δ = Δ 0 (T )[e iϕL Θ(−x − a/2) + e iϕR Θ(x − a/2)], where Δ 0 (T ) is temperature dependent and it follows that Δ 0 (T ) = Δ 0 tanh(1.74 (T c /T − 1)), where T c is the superconducting critical temperature [33] for a widely used s-wave superconductor like lead is 7.2 K, ϕ L and ϕ R being superconducting phases for the left and right superconductors, respectively. The Bogoliubov-de Gennes equation for our junction is [34]…”