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Resistivity Due to Domain Wall Scattering
Levy, P.M. & Zhang, S., 1997. Resistivity due to Domain Wall Scattering. Phys. Rev. Lett. 79, 5110
Essay about this article
The study of GMR evolved rapidly since its discovery to encompass effects in which spin currents, rather than charge currents, played the dominant role. To distinguish these from other electrical transport phenomena a new word, “spintronics,” was coined. Spintronics denotes control of current through the spin of an electron in contradistinction to electronics, which denotes control of current through the charge of the electron. At first the word magnetoelectronics was tried, but it readily gave way to spintronics. Under this new banner came all effects where the electron’s spin played a role in controlling the current, e.g., GMR, TMR, and current driven spin torque.
The new focus on spin currents also reopened some long-standing, unresolved issues. One of them was the increase in resistivity of a ferromagnetic metal when domains are formed in the bulk of the metal. Domains are regions where the magnetic moments of the atoms are aligned in parallel; they are separated from other domains, where the magnetization is at an angle to the domain under consideration, by a domain wall. Within a wall the magnetic moments continuously rotate between the magnetization of the adjacent domains. In the 1960’s experiments on iron whiskers [a pure form of iron with few impurities, in the shape of a needle] showed that when one applied an external field strong enough to saturate the magnetization of the whisker, and thereby erase the domains, the resistivity decreased. The existence of domains arises from a competition between exchange energy--which favors parallel, collinear, alignment of moments--and the magnetostatic, or magnetic dipole-dipole energy, which favors non-collinear arrangements. Whiskers are elongated objects such that domains form with their magnetization aligned parallel or antiparallel to the major axis of the needle. It is this configuration that minimizes the leakage of magnetic flux emanating from the whisker and thereby the magnetostatic energy [2]. As the resistivity of an iron whisker is considerably smaller than the resistivity of bulk iron, even the small difference in the resistivity between the whisker with and without domains was enough to produce a large MR ratio. Ratios can be deceptive and often differences in resistivity are more relevant than ratios.
Initially, explanations for this magnetoresistive effect focused on two aspects of conduction across a domain wall; first, the scattering at the boundary at the interfaces between the wall and domains and, second, from the effects “due to the zigzagging character of the electron orbits when going between up and down regions of the magnetization.[1]” The first was estimated to be relevant only for very narrow domain walls on the order of several angstroms. While most walls were considerably wider; the extremely low resistivity of whiskers is indicative of little electron scattering in the domains, so that the effect of zigzagging of electron orbits may be relevant for domain walls producing resistance. However, for most bulk ferromagnetic metals the resistivity is considerable larger, so that the latter mechanism is not a viable candidate for producing the resistivity associated with domain walls.
Domain Wall Resistivity (DWR), as its now know, received new attention in 1996 when experiments were performed on thin films of cobalt where workers were able to obtain definitive data on the resistivity created by these walls [3]. The explanation proposed was that scattering of conduction electrons by domain walls is due to a combination of (1) how well the precessional behavior of the carrier spins allows it to track the changing local exchange field direction as it traverses the wall, and (2) the same type of spin dependent scattering due to impurities that gives rise to, among other things, giant magnetoresistance. In 1997, later Shufeng Zhang and I picked up on the explanation given by Gregg, et al. and developed an alternative view that explained the increase in resistivity by using their ingredients, but a different formalism. In our picture the continuously rotating background magnetization induced an admixture of the opposite spin in each of the two spin channels, i.e., admixtures in the wavefunctions for the electrons in the two channels. This has the effect of diminishing the difference in resistivities between the channels and thereby decreasing the short-circuit effect that exists for the current within the domains where the two spin channels are not mixed.
[1] G. G. Cabrera and L. M. Falicov, Phys. Status Solidi (b) 61, 539 (1974); ibid 62, 217 (1974).
[2] Depolarization factors are used to discuss the electric and magnetic polarization of continuous media, i.e., bulk materials. They are used to calculate the difference between the external field applied to a sample and the internal field felt by the electric or magnetic moments inside; microscopically it arises from the electric and magnetic dipole-dipole energy.
[3] J. F. Gregg, W. Allen, K. Ounadjela, M. Viret, M.Hehn, S.M. Thompson, and J.M.D. Coey, Phys. Rev. Lett. 77, 1580 (1996).
Discussion Question
What differentiates electron scattering in domain walls from the scattering in the domains themselves?
The above article is reprinted with permission from the author(s) of Levy, P.M. & Zhang, S., 1997. Resistivity due to Domain Wall Scattering. Phys. Rev. Lett. 79, 5110. Copyright (1997) by the American Physical Society. Readers may view, browse, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modified, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the American Physical Society.
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