Micromagnetic understanding of current-driven domain wall motion in patterned nanowires

Abstract

In order to explain recent experiments reporting a motion of magnetic domain walls (DW) in nanowires carrying a current, we propose a modification of the spin transfer torque term in the Landau-Lifchitz-Gilbert equation. We show that it explains, with reasonable parameters, the measured DW velocities as well as the variation of DW propagation field under current. We also introduce coercivity by considering rough wires. This leads to a finite DW propagation field and finite threshold current for DW propagation, hence we conclude that threshold currents are extrinsic. Some possible models that support this new term are discussed.Recent research on magnetic nanostructures has shown that effects caused by an electric current flowing across a nanostructure may dominate over the effects due to the field generated by the same current [1,2]. Most of the work up to now, experimental and theoretical, has been devoted to the 3-layer geometry (2 magnetic layers separated by a normal metal spacer, with lateral dimensions well below the micrometer so as to get single domain behaviour). Under current, generation of spin waves [3], layer switching [2] and precession of magnetization [4] have been observed. All these results could be qualitatively explained by the spin transfer model [1]. On the other hand, the situation with an infinite number of layers, namely a magnetic nanowire containing a magnetic domain wall (DW), has just started to be studied. Here, under the sole action of a current, the DW may be moved along the wire, as confirmed by several experiments [5][6][7][8][9][10]. The situation is however more complex than with 3 layers, as the evolution of the current spin polarization across the DW has to be described, so that a deep connection with the problem of DW magnetoresistance exists. Two limits have been identified by the theories, namely the thin and thick DW cases. The length to which the DW width has to be compared is, depending on the model, the spin diffusion length [11], the Larmor precession length [12], or the Fermi wavelength [13]. These lengths are below or of the order of a nanometer in usual ferromagnetic metals. In the experiments cited above (nanowires of typical width 100 nm and thickness 10 nm), the DW width is of the order of 100 nm, much c EDP Sciences * * * AT acknowledges fruitful discussions with F. Piéchon and N. Vernier.

Current-induced spin–orbit torques

“…The general form of the modified Landau-Lifshitz-Gilbert equation that takes into account STT terms [70,72] together with the SO interaction in a single magnetic layer characterized by inversion asymmetry can be written as…”

Spin pumping by a field-driven domain wall

“…11 The opposite effect, i.e., the manipulation of magnetization with spin current, is called spin transfer. [12][13][14][15] Recently, the possibility of manipulating with current the position of a magnetic domain wall via spin transfer torques has attracted a great deal of theoretical [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] and experimental [31][32][33][34][35][36][37][38] interest. Although the subject is still controversial, 18,21 it is by now established that in the longwavelength limit, the equation of motion for the magnetization direction ⍀, which in the absence of current describes damped precession around the effective field −␦E MM ͓⍀͔ / ͑ប␦⍀͒, is given by…”

Current-driven magnetic domain wall motion and its real-time detection

“…Figure 2 show the DW velocity as a function of current density for several β based on a one dimensional 1D model. 9) For β = 0, the threshold current required to move the DW is clearly observed. For β ≠ 0, on the other hand, a finite DW velocity is observed even below the threshold current.…”