Fig. 3: Anomalous magnetic oscillation in the \(\Delta {\sigma }_{xy}^{{{{{{\rm{PHE}}}}}}}(\phi,H=\pm 9\,{{{{{\rm{T}}}}}})\) of the NIO-227 thin film.
From: Higher harmonics in planar Hall effect induced by cluster magnetic multipoles
a Schematic diagram of the \({{{{\Delta }}}}\,{{{{{\sigma }}}}}_{{{{{xy}}}}}^{{{{{{{{\rm{PHE}}}}}}}}}\left({{{{\phi }}}}\right)\) measurement geometry. In this geometry, I is applied along the \(\left[1\bar{1}0\right]\) direction and Hext is rotated within the sample plane. b \({{{{\Delta }}}}\,{{{{{\sigma }}}}}_{{{{{xy}}}}}^{{{{{{{{\rm{PHE}}}}}}}}}\left({{{{\phi }}}}\right)\) curves at 20 and 2 K. At 20 K, the \({{{{\Delta }}}}\,{{{{{\sigma }}}}}_{{{{{xy}}}}}^{{{{{{{{\rm{PHE}}}}}}}}}\left({{{{\phi }}}}\right)\) curve has a sin (2ϕ) oscillation. At 2 K, the \({{{{\Delta }}}}\,{{{{{\sigma }}}}}_{{{{{xy}}}}}^{{{{{{{{\rm{PHE}}}}}}}}}\left({{{{\phi }}}}\right)\) curve has an inhomogeneous oscillation, indicating a hidden magnetic origin. c Contour plot of all \({{{{\Delta }}}}\,{{{{{\sigma }}}}}_{{{{{xy}}}}}^{{{{{{{{\rm{PHE}}}}}}}}}\left({{{{\phi }}}}\right)\) curves below 30 K. A gradual appearance of the abovementioned peaks can be seen (red region). While the peaks at ϕ = 120° and 300° (green region) exist above T ~ 15 K, the peaks near ϕ = 60°, 180°, 240°, and 340° (red region) appear below T ~ 15 K. d FFT results of all \({{{{\Delta }}}}\,{{{{{\sigma }}}}}_{{{{{xy}}}}}^{{{{{{{{\rm{PHE}}}}}}}}}\left({{{{\phi }}}}\right)\) curves with different T. The FFT intensities of the second, fourth, and sixth harmonics are related to magnetization from the dipole, OM induced by the A2-CMO, and OM induced by the T1-CMO, respectively. The inset shows the temperature dependence of the sixth harmonic below 30 K. Clearly, the sixth harmonic order emerges at 15 K, which indicates the role of the T1-CMO.
