Action of current on ferrimagnetic domain wall: 2 propagation regimes in creep and influence of domain wall structure

The possibility of manipulating magnetic domain walls (DWs) using electrical current is very attractive for magnetic devices that store and process non-volatile information [1]. To estimate the efficiency of current acting on a magnetic texture (by Spin Transfer Torque for instance), the relevant quantity is a drift speed $\mathrm {u}=( \mathrm {g}\mu _{B}\mathrm {P}) /$(2eMs) J where J is the current density, P its spin polarisation in the magnetic media, Ms the net magnetisation, g the Landé factor, $\mu _{B}$ the Bohr magneton, e the electron charge [2]. The analytical $\mathrm {q}- \varphi $ model of DW motion along 1D wire shows that DW motion induced just by field or just by STT exhibits 2 different DW propagation regimes [3]. For low field or low current (low u), the DW moves steadily with just a tilt of its central magnetisation. This regime is called translational regime. For stronger field or current (strong u), the DW moves with a continuous precession of its central magnetisation. This regime is called precessional regime. In both regimes, speeds are proportional to H or u. The 2 regimes are separated by a critical field (or critical current) called Walker field (or current). Since the velocity is linear with H or u, it is possible to convert a current density acting on the DW into an equivalent field Heq defined as the field necessary to induce the same macroscopic velocity as the current density. In this equivalent field approach, Heq is proportional to u, with a proportionality constant for each regime. In classical ferromagnetic materials that have been mostly studied, P and Ms have the same physical origin and thermal dependence. Therefore, for those materials, the ratio P/ Ms entering u which governs efficiency of STT is fixed. To play with P/ Ms, we focused on more exotic materials namely Rare Earth/ Transition Metal (RETM) ferrimagnetics alloys [4] in which it is possible to tune independently Ms or P by composition or temperature. Indeed, in RETM, two populations of magnetic moments are antiferromagnetically coupled: 3d TM moments are antiparallel to 5d and localised 4f RE moments. The alloys net magnetisation is the difference of moments of the 2 populations whereas spin polarisation P arises only from that of RE and TM conduction electrons. We measured amorphous ferrimagnetic TbFe alloys thin films grown by coevaporation. They exhibit perpendicular magnetic anisotropy and P and Ms have clearly different thermal dependence (Fig 1a). The propagation of DWs in TbFe microtracks was analysed using Kerr microscopy. In a first step, we measured the velocity under continuous field (without current pulses) at different temperatures. We observed a nonlinear behaviour of velocity versus field and a strong dependence with temperature (Fig 1b). This type of DW dynamic is called creep regime. In this regime, the DWM is characterised by discrete hopping of the DW between weak pinning centres acting collectively and the DW velocity is described by an Arrhenius law. The energy barrier to overcome by thermal activation depends on the applied field H weighted by a universal exponent $(\mu = -1/4)$ that describes the motion of 1D elastic system in 2D random disorder media [5]. Fig 2a illustrates our original results demonstrating Current Induced DW Motion in TbFe wires under combined field and current and Fig 1c shows DW velocities for a few current densities. Two main observations can be done. The STT-like action pushes DWs along the electrons flow and can add or substract to the field action: a signature of STT is the increase of the split between fast (up-triangle) and slow (down-triangle) DWs. Joule heating modifies the creep dynamic and makes DWMs easier in both directions: the mean speed increases. A very careful analysis of the creep velocity was performed taking into account field, current and temperature versus time. We could evaluate Joule heating and the current contribution in terms of equivalent field Heq. In Fig 2b, Heq is reported versus current density (J) and clearly presents 2 regimes. Heq is not proportional to J P/Ms over the entire range (dashed line - material parameters from Fig 1a), as expected in conventional STT [3]. Based on an extended $\mathrm {q}- \varphi 1\mathrm {D}$ model, we describe two regimes separated by a Walker-like threshold above which the CIDWM is more efficient, maybe thanks to changes of DW structure such as the creation of Néel lines [6].