Improved spin–orbit torque induced magnetization switching efficiency by helium ion irradiation

Increasing the efficiency of spin–orbit torque (SOT) is of great interest in spintronics devices because of its application to the non-volatile magnetic random access memory and in-logic memory devices. Accordingly, there are several studies to alter the magnetic properties and reduce the SOT switching current with helium ion irradiation, but previous researches are focused on its phenomenological changes only. Here, the authors observe the reduction of switching current and analyze its origins. The analyzed major reasons are improved spin Hall angle represented as the changed resistivity of heavy metal layer and the reduction of surface anisotropy energy at interface between heavy metal and ferromagnet. It is confirmed that almost linear relation between changed SHA and Pt resistivity by helium ion irradiation, which is attributed because of the increase in the scattering sources induced by structural distortion during ion penetration. From the calculated power consumption ratio based on the derived parameter, the requiring power decreases according to the degree of ion irradiation. Our results show that helium ion penetration induced layer and interfacial disturbance affects SOT induced magnetization switching current reduction and may provide possibility about helium ion irradiation based superior SOT device engineering.

obtaining only changed properties, we need to cover He + ion irradiation area wider than Hall cross area for avoiding mix-up of signals between irradiation and non-irradiation part. In the magnetization switching process with the magnetic field, the experimentally observed switching (coercivity) field is much smaller than the anisotropy field, which is so called Brown paradox [1]. According to the Brown paradox, the switching at the anisotropy field is only valid in single domain model, and real switching field can be gratefully reduced by formation of multi-domain state and domain wall motion. Such discrepancy is also found in the SOT induced switching in our study.

Supplementary
The macro-spin model using the single domain model and the actual observed values are quite different, which is thought to be due to the generation of multi-domain states during the switching process. We observed that different domain nucleation states appear according to the magnitude of in-plane direction external magnetic field. In Fig. S2a, initially abrupt switching occurs, but slow switching is dominant at the end of switching for 3.1 kOe loop. However, multi-domain effect is more dominant in the low field region. In the case of a small field (0.7 kOe), a middle-step at blue circles in Fig. S2a is observed, and it is assumed that switching occurs by formation of the bubble domains by the reason that sufficient SOT is not applied for forming the domains. However, as the field increases, the middle-step disappears, and it is assumed that the switching proceeds to single-domain nucleation due to sufficient SOT. Therefore, we considered that the two domain nucleation states are in different causes, and thought that it would be difficult to directly compare the small field region with the higher field region. In fact, as shown in Fig S2b, the switching current reduction ratio at 0.7 kOe showed a tendency to decrease according to the dose amount (middle steps are observed) while increasing tendency is observed in another external field region (no middle steps). Because the modulated area by ion irradiation in our system is micron scale size, it is hard to directly measure or configure changed magnetic anisotropy energy by irradiations. So, we follow the generalized Sucksmith-Thompson (GST) method [2,3] to extract the 1st and 2nd order perpendicular magnetic anisotropy (PMA) field. We used AHE measurement to apply GST method, where AHE is proportional to the zcomponent of the magnetization. And the more than whole Hall cross area are irradiated to guarantee to exclude the un-irradiated area signal as shown in Fig. 1a. The GST method follow the equations,

Supplementary Note 3: Generalized Sucksmith-Thompson method
Here, is the first order PMA effective field, ,2 is the second order PMA field, = cos , is the polar angle of magnetization and is the polar angle of external magnetic field . FIG. S2 shows the fitted result using equation (1) and (2). The result in Fig.1 is shown with measured data under direction of = 0° and = 80° with the pristine sample. As seen in Fig. S2, although the applied field is much smaller than PMA field of sample, precise determination and ,2 is possible. The obtained and ,2 are depicted in Fig. 2d as a function of dose amount.

Supplementary Note 4: The method of Distinguish the anomalous and planar Hall effect contributions
In Hall measurements, if the applied magnetic field is out-of-plane, only anomalous Hall effect (AHE) is detected. And only the planar Hall effect (PHE) is considered for the in-plane direction in PMA. However, with general direction field as like harmonic measurements, we have always mixed signals of AHE and PHE.
Therefore, careful analysis is required to distinguish both contributions in the harmonic measurements. In normally, the AHE measurement only needs small external field near coercivity, but PHE contribution change are detected with azimuthal angle ( ) dependence inside external in-plane direction magnetic field exceeding PMA effective anisotropy field. However, in our system, the PMA field has high enough, few thousand to ten thousand Oersted scale, we follow the separating method between AHE and PHE contribution using asymmetrically measured Hall voltage [4] to extract the ion irradiation induced AHE and PHE contribution change within field magnitude of 1 T. Fig. S3a and Fig. S3b show the separated plot, measurement of +B to -B and -B to +B, in original loop and only -B to +B part reversed loop in B = 80° and = 40°. Fig. S3b clearly show asymmetricity by measurement direction caused by PHE contribution. Adding and subtracting each measurement results, we can calculate AHE and PHE contributions as shown in Fig. S3c and Fig. S3d .
From the AHE contribution, we can calculate AHE resistance and following, The SOT analysis method using the 1st and 2nd order harmonic Hall signals with AC current is commonly utilized because of its ability to classify two different contributions of SOT and easy measurement process. At first many researches is conducted on much lower external magnetic field comparing anisotropy field, so only 1st order PMA effective field is under consideration [5,6,7]. However, as the studies on angular dependence of DLT and FLT effective field progress, it is also known that the 2nd order PMA field plays an important role in accurate analysis on harmonic Hall signals [4,8,9]. So, we consider only the 1st PMA on our data and show the importance of contribution of 2nd PMA in the harmonic Hall signal analysis for accurate SOT induced effective field calculation. Because the Hall voltage follows, And here, 1 and 2 is the first order and the 2nd order harmonic Hall voltages, respectively, and expressed as, So, Δ and Δ can be calculated by measured 1 and 2 at each direction. The calculated DLT and FLT effective field can be rewritten as form like and , , 0 and 0 is defined as With above equations, we can replot the harmonic Hall voltage to DLT and FLT effective fields as function of , as shown in Fig. S4a and Fig. S4b. These results show quite different angular dependence at high tilting angle and the dose amount dependent tendency does not appear well at smaller angle case comparing with case of considering 2nd order PMA. This suggests that the 2nd order PMA has a large enough influence on analysis of harmonic Hall signal at not only high angle magnetization tilting case, but also on calculation on effective fields in small tilting angle. For understanding influence caused by ion irradiation induced Pt layer characteristic change, we measure the longitudinal and transverse resistivity by low-temperature resistance and ordinary Hall effect measurement, respectively. The Fig. S5a show the temperature dependent resistivity on Pt single layer from 5 K to 225 K and extracted temperature coefficient and residual-resistivity ratio (RRR) is seen in Fig. S5b. The temperature coefficient follows equation of = 0 (1 + • ( − 0 )) in linear resistivity region, here the is temperature coefficient, one can easily extract using linear fitting. In RRR case, defined as 300 / 5 in here, we pick the resistivity at 5 K instead of 0 K for calculation of RRR because of measurement limitation and resistivity of 300 K is calculated extending with linear fitting as shown in FIG.

Supplementary
S5a. Not only longitudinal resistivity, transverse resistivity also can be inferred with ordinary Hall effect (OHE) measurement. The measured Hall voltage and its Hall coefficient is shown in Fig. S5c-d, respectively. From this result, we can suggest that the ion irradiation process increases longitudinal and transverse resistivity both.