Thickness-dependent, tunable anomalous Hall effect in hydrogen-reduced PdCoO₂ thin films

Ferromagnetic materials exhibit anomalous Hall effect (AHE), which is an extra contribution added to the ordinary Hall effect and is usually proportional to their magnetization (thus frequently hysteretic). One of the common characters of any AHE is its well-defined sign: depending on how its magnetization couples with the mobile carriers, AHE can be either positive or negative against the applied external magnetic field. In clean materials, the net Berry curvature, integrated at the Fermi level of the materials band structure, determines the sign of AHE. However, in materials with structural disorders or impurities, both magnitude and sign of AHE can be dominated by extrinsic factors such as defect scattering. Regardless, in most ferromagnetic materials, the AHE sign is not switchable, but certain materials such as SrRuO₃ [1], chiral magnets [2, 3, 4], and magnetic topological insulators [5, 6], can exhibit AHE sign reversal depending on external stimulations.

The non-magnetic, metallic delafossites PtCoO₂ and PdCoO₂ are the most conducting oxides, with PdCoO₂ having the longest mean free path of 20 $\mu$m among oxides [7, 8]. Although PdCoO₂ is not magnetic, it exhibits itinerant surface magnetism [9, 10, 11], and recent work on hydrogenated PdCoO₂ reported the emergence of bulk magnetism with strong perpendicular magnetic anisotropy (PMA). It was shown that these hydrogenated films exhibit sign change of AHE with hydrogenation parameters [12, 13], likely due to structural changes when PdCoO₂ is reduced. Here, we expand on this previous study with comprehensive experiments on over 80 hydrogenated PdCoO₂ samples of various thickness and find that as the film gets thicker, PMA gradually turns into in-plane magnetic anisotropy (IMA) and the sign-tunability of AHE also disappears.

We grew PdCoO₂ films on Al₂O₃ (0001) substrates using oxygen plasma assisted molecular beam epitaxy (MBE) [14]. The films were grown at 300 ^∘C in a background pressure of $4\times 10^{-6}$ Torr plasma oxygen in a layer-by-layer fashion. Plasma is generated using a 13.6 MHz RF source at a power of 450 W. After the growth, hydrogenation is carried out at ambient pressure by annealing in a 10% H₂/90% Ar mixture gas at various temperatures for different duration. All thickness values correspond to the nominal PdCoO₂ thickness. Transport measurements were carried out using standard DC van der Pauw technique.

In Figure 1, we demonstrate the effects of anneal temperature and film thickness on the magnetic and transport properties of the PdCoO₂ films. Previously, annealing time ($t_{A}$) and temperature ($T_{A}$) were used to switch the AHE sign [12]. Here we use T_A as the main tuning parameter. Except for the thinnest film (3.5 nm), no sign change occurs for T_A $<$ 100 ^∘C. With slightly higher T_A ($\sim$100 - 200 ^∘C), AHE with positive sign appears (positive AHE is defined as R${}_{xy}^{sat}>0$ for H$>0$). With higher T_A, positive AHE abruptly switches to negative in films with thickness up to 25 nm. At even higher anneal temperatures, the AHE sign reverses back to positive. Robust PMA with well-defined coercive fields is present in films with thickness up to 25 nm. As the film gets thicker than 25 nm, the AHE shows only IMA behavior and no switching is observed. The switching behavior is generally reproducible across many samples and anneal parameters. For example, in the case of the 9 nm thick film shown in Figure 1, annealing at 100 ^∘C leads to AHE with positive sign and robust PMA. When this film is annealed at 200 ^∘C, the AHE sign becomes negative, the shape of the curve changes and the coercive field becomes larger. After annealing at 300 ^∘C, the $R_{xy}$ value shrinks significantly, and although the sign is positive, hump-like features are present suggesting that there are two competing channels with different AHE signs [15, 16]. When annealed at 400 ^∘C, the AHE sign becomes positive, and the coercivity is also enhanced compared to annealing at 100 ^∘C.

Rutherford backscattering, x-ray photoelectron spectroscopy and x-ray diffraction show reduction of the films to a Pd-Co alloy state after hydrogenation [12], which explains the emergence of PMA and AHE behavior. However, unlike traditional PdCo alloys, hydrogenation of PdCoO₂ is unique due to intermixing of Pd and Co along with with trace amounts of oxygen and hydrogen and a novel layered structure can also be realized [12]. This may be why the PMA is present in thinner films only. In general, the strength and direction of magnetic anisotropy is determined by many factors such as the crystalline environment (magnetocrystalline anisotropy), strain (magnetostriction), interface and shape [17, 18]. In the case of Pd/Co multilayers, layer thickness and interface have been found to play critical roles in the development of PMA. A recent study of PdCo alloys found that the surface anisotropy contribution is dominant in thinner films, while shape and magnetoelastic anisotropy dominates thicker films, which can be used to change between IMA and PMA [19]. In a similar manner, the differences in the hysteretic behavior across thickness in our films may be due to similar nanostructural changes resulting from the annealing process.

These results suggest that there may be a continuous transformation of AHE across T_A: initially a positive AHE appears, changes to negative with higher T_A, then changes back to positive with even higher T_A. There are some minor changes in the overall squareness of the curves, but the PMA is preserved. The fact that sign change is limited to thinner films suggests a potentially large role played by interfaces. To understand the sign change, we may consider two competing channels corresponding to the two signs. Initially a positive channel is largely responsible for the positive AHE. After extended annealing, the negative channel dominates and results in a net negative AHE. Finally, with more annealing, the same (or different) positive channel results in positive AHE. To understand this, we discuss how AHE varies across measurement temperatures for the different annealing conditions, i.e. across each of the different AHE signs.

In Figure 2(a), we show the variation in positive and negative AHE across measurement temperatures in 9 nm thick samples. At the lowest anneal temperature of 100 ^∘C, AHE is positive and $|\rho_{xy}|$ increases with temperature. At T_A = 200 ^∘C, AHE is negative, but $|\rho_{xy}|$ decreases with temperature, which is opposite to the previous case. With an even higher anneal temperature of 400 ^∘C, the AHE switches to positive and $|\rho_{xy}|$ increases with temperature. When $\rho_{xy}$ values for each T_A are compared to the lowest measured temperature, as shown in Figure 2(b), we find that at a field of 1 T, where $\rho_{xy}$ is saturated, samples at all anneal temperatures show similar response. This quantity, which we define as $\Delta\rho_{xy}^{1T}=\rho_{xy}^{1T}(T)-\rho_{xy}^{1T}(10K)$, shows that although the overall sign of AHE is different between the different anneal conditions, temperature-dependent contribution to AHE remains little changed. This suggest that there are at least two distinct mechanisms responsible for the observed AHE. One is the temperature-independent part, whose sign depends strongly on the annealing parameter, and the other is the temperature-dependent contribution, which always remains positive and grows with temperature, and is little dependent on the annealing conditions. It should be noted that the Curie temperature (T_C) of these films are beyond room temperature [12], and the appearance of two contributions may be a result of two different scattering channels.

Sign change in AHE was previously reported in a few materials including elemental metals [20, 21] and multilayers [22], but its origin is not always clear. Sometimes, such a sign change can occur when the dominant contribution for AHE changes between extrinsic and intrinsic mechanism [23]. Disorder can also strongly influence carrier scattering and lead to changes in AHE [24, 25, 26], which includes examples such as the metallic oxide SrRuO₃ [15, 16, 27, 28], intermetallic alloys such as MnGa [29] and magnetic topological insulators [5, 6]. Considering that the bands in hydrogen-reduced PdCoO₂ are derived from Pd and Co states, and since the film structures are intermediate between single-crystalline and polycrystalline, the sign change of AHE is likely a combined result of both extrinsic (scattering) and intrinsic (Berry curvature) mechanisms. The resistivity of our films lie close to the region where crossover between extrinsic and intrinsic mechanisms occurs [20], providing another hint that the two competing channels may be due to different mechanisms. Also, the fact that thickness plays a role shows that the interfaces may have an important contribution and, as evidenced from Figure 1, thickness and PMA may also be correlated and the sign change may be dependent on the PMA. Yet, considering the structural complexity of these films, it will be difficult to pinpoint the exact origin of the sign change. Regardless, the very fact that the desired AHE sign can be reproducibly achieved with a simple annealing procedure suggests that this effect may be harnessed in this material for further studies on AHE and/or applications. Similarly, it would be interesting to examine the extrapolation of these results to similar systems.

The longitudinal resistivity ($\rho_{xx}$) values with different T_A for the hydrogen-reduced films are shown in Figure 3(a). In general, the hydrogenated films are more resistive than pristine PdCoO₂ [14]. It is also notable that the residual resistivity ratio (RRR), defined as $RRR=\rho(295K)/\rho(10K)$, is substantially reduced after hydrogenation. Quantitatively, while RRR in pristine PdCoO₂ thin films grows with thickness and reaches about 16 at 100 nm, it is relatively constant at about 1.2 $\pm$ 0.1 for all the hydrogenated films, regardless of thickness. Both increased resistivity and reduced RRR after hydrogenation show that the hydrogenated films have substantially higher level of defect scatterings than the pristine films. Furthermore, as shown in Figure 3(b), $\rho_{xx}$ is usually higher for negative AHE, suggesting that the additional scattering channel responsible for the higher resistivity is responsible for the negative AHE. Figure 3(c,d) compiles the relationship between thickness, anneal temperature and AHE which provides a guide to tune the sign and magnitude of AHE in different films by varying the anneal parameter T_A. It is notable that negative AHE can show up only within a narrow region of the phase space.

In summary, we showed that below a critical thickness of about 25 nm, magnetic and electronic properties of the hydrogen-reduced PdCoO₂ films can be effectively tuned with the annealing temperature. Then, beyond the critical film thickness, PMA with sign tunable AHE changes to IMA with a fixed sign of AHE. Competitions between different scattering mechanisms, coupled with out-of-plane anisotropy, may lead to the AHE sign change.

This work is supported by National Science Foundation (NSF) Grant No. DMR2004125 and Army Research Office (ARO) Grant No. W911NF2010108. We thank Shriram Ramanathan for helpful discussions.