Extraordinary Hall Effect in Freestanding Oxide Heterostructures

: Recently, Topological Hall Effect (THE) has been unravelled in various perovskite iridate, ruthenate and manganite interfaces, suggesting the presence of magnetic Skyrmion-like bubbles. Among the materials and sample structures investigated so far, the physical properties were not free from influences of substrates, which are templates for crystalline epitaxial growth. Dzyaloshinskii-Moriya Interaction or Berry curvatures by the substrates may originate from several structural factors such as in-plane strain, octahedral rotation or terminations. In this report, we employ the water-soluble Sr 3 Al 2 O 6 sacrificial buffer layer to prepare freestanding SrRuO 3 /SrIrO 3 heterostructures with high-quality interfaces, and THE-like humps are observed up to 90 K. Analysing the Hall signal with the rotation of magnetic field direction suggests there are magnetically decoupled regions. This scheme also paves the way for several magnetic texture imaging techniques in transmission mode for future studies.

Among the myriad perovskite oxides available across the Periodic Table, the SrRuO3 (SRO)/SrIrO3 (SIO) interface stands out as the robust candidate for exploring the physics of Topological Hall Effect (THE) 1, 2, 3, 4, 5 . This is true considering their several valuable properties: (i) both the Ru 4+ (4d t2g 4 eg 0 , L=1, S=1) and Ir 4+ (5d t2g 5 eg 0 , Jeff=1/2) are heavy metal cations in perovskite environment contributing strong spin-orbit coupling (SOC). (ii) The bulk SRO has a minority-spin double-exchange mechanism 6 that creates a metallic ferromagnetic ground state with a net moment of ~1.6 µB/Ru and strong perpendicular magnetic anisotropy (PMA) 7 ; yet the bulk SIO is a paramagnetic semimetal due to its low Mott-Hubbard interaction (U) and Hund's coupling (JH) 8,9 . (iii) SRO and SIO perovskites are blessed with optimal Goldschmidt tolerance factor of ~0.9 that facilitates the growth of high quality crystalline ultrathin films and sharp interfaces, easily accessible with a physical vapour deposition technique. Owing to the topologically non-trivial t2g band structure of SRO in k-space 10 , factor (ii) produces a large Anomalous Hall Effect (AHE) below its Curie temperature (TC). Combining factor (i) and (iii) may result in strong interfacial Dzyaloshinskii-Moriya Interaction (DMI) 11,12 and may host Neel-type magnetic Skyrmions 13,14,15 , which are distinct to the Bloch-type ones arisen from bulk inversion asymmetry 16 .
Thus far, the origin of the hysteretic antisymmetric humps in Hall Effect is subjected to debates. On the one hand, Bruno first derived the theory of THE from a real-space Berry curvature perspective. At a Skyrmion phase, by assuming a strong Hund's coupling between the free electrons' spin and local moments, a Berry phase is gained during the hopping process of free electrons across non-collinear spin textures 17,18 . Nakazawa further improvised the theory by accounting for Mott-Hubbard interaction and weak Hund's coupling 19 . Note that this can be generalized to any non-collinear moments 20 where sgn(A1)=-sgn(A2), HC1≠HC2 and J1≠J2. The latter is coined as the "Bi-Langevin" interpretation here, and it has been perceived to not containing THE signal but merely a mathematical artefact from two AHE signals 23,24 , either intrinsic or extrinsic. An example is illustrated in supplementary Fig S1a- First, we compared the properties among three samples structures (Fig. 1a, 3a, 3c), with the details of sample fabrication are clarified in Methods. In Figure 1a, the AHE and hump signals are present in both structures A and B, yet their low temperature (ground state) AHE have opposite signs. The low-temperature negative AHE in structure A is consistent with the reported behaviours for SIO/SRO bilayers and SRO single layer 1, 4 . This can likely be attributed to the minority spin double-exchange mechanism in bulk SRO with threefold-degeneracy ( Fig. 1c, left). Since the mobile electron's spin is opposite to the local magnetization, we may expect a negative spin polarization q = , which has been reported to be -9.5% at 0.31 K 28 . However, the AHE sign-reversal at a higher temperature (near TC) can be understood as thermally-driven EF shifting across band structure anti-crossings 29,30 , which are gaps opened by SOC acting as sources/sinks of Berry curvature 31,32 . On the other hand, the ultrathin SRO layer grown on SIO in structure B has more severe carrier localization (Mott-insulating) and }~ orbital is theorized to have reduced intra-site Coulomb repulsion compared to }•,~• orbitals, lifting their degeneracy 33,34 . The Ru 4+ electronic configuration is hence fixed at "ferro-orbital" } Next, the quality of the freestanding structure is carefully optimized. Preliminary experiments indicated prolonged exposure to water might deteriorate the sample quality, probably due to oxygen vacancy migration. Hence, a good strategy is to minimize the float time of samples in water (5-10 minutes), before scooping out onto respective supports.
This requires the SAO sacrificial layer to be thick enough (100 nm) for fast water dissolution, yet maintaining layer-by-layer growth with a surface roughness of ~0.16 nm.
We speculate that the ultrathin SRO/SIO structures A-C be too fragile for convenient scooping during the water dissolution process. Thus a 40-nm-thick STO buffer is inserted above SAO as a mechanical support. Its thickness is optimal to produce elongated flakes convenient for Hall bar fabrication, above which the flakes would roll along their short axes due to imbalanced surface tension (Fig. 2a), similar to reference 37 . The rolls would inhibit successful photolithography and Cu electrode lift-off since their Van der Waals adhesion with the SiO2//Si substrate is weak, hence undesirable. Finally, after transferring onto the SiO2//Si substrates (Fig. 2b), the flakes maintained a smooth topography of ~0.23 nm roughness.
To obtain a sufficiently strong signal in magnetometry measurement, we exfoliated a large (mm-scale) flake of structure Cf by attaching the sample surface to a Kapton tape before immersing into the water; nevertheless, the large flake contains countless cracks due to strain relaxation (Fig. 2c). A clear TC~100 K can be inferred from the moment versus temperature (M-T) curves (Fig. 2d, left panel), where the bifurcation between field-cooled (FC) and zero-field-cooled (ZFC) M-T curves is similar to SRO films having a competition between ferromagnetic and antiferromagnetic interaction between Ru 4+ . In the moment versus field (M-H) loops (Fig. 2d, right panel), clear double-hysteresis loops can be seen at a low temperature of 20 K, with the wider coercive field µoHC~1 T, which is similar to the HC of Hall Effect to be discussed in Fig. 3g . S2). Surprisingly, large continuous flakes can be produced with few cracks, yet the magnetic property is completely diminished, likely due to chemical reaction with the acid.
Next, Cu electrodes are patterned onto freestanding flakes Af, Bf and Cf by standard photolithography and lift-off, as shown in Fig. 3a Fig. S3c-d).
The "Bi-Langevin" interpretation is perhaps incomplete to decipher the mystery of the hump signals -doubts still arise in the reason of decoupling between L1,2 at the hump's emergence, and their sensitivity towards the magnetic field direction. Therefore, it would be insightful to study the Hall Effect evolution by rotating the external magnetic field direction from out-of-plane (Hz, θ=0 o ) to in-plane (Hy, θ=90 o ) (schematic in Fig. 4b, inset).
As seen in Fig. 4a