Post-synthesis control of Berry phase driven magnetotransport in ${\mathrm{SrRuO}}_3$ films

Controlling electronic band structure is an important step toward harnessing quantum materials for practical uses. This is exemplified in the spin-polarized bands near the Fermi level of a ferromagnet where small variation to the Berry curvature can be used to control the intrinsic anomalous Hall effect (AHE). Since these pathways are highly sensitive to crystal structure, iterative post-synthesis manipulation of the underlying lattice can act as a fundamental probe and provide new opportunities for functionalization. In this work, depth-dependent magnetic inhomogeneity in a $4d$ itinerant ferromagnet ${\mathrm{SrRuO}}_3$ film is controlled by applying low energy He ion irradiation. Combined magnetometry, polarized neutron reflectometry, and magnetotransport experiments demonstrate that the Berry phase and associated AHE can be continuously and iteratively modified post-synthesis. The findings of this work should be widely applicable to other quantum materials where crystal distortions and symmetry are tightly bound to band structure and resulting Berry phase effects.

Figure 1

(a) Illustration of the octahedral rotations of ${\mathrm{SrRuO}}_3$ in the orthorhombic ($M$-SRO) and tetragonal ($T$-SRO) phases. (b) Epitaxial relationship between the $M$-SRO and pseudocubic (pc) indices. (c) $\theta –2\theta$ scans of the ${\mathrm{SrRuO}}_3$ thin films grown on ${\mathrm{SrTiO}}_3$ (001) substrates with different helium dosages. (d) The out-of-plane lattice parameter changes as a function of the helium dose labeled according to the pseudocubic unit cell as $c_{\text{pc}}$. (e) Reciprocal space map around the ${\left(103\right)}_{\text{pc}}$ reflection of the as-grown sample is consistent with the typical orthorhombic phase, whereas (f) a nearly full transition to the undistorted tetragonal phase is indicated with the largest lattice expansion.

Figure 2

(a) Resistivity ${\rho }_{\text{xx}}$ and (b) saturation magnetization $M_{\text{S}}$, are shown as a function of temperature, in addition to (c) the ferromagnetic Curie temperature $T_{\text{C}}$ determined from ${\rho }_{\text{xx}}\left(T\right)$.

Figure 3

Hall effect measurements of as-grown and helium irradiated ${\mathrm{SrRuO}}_3$ films. Definitions for the anomalous Hall resistivity ${\rho }_{\text{AHE}}$ and coercive field $H_{\text{C,AHE}}$ are indicated at curves for the as-grown film measured at 10 K. Note the scale differences labeled on the vertical axis, and curves at different temperatures are shown with a constant offset for clarity.

Figure 4

The (a) zero crossing of the AHE with applied magnetic field, $H_{\text{C,AHE}}$, (b) ${\rho }_{\text{AHE}}$, and (c) peak amplitude of the hump-like feature ${\rho }_{\text{M}}$ are shown for as-grown and helium irradiated films. (d) Detailed temperature scans of the largest lattice expanded film for $T\sim T_{\text{R}}$ showing the clear hump-like feature.

Figure 5

A comparison of the normalized magnetization and anomalous Hall resistivity at (a) 10 K and (b) 60 K for helium irradiated ${\mathrm{SrRuO}}_3$ with the largest lattice expansion. Illustration of multicomponent field-dependent reversal of the (c) magnetization and (d) Hall effect resistivity for two arbitrary superimposed components with opposite sign anomalous Hall coefficient and different magnetic coercivities.

Figure 6

Polarized neutron reflectometry (PNR) of helium irradiated ${\mathrm{SrRuO}}_3$. The experimental and fitted normalized (a) neutron reflectivity ($R/R_{\text{F}}$) and (b) spin asymmetry ($SA$). (c) Illustration of the PNR experiment, and inhomogeneous magnetization profile of helium irradiated ${\mathrm{SrRuO}}_3$ film. (d) The best fit of the depth-dependent nuclear density and magnetization profiles. Further detail of the fitting method used to obtain the result in (d) can be found in SM Sec. 3 [41].

Figure 7

Anomalous Hall effect sign reversal modeled using the depth-dependent magnetic profile obtained from neutron experiments. (a) ${\rho }_{\text{xy}}$ of the surface and interface components which define the limits of the profile distribution of the model (at 60 K), and (b) shown for all temperatures where the black line indicates the film average identical to Figs. 4 and 4. (c) Comparison of the experimental Hall effect measurement for the ${\mathrm{SrRuO}}_3$ film with the largest $c_{\text{pc}}$-axis expansion, and the model from the PNR-derived inhomogeneity profile, and distribution in ${\rho }_{\text{xy}}$ and $H_{\text{C}}$ from (b).