{"title":"Spin-deformation coupling in two-dimensional polar materials","authors":"J. A. Sánchez-Monroy, Carlos Mera Acosta","doi":"10.1103/physrevb.110.205412","DOIUrl":null,"url":null,"abstract":"The control of the spin degree of freedom is at the heart of spintronics, which can potentially be achieved by spin-orbit coupling or band topological effects. In this paper, we explore another potential controlled mechanism under debate: the spin-deformation coupling (SDC)—the coupling between intrinsic or extrinsic geometrical deformations and the spin degree of freedom. We focus on polar-deformed thin films or two-dimensional compounds, where the Rashba spin-orbit coupling (SOC) is considered as an <mjx-container ctxtmenu_counter=\"10\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(6 0 5 (4 1 2 3))\"><mjx-mrow data-semantic-annotation=\"clearspeak:simple\" data-semantic-children=\"0,4\" data-semantic-content=\"5,0\" data-semantic- data-semantic-owns=\"0 5 4\" data-semantic-role=\"prefix function\" data-semantic-speech=\"SU left parenthesis 2 right parenthesis\" data-semantic-type=\"appl\"><mjx-mtext data-semantic-font=\"normal\" data-semantic- data-semantic-operator=\"appl\" data-semantic-parent=\"6\" data-semantic-role=\"prefix function\" data-semantic-type=\"function\" style='font-family: MJX-STX-ZERO, \"Helvetica Neue\", Helvetica, Roboto, Arial, sans-serif;'><mjx-utext style=\"font-size: 90.6%; padding: 0.828em 0px 0.221em; width: 18px;\" variant=\"-explicitFont\">SU</mjx-utext></mjx-mtext><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"appl\" data-semantic-parent=\"6\" data-semantic-role=\"application\" data-semantic-type=\"punctuation\"><mjx-c></mjx-c></mjx-mo><mjx-mrow data-semantic-added=\"true\" data-semantic-children=\"2\" data-semantic-content=\"1,3\" data-semantic- data-semantic-owns=\"1 2 3\" data-semantic-parent=\"6\" data-semantic-role=\"leftright\" data-semantic-type=\"fenced\" space=\"2\"><mjx-mo data-semantic- data-semantic-operator=\"fenced\" data-semantic-parent=\"4\" data-semantic-role=\"open\" data-semantic-type=\"fence\" style=\"vertical-align: -0.02em;\"><mjx-c>(</mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"4\" data-semantic-role=\"integer\" data-semantic-type=\"number\"><mjx-c>2</mjx-c></mjx-mn><mjx-mo data-semantic- data-semantic-operator=\"fenced\" data-semantic-parent=\"4\" data-semantic-role=\"close\" data-semantic-type=\"fence\" style=\"vertical-align: -0.02em;\"><mjx-c>)</mjx-c></mjx-mo></mjx-mrow></mjx-mrow></mjx-math></mjx-container> non-Abelian gauge field. We demonstrate that the dynamics between surface and normal electronic degrees of freedom can be properly decoupled using the thin-layer approach by performing a suitable gauge transformation, as introduced in the context of many-body correlated systems. Our work leads to three significant results: (i) gauge invariance implies that the spin is uncoupled from the surface's extrinsic geometry, challenging the common consensus; (ii) the Rashba SOC on a curved surface can be included as an <mjx-container ctxtmenu_counter=\"11\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(6 0 5 (4 1 2 3))\"><mjx-mrow data-semantic-annotation=\"clearspeak:simple\" data-semantic-children=\"0,4\" data-semantic-content=\"5,0\" data-semantic- data-semantic-owns=\"0 5 4\" data-semantic-role=\"prefix function\" data-semantic-speech=\"SU left parenthesis 2 right parenthesis\" data-semantic-type=\"appl\"><mjx-mtext data-semantic-font=\"normal\" data-semantic- data-semantic-operator=\"appl\" data-semantic-parent=\"6\" data-semantic-role=\"prefix function\" data-semantic-type=\"function\" style='font-family: MJX-STX-ZERO, \"Helvetica Neue\", Helvetica, Roboto, Arial, sans-serif;'><mjx-utext style=\"font-size: 90.6%; padding: 0.828em 0px 0.221em; width: 18px;\" variant=\"-explicitFont\">SU</mjx-utext></mjx-mtext><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"appl\" data-semantic-parent=\"6\" data-semantic-role=\"application\" data-semantic-type=\"punctuation\"><mjx-c></mjx-c></mjx-mo><mjx-mrow data-semantic-added=\"true\" data-semantic-children=\"2\" data-semantic-content=\"1,3\" data-semantic- data-semantic-owns=\"1 2 3\" data-semantic-parent=\"6\" data-semantic-role=\"leftright\" data-semantic-type=\"fenced\" space=\"2\"><mjx-mo data-semantic- data-semantic-operator=\"fenced\" data-semantic-parent=\"4\" data-semantic-role=\"open\" data-semantic-type=\"fence\" style=\"vertical-align: -0.02em;\"><mjx-c>(</mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"4\" data-semantic-role=\"integer\" data-semantic-type=\"number\"><mjx-c>2</mjx-c></mjx-mn><mjx-mo data-semantic- data-semantic-operator=\"fenced\" data-semantic-parent=\"4\" data-semantic-role=\"close\" data-semantic-type=\"fence\" style=\"vertical-align: -0.02em;\"><mjx-c>)</mjx-c></mjx-mo></mjx-mrow></mjx-mrow></mjx-math></mjx-container> non-Abelian gauge field in curvilinear coordinates; and (iii) we identify a previously unnoticed scalar geometrical potential dependent on the Rashba SOC strength. This scalar potential, independent of spin, represents the residual effect remaining after decoupling the normal component of the non-Abelian gauge field. The outcomes of our paper open alternative pathways for exploring the manipulation of spin degrees of freedom through the use of the SDC.","PeriodicalId":20082,"journal":{"name":"Physical Review B","volume":null,"pages":null},"PeriodicalIF":3.7000,"publicationDate":"2024-11-08","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.110.205412","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 control of the spin degree of freedom is at the heart of spintronics, which can potentially be achieved by spin-orbit coupling or band topological effects. In this paper, we explore another potential controlled mechanism under debate: the spin-deformation coupling (SDC)—the coupling between intrinsic or extrinsic geometrical deformations and the spin degree of freedom. We focus on polar-deformed thin films or two-dimensional compounds, where the Rashba spin-orbit coupling (SOC) is considered as an SU(2) non-Abelian gauge field. We demonstrate that the dynamics between surface and normal electronic degrees of freedom can be properly decoupled using the thin-layer approach by performing a suitable gauge transformation, as introduced in the context of many-body correlated systems. Our work leads to three significant results: (i) gauge invariance implies that the spin is uncoupled from the surface's extrinsic geometry, challenging the common consensus; (ii) the Rashba SOC on a curved surface can be included as an SU(2) non-Abelian gauge field in curvilinear coordinates; and (iii) we identify a previously unnoticed scalar geometrical potential dependent on the Rashba SOC strength. This scalar potential, independent of spin, represents the residual effect remaining after decoupling the normal component of the non-Abelian gauge field. The outcomes of our paper open alternative pathways for exploring the manipulation of spin degrees of freedom through the use of the SDC.
期刊介绍:
Physical Review B (PRB) is the world’s largest dedicated physics journal, publishing approximately 100 new, high-quality papers each week. The most highly cited journal in condensed matter physics, PRB provides outstanding depth and breadth of coverage, combined with unrivaled context and background for ongoing research by scientists worldwide.
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