Crystal Symmetry-Dependent In-Plane Hall Effect
Abstract
The Hall effect has played a vital role in unraveling the intricate properties of electron transport in solid materials. Here, we report on a crystal symmetry-dependent in-plane Hall effect (CIHE) observed in a CuPt/CoPt ferromagnetic heterostructure. Unlike the planar Hall effect (PHE), the CIHE in CuPt/CoPt strongly depends on the current flowing direction (ϕ$_I$) relative to the crystal structure. It reaches its maximum when the current is applied along the low crystal-symmetry axes and disappears when applied along the high crystal-symmetry axes, exhibiting an unconventional angular dependence of cos(3ϕ$_I$). Utilizing a symmetry analysis based on Invariant Theory, we demonstrate that the CIHE could exist in magnetic crystals with C$_3$$_v$ symmetry. Using a tight-binding model and realistic first-principles calculations on the metallic heterostructure, we find that the CIHE originates from the trigonal warping of the Fermi surface. Our observations highlight the critical role of crystal symmetry in generating novel Hall effects.
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