{'fraction_non_alphanumeric': 0.04378864172350054, 'fraction_numerical': 0.013831346803492893, 'mean_word_length': 4.680666183924692, 'pattern_counts': {'":': 0, '<': 3, '<?xml version=': 0, '>': 5, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Complementary logic operation based on electric-field controlled spin-orbit torques

Spintronic devices as alternatives to traditional semiconductor-based electronic devices attract considerable interest as they offer zero quiescent power, built-in memory, scalability, and reconfigurability. To realize spintronic logic gates for practical use, a complementary logic operation is essential but still missing despite a recent progress in spin-based logic devices. Here, we report the development of a complementary spin logic device using electric-field controlled spin-orbit torque (SOT) switching. In heavy metal/ferromagnet/oxide structures, the critical current for SOT-induced switching of perpendicular magnetization is efficiently modulated by an electric field via voltage-controlled magnetic anisotropy (VCMA) effect in a non-volatile manner. Moreover, the polarity of the VCMA is tuned by the modification of oxidation state at the ferromagnet/oxide interface. This allows us to fabricate both n-type and p-type spin logic devices and to enable a complementary logic operation, paving the way for the development of non-volatile and reconfigurable logic devices.

Spintronic devices for information processing have attracted considerable interest owing to their potential advantages of improved computational capability and reduced power consumption [1][2][3]. Up to now, spin-based logic devices have been developed in two different approaches. The first is to add the electron spin as a variable parameter into existing semiconductor devices [4], such as the spin field-effect transistor (FET) proposed by Datta and Das [5]. Despite recent successes in the operation of the spin FET with a semiconducting channel [6][7][8], further developments are required to improve the signal at room temperature and to secure the device scalability. The second approach is to utilize metallic structures in which a logic operation is performed by using domain wall motion [9][10][11][12], magnetization switching [13,14], and spin wave propagation [15]. These metal-based spintronic devices are advantageous as they operate at room temperature. However, the screening effect of metals inhibits implementing electric-gating-induced field-effect functions, which are indispensable for complex logic operations. More importantly, a spintronic device performing complementary logic operation analogous to the conventional CMOS has not been developed yet.
In this work, we experimentally demonstrate a spin logic device capable of performing complementary logic operation which is based on the spin-orbit torque (SOT) [16][17][18][19][20][21] and its controllability using an electric field [22,23]. The SOT is a spin-transfer torque originating from the spin-orbit coupling in heavy metal (HM)/ferromagnet (FM)/oxide structures and enables magnetization switching by an in-plane current. The critical current of the SOTinduced switching can be modulated by a perpendicular gate voltage (see Fig. 1a) which induces the change in the magnetic anisotropy of the trilayer structures via voltage-controlled magnetic anisotropy (VCMA) effect [24][25][26][27][28][29][30][31][32]. Therefore, the combination of SOT and VCMA allows us to control our device to be either switchable or non-switchable for a given input clock current. This is the first working principle of our spin logic device. The second principle is based on the finding that the polarity of the electric-field effect on the magnetic anisotropy (or VCMA effect) can be reversed by modulating oxidation state at the FM/oxide interface. As we show below, for an under-oxidized interface, a positive (negative) gate voltage decreases (increases) the magnetic anisotropy, whereas for an over-oxidized interface, the reversed VCMA effect occurs. This opposite dependence of VCMA effect on the sign of gate voltage allows us to form an "n-type" or a "p-type" spin logic device by controlling the oxidation state.
Having these two types of devices (i.e., n-type and p-type), we realize the complementary functionality of spin logic devices as we demonstrate below.

Electric-field controlled spin-orbit torque switching
In order to prove the working principles in our devices, we carry out SOT-switching experiment combined with the application of a gate voltage for Ta(5 nm)/CoFeB(1 nm)/MgO(1.6 nm)/AlOx(1.8 nm) Hall bar structures, where perpendicular magnetic anisotropy (PMA) is established in the CoFeB (see Fig. 1a and Methods). We integrate the gate oxide (ZrO2) and electrode (Ru) on top of a square-shaped CoFeB/MgO/AlOx island for gating. We vary the oxidation time (tox) for AlOx formation from 25 sec to 125 sec in order to control the oxidation state at the CoFeB/MgO interface and to modify the dependence of magnetic anisotropy on the voltage polarity. In order to estimate VCMA effect, we measure the anomalous Hall resistance (Rxy) as a function of the in-plane magnetic field (Bx) under a gate voltage (VG), where Rxy represents the z-component of magnetization. Analysing the decrease in Rxy with increasing Bx allows us to estimate the perpendicular anisotropy field (HK). We find that the HK maximizes at tox = 75 sec, referred to as the optimal oxidation time tox,op, and slightly decreases for tox either longer or shorter than tox,op (See Supplementary Note 1). Figures 1b -1d show the dependence of magnetic anisotropy on the gate voltage polarity for samples with different oxidation times. The sample with tox = 25 sec (< tox.op) shows that the Bx-dependent decreasing rate of Rxy is larger for VG of +22 V than for VG of -20 V (Fig. 1b), indicating that a negative (positive) VG increases (decreases) HK. Remarkably, the VCMA effect is reversed in its sign for the sample with tox = 125 sec (> tox,op; Fig. 1d). On the other hand, the VCMA effect is negligible in the sample with tox = 75 sec (= tox,op; Fig. 1c). The dependence of VCMA effect on tox is summarized in Fig. 1e. This dependence can be explained by the modification in the oxidation state at the CoFeB/MgO interface and the resultant change in PMA [33]. The application of an electric voltage induces the relocation of oxygen ions either towards or away from the interface depending on its polarity [34], which modulates HK accordingly. For example, in the under-oxidation condition (tox < tox.op), a negative bias supplies oxygen ions to the interface that is initially at the oxygen-deficient state, and consequently increases HK. The opposite VCMA effect occurs in the over-oxidation condition (tox > tox.op) for which a negative bias decreases HK. This voltage-induced change in oxidation state is supported by a nonvolatile behaviour of the VCMA effect; HK remains the same even after VG is removed (Supplementary Note 2).
We next investigate the effect of VG on SOT-induced switching performance. We note that in all SOT switching experiments, we apply an external in-plane field along the current direction (+x direction) for the deterministic switching. We note that this external field can be replaced by an internal exchange bias field [35,36]. The critical current (IC) for SOT-induced magnetization switching is known to be proportional to HK [37] so that VG is able to control IC through the modification of HK. As expected, the SOT-induced switching experiment under VG for the samples with different tox's demonstrates a clear dependence of IC on VG (Figs. 1f -1h).
The absolute value of IC of the under-oxidized sample (tox = 25 sec) is 6.5 mA for VG of +24 V, which is noticeably smaller than 8.8 mA for VG of -24 V (Fig. 1f). The over-oxidized sample (tox = 125 sec) shows the opposite behaviour; |IC| for a negative VG is smaller than that for a positive VG (Fig. 1h). On the other hand, the sample with tox = 75 sec shows a negligible modulation in IC by VG (Fig. 1g). Figure 1e shows that the modulation of the IC is closely correlated with that of the HK. We note, however, that the change in IC of ~30% is much greater than that in HK of ~2%, which implies the VCMA may not be the only source causing the electric-field controlled SOT.
These results presented in Fig. 1 demonstrate two working principles required for the realization of the spin logic devices; the first is that IC for SOT-induced switching can be effectively tuned by VG and the second is that the dependence of IC on VG can be designed by the oxidation time. In particular, the second principle allows us to mimic p-type or n-type semiconductor device by defining a SOT device as p-type (n-type) when the device switches its magnetization by an in-plane input clock current IIN for a negative (positive) VG.

Programmable logic operation of spin logic device
With these working principles, we first demonstrate a logic operation using a single device in which the gate voltage (VG) and the input current (IIN) are used as two input parameters (Fig. 2a). The tox is 125 sec of the device (> tox.op; over-oxidation condition), which is thus p-type where |IC| for a negative VG is smaller than that for a positive VG (Fig. 2b). By setting the in-plane input clock current IIN of ±13 mA and VG of -24 V, the magnetization switches from the UP magnetization (//+z) to the DOWN magnetization (//-z) or vice versa, depending on the polarity of IIN. Figure 2c shows the operation of the given spin logic device, which allows us to construct a truth table (Fig. 2d). Here, we define the positive values of the inputs (VG = +24 V, IIN = +13 mA) as digital input "1" whereas their negative values (VG = -24 V, IIN = -13 mA) as digital input "0". Those inputs determine the output of the spin logic device, the magnetization direction which is monitored by measuring anomalous Hall resistance Rxy; UP magnetization (Rxy > 0) is equivalent to digital output "1" and DOWN magnetization (Rxy < 0) is equivalent to digital output "0". Figure 2d demonstrates that two logic operations are possible depending on the initial magnetization state; the device operates the OR function of IIN and VG when it is initialized as "1" state (magnetization UP), and the AND function of IIN and VG' (NOT VG) when initialized as "0" state (magnetization DOWN). This offers the realization of multi-functional or programmable spin logic devices.
The logic operations can be also performed by the combination of two spin logic devices with the same type. The sample is fabricated by defining two nominally identical CoFeB/MgO/AlOx islands on a common Ta underlayer, which are designated as spin logic devices A and B, respectively (Fig. 3a). We note that both devices A and B are of p-type (tox = 125 sec) and |IC| is 12.

Complementary functionality of spin logic devices
The next demonstration is for the complementary operation of the spin logic devices, in which n-type device (tox = 25 sec; under-oxidation condition) and p-type device (tox = 125 sec; over-oxidation condition) are electrically connected and incorporated with a common gate electrode VG (Fig 4a). The n-type characteristic of the former device is shown in Supplementary Note 4. Before the operation, we initialize the devices to be UP magnetizations (Rxy,n = Rxy,p = +2) corresponding to the digital output "1" state and use the IIN of ±12 mA. Figure 4b shows the complementary operation of the spin logics; when we apply VG = +24 V (red-shaded region), the magnetization or digital state of the n-type device is manipulated by the IIN while that of the p-type device remains unchanged. In contrast, when we apply VG = -24 V (blue-shaded region), the digital state in the p-type device is selectively controlled by the IIN. Therefore, our devices perform the n-type (p-type) function exclusively for the positive (negative) VG, confirming the complementary functionality of the spin logic device. This is a spin analogue to the conventional CMOS, which can facilitate the spin-based logic devices. Furthermore, when we apply an IIN greater than 14 mA, both devices are simultaneously controlled regardless of the gate voltage (grey-shaded region). This is a unique function of the spin logic devices based on SOT, which allows for initializing or erasing all the information at the same time [38].

Discussion
We finally discuss several advantages of our spin logic device over conventional CMOSbased device: (i) it does not require refreshing in quiescent mode because of its non-volatile characteristic of magnetic state as well as VCMA effect (Fig. S2), resulting in a substantial reduction in power consumption. (ii) The n-type or p-type character of the spin logic device is determined by the oxidation state at the FM/oxide interface, which in principle can be controlled by a gate voltage for an improved VCMA effect. This reconfigurable spin logic device offers great flexibility for various logic algorithms. (iii) The device does not include semiconductors, meaning that three-dimensional integration of the devices would be possible, which can result in considerably increased device density. (iv) It can also serve as a built-in memory cell within a logic circuit, reducing power dissipation required for transferring signals between commonly separate logic and memory cells. (v) The switching of the SOT-based device is fast [39], which are prerequisites for logic operations. We note that the signal of our device can be considerably improved by introducing a magnetic tunnel junction to read the output of the device [40,41]. This together with above advantages promises that the further development of our spin logic device could provide an efficient logic unit with high density and fast speed.     versus Bx is shown in the inset of each graph, from which the HK is extracted (Fig. S1f). Note that all the measurements are done without a gate voltage (as-deposited state). We find that the HK is the largest for tox = 75 sec, referring to as the optimal oxidation state, tox,op, and HK decreases for tox either longer or shorter than tox,op.

Supplementary Note 2. Non-volatility of voltage-controlled magnetic anisotropy
As shown in Fig. 1 of the main text, the magnetic anisotropy field (HK) of the over-oxidized sample (tox = 125 sec) decreases by a gate voltage VG of -20 V, which is demonstrated in Fig.   S2, where the black (red) symbols represent the normalized Rxy versus Bx curve under 0 V (-20V). We repeated the same measurement after removing the VG, which is indicated as the blue symbols in Fig. S2, demonstrating the HK remains the same as the previously-measured value under -20 V. This clearly shows non-volatile behavior of the voltage-controlled magnetic anisotropy in our samples.

Supplementary Note 3. Logic operation of spin logic device
Table S1 summarizes the logic operation of the device of Fig. 3 on the main text when both devices are initialized as DOWN magnetization and the input clock current is positive (IIN > 0). By changing the initial magnetization states, the same device exhibits different Boolean equations from those in Fig. 3d of the main text; demonstrating that the logic operation can be programmed by the initial magnetization direction. Table S1. Logic operation of two p-type spin logic devices for initial magnetization DOWN and the positive IIN. Supplementary Note 4. Electric-field controlled spin-orbit torque switching in n-type spin logic device Figure S3 shows the dependence of the spin-orbit torque (SOT) switching on the gate voltage VG for the n-type device (tox= 25) in the complementary spin logic devices presented in Fig. 4 of the main text. The IC in the n-type spin logic device increases (decreases) when a negative (positive) VG of 24 V is applied, which is the opposite to that in p-type device, which is summarized in Table S2.