You would think that, by now, we would have figured out basically all there is to know about comparatively simple metals conduct electricity, even in the presence of a magnetic field. I mean, Maxwell and Faraday etc. were figuring out electric and magnetic fields a century and a half ago. Lorentz wrote down the force on a moving charge in a magnetic field in 1895. The Hall Effect goes back to 1879. Sommerfeld and his intellectual progeny laid the groundwork for a quantum theory of electronic conduction starting about a hundred years ago. We have had good techniques for measuring electrical resistances (that is, sourcing a current and measuring the voltage differences between different places on a material) for many decades, and high quality magnets for around as long.
Surprisingly, even in very recent times we are still finding out previously unknown effects that influence the resistance of a metal in a magnetic field. Let me give you an example.
I'd written here about the spin Hall effect and its inverse, which were only "discovered" relatively recently. In brief, because of strong spin-orbit coupling (SOC) effects on the electronic structure of comparatively heavy metals (Pt, Ta, W), passing a current through a thin film strip of such a material generates a spin current, leading to the accumulation of spin at the top and bottom of the strip. If those interfaces are in contact with magnetic materials, exchange processes can take place so that there is a net transfer of angular momentum between the metal and the magnetic system.
There is actually a correction to the resistance of the SOC metal: The spin accumulation can lead to a diffusive spin current between the top and bottom surfaces, which (thanks to the inverse spin Hall effect, ISHE) gives an additive kick to the charge current (and effectively lowers the resistance of the metal from what it would be in the absence of the spin Hall physics). If the top and bottom interfaces are in contact with a magnetic system and therefore affect the spin accumulation, that correction can be modified depending on the orientation of the magnetization of the magnetic material, leading to the spin Hall magnetoresistance.
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| Spin Hall/inverse spin Hall resistive correction, adapted from here. |
That's not the end of the story, however. Even without an adjoining magnetic material, there is an additional magnetoresistive correction, \(\delta \rho(\mathbf{H})\) to the resistivity of the SOC metal. If the magnetic field has a component transverse to the direction of the SHE accumulated spins, the spins will precess about that field, and that can affect the ISH correction to the resistivity. This was predicted in 2007 by Dyakanov (arxiv, PRL), and it was found experimentally several years later, as reported in PRL (arxiv version here). There are readily measurable effects in both the longitudinal resistivity \(\rho_{xx}\) (voltage measured along the direction of the current) and the transverse resistivity \(\rho_{xy}\) (voltage measured transverse to the current, as in the Hall effect, but this holds even when the external magnetic field is in the plane of the film).
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| Hanle magnetoresistance idea, adapted from here. |
This correction is called the Hanle magnetoresistance.
(Aside: There is some interesting scientific history behind the name. Hanle was the first to explain an atomic physics optical effect, where the precession of magnetic moments of a gas of atoms in a magnetic field affects the polarization of light passing through the gas. In condensed matter, the name "Hanle effect" shows up in discussions of spin transport in metals. The first time I ever encountered the term was in this paper, which foreshadows the discovery of giant magnetoresistance. A ferromagnetic emitter contact is used to inject spin-polarized electrons into a non-magnetic metal, aluminum. Those electrons diffuse over to a second ferromagnetic collector contact, where their ability to enter that contact (and hence the resistance of the gadget) depends on the relative alignment of the spins and the magnetization of the collector. If there is a magnetic field perpendicular to the plane of the device, the spins precess while the electrons diffuse, and one can analyze the magnetoresistance to infer the spin relaxation time in the metal.)
One of my students and I have been scratching our heads trying to see if we really understand the Hanle magnetoresistance, which we have been measuring recently as a by-product of other work. I think it's pretty amazing that we are still discovering new effects in something as simple as the resistance of a metal in a magnetic field.
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