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Discovering the compact、stable and easily controllable nanoscale non-trivial topological magnetic structures---magnetic skyrmions,is the key to develop next-generation high-density, high-speed,and low-energy non-volatile information storage devices.Based on the topological generation mechanism,magnetic skyrmions could be generated through the Dzyaloshinskii–Moriya Interaction (DMI) induced by space-reversal symmetry broken.Two dimensional (2D) non-centrosymmetric Janus could generate vertical built-in electric fields to break spatial inversion symmetry. Therefore, seeking 2D Janus with intrinsic magnetism is fundamental to develop the novel chiral magnetic storage technologies.In this work, we combined detailed machine learning techniques and first-principles calculations to discover the magnetism of the unexplored 2D janus. we first collected 1179 2D hexagonal ABC-type Janus based on the Materials Project database, and used elemental composition as feature descriptors to construct four machine learning models: Random Forest (RF), Gradient Boosting Decision Trees (GBDT), Extreme Gradient Boosting (XGB), and Extra Trees (ET). These algorithms and models were constructed to predict lattice constants, formation energies, and magnetic moment, via hyperparameter optimization and ten-fold cross-validation. GBDT exhibits the highest accuracy and best prediction performance for magnetic moment classification. Subsequently, the collected data of 82,018 yet-undiscovered 2D Janus,were input into the trained models to generate 4,024 high magnetic moment 2D Janus with thermal stability. First-principles calculations were employed to validate random sample of 13 Janus with high magnetic moment. This study provides an effective machine learning framework for magnetic moment classification and high-throughput screening of 2D Janus, accelerating the exploration of magnetic properties in 2D Janus structures.
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Keywords:
- machine learning /
- two-dimensional Janus materials /
- magnetic moment /
- first-principles calculations
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图 1 机器学习结合DFT发掘高磁矩Janus材料步骤
Figure 1. Steps for discovering high magnetic moment Janus materials by combining machine learning with DFT.
图 2 六角晶系ABC型Janus材料原子结构的(a)侧视图和(b)俯视图
Figure 2. (a) Side view and (b)top view of atomic structures of hexagonal ABC-type Janus materials.
图 3 数据集中二维 Janus 材料的(a)晶格常数 a 和b, (b)晶格常数 c, (c)形成能和(d)总磁矩的分布
Figure 3. The distribution of (a) lattice constants a and b, (b) lattice constant c, (c) formation energy and (d) total magnetic moment of the dataset of 2D Janus materials.
图 4 晶格常数预测: 最优模型在十折交叉验证中的散点图. (a) Lattice a = b预测任务最优模型: 极端随机树, (b) Lattice c预测任务最优模型: 极端梯度提升
Figure 4. Prediction of lattice constants: scatter plots for the optimal models in ten-fold cross-validation. (a) The optimal model for the lattice a=b prediction task:ET, (b) The optimal model for the lattice c prediction task:XGB.
图 5 形成能预测: 四种模型在十折交叉验证上的散点图. (a)随机森林, (b)梯度提升决策树, (c)极端梯度提升(d)极端随机树
Figure 5. Prediction of formation energy: scatter plots for four models in ten-fold cross-validation. (a) RF (b) GBDT, (c) XGB, (d) ET.
图 6 磁矩分类预测: 四种模型在十折交叉验证上的混淆矩阵. (a)随机森林, (b)梯度提升决策树, (c)极端梯度提升(d)极端随机树
Figure 6. Prediction of magnetic moment classification: confusion matrices for four models in ten-fold cross-validation. (a) RF, (b) GBDT, (c) XGB, (d) ET.
图 7 13种二维六角晶系Janus原子结构的侧视图
Figure 7. Side view of atomic structures of 13 two-dimensional hexagonal Janus materials.
表 1 不同训练任务中机器学习最优模型的超参数
Table 1. The hyperparameters of the optimal machine learning models in various training tasks.
模型 超参数 GBDT(磁矩分类) learning_rate = 0.01603011, max_depth = 5, n_estimators = 272, subsample = 0.69895067 GBDT(形成能) learning_rate = 0.02, max_depth = 6, n_estimators = 353, subsample = 0.93030056 ET(晶格常数a和b) max_depth = 10, max_features = 0.60, n_estimators = 100,
min_samples_leaf = 2, min_samples_split = 4XGB(晶格常数c) learning_rate = 0.02, n_estimators = 300, max_depth = 5,
subsample = 0.8, colsample_bytree = 0.49613519
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表 2 晶格常数预测
Table 2. Prediction of lattice constants.
模型 Lattice a=b Lattice c MAE RMSE $R^2$ MAE RMSE $R^2$ RF 0.5485 0.8104 0.7375 0.6491 1.0001 0.6872 GBDT 0.4477 0.7350 0.7829 0.6679 0.9924 0.6923 XGB 0.5427 0.7968 0.7462 0.5953 0.9474 0.7186 ET 0.3469 0.6808 0.8137 0.6534 1.0103 0.6817
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表 3 形成能预测: 四种机器学习模型的评价指标
Table 3. The Prediction of formation energy: evaluation metrics of four machine learning models.
模型 MAE RMSE $R^2$ RF 0.1054 0.1697 0.8671 GBDT 0.0798 0.1411 0.9070 XGB 0.0959 0.1533 0.8930 ET 0.1120 0.1701 0.8657
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表 4 磁矩分类预测: 四种机器学习模型的评价指标
Table 4. Prediction of magnetic moment classification.: evaluation metrics of four machine learning models.
模型 Accuracy Precision Recall F1 score RF 0.8770 0.8459 0.7636 0.7862 GBDT 0.8948 0.8498 0.8182 0.8263 XGB 0.8762 0.8398 0.7697 0.7883 ET 0.8795 0.8392 0.7778 0.7965
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表 5 13种结构优化后的六角晶系ABC型Janus材料的晶格常数, 形成能和磁矩
Table 5. Optimized lattice constants, formation energies and magnetic moments of 13 two-dimensional hexagonal ABC-type Janus materials.
Formula Lattice constants Formation energy (eV) $ |\mu| $ ($ \mu_B $) a = b(Å) c(Å) A B C ErFeTb 3.35 18.25 –2.02 2.51 3.03 6.24 FeNO 2.92 15.00 –11.87 1.17 0.08 0.47 HoRuSr 4.90 18.79 –6.66 3.79 0.02 0.05 DyOsSr 4.18 18.87 –6.89 4.89 0.00 0.13 EuSbSr 5.43 18.69 –5.53 6.85 0.01 0.05 HoIrSr 4.58 18.79 –7.24 3.72 0.00 0.05 LiUZn 2.89 18.13 –0.44 0.00 1.65 0.01 PuSZn 4.52 18.13 –6.75 5.61 0.10 0.01 GdKU 7.46 18.13 –2.39 7.33 0.00 2.96 LuNbTi 3.02 18.13 –1.76 0.02 0.28 1.67 GdHfSe 5.03 18.93 –8.46 7.33 0.34 0.02 NaTbZn 4.65 18.69 –1.87 0.02 6.00 0.00 HoNpSr 3.69 18.46 –1.80 3.81 4.38 0.08
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