Thermodynamic theory for thermal-gradient-driven domain-wall motion

Abstract

Spin waves (or magnons) interact with magnetic domain walls (DWs) in a complicated way that a DW can propagate either along or against magnon flow. However, thermally activated magnons always drive a DW to the hotter region of a nanowire of magnetic insulators under a temperature gradient. We theoretically illustrate why it is surely so by showing that DW entropy is always larger than that of a domain as long as material parameters do not depend on spin textures. Equivalently, the total free energy of the wire can be lowered when the DW moves to the hotter region. The larger DW entropy is related to the increase of magnon density of states at low energy originated from the gapless magnon bound states. Manipulation of a magnetic domain wall (DW) in a nanostructure has attracted much attention due to its application prospects in logical operations [1] and data storage [2]. Moving DWs in a controlled manner is an important issue in those applications. Magnetic fields via energy dissipation [3][4][5] and electric current via angular momentum transfer [6][7][8] are well-known control parameters for DW motion. To overcome the Joule heating [7] in current driven magnetization reversal, heat itself has recently been proposed [9] as an efficient control parameter for spin manipulation. A temperature gradient can generate spin current [10][11][12] due to electron and/or magnon flow. This thermoelectric phenomenon of spin current generation is called spin Seebeck effect that has been experimentally observed through the inverse spin Hall effect [10]. The spin Seebeck effect has also been suggested [13,14] as a control parameter for DW manipulation. As spin-1 carriers, magnons can mediate a spin transfer torque (STT) [15] on a magnetic texture like a DW in a similar way as the electrons do. It was predicted [13,14] that a thermal-magnon-driven DW can propagate along a wire at a high speed, and this prediction was confirmed in a recent experiment [16].There is little doubt that magnonic STT can drive a DW to move. In terms of DW propagation direction, the pure magnonic STT predicts [15] a DW moving against magnon propagation direction. However, a DW may also propagate along magnon flow direction [17][18][19]. This is very similar to electric-current-driven DW motion: A DW propagates along or against electron flow direction, depending on detailed spin-orbit interactions and DW types [20][21][22]. It is not clear whether magnon-driven "wrong" DW propagation direction shares a similar physics origin as its electron counterpart. In principle, angular momentum does not dictate DW motion since its governing dynamics, Landau-Lifshitz-Gilbert (LLG) equation, does not conserve the total angular momentum when the spin-lattice and spin-orbital interactions are involved. Nevertheless, all studies [13,14,16] showed that a DW propagates to the hotter part of a wire under a temperature gradient. Although this result is consistent with the STT prediction, magnonic STT cannot be the sole physics behind. It is thus * Corresponding author: phxw...

Domain wall motion by localized temperature gradients

“…The DW is inside the TG (∇T (X DW ) = 0) and its motion can be attributed mostly to the ET. [19][20][21] In the Magnonic case the motion could be given by a magnons stream passing adiabatically through the DW, but also by the effect of an averaged ET. Note that thermal magnons, apart from the µST T , also introduce an averaged ET 21,23 : where the temperature is higher, the averaged M s (over more cells) is lower (as in the Entropic case) due to higher thermal fluctuation.…”

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“…This would also allow one to investigate novel phenomena such as domain-wall motion in a magnetic insulator, which is in contrast to the well-established domain-wall motion in conductors, not driven by electronic spin currents [27] but by spin waves [28,29]. Recent results in the field of spin caloritronics have shown that the spin waves can also be thermally excited by the spin Seebeck effect [30] and are capable of moving magnetic domains [31][32][33][34][35]. However, a more detailed analysis of the thermally excited domain wall motion has not been possible, so far, as experimental observations are currently limited only to bulk materials due to the relatively weak signal in YIG.…”

Equations of motion and frequency dependence of magnon-induced domain wall motion

“…14,15 However, a domain wall in a temperature gradient can experience additional torques besides the purely magnonic ones, for instance the exchange stiffness can vary with temperature. 5,[16][17][18][19][20][21] Characteristically, these torques can induce a Walker breakdown, upon which the domain wall is deformed as it moves. 22 In ferromagnets, previous studies of domain wall dynamics due to magnonic torques have considered the response of a static wall to first-order spin-wave excitations.…”