Fig. 1: Schematic illustration of the in-plane Hall effect in rutile (1 1 1) films.
From: Unveiling an in-plane Hall effect in rutile RuO2 films
a Illustration of the two different Cartesian coordinate systems, P- and L-frames. The bases of the P-frame, {\({\hat{{{\boldsymbol{e}}}}}_{{{\mathbf{{1}}}}}^{{{\boldsymbol{P}}}},{\hat{{{\boldsymbol{e}}}}}_{{{\mathbf{{2}}}}}^{{{\boldsymbol{P}}}},{\hat{e}}_{{{\mathbf{{3}}}}}^{{{\boldsymbol{P}}}}\)}, are formed by the orthogonal crystallographic a, b, and c axes, and those of the L-frame, {\({\hat{{{\boldsymbol{e}}}}}_{{{\mathbf{{1}}}}}^{{{\boldsymbol{L}}}},{\hat{{{\boldsymbol{e}}}}}_{{{\mathbf{{2}}}}}^{{{\boldsymbol{L}}}},{\hat{e}}_{{{\mathbf{{3}}}}}^{{{\boldsymbol{L}}}}\)}={\({\hat{{{\boldsymbol{e}}}}}_{{{\boldsymbol{x}}}},{\hat{{{\boldsymbol{e}}}}}_{{{\boldsymbol{y}}}},{\hat{{{\boldsymbol{e}}}}}_{{{\boldsymbol{z}}}}\)}, are defined by the (1 1 1) facet, for which transport measurements were performed. \({\hat{{{\boldsymbol{e}}}}}_{{{\mathbf{{3}}}}}^{{{\boldsymbol{L}}}}=\,{\hat{{{\boldsymbol{e}}}}}_{{{\boldsymbol{z}}}}\) in the L-frame is close to the [1 1 2] direction of the rutile structure due to a = b ≈ √2 c. b, c Illustrations of the Hall-resistivity vector ρHall (b) without and (c) with an out-of-plane (oop) component when the magnetic field is applied along the [1 ‒1 0] (y-axis) and [‒1 ‒1 2] (x-axis) directions, respectively.
