A Theory for Anisotropic Magnetoresistance in Materials with Two Vector Order Parameters

Abstract

Anisotropic magnetoresistance (AMR) and related planar Hall resistance (PHR) are ubiquitous phenomena of magnetic materials. Although the universal angular dependences of AMR and PHR in magnetic polycrystalline materials with one order parameter are well known, no similar universal relation for other class of magnetic materials are known to date. Here a general theory of galvanomagnetic effects in magnetic materials is presented with two vector order parameters, such as magnetic single crystals with a dominated crystalline axis or polycrystalline non-collinear ferrimagnetic materials. It is shown that AMR and PHR have a universal angular dependence. In general, both longitudinal and transverse resistivity are non-reciprocal in the absence of inversion symmetry: Resistivity takes different values when the current is reversed. Different from simple magnetic polycrystalline materials where AMR and PHR have the same magnitude, and π/4 out of phase, the magnitudes of AMR and PHR of materials with two vector order parameters are not the same in general, and the phase difference is not π/4. Instead of π periodicity of the usual AMR and PHR, the periodicities of materials with two order parameters are 2π.

Anisotropic Magnetoresistance Effect of Intercalated Ferromagnet FeTa3S6

“…It can be seen in this figure that R xx reaches its maximum at θ = 90 °and 270 °, and R xx reaches its minimum at θ = 0 °, 180 °, and 360 °, which means that the magnetoresistance is maximum when the magnetic field is parallel to ab-plane, and the magnetoresistance is minimum when the magnetic field is perpendicular to ab-plane, which is consistent with the property of conventional metal ferromagnets [46]. Experimental data suggest an inversion symmetry for this sample; AMR has a two-fold symmetry and is dominated by M and c-axis when field rotates in ac and bc planes [47]. At low temperatures (approximately below the Curie temperature), the curve has a sharp peak at θ = 90 °and 270 °, and it is caused by the sudden flip of the magnetization when the magnetic field is parallel to the sample [48], which causes the curve not to conform to the form of sin 2 θ.…”

On universal butterfly and antisymmetric magnetoresistances

“…respectively according to the generalized Ohm's law in amorphous or polycrystalline magnetic materials [43][44][45]. R 1 and A 1 are material parameters whose values depends on microscopic interactions.…”

A theory of unusual anisotropic magnetoresistance in bilayer heterostructures

“… is the longitudinal resistivity of the heterostructure when the magnetization is along the y -direction. In addition to the term of for usual AMR and planar Hall resistance 15 , is the newly discovered UAMR that people cast wrongly as 5 although it is mathematically the same as after replacing by , where denotes the unit vector of the current. R and are the amplitudes of one-fold and three-fold angular dependence of unusual planar Hall resistance accompanied the UAMR 3 – 13 .…”

“…This observation is difficult to understand within the SMR theory, but is a natural outcome of the case of in the present theory. The slightly different angular dependence of usual AMR curve can be naturally understood from the contribution of the poor single crystal metal of 15 . Whether is an intrinsic parameter of materials is an interesting question.…”

“…In a short summary, there are experimental ways to distinguish the current theory from the popular SMR theory. One important remark is to exclude the metallic single crystal that will introduce extra contributions to the angular dependences of magnetoresistance 15 .…”