{"title":"过渡金属二聚体中 Dzyaloshinskii-Moriya 相互作用的可逆电场控制","authors":"Byungryul Jang, G. M. Pastor","doi":"10.1103/physrevb.110.014443","DOIUrl":null,"url":null,"abstract":"The anisotropic antisymmetric Dzyaloshinskii-Moriya (DM) interactions between local magnetic moments <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mrow><mi mathvariant=\"bold-italic\">μ</mi></mrow><mi>i</mi></msub></math> and <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mrow><mi mathvariant=\"bold-italic\">μ</mi></mrow><mi>j</mi></msub></math>, which can be induced by an external electric field (EF) are investigated in the framework of density functional theory by considering all <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mn>3</mn><mi>d</mi></mrow><mo>,</mo><mo> </mo><mrow><mn>4</mn><mi>d</mi></mrow></math>, and <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mn>5</mn><mi>d</mi></mrow></math> freestanding transition metal dimers. The possibilities of triggering and reversibly tuning chiral magnetic couplings by electric means are demonstrated. The dependence of the DM-coupling vector <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi mathvariant=\"bold-italic\">D</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub></math> on the EF strength <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>E</mi></math> is shown to be approximately linear for <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mo>|</mo><mi>E</mi><mo>|</mo><mo>≤</mo><mn>0.6</mn></mrow></math> V/Å, with only minor third-order corrections. The first- and third-order zero-field electric susceptibility of the DM couplings are determined and analyzed as a function of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>d</mi></math>-band filling. The correlations between them and the chirality of the spin-orbit energy are displayed. From a microscopic perspective, the EF-induced DM couplings are shown to stem from the permanent electric dipole moments <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msup><mrow><mi mathvariant=\"bold-italic\">p</mi></mrow><mn>0</mn></msup></math> that are already present in the field-free dimers whenever their local magnetic moments are not collinear. The symmetry rules governing <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msup><mrow><mi mathvariant=\"bold-italic\">p</mi></mrow><mn>0</mn></msup></math> and its chirality are discussed. Finally, the dependence of the EF-induced DM couplings on the degree of noncollinearity of the magnetic order is quantified by varying systematically the angle <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>θ</mi></math> between the local moments. While the electronic calculations show that the changes in the effective <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi mathvariant=\"bold-italic\">D</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub></math> can be quite important for arbitrary <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>θ</mi></math>, one also observes that <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi mathvariant=\"bold-italic\">D</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub></math> depends weakly on <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>θ</mi></math> and is thus transferable within a limited range of noncollinear magnetic arrangements, provided that they are not too far from the lowest-energy configuration.","PeriodicalId":20082,"journal":{"name":"Physical Review B","volume":null,"pages":null},"PeriodicalIF":3.7000,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Reversible electric field manipulation of the Dzyaloshinskii-Moriya interactions in transition metal dimers\",\"authors\":\"Byungryul Jang, G. M. Pastor\",\"doi\":\"10.1103/physrevb.110.014443\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The anisotropic antisymmetric Dzyaloshinskii-Moriya (DM) interactions between local magnetic moments <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><msub><mrow><mi mathvariant=\\\"bold-italic\\\">μ</mi></mrow><mi>i</mi></msub></math> and <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><msub><mrow><mi mathvariant=\\\"bold-italic\\\">μ</mi></mrow><mi>j</mi></msub></math>, which can be induced by an external electric field (EF) are investigated in the framework of density functional theory by considering all <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><mrow><mn>3</mn><mi>d</mi></mrow><mo>,</mo><mo> </mo><mrow><mn>4</mn><mi>d</mi></mrow></math>, and <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><mrow><mn>5</mn><mi>d</mi></mrow></math> freestanding transition metal dimers. 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From a microscopic perspective, the EF-induced DM couplings are shown to stem from the permanent electric dipole moments <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><msup><mrow><mi mathvariant=\\\"bold-italic\\\">p</mi></mrow><mn>0</mn></msup></math> that are already present in the field-free dimers whenever their local magnetic moments are not collinear. The symmetry rules governing <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><msup><mrow><mi mathvariant=\\\"bold-italic\\\">p</mi></mrow><mn>0</mn></msup></math> and its chirality are discussed. Finally, the dependence of the EF-induced DM couplings on the degree of noncollinearity of the magnetic order is quantified by varying systematically the angle <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><mi>θ</mi></math> between the local moments. 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引用次数: 0
摘要
通过考虑所有 3d、4d 和 5d 独立过渡金属二聚体,在密度泛函理论的框架内研究了局部磁矩 μi 和 μj 之间的各向异性不对称 Dzyaloshinskii-Moriya (DM) 相互作用,这种作用可以由外部电场 (EF) 引起。研究证明了通过电手段触发和可逆调节手性磁耦合的可能性。在 |E|≤0.6 V/Å 时,DM 耦合矢量 Dij 与 EF 强度 E 的关系近似线性,仅有微小的三阶修正。确定并分析了 DM 耦合的一阶和三阶零场电感应强度与 d 波段填充的函数关系。并显示了它们与自旋轨道能的手性之间的相关性。从微观角度看,EF 引起的 DM 耦合源于永久电偶极矩 p0,只要无场二聚体的局部磁矩不是共线的,这些永久电偶极矩就已经存在于无场二聚体中。讨论了 p0 及其手性的对称性规则。最后,通过系统地改变局部磁矩之间的角度θ,量化了 EF 引发的 DM 耦合对磁序非共线性程度的依赖。电子计算结果表明,有效 Dij 的变化对任意 θ 都非常重要,同时我们还观察到 Dij 对 θ 的依赖性很弱,因此可以在有限的非共轭磁排列范围内转移,只要它们与最低能量构型相差不太远。
Reversible electric field manipulation of the Dzyaloshinskii-Moriya interactions in transition metal dimers
The anisotropic antisymmetric Dzyaloshinskii-Moriya (DM) interactions between local magnetic moments and , which can be induced by an external electric field (EF) are investigated in the framework of density functional theory by considering all , and freestanding transition metal dimers. The possibilities of triggering and reversibly tuning chiral magnetic couplings by electric means are demonstrated. The dependence of the DM-coupling vector on the EF strength is shown to be approximately linear for V/Å, with only minor third-order corrections. The first- and third-order zero-field electric susceptibility of the DM couplings are determined and analyzed as a function of -band filling. The correlations between them and the chirality of the spin-orbit energy are displayed. From a microscopic perspective, the EF-induced DM couplings are shown to stem from the permanent electric dipole moments that are already present in the field-free dimers whenever their local magnetic moments are not collinear. The symmetry rules governing and its chirality are discussed. Finally, the dependence of the EF-induced DM couplings on the degree of noncollinearity of the magnetic order is quantified by varying systematically the angle between the local moments. While the electronic calculations show that the changes in the effective can be quite important for arbitrary , one also observes that depends weakly on and is thus transferable within a limited range of noncollinear magnetic arrangements, provided that they are not too far from the lowest-energy configuration.
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