Bulk Rashba‐Type Spin Splitting in Non‐Centrosymmetric Artificial Superlattices

Abstract Spin current, converted from charge current via spin Hall or Rashba effects, can transfer its angular momentum to local moments in a ferromagnetic layer. In this regard, the high charge‐to‐spin conversion efficiency is required for magnetization manipulation for developing future memory or logic devices including magnetic random‐access memory. Here, the bulk Rashba‐type charge‐to‐spin conversion is demonstrated in an artificial superlattice without centrosymmetry. The charge‐to‐spin conversion in [Pt/Co/W] superlattice with sub‐nm scale thickness shows strong W thickness dependence. When the W thickness becomes 0.6 nm, the observed field‐like torque efficiency is about 0.6, which is an order larger than other metallic heterostructures. First‐principles calculation suggests that such large field‐like torque arises from bulk‐type Rashba effect due to the vertically broken inversion symmetry inherent from W layers. The result implies that the spin splitting in a band of such an ABC‐type artificial SL can be an additional degree of freedom for the large charge‐to‐spin conversion.


S1. Magnetic anisotropies of the SLs estimated by the generalized Sucksmith-Thompson method and Dzyaloshinskii-Moriya interaction (DMI) of the [Pt/Co/W 0.6 nm]-SL
The magnetic anisotropies of SLs in this sutdy are obtained suing the generalized Sucksmith-Thompson (GST) method [S1]. In this measurement, as presented in Figure S1(a), the anomalous Hall resistance is measured with applied magnetic field in different polar angles (Here, θ = 60 º and 80º).
The Rxy vs H plots of the SL samples show typical characteristics with perpendicualr magnetic anisotropy (PMA). Then, the first and second order of magnetic anisotropy energy can be calculated as following equations, Here, m is the normalized magnetization in z direction, M S is the saturation magnetization and H is external magnetic field applied in polar angle θ. Figure S1  We could also confirm that Dzyaloshinskii-Moriya interaction (DMI) exists in the superlattice system. We measured the DMI-effective-field induced in the [Pt 1.0/Co 0.6/W 0.6 (nm)] 12 superlattice using the extended Droplet model (see ref. 25 in the main manuscript). According to the model, when a system is perpendicularly magnetized under both B z (//B n ) and B x , the B n vs. B x curve shows threshold behavior owing to the DMI. Here, B n is a nucleation field. From the critical field, we can estimate the DMI-induced effective field. Figure R4 shows the measured B n in terms of B x , and the film shows the threshold behavior marked with the yellow dotted line in the figure. Thus, the DMIinduced field B DMI is about 50 mT. It has been reported that a system can have sizable DMI energy with non-centrosymmetry (see ref. 25 in the main manuscript). Therefore, DMI in our superlattice originates from the non-centrosymmetric superlattice. Figure S2. B n vs. B x curve measured with the [Pt 1.0/Co 0.6/W 0.6 (nm)] 12 superlattice. The yellow dotted line indicates the DMI-induced effective field.

S2. Estimation of current shunting in [Pt/Co/W] superlattice
The injected current density is calculated by considering the resistivity of each material. The resistivity of the materials with different thickness can be obtained from the following process. First of all, the resistivity of Ta(1.5 nm)/X (t nm)/MgO(2 nm)/Ta(3 nm) structure is measured (X = Pt (1 ~ 5 nm), Co (0.6 nm), and W (0.2 ~ 1 nm)). Then, the resistivity of Ta(1.5 nm) is measured in Ta The resistivity of the materials is consistent with the previous research measured in similar thickness [S2, S3]. The fairly high resistivity of W ( suggests that W could have a mixture of alpha and beta phase [S4]. On the other hand, XRD spectrum cannot clearly distinguish α and β-W in

S3. Subtraction of thermoelectric effect contributions
In addition to the PHE, the thermoelectric effect due to the temperature gradient in x and z direction ( and ) contribute to the 2 nd harmonic voltage [S5, S6]. In particular, which is caused by the different thermal conductivity between the wafer and the air affects to the slope of when the field is applied in x direction ( ), thereby easily overestimating H DL . Therefore, one must subtract this contribution from the raw data of . Actually, in the raw data, the thermoelectric effect due to anomalous Nernst effect (ANE) and spin Seebeck effect (SSE) is dominant over DL-SOT under high magnetic field (= 9 T) in this series of samples as shown in the Fig. S4 (a). (The example is only shown for the case of [Pt/Co/W(0.6)]-SL.) Therefore, the maximum value of is considered entirely from thermoelectric effects because the DL-SOT becomes '0' under strong magnetic field.
The thermoelectric signal is reconstructed from the first harmonic data as shown in Figure S4 (b). The due to pure DL-SOT is obtained as in Figure S4 (c) after subtracting the reconstructed ANE signal from the raw data. The from thermoelectric effects are plotted in Figure S4  Especially, we would like to note that most of the previous research investigating spin-orbit torque in magnetic multilayer system overlooked these thermoelectric contributions, thereby obtaining misleading value of spin Hall angle [S7, S8]. Since both ANE and SSE are significant in multilayer system are significant in magnetic multilayer system [S9, S10], one needs to be cautious about quantifying the spin-orbit torque.

S4. Subtraction of planar Hall contribution for quantifying SOT and confirmation of the SOT with the current-induced magnetization switching
In order to quantify the spin-orbit effective field, one needs to consider about the contribution from the planar Hall effect (PHE). The planar Hall resistance ( ) is the transverse component of the anisotropic magnetoresistance (AMR). During the harmonic Hall voltage measurement, this PHE also generates transverse Hall voltage [S11]. Therefore, the PHE correction is necessary when analyzing SOT effect. Figure S5   We also compared the SOT effective values with and without PHE correction as listed in Table S1. We can find that the values are different from each other, but the trend is the same; ξ FL / ξ DL <1 when t Pt >2 nm, otherwise ξ FL / ξ DL >1. The obtained ξ values are similar to previously reported values as displayed in Fig. 3 of the main manuscript. In these points of view, we would like to carefully emphasize that our main argument about the mechanism transition from Rashba to bulk spin Hall effect is reasonable. superlattice. We successfully observed the SOT-induced magnetization switching behavior of the device under B x = 47.5 mT as shown in Fig. S6. The observed switching polarity depends on the B x direction, which indicates the SOT-induced switching. For both cases, the switching current is ~72 mA, whose current density is . Adopting the anisotropy B k =1.5 T, the estimated SOTswitching efficiency [(J c /B k ) -1 ] is ) which is much larger than the Pt/Co bilayer cases ~0.1 [S12]. This trend (enhancement in the SOT-switching efficiency) is consistent with our 2 nd harmonic measurement results. Therefore, the second harmonic measurement results are reliable.

S5. X-ray reflectivity of the [Pt/Co/W]-SLs
The series of superlattices with accurately controlled thickness in a mono-atomic level with a sharp interface are the essential necessity of this research. Therefore, the sputtering power and time are delicately manipulated. For example, when an element having a large mass such as W is deposited on the Co, the interface between Co/W could be damaged because of the bombardment energy during the sputtering process. Therefore, the sputtering power is optimized to create the superlattice with less damaged interface which is deduced from the roughness in XRR spectra. Figure S7 shows the XRR spectra from each superlattice with varied W thickness and their fitting. From the fitting, the thickness and roughness are obtained as

S7. Ratio between orbital and effective spin moments estimated from XAS and XMCD spectra
X-ray absorption spectra (XAS) are recorded in a range between Co L 3 and L 2 edge (740 ~ 840 keV) with normal and grazing incidence at 0 º and 70º. The applied magnetic field is ± 2 T which is high enough to saturate the magnetization. The parallel and antiparallel magnetic field to the film plane provides different absorption coefficient of the photon. The difference between the right and the left circularly polarized spectra corresponds to the XMCD spectrum. All the measurements are performed in the ultrahigh vacuum and at the room temperature. The backgrounds of XAS and XMCD were subtracted using a linear function and an arctangent step function. The results after the subtraction of XAS and XMCD spectra are shown in Figure S9(a) and (b). From the integrated XMCD and XAS spectra, the orbital moment contribution to the effective spin moment ) can be calculated by the following equations usually called sum rules [S14] as follows; where, is 3d electron occupation number of Co, 〈 〉 is the expectation value of the dipolar operator and 〈 〉 is in Hartree atomic units. Here, the value of p and q are the integrals over L 3 edge and both L 3 and L 2 edges, respectively in XMCD spectra. The value of r can be calculated from the integration of L 3 and L 2 edges in XAS spectra. In addition, we quantified and confirmed that the 〈 〉 is much smaller compared to 〈 〉. Therefore, the orbital moment to the effective spin moment can be calculated by using last equation with neglecting the contribution from 〈 〉 〈 〉 . Figure S9.