As observed in Heusler Alloys, atomic damage plays an important role in insulating tunnel barrier materials in MTJs. Examples include spinel-type oxides ab2o4that identification is advantageous for lattice matched heterointerfaces of BCC-based ferromagnetic materials with high TMR ratio and/or low resistance area products (ra))34,35,36,37. The physical properties of TMR junctions desired for spitronic applications can be potentially addressed by wide variations of components, such as their composition and atomic damage. To tackle this complexity, data-driven material design has opened up a new era of material science, but exploration of materials using traditional machine learning models such as Bayesian optimization and Monte Carlo Tree search can make efficient material exploration difficult due to the numerous combinational explosions from the freedom of the material itself.
To address the above issues, another approach is presented here. This is not just using first principle calculations and machine learning, but also combining it with quantum annealing (QA), inspired by recently available quantum computing technologies. Focusing on the atomic damage of MGGA2o4 For example, MTJ, that is, Fe/Atomic-Dording Mgga2o4/fe(001) system, demonstrates proof-of-concept research searching for appropriate MTJs in energy-stable points (low \(\delta {e} _{{\rm {total}} \)), higher TMR ratio and lower ra Numbers by optimizing the atomic arrangement of Mg and Ga in Mgga.2o4 Tunnel barrier.
MTJ with reverse spinel MGGA2o4 As shown in Figure 9a, all Mg and half of the Ga atoms randomly occupy the octahedral site (orange site in Figure 9a), and the remaining Ga atoms occupy the tetrahedral site (green site in Figure 9a). In this work, the atomic arrangement of Mg and GA at the octahedral site, and the number of total combinations can be defined as follows: \({10}_{{c}_{5}} = 252 \)can be optimized by first-principles calculations of density sensory theory (DFT), machine learning, and QA technology. In a QA-based framework, the combination optimization problem is replaced by the ISING model, where QA obtains the lowest ISING energy of a particular ISING Hamiltonian. ISING Model Hamiltonians can be built using machine learning, so-called factorization machines (FM).38. In the FM model, the target properties of interest can be expressed by the atomic arrangement of MG and GA as follows:
$$f({\boldsymbol {x}})=b+\mathop{\sum}\limits_{i=1}^{n}{q}_{i}{i}{x}_{i}+\mathop{\sum}}\limits_{i=1}}\limits_{j=i+1}^{n}\langle{v}_{i},{v}_{j}\rangle{x}_{i}{i}{x}_{j},$$
(4)
where \(n \) The number of qubits corresponding to the site of damage [\(N=10\) in this work as shown in Fig. 9a] And vector \({\boldsymbol {x}} = {\boldsymbol {\{}}{x}_{1}, \,{x}_{2}, \,\ldots, \,{x}_{{n}{\boldsymbol {\}}} A descriptor that defines the atomic arrangement of Mg and Ga (\({x} _{i} = 0 \) mg and \({x} _{i} = 1 \) In case of GA in a disturbed area \(I\)). Fitting model parameters are bias terms \(b \)linear terms \({q} _ {i} \) and secondary terms \(\langle {v}_{i}, {v}_{j}\rangle={\sum}_{k}^{k}{v}_{ik}{v}_{jk}\) {v}_{jk}\). Hyperparameters \(k \) Determined the rank of the FM model and optimized to 7, 2, and 3 for optimization \(\delta {e} _{{\rm {total}} \)TMR, and RA, respectively. Fit model parameters, \({q} _ {i} \) and \(\langle {v}_{i}, {v}_{j}\rangle \)to solve the ISING model by QA, you can convert it to the following quadratic unconstrained binary optimization (QUBO) form:
$$\begin{array}{rcl}{q}_{ij}=\left\{\begin{array}{l}{q}_{i}\,(i=j)\\langle,{v}_{i}\,(i\,\ne\,j)\end{array}\right. \end {array}. $$
(5)
a MTJ structure of Fe/atomic damage MGGA2o4/Fe (001). Here, Mg and Ga atoms randomly occupy the octahedral sites (orange sites). b Calculation amounts combined with QA, FM and DFT40.
Ising Hamiltonian has been called hqubo Next is given as
$${h}_{{\rm{q}}{\rm{u}}{\rm{b}}{\rm{o}}} = \mathop {\sum}\limits_{i < j}{q}_{ij}{x}_{i}{x}_{j}+\alpha {\left(\mathop {\sum }_{i=1}^{n}{x}_{i} - \frac {n}{2}\right)}^{2}. $$
(6)
The first term is a cost function, and the second term is a penalty term that limits the atomic composition of Mg and GA to 1:1. Hyperparameters \(\alpha\) (real numbers, \(\ alpha> 0 \)) to control the intensity of the penalty period. QA solves hqubo And the solution with the lowest ISING energy is the next candidate for the MG/GA atomic arrangement, which requires the evaluation of the target's physical properties by DFT calculations. Total energy, ground state electronic structures, and spin transport properties, along with the basis of linear combinations of atomic orbitals implemented in the Quantum Atomistix Toolkit (Quantum-ATK) simulations, are derived from first-principles calculations with the basis of linear combinations of atomic orbitals.39. GGA is used in exchange correlation function18,For more information on calculation methods, see the reference. 40. The calculation flow, FM + QA + DFT, is shown in Figure 9b. FM + QA + DFT is referred to below as FM + QA (DFT is omitted).
Figure 10 shows the FM+QA results for the search history to obtain the appropriate MTJ. \(\delta {e} _{{\rm {total}} \)TMR, and RA. To investigate the effectiveness of FM+QA, FM+simulation annealing (FM+SA), FM+Exact Solver (FM+ES), FM+Exact Solver (FM+ES), ISING energy is evaluated for all atomic configurations.x's) training data, and the vector x that gives the lowest equal energy, are always chosen as the next candidate. ), Bayesian optimization (BO), and random search (RS) were also performed, with 10 trials performed using different initial training datasets containing randomly selected 20 MTJ structures. for \(\delta {e} _{{\rm {total}} \)As shown in Figure 10A, FM+QA successfully obtains the appropriate MTJ within approximately 50 structures (including training data for 20 structures), which is comparable to that of FM+ES (Figure 10C), confirming the FM+QA method. The efficiency obtained from FM+QA is slightly faster than FM+SA (see Figure 10b), and significantly more than BO and RS (see Figure 10D, E). For TMR, similar search efficiencies are obtained between FM+QA, FM+SA, and FM+ES (Figures 10F–H), which is much better than those of BO and RS (see Figures 10I, J). Therefore, from these results, FM+QA may be a promising approach in searching for preferred MTJs with energetically stable atomic damage and best TMR properties.
a–e \(\delta {e} _{{\rm {total}} \)(f) – (j)tmr, and (k) – (o) RA obtained by FM+QA, FM+SA, FM+ES, BO, and RS, respectively. Ten trials were performed using a training dataset containing 20 MTJ structures for each property and method. The horizontal axis contains the initial training dataset, and its range varies between RS and others40.
On the other hand, it is difficult to optimize the atomic arrangement of MTJs using low RA using FM+QA. Figure 10K shows that the variation in the number of structures required to optimize is very wide, very wide depending on the initial training dataset, with a maximum of over 150 structures required (see Inset). This feature has also been confirmed in FM+SA and FM+ES (see Figure 10M, N). These results appear to reflect the inaccuracy of FM training. hqubo It's built rather than QA solver performance. Therefore, it is difficult to reach the optimal solution, i.e. low MTJ rasuch hqubo. In contrast, BO efficiently reaches the best MTJ with the lowest ra.
Here, potential solutions to improve the robustness of FM models ra Here's a discussion of optimization. Hyperparameters can be used to improve performance of FM models k Bigger k = 10, kSet to 3 and brings you the best performance from internally verified pre-tests k = 1-10 in this proof-of-concept study. Additionally, the size of the database used in this demo: That is . , 20 training data may be too small and/or too hungry, raAtomic arrangement in the FM model. The latter becomes more serious in defining the generalizability of the FM model, but it is expected to be mitigated in a natural way at the actual level of FM+QA(+DFT) where combinatorial explosions occur, and the number of training data sets will be greater than this demonstration. Furthermore, in real-world problems, finding some good material candidates is beneficial for device development through materials informatics, rather than finding just one best solution. In this context, our demonstration still offers efficient search performance of BO, although it is inferior to BO. \(\delta {e} _{{\rm {total}} \) and TMR ratio raOptimization (“Efficiency Search Results””ra*” in Figure 4 of ref.37).
In conclusion, we proposed an alternative approach that can be adapted to the combinatorial explosion problem by combining cutting-edge QA, FM and DFT technologies, and applied it to the MTJ atomic damage optimization problem.2o4. Our proof-of-concept research has left room for achieving higher search efficiency with specific physical properties and improving methods, such as Bayesian optimization. Current approaches may provide breakthroughs to overcome combinatorial explosions that are inaccessible to traditional machine learning, regardless of whether the system is ordered and impaired. More specifically, FM+QA+DFT can be applied to multicomponent materials such as the Heusler Alloy family when atomic elements, composition, defects, crystal structures, and other combinational optimization problems of degrees of freedom of interest map to the ISING model.
