Field-direction control of the type of charge carriers in nonsymmorphic ${\mathrm{IrO}}_2$

In the quest for switching of the charge carrier type in conductive materials, we focus on nonsymmorphic crystals, which are expected to have highly anisotropic folded Fermi surfaces due to symmetry requirements. Following a simple tight-binding model simulation, we prepare nonsymmorphic ${\mathrm{IrO}}_2$ single-crystalline films with various growth orientations by molecular beam epitaxy, and systematically quantify their Hall effect for the corresponding field directions. The results clearly demonstrate that the dominant carrier type can be intrinsically controlled by the magnetic field direction, as also evidenced by first-principles calculations revealing nontrivial momentum dependence of the group velocity and mass tensor on the folded Fermi surfaces and its anisotropic nature for the field direction.

Figure 1

(a) Schematic Fermi surface at half filling for an upper body-centered-tetragonal lattice. (b) Antiferromagnetic spin configuration on sites A and B, and the resultant gapped Fermi surface in the folded Brillouin zone. (c) A rutile structure as an example of nonsymmorphic lattices, where crystallographically nonequivalent sites A and B with opposite ligand configurations are interconnected by symmetry operations of screw rotation and glide mirror. Folded Fermi surfaces with strong anisotropy are then realized near the zone boundary without a gap opening. (d) Energy bands calculated for a nonsymmorphic body-centered-tetragonal model as shown in the inset, where an anisotropic orbital and its ${90}^{\circ }$ rotated one are respectively placed on the two sites to reproduce nonsymmorphicity. Tight-binding parameters $t_a=0.5t,t_b=0.4t,$ and $t_c=-0.8t \left(t<0\right)$ are used, and the Fermi energy $E_{\mathrm{F}}$ is defined as the energy of the half-filled level. (e) Hall coefficient depending on the field direction, derived in the tight-binding model for $t<0$ or $t>0$.

Figure 2

(a) X-ray diffraction $\theta \text{−}2\theta$ scan of an ${\mathrm{IrO}}_2$ film grown on a (110) ${\mathrm{TiO}}_2$ substrate, and (b) rocking curve of the (110) film peak with a full width at half maximum (FWHM) of 65 arcsec. (c) Atomic force microscopy image of a 10 nm (110) ${\mathrm{IrO}}_2$ film. The root mean square (rms) roughness is 0.09 nm. (d) Cross-sectional high-resolution transmission electron microscopy image and (e) its magnified view around the interface. Reciprocal space mappings of (f) (110) and other (g) (100), (h) (001), (i) (101), and (j) (111) oriented ${\mathrm{IrO}}_2$ films, epitaxially grown on the corresponding ${\mathrm{TiO}}_2$ orientations. Crosses denote the respective peak positions calculated from bulk lattice parameters [33, 34].

Figure 3

(a) Longitudinal resistivity of the series of the ${\mathrm{IrO}}_2$ oriented films. (b) Geometry of field directions and film orientations for the Hall measurement. The ${\mathrm{IrO}}_2$ rutile structure is shown in the inset with the same orientation. (c) Field-direction dependence of the Hall resistivity measured at 2 K. (d) Temperature dependence of the ordinary Hall coefficient along the various field directions.

Figure 4

(a) Band structure and (b) in-plane Fermi surface cuts of ${\mathrm{IrO}}_2$, calculated with bulk parameters [34]. Distribution of ${\sigma }_{\alpha \beta \gamma ,i\mathbf{k}}$ on the two Fermi surfaces $\left(i=1,2\right)$, for the cases of applying the field along the (c) [100] and (d) [001] directions. (e) Field-direction dependence of the ordinary Hall coefficient derived from the electronic structure. (f) Comparison between the experimental and theoretical values of the Hall coefficient, plotted for the field-direction vector on the spherical coordinate. A dominant type of charge carrier is intrinsically switched from electron to hole by inclining the magnetic field from the $c$ axis onto the $ab$ plane. The five directions investigated for interpolation are represented by the colored dots.