{"title":"处理过氧化物中极子与氧空位之间的相互作用","authors":"Dylan Windsor, Haixuan Xu","doi":"10.1103/physrevmaterials.8.094406","DOIUrl":null,"url":null,"abstract":"Interactions between polarons and oxygen vacancies in oxides, which cause them to modify one another's physical properties, are highly important for applications such as photovoltaics and ferroelectrics. While the difficulty in modeling polarons using density functional theory (DFT) calculations has been alleviated by the recent development of various techniques, including, e.g., the Hubbard-U parameter and finite-size corrections, the underlying physics of polaron interactions with defects remains unknown. Here, we demonstrate that the polaron-vacancy complexes in <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>PbTi</mi><msub><mi mathvariant=\"normal\">O</mi><mn>3</mn></msub></mrow></math> have a preferred orbital configuration, different from the orbital configuration of the bulk polaron, by exploring multiple nearby local minima using <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>DFT</mi><mo>+</mo><mi mathvariant=\"normal\">U</mi></mrow></math>. To address the issue of polaron property dependence on the Hubbard-U value, we determine the U value via enforcement of piecewise linearity, and we employ finite-size corrections. Three local minima with different electronic configurations are found by varying the initial conditions: (i) a polaron trapped in a <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mrow><mi>Ti</mi><mtext>−</mtext></mrow><mn>3</mn><msub><mi>d</mi><mrow><mi>e</mi><mi>g</mi></mrow></msub></mrow></math> orbital on the first-nearest-neighbor Ti-ion of the oxygen vacancy (<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>e</mi><mi>g</mi></mrow></math> complex), (ii) a polaron trapped in a <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mrow><mi>Ti</mi><mtext>−</mtext></mrow><mn>3</mn><msub><mi>d</mi><mrow><mi>t</mi><mn>2</mn><mi>g</mi></mrow></msub></mrow></math> orbital at the same position (<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>t</mi><mn>2</mn><mi>g</mi></mrow></math> complex), and (iii) electrons delocalized across several nearby sites and both spin channels, resulting in a semilocalized state. We find that the <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>e</mi><mi>g</mi></mrow></math> complex is the most energetically favorable state, revealing a change in the orbital of the polaron when trapped by an oxygen vacancy, since the bulk polaron is found to be in a <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>t</mi><mn>2</mn><mi>g</mi></mrow></math> orbital. Furthermore, we demonstrate that great care must be taken to find the correct physical picture with <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>DFT</mi><mo>+</mo><mi mathvariant=\"normal\">U</mi></mrow></math>, since a small change in the initial conditions results in finding different local minima.","PeriodicalId":20545,"journal":{"name":"Physical Review Materials","volume":null,"pages":null},"PeriodicalIF":3.1000,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Treating interactions between polarons and oxygen vacancies in perovskite oxides\",\"authors\":\"Dylan Windsor, Haixuan Xu\",\"doi\":\"10.1103/physrevmaterials.8.094406\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Interactions between polarons and oxygen vacancies in oxides, which cause them to modify one another's physical properties, are highly important for applications such as photovoltaics and ferroelectrics. While the difficulty in modeling polarons using density functional theory (DFT) calculations has been alleviated by the recent development of various techniques, including, e.g., the Hubbard-U parameter and finite-size corrections, the underlying physics of polaron interactions with defects remains unknown. Here, we demonstrate that the polaron-vacancy complexes in <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><mrow><mi>PbTi</mi><msub><mi mathvariant=\\\"normal\\\">O</mi><mn>3</mn></msub></mrow></math> have a preferred orbital configuration, different from the orbital configuration of the bulk polaron, by exploring multiple nearby local minima using <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><mrow><mi>DFT</mi><mo>+</mo><mi mathvariant=\\\"normal\\\">U</mi></mrow></math>. To address the issue of polaron property dependence on the Hubbard-U value, we determine the U value via enforcement of piecewise linearity, and we employ finite-size corrections. Three local minima with different electronic configurations are found by varying the initial conditions: (i) a polaron trapped in a <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><mrow><mrow><mi>Ti</mi><mtext>−</mtext></mrow><mn>3</mn><msub><mi>d</mi><mrow><mi>e</mi><mi>g</mi></mrow></msub></mrow></math> orbital on the first-nearest-neighbor Ti-ion of the oxygen vacancy (<math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><mrow><mi>e</mi><mi>g</mi></mrow></math> complex), (ii) a polaron trapped in a <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><mrow><mrow><mi>Ti</mi><mtext>−</mtext></mrow><mn>3</mn><msub><mi>d</mi><mrow><mi>t</mi><mn>2</mn><mi>g</mi></mrow></msub></mrow></math> orbital at the same position (<math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><mrow><mi>t</mi><mn>2</mn><mi>g</mi></mrow></math> complex), and (iii) electrons delocalized across several nearby sites and both spin channels, resulting in a semilocalized state. We find that the <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><mrow><mi>e</mi><mi>g</mi></mrow></math> complex is the most energetically favorable state, revealing a change in the orbital of the polaron when trapped by an oxygen vacancy, since the bulk polaron is found to be in a <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><mrow><mi>t</mi><mn>2</mn><mi>g</mi></mrow></math> orbital. Furthermore, we demonstrate that great care must be taken to find the correct physical picture with <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><mrow><mi>DFT</mi><mo>+</mo><mi mathvariant=\\\"normal\\\">U</mi></mrow></math>, since a small change in the initial conditions results in finding different local minima.\",\"PeriodicalId\":20545,\"journal\":{\"name\":\"Physical Review Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":3.1000,\"publicationDate\":\"2024-09-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Physical Review Materials\",\"FirstCategoryId\":\"88\",\"ListUrlMain\":\"https://doi.org/10.1103/physrevmaterials.8.094406\",\"RegionNum\":3,\"RegionCategory\":\"材料科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATERIALS SCIENCE, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physical Review Materials","FirstCategoryId":"88","ListUrlMain":"https://doi.org/10.1103/physrevmaterials.8.094406","RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, MULTIDISCIPLINARY","Score":null,"Total":0}
Treating interactions between polarons and oxygen vacancies in perovskite oxides
Interactions between polarons and oxygen vacancies in oxides, which cause them to modify one another's physical properties, are highly important for applications such as photovoltaics and ferroelectrics. While the difficulty in modeling polarons using density functional theory (DFT) calculations has been alleviated by the recent development of various techniques, including, e.g., the Hubbard-U parameter and finite-size corrections, the underlying physics of polaron interactions with defects remains unknown. Here, we demonstrate that the polaron-vacancy complexes in have a preferred orbital configuration, different from the orbital configuration of the bulk polaron, by exploring multiple nearby local minima using . To address the issue of polaron property dependence on the Hubbard-U value, we determine the U value via enforcement of piecewise linearity, and we employ finite-size corrections. Three local minima with different electronic configurations are found by varying the initial conditions: (i) a polaron trapped in a orbital on the first-nearest-neighbor Ti-ion of the oxygen vacancy ( complex), (ii) a polaron trapped in a orbital at the same position ( complex), and (iii) electrons delocalized across several nearby sites and both spin channels, resulting in a semilocalized state. We find that the complex is the most energetically favorable state, revealing a change in the orbital of the polaron when trapped by an oxygen vacancy, since the bulk polaron is found to be in a orbital. Furthermore, we demonstrate that great care must be taken to find the correct physical picture with , since a small change in the initial conditions results in finding different local minima.
期刊介绍:
Physical Review Materials is a new broad-scope international journal for the multidisciplinary community engaged in research on materials. It is intended to fill a gap in the family of existing Physical Review journals that publish materials research. This field has grown rapidly in recent years and is increasingly being carried out in a way that transcends conventional subject boundaries. The journal was created to provide a common publication and reference source to the expanding community of physicists, materials scientists, chemists, engineers, and researchers in related disciplines that carry out high-quality original research in materials. It will share the same commitment to the high quality expected of all APS publications.