{"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. 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":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physical Review B","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1103/physrevb.110.014443","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Physics and Astronomy","Score":null,"Total":0}
引用次数: 0
Abstract
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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