Programmable and non-volatile spin-based logic devices have attracted significant interest for use in logic circuits. Realization of logic operations via spin–orbit torque (SOT) driven magnetization switching could be a crucial step in the direction of building logic-in-memory architectures. In this work, we demonstrate experimentally, the realization of four logic operations in a heavy metal/ferrimagnet bilayer structure via SOT switching. We also propose a general scheme for choosing input parameters to achieve programmable logic operations. The bulk and tunable perpendicular magnetic anisotropy and relatively lower saturation magnetization in ferrimagnets are found to make them more energy efficient in performing logic operations, as compared to conventional ferromagnets. Thus, ferrimagnets are promising candidates for use in logic-in-memory architectures, leading to the realization of user-friendly spin logic devices in the future.

## I. INTRODUCTION

The search for alternatives to traditional complementary metal oxide semiconductor (CMOS) based logic devices has attracted significant interest in the last few decades. The possibility of realizing low power, ultrafast, in-memory computation using the spin of the electron, rather than its charge, has made spin logic devices a very promising alternative. Several types of spin-based logic schemes have been proposed thus far, including magnetic cellular automata,^{1,2} spin-based semiconductors,^{3,4} magnetoelectric spin–orbit devices,^{5} magnonic devices,^{6–8} exchange^{9} or domain wall^{10,11} driven magnets, skyrmions,^{12} etc. Some of the above schemes have been realized experimentally as well. However, one significant drawback faced by all the above schemes is the need for additional circuitry to realize different logic operations. This, in turn, leads to an increase in the total circuit area, thus negating the advantage of utilizing spin logic as compared to CMOS. Programmable logic devices, which can implement multiple logic operations by changing a control variable, are more viable in this regard.

Such a programmable logic prototype, utilizing the phenomenon of spin orbit torque (SOT) driven perpendicular magnetization switching,^{13–15} has been demonstrated.^{16} The external magnetic field which assists in the magnetization switching process acts as the control variable, enabling different logic operations on the same device. The spin logic device in Ref. 16 consists of a heavy metal (HM)/ferromagnet (FM)/oxide heterostructure annealed at 400 °C, with an ultrathin Co layer (0.8 nm) as the FM. In such a heterostructure, the interfacial magnetic anisotropy at the FM/oxide interface is responsible for perpendicular magnetic anisotropy (PMA).

In this work, we utilize a HM/rare earth (RE)–transition metal (TM) alloy (namely, GdFe) ferrimagnet (FiM) bilayer to realize various logic operations via SOT driven magnetization switching. Replacing the FM with a FiM having tunable thickness and composition enables greater flexibility in magnetic properties, which, in turn, offers several advantages. First, it is comparatively easier to obtain PMA in HM/FiM bilayers over a wide range of FiM thicknesses and compositions due to the relatively lower saturation magnetization for FiMs.^{17} Second, the perpendicular anisotropy field H_{p} of the FiM can be manipulated, thus enabling control over the critical current required for SOT driven magnetization switching.^{18} Third, the opposite angular momenta of Gd and Fe make it possible to control the net angular momentum and, thereby, manipulate domain wall velocities in the FiM, allowing for the realization of faster domain wall motion,^{19,20} leading to a more efficient SOT driven magnetization reversal. All the above advantages make HM/FiM bilayers a promising candidate for realizing ultrafast and efficient spin logic devices. We utilize the external magnetic field as the control variable to program different logic operations on the same device, keeping all other input parameters fixed.

## II. RESULTS AND DISCUSSION

### A. Material preparation and characterization

A thin film stack consisting of Pt(5)/Gd_{25}Fe_{75}(10)/SiN(10 nm) was deposited on thermally oxidized Si substrates by magnetron sputtering. The GdFe amorphous layer was deposited by co-sputtering Fe and Gd targets at room temperature. The SiN layer served as the capping layer, preventing oxidation of GdFe. The 5 nm thick Pt underlayer was employed as a spin current source to provide SOT via the spin Hall effect (SHE). The saturation magnetization M_{S} and H_{p} of the sample were measured by vibrating sample magnetometry and found to be 200 and 160 mT, respectively (S1 in the supplementary material). Hall crosses of different dimensions were patterned by ultraviolet photolithography and Ar ion milling. Ti(10)/Al(200 nm) electrodes were sputtered onto the sample to perform electrical measurements.

### B. Spin–orbit torque (SOT) driven magnetization switching

All results of this work are based on measurements performed on a Hall cross having current channel and voltage channel widths of 60 *μ*m, unless stated otherwise. The schematic diagram in Fig. 1(a) shows the setup for measuring the Hall voltage V_{Hall} under an out-of-plane external field sweep H_{z}. The obtained square loop in Fig. 1(b) confirms PMA in the device, identifies the GdFe composition to be Fe-dominated, and defines the values of V_{Hall} corresponding to when the magnetization is oriented along +z or −z [±0.22 mV for a measuring current I_{M} of +1 mA flowing along +x, as shown in Fig. 1(b)]. H_{p} was estimated by measuring V_{Hall} under an in-plane external field sweep H_{x} and found to be 160 mT (S1 in the supplementary material). We also performed harmonic Hall measurements to confirm the SOT from Pt (S2 in the supplementary material). Figure 1(c) depicts the experimental setup for performing SOT driven magnetization switching. Due to the SHE in Pt, charge current I_{C} flowing along +x leads to a spin current I_{S}, with polarization $\sigma $ along –y, flowing along +z. I_{S} flowing into GdFe results in a damping-like SOT $ \tau DL ^$ along $ m ^\xd7( \sigma ^ \xd7 m ^)$. This SOT is responsible for switching the magnetization from +z to −z in the presence of an external magnetic field H_{ext} along +x. Depending on the polarity of switching to be achieved, we initialize the magnetization along ±z by applying H_{z} of ±100 mT, respectively. After this initialization, a small H_{x} is applied to assist magnetization switching. The applied current I_{C} is swept along ±x and V_{Hall} is measured with I_{M} of +1 mA. As shown in Fig. 1(d), reversible switching is observed in a single current loop. The sense of switching can be reversed further by reversing the direction of H_{x}. The gradual change observed in V_{Hall} with I_{C} indicates that switching proceeds via nucleation and expansion of reversed domains. This has been confirmed by polar magneto-optic Kerr effect (PMOKE) imaging (S3 in the supplementary material). The difference in V_{Hall} amplitude between the signals in Figs. 1(b) and 1(d) can also be understood in terms of the change in the domain structure observed in the Hall cross by PMOKE. We define the critical switching current I_{sw} as the current at which V_{Hall} reverses its polarity. I_{sw} for different values of H_{x} are shown in Fig. 1(e).

### C. Realization of NAND operation

To realize logic operations using SOT driven magnetization switching, we first define two different current levels I_{0} and I_{1} as corresponding to the input logic states “0” and “1,” respectively. Throughout this work, we define I_{0 }= 1 mA and I_{1 }= 36 mA, unless stated otherwise. Two separate current sources, named A and B, are used to provide the two input currents I_{A} and I_{B}, respectively. For example, the input (0, 1) corresponds to (I_{A}, I_{B}) = (1 mA, 36 mA). The different combinations of inputs are shown in Fig. 2(a), along with the switching curve corresponding to *μ*_{0}H_{x} = +5 mT. We define the outputs “0” and “1” as corresponding to when the magnetization points along ±z. This is detected by classifying V_{Hall} values below and above zero as “0” and “1”, respectively.

The measurement sequence is as follows: first, *μ*_{0}H_{z }= +100 mT is applied to initialize the magnetization along +z. Second, in the presence of an in-plane field *μ*_{0}H_{x} = +5 mT, the input pair (0,0) is applied to the device using current sources A and B. This corresponds to a total current of 2 mA flowing through the device. Third, after the input pair (0,0) is turned off, a sense current I_{M} of +1 mA is applied to measure V_{Hall} and, thereby, detect the magnetization state. Finally, a reset current I_{Reset} (=−60 mA) is applied to bring the magnetization state to +z. The steps listed above, excluding initialization, are repeated multiple times for different input pairs of currents and the output V_{Hall} corresponding to each input pair is measured. The outputs measured corresponding to multiple input pairs are given in Fig. 2(b). Based on the threshold for determining “0” and “1” discussed previously, we see that the truth table for this operation is that of a NAND gate [Fig. 2(c)].

### D. Realization of NOR operation

Having realized the NAND operation, keeping all other previously defined parameters the same, we increase *μ*_{0}H_{x} from +5 to +30 mT. As seen from the switching curve in Fig. 3(a), the increased H_{x} will result in the magnetization being switched for all input pairs, except for (0, 0). Using the same measurement sequence as in the NAND operation, we measure V_{Hall} and plot the outputs for multiple input pairs [Fig. 3(b)]. The truth table for this operation is found to resemble that of a NOR gate [Fig. 3(c)].

### E. Realization of AND and OR operations

We have realized NAND and NOR operations using positive in-plane fields *μ*_{0}H_{x }= +5 and +30 mT, respectively, to switch the magnetization from “1” to “0.” By reversing the polarity of *μ*_{0}H_{x} and initializing the magnetization from “0,” we should be able to achieve the opposite sense of switching and, thus, realize the AND and OR operations. This was realized utilizing the switching curves for *μ*_{0}H_{x }= −5 and −30 mT, as shown in Figs. 4(a) and 4(b), respectively. Note that the initial state of magnetization corresponds to “0,” and I_{Reset}, in this case, brings the magnetization to −z. The outputs corresponding to multiple input pairs and the obtained truth tables for both AND and OR operations are shown in Figs. 4(c) and 4(d).

### F. General scheme of choosing currents for programmable logic

_{sw}for different values of H

_{x}are shown in Fig. 5(a), along with the logic operation realized using different H

_{X}. We define I

_{sw(Hi)}and I

_{sw(Lo)}as the critical switching currents corresponding to the lower and higher H

_{x}magnitudes that have been chosen. In all the above realized logic operations, we require that the input (0, 0) should not switch the initialized magnetization state, while the input (1, 1) should necessarily switch the initialized magnetization state. This requires all allowed (I

_{0}, I

_{1}) pairs to satisfy the inequalities,

Combining (1) and (2) and using I_{sw(Lo) }= 26 mA (for *μ*_{0}H_{x }= ±30 mT) and I_{sw(Hi) }= 40 mA (for *μ*_{0}H_{x }= ±5 mT), we obtain the operation window, indicated in the shaded area of Fig. 5(b), where different (I_{0}, I_{1}) combinations will be able to realize all four of the above logic operations. Depending on the choice of (I_{0}, I_{1}), the output of the (0, 1) and (1, 0) inputs may be closer to the defined threshold of the zero Hall voltage.

Additionally, we confirm the repeatability of the switching curve (S4 in the supplementary material) and also estimate the error in different logic operations for 100 random input pairs (S5 in the supplementary material). To highlight the advantage of using the SOT driven magnetization switching of the GdFe FiM over conventional FMs, we compare the switching energy of the device presented in this work with that of a HM/CoFeB system (S6 in the supplementary material). After accounting for the difference in the magnetic properties and other parameters, the FiM system is found to be more energy efficient in its switching operation, highlighting the advantage of FiMs over FMs.

## III. CONCLUSION

We realized programmable spin logic in a Pt/GdFe bilayer by utilizing SOT driven magnetization switching. Four different logic operations, namely, NAND, NOR, AND, and OR, were realized by changing the in-plane external magnetic field. A general scheme for choosing the input currents corresponding to the logic inputs was also developed. Comparing the switching energy efficiency of the proposed ferrimagnet system with a conventional ferromagnet system, the former was found to be more energy efficient. However, a few challenges remain to be addressed before such proposed spin logic devices can become commercially viable. The temperature dependence of the gyromagnetic ratio γ of RE–TM alloy FiMs can result in magnetic properties of the FiM having a strong temperature dependence, which, in turn, is undesirable for device applications.^{21} Yet, another aspect that needs to be considered is the reduction in the critical switching current. One possibility in this regard is to improve the spin Hall effect in the HM by methods such as ion implantation^{22–25} and sputtering.^{26}

These challenges need to be addressed before spin logic devices, like those proposed in this work, can be ready for large scale production. In conclusion, this work presents a spin logic prototype, based on SOT driven switching in a HM/FiM bilayer, compatible with logic-in-memory architectures, for future commercial use.

## SUPPLEMENTARY MATERIAL

See the supplementary material for additional details.

## ACKNOWLEDGMENTS

Yasuhiro Fukuma and Hironori Asada would like to acknowledge JSPS Grant-in-Aid (KAKENHI No. 22K04198), KIOXIA Corporation, and Iketani Science and Technology Foundation.

## AUTHOR DECLARATIONS

### Conflict of Interest

The authors have no conflicts to disclose.

### Author Contributions

**Arun Jacob Mathew:** Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Validation (equal); Writing – original draft (equal). **Yufei Gao:** Data curation (equal); Formal analysis (equal); Investigation (equal); Validation (equal). **Junwen Wang:** Data curation (equal); Formal analysis (equal); Investigation (equal); Validation (equal). **Mojtaba Mohammadi:** Supervision (equal); Visualization (equal); Writing – review & editing (equal). **Hiroyuki Awano:** Resources (equal); Supervision (equal); Visualization (equal); Writing – review & editing (equal). **Masaaki Takezawa:** Resources (equal); Supervision (equal). **Hironori Asada:** Funding acquisition (equal); Resources (equal); Supervision (equal); Visualization (equal); Writing – review & editing (equal). **Yasuhiro Fukuma:** Conceptualization (equal); Funding acquisition (equal); Project administration (equal); Resources (equal); Supervision (equal); Visualization (equal); Writing – review & editing (equal).

## DATA AVAILABILITY

The data that support the findings of this study are available from the corresponding author upon reasonable request.