Role of interface quality for the spin Hall magnetoresistance in nickel ferrite thin films with bulk-like magnetic properties

The advent of (spin) angular momentum transport without an accompanying charge current, i.e., the flow of pure spin currents, has led to the discovery of several remarkable effects that are relevant for next generation spin electronic devices.^1–3 Among these effects is the spin Hall magnetoresistance (SMR)^3–9 in magnetically ordered insulator (MOI)/normal metal (NM) heterostructures, which enables the detection of novel magnetic phases in MOIs.^10–12 While initial investigations of the SMR heavily relied on yttrium iron garnet (YIG), reports on the observation of the SMR in many other MOIs ranging from ferrimagnetic^5,13,14 to antiferromagnetic^15–19 order confirm the universality of this effect. The magnitude of the SMR effect crucially depends on the transparency of the MOI/NM interface, as well as the spin Hall effect (SHE) and the spin diffusion length of the NM. Nevertheless, there are only a few publications dealing with the impact of the interface quality on the SMR response.^20,21 In this publication, we experimentally investigate the SMR amplitude in nickel ferrite thin films with bulk-like magnetic properties²² interfaced with Ta or Pt and find that the interface quality affects the resistivity as well as the SMR amplitude in NFO/Pt heterostructures.

The heterostructures investigated in this study are NFO/NM bilayers, where the NM is Pt and Ta. The ferrimagnetic NFO thin films (≈ 100 nm) are grown on (001)-oriented MgGa₂O₄ (MgGO) substrates via pulsed laser deposition. The bulk MgGO single crystals were grown by the Czochralski method at the Leibniz-Institut für Kristallzüchtung, Berlin, Germany,²³ and those substrates were then polished and formatted by CrysTec GmbH, Berlin, Germany. During the film growth, the substrate was kept at $700° C$ in an oxygen atmosphere with 10 mTorr. For the magnetotransport experiments, we defined NM Hall bar structures on top of the NFO with a width of 80 μm and a length of 800 μm via optical lithography, sputter deposition of the NM, and lift-off. For the NMs, we used Ta and Pt layers, that were deposited ex-situ in an ultrahigh vacuum sputtering system with a base pressure of 2 × 10^–9 mbar. The deposition was carried out in an argon atmosphere at 5 × 10^–3 mbar and a growth rate of 2 Å/s for both materials. The magnetotransport experiments were carried out in two superconducting magnet cryostats at temperatures T ranging from 5 K to 300 K. One transport setup is based on a 2D-vector magnet with magnetic fields limited to μ₀H = 7 T and a second has full 3D magnetic field vector control (⁠$μ0H≤2.5 T$⁠). For the resistance measurements, we applied a DC of 10 μA to the Hall bar and measured the longitudinal DC voltage drop. To rule out any spurious thermal voltages, we utilized the current reversal technique as detailed in Refs. 24 and 25 and in the supplementary material.

As a first step, we investigated the orientation of the sputter deposited Pt layer on top of the NFO layer on (001)-oriented MgGO substrates by x-ray diffraction using a reference sample with a blanket 10 nm thick Pt film. The obtained results for the 2θ-ω scan are shown in Fig. 1(a). The sample exhibits peaks from the (001)-oriented NFO thin film and the low intensity (111)-peak of Pt suggests that Pt grows (111)-textured on top of the NFO layer. Due to the low intensity of the Pt peak, we were unable to investigate any in-plane epitaxial relationship between Pt and NFO. For a Ta reference sample, no peaks originating from the Ta layer were found, thus we do not have information on the growth of Ta on our NFO thin films.

For the magnetotransport experiments, we utilized two differently oriented NM Hall bars with respect to the crystalline orientation of the NFO layer, as illustrated in Fig. 1(b). This allows us to investigate the SMR for two different current directions: along the [100]-direction and the [110]-direction of NFO. For the study of the SMR in these samples, we used angle-dependent magnetoresistance (ADMR) experiments.²⁶ In the ADMR experiments, an external magnetic field with a fixed magnitude μ₀H is applied to the sample, while measuring the longitudinal resistivity ρ_long of the Hall bar as a function of the orientation of the magnetic field direction h = H/H. In our experiments, we rotated the external magnetic field in several planes to investigate the observed magnetoresistance (MR). The first plane is the in-plane (ip) rotation of the external magnetic field, where α is defined as the angle between the charge current direction and h [see the inset in Fig. 2(a)]. Four more rotation planes have been used in these experiments. Two rotation planes perpendicular to the two charge current directions [oopj, with β defined in the inset of Fig. 2(b)] and two rotation planes residing in the plane defined by each charge current direction and the surface normal [oopt, with γ defined in the inset of Fig. 2(c)]. We determined the minimum value of ρ_long for each ADMR measurement and calculated the relative MR amplitude as the difference with respect to this minimum value divided by this value.

In Fig. 2, we show the ADMR results obtained for Pt(3.5 nm) and Ta(5 nm) Hall bars on NFO(100 nm) thin films at 300 K and μ₀H = 2.5 T. We first look into the MR response of the Pt Hall bars for the in-plane rotation plane [see Fig. 2(a)]. Clearly, for both Hall bars, we observe two maxima and two minima over the full $360°$ rotation and the MR follows a sin²-dependence. For both current directions, we observe maxima in the MR for $h ⊥ t$ and minima for $h∥t$⁠, in agreement with the SMR theory.^3,8,9 However, the extracted maximum MR for the two current directions is different: for j along the NFO [100]-direction, we find a maximum MR of 8.1 × 10^–4, while for j along the NFO [110]-direction, we obtain 1.2 × 10^–3. This is a 50% change in the maximum MR for these two current directions and appears to relate to a difference in the interface morphology depending on the position of the Hall bar on the sample and not on the current direction. This difference in the interface morphology is also correlated with a change in Pt resistivity, as discussed further below. In addition, the MR for the [110]-direction is comparable to SMR values obtained for YIG/Pt heterostructures, where the current was oriented along the $[11¯0]$- and the $[12¯1]$-directions of the YIG film.^3,5

To further investigate whether the increase in the maximum MR for the in-plane rotation for j along the NFO [110]-direction is only due to the SMR, we also conducted ADMR experiments in the oopj- and oopt-configuration for both charge current directions. These results are shown in Fig. 2(b) for the oopj-configuration and in (c) for the oopt-configuration. For the oopj-configuration, we see that the MR does not follow a typical $cos2$-dependence, which can be explained by the large uniaxial anisotropy with the hard axis along the surface normal for NFO.²² Thus, for the applied field of 2.5 T, it is not possible to fully align the magnetization direction m along the out-of-plane direction. Nevertheless, we observe distinct maxima for $h ⊥ t$ and minima for $h∥t$⁠. Again, we observe in the oopj-configuration a larger maximum MR for j along the NFO [110]-direction than for j along the NFO [100]-direction. In the oopt-configuration, we only observe a negligible angle-dependence of the MR signal (due to the fact that the magnetic anisotropy in NFO still plays a role at the investigated magnetic field magnitude) for both current directions, in agreement with the SMR theory.^5,8 Thus, for both current directions, we observe the typical SMR fingerprint in ADMR experiments and can conclude that the observed difference in MR originates from the SMR. We note that similar results have been obtained in the investigated temperature range from 5 K to 300 K for all three rotation planes. Moreover, we conducted the ADMR experiments on a NFO/Pt sample with a Pt thickness of 7 nm with several devices and found, within our experimental error, no significant change in the SMR response as detailed in the supplementary material. These findings suggest that the observed change in the SMR amplitude only persists for very thin Pt layers (below 7 nm). We also note that this difference in MR persists for field-dependent magnetoresistance measurements as shown in the supplementary material.

For comparison, we also investigated the SMR for different charge current directions in Ta/NFO Hall bar structures. The extracted MR is shown in Fig. 2(d) for the ip-, (e) for the oopj-, and (f) for the oopt-configuration, respectively. Also for Ta, we find an angle-dependence of the MR for the ip and oopj-configuration for both current directions and negligible angle-dependence for the oopt-configuration. Thus also for the Ta layer, the sole cause for the observed MR is the SMR. In contrast to the Pt Hall bars, the maximum MR is now larger for j along the NFO [100]-direction (8.4 × 10^–4 for the [100]-direction and 7.7 × 10^–4 for the [110]-direction). The difference in the maximum MR for Ta is small and thus the observed difference in SMR may be fully explained by variations due to the fabrication process.

In order to further investigate this difference in the SMR amplitude and to distinguish it from effects originating from magnetic anisotropy, we conducted ADMR experiments in all three orthogonal rotation planes for temperatures 5 K ≤ T ≤ 300 K and in the external magnetic field range $0.1 T≤μ0H≤7 T$⁠. To extract the SMR amplitude from these measurements, we simulated the SMR response of ρ_long using:^3,8,9

where ρ₀ is the resistivity of the NM layer, when m is collinear to the spin polarization of the spin accumulation in the NM layer induced by the SHE. The SMR amplitude is described by ρ₁ and m_t is the projection of m onto the t-direction (⁠$t=n×j$⁠). For our simulations, we assumed ρ₀ to be field dependent, while ρ₁ is field-independent. For the determination of the magnetization direction for each field direction, we globally optimized the free enthalpy density normalized to the saturation magnetization of the NFO:^5,26

with B₀₀₁ being the uniaxial out-of-plane anisotropy field, B_c the cubic anisotropy field, and m_hkl the projection of m onto the [hkl]-direction of NFO. For each temperature, we then optimized a set of ρ_i and B_i parameters until an excellent agreement (reduced $χ2≤1×10−6$⁠) between the simulation and experimental data was obtained in all rotation planes and for all μ₀H. This approach allows us to disentangle the magnetoresistance effects from the changes in resistance arising from the fact that m is not parallel to h due to magnetic anisotropy (for more details see the supplementary material). For the cubic magnetic anisotropy of the NFO thin film, we found a temperature independent value of B_c = 10 mT, corresponding to the in-plane magnetic easy axes along the [110]-direction and $[11¯0]$-direction, which agrees with ferromagnetic resonance studies on samples grown under the same conditions.²² 

To better analyze the temperature dependence of the other parameters, we first plot the SMR magnitude $SMR=ρ1/[ρ0(μ0H=7 T)]$ for Ta and Pt as a function of T for the two different charge current directions in Fig. 3(a). As evident from this plot, the difference in SMR for the two charge current directions persists for all investigated temperatures. For Pt, SMR is larger for j along the NFO [110] direction over the whole temperature range. At low temperatures (T ≤ 25 K), the difference in SMR magnitude for the current directions in Pt is smaller than at higher temperatures. For the two Ta Hall bars, we find that the SMR is larger for j along the NFO [100] direction, albeit the difference is less pronounced than for Pt. Moreover, for T ≤ 75 K, the SMR in Ta is larger than in Pt, suggesting that Ta might be a better choice for SMR investigations at low temperatures.

For magnetic anisotropy determined from these ADMR experiments, we find that B₀₀₁ monotonically increases with decreasing temperature as illustrated in Fig. 3(b). Such a behavior could be either explained by the increase in saturation magnetization or due to strain effects caused by the difference in thermal expansion of the MgGO substrate and the NFO layer. From additional magnetometry measurements (see the supplementary material), we determined the saturation magnetization M_s of the NFO layer as a function of temperature and calculated the shape anisotropy contribution in the thin film limit $Bshape=0.5μ0Ms$⁠, which is also plotted in Fig. 3(b). Clearly, the extracted B₀₀₁ is much larger than B_shape. Thus, we conclude that B₀₀₁ is dominated by the strain in the NFO layer. This finding agrees well with the previous analysis of the uniaxial out-of-plane magnetic anisotropy in bulk-like NFO thin films.²² 

In order to further investigate the origin of the observed difference of the SMR, we fabricated additional NFO(100 nm)/Pt(3.5 nm) Hall bars oriented along the [110]-and [100]-directions of NFO on a single sample. From ADMR experiments, we then extract SMR and ρ_Pt for these additional structures. In Fig. 4(a), we plot SMR as a function of ρ_Pt for all investigated NFO(100 nm)/Pt(3.5 nm) structures. As detailed in the supplementary material, we expect that the SMR scales linearly with ρ_NM, assuming that only the spin Hall angle and spin diffusion length of the NM depend on ρ_NM.^27,28 Thus, from this simple estimation we would expect that the SMR increases with increasing resistivity. This is in contrast to our experimental results as shown in Fig. 4(a). In our NFO/Pt samples, the SMR is the largest for the structure with the lowest ρ_Pt, and with increasing ρ_Pt, the SMR appears to decrease linearly. We attribute the change of ρ_NM for a constant Pt thickness to different morphologies of the NFO/Pt interface, which seems to depend on the position of the Hall bar on the NFO.²⁹ Atomic force microscopy performed on pristine NFO samples did not reveal any clear position dependence of the surface morphology. However, a different surface morphology nicely explains the different values obtained for ρ_Pt at a constant Pt thickness. Due to the low Pt thickness, changes in the interface roughness greatly affect the resistivity of the Pt layer. Moreover, it is then reasonable to expect a change in the interfacial spin mixing conductance^30–32 for different values of the surface roughness. Following this argument, a lower ρ_Pt in our samples indicates a smoother interface, i.e., less contribution from interface scattering to the total resistance of the Pt layer. This smooth interface is also beneficial for the spin mixing conductance and thus leads to an increase in SMR. This change in spin mixing conductance seems to dominate in our NFO/Pt samples over the dependence of the spin Hall angle and the spin diffusion length on ρ_Pt. While the interface morphology evidently influences the spin mixing conductance, it may be also possible that different ρ_Pt leads to changes in the s-d exchange across the NFO/Pt interface, which also will influence the spin mixing conductance.^33–37 

To further illustrate this relation between ρ_NM and SMR, we compare the temperature evolution of the ratios of the SMR on the one hand and the ratios of the resistivities ρ_NM for the two different current directions on the other hand for Pt and Ta. The result of this analysis is shown in Figs. 4(b) and 4(c). As evident from Fig. 4(b), the difference in ρ_Pt and SMR persists over the whole investigated temperature range. While we obtain $ρPt[100]/ρPt[110]>1$ for all temperatures, $SMRPt[100]/SMRPt[110]<1$⁠. Interestingly, when we multiply $ρPt[100]/ρPt[110]$ with a factor of 0.55 [red line in Fig. 4(b)], we obtain a good agreement with the temperature dependence of $SMRPt[100]/SMRPt[110]$⁠. This again indicates that not only the spin Hall angle and the spin diffusion length depend on ρ_Pt, but also the value of ρ_Pt acts an indicator for the spin mixing conductance.

For Ta, as illustrated in Fig. 4(b), $ρTa[100]/ρTa[110]$ remains essentially constant over the whole temperature range with a value of 0.99. For $SMRTa[100]/SMRTa[110]$⁠, we find a slight decrease with decreasing temperature from 1.09 at room temperature down to 1.07 at T = 5 K. Again, we can map the evolution of these two ratios with temperature by multiplying $ρTa[100]/ρTa[110]$ with a factor of 1.11.

In summary, we showed that the SMR from our NFO/NM heterostructures is comparable to the results obtained on the prototype ferrimagnetic insulator YIG. Thus, these NFO/NM heterostructures are well suited for further pure spin current experiments.^38,39 Our results further illustrate that one can tune the SMR amplitude via the interface roughness and utilize the resistivity of the NM as an indicator for the interface quality. Thus, not only the spin Hall angle and the spin diffusion length are affected by ρ_NM, but ρ_NM also acts as an indicator for the spin mixing conductance at the interface. From this perspective, further experiments are expected to allow for a clarification of possible microscopic origins of this correlation. Moreover, a more systematic investigation of the resistivity scaling of the SMR effect in NFO/Pt bilayers may allow to more clearly address the interface morphology. Our results presented here open up a new avenue for engineering the charge current to spin current conversion in magnetically ordered insulator/normal metal heterostructures.

See the supplementary material for the magnetic characterization of the NFO films, details on the ADMR measurements, discussion on the resistivity dependence of the spin Hall magnetoresistance, and the measured field-dependent magnetoresistance data.

We thank Timo Kuschel, Juan Shan, and Jutta Schwarzkopf for the fruitful discussions. We gratefully acknowledge financial support by the DFG via Project No. AL 2110/2-1. The work at the University of Alabama was supported by NSF Grant No. ECCS-1509875.