Anisotropic RKKY interaction in doped monolayer germanene: spin–orbit coupling effects

IF 1.9 4区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Pramana Pub Date : 2024-05-11 DOI:10.1007/s12043-024-02763-w
Farshad Azizi, Hamed Rezania
{"title":"Anisotropic RKKY interaction in doped monolayer germanene: spin–orbit coupling effects","authors":"Farshad Azizi,&nbsp;Hamed Rezania","doi":"10.1007/s12043-024-02763-w","DOIUrl":null,"url":null,"abstract":"<div><p>We study exchange interaction between two magnetic impurities, i.e. the Ruderman–Kittel–Kasuya–Yosida (RKKY), in doped germanene layer by directly computing Green’s function within the full band method. Kane–Mele model Hamiltonian in the presence of spin–orbit coupling and longitudinal magnetic field has been applied to describe electron dynamics. The behaviour of RKKY interaction as a function of distance between the localised moments has been analysed for different values of magnetic field and spin–orbit coupling strength for electrons. Also, the effects of electron doping as the variation of chemical potential on behaviours of RKKY interaction have been investigated. It has been shown that a magnetic field along the <i>z</i>-axis mediates an anisotropic interaction which corresponds to an XXZ model interaction between two magnetic moments. The exchange interaction along the arbitrary direction between two magnetic moments has been obtained using the static spin susceptibilities of doped germanene layer in the presence of spin–orbit coupling. The effects of magnetic field, electron doping and spin–orbit coupling on the dependence of exchange interaction on distance between moments are investigated by calculating the correlation function of the spin density operators. Our results show that the electron doping impacts the spatial behaviour of RKKY interaction. Moreover, spin–orbit coupling effects on both longitudinal and transverse RKKY interactions have been investigated for doped germanene monolayer. Finally, we have studied in detail the temperature dependence of RKKY interactions for various amounts of spin–orbit coupling strengths.</p></div>","PeriodicalId":743,"journal":{"name":"Pramana","volume":"98 2","pages":""},"PeriodicalIF":1.9000,"publicationDate":"2024-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Pramana","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1007/s12043-024-02763-w","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0

Abstract

We study exchange interaction between two magnetic impurities, i.e. the Ruderman–Kittel–Kasuya–Yosida (RKKY), in doped germanene layer by directly computing Green’s function within the full band method. Kane–Mele model Hamiltonian in the presence of spin–orbit coupling and longitudinal magnetic field has been applied to describe electron dynamics. The behaviour of RKKY interaction as a function of distance between the localised moments has been analysed for different values of magnetic field and spin–orbit coupling strength for electrons. Also, the effects of electron doping as the variation of chemical potential on behaviours of RKKY interaction have been investigated. It has been shown that a magnetic field along the z-axis mediates an anisotropic interaction which corresponds to an XXZ model interaction between two magnetic moments. The exchange interaction along the arbitrary direction between two magnetic moments has been obtained using the static spin susceptibilities of doped germanene layer in the presence of spin–orbit coupling. The effects of magnetic field, electron doping and spin–orbit coupling on the dependence of exchange interaction on distance between moments are investigated by calculating the correlation function of the spin density operators. Our results show that the electron doping impacts the spatial behaviour of RKKY interaction. Moreover, spin–orbit coupling effects on both longitudinal and transverse RKKY interactions have been investigated for doped germanene monolayer. Finally, we have studied in detail the temperature dependence of RKKY interactions for various amounts of spin–orbit coupling strengths.

Abstract Image

查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
掺杂单层锗烯中各向异性的 RKKY 相互作用:自旋轨道耦合效应
我们研究了掺杂锗层中两个磁性杂质(即 Ruderman-Kittel-Kasuya-Yosida(RKKY))之间的交换相互作用,采用全带方法直接计算格林函数。在存在自旋轨道耦合和纵向磁场的情况下,Kane-Mele 模型哈密顿应用于描述电子动力学。针对不同的磁场值和电子自旋轨道耦合强度,分析了 RKKY 相互作用作为局部矩之间距离函数的行为。此外,还研究了电子掺杂以及化学势变化对 RKKY 相互作用行为的影响。研究表明,沿 Z 轴的磁场介导了一种各向异性的相互作用,相当于两个磁矩之间的 XXZ 模型相互作用。在存在自旋轨道耦合的情况下,利用掺杂锗烯层的静态自旋感性,得到了两个磁矩之间沿任意方向的交换相互作用。通过计算自旋密度算子的相关函数,研究了磁场、电子掺杂和自旋轨道耦合对交换相互作用取决于磁矩间距离的影响。结果表明,电子掺杂会影响 RKKY 相互作用的空间行为。此外,我们还研究了掺杂锗单层的自旋轨道耦合对纵向和横向 RKKY 相互作用的影响。最后,我们详细研究了不同自旋轨道耦合强度下 RKKY 相互作用的温度依赖性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
Pramana
Pramana 物理-物理:综合
CiteScore
3.60
自引率
7.10%
发文量
206
审稿时长
3 months
期刊介绍: Pramana - Journal of Physics is a monthly research journal in English published by the Indian Academy of Sciences in collaboration with Indian National Science Academy and Indian Physics Association. The journal publishes refereed papers covering current research in Physics, both original contributions - research papers, brief reports or rapid communications - and invited reviews. Pramana also publishes special issues devoted to advances in specific areas of Physics and proceedings of select high quality conferences.
期刊最新文献
The effects of q-deformed Rosen–Morse potential on the behaviour of interacting BEC systems The improved saturation model in the nuclei Stefan blowing impact and chemical response of Rivlin–Reiner fluid through rotating convective disk Impact of gold and silver nanoparticles on the thermally radiating MHD slip blood flow within the stenotic artery using stability analysis and entropy optimisation Study of the bubble motion inside a peristaltic tube
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1