<p>Two-dimensional materials with Rashba-like spin splitting near the Fermi level hold significant potential for next-generation spintronic devices. Using density functional theory based calculations, we demonstrate that spin-orbit coupling along with broken out-of-plane mirror symmetry induces strong Rashba splitting in the lowest conduction states of SbSeI Janus layer. This allows the possibility of spin control via an external electric field. The Rashba spin split bands are isotropic around the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\Gamma\)</EquationSource> </InlineEquation> point due to the presence of three-fold rotational <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(C_3\)</EquationSource> </InlineEquation> symmetry. The values of Rashba splitting characteristics, namely Rashba energy <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(E_\text{R}\)</EquationSource> </InlineEquation>, crystal momentum offset <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(k_\text{R}\)</EquationSource> </InlineEquation>, and Rashba parameter <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\alpha _\text{R}\)</EquationSource> </InlineEquation>, are found to be 39.3 meV, 0.05 Å<InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\phantom{0}^{-1}\)</EquationSource> </InlineEquation>, and 1.57 eV Å, respectively. The lowest conduction states around the <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(\Gamma\)</EquationSource> </InlineEquation> point possess a dominant contribution from the <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(p_z\)</EquationSource> </InlineEquation> orbital of Sb atoms. The spin-textures of the stronger <InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(S_x\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq10"> <EquationSource Format="TEX">\(S_y\)</EquationSource> </InlineEquation> components show opposite phases while that of the weaker <InlineEquation ID="IEq11"> <EquationSource Format="TEX">\(S_z\)</EquationSource> </InlineEquation> component retains the <InlineEquation ID="IEq12"> <EquationSource Format="TEX">\(C_3\)</EquationSource> </InlineEquation> symmetry of the system. In addition, our calculations reveal that mechanical strain and external static electric field can effectively modulate the strength of spin-orbit coupling and thus, control the Rashba splitting. Rashba parameter <InlineEquation ID="IEq13"> <EquationSource Format="TEX">\(\alpha _\text{R}\)</EquationSource> </InlineEquation> remains robust under the biaxial strain and its value reduces less than 10% for strain ranging from -4% to +6%. Interestingly, uniaxial strain breaks the <InlineEquation ID="IEq14"> <EquationSource Format="TEX">\(C_3\)</EquationSource> </InlineEquation> symmetry which creates significant anisotropy in Rashba split bands around the <InlineEquation ID="IEq15"> <EquationSource Format="TEX">\(\Gamma\)</EquationSource> </InlineEquation> point. On the other hand, application of electric field leads to nearly linear variations of the above mentioned Rashba characteristics versus the field. The <InlineEquation ID="IEq16"> <EquationSource Format="TEX">\(\alpha _R\)</EquationSource> </InlineEquation> can be tuned from 1.45 to 1.70 eV Å for the field strength ranging from -1.12 to 1.12&#xa0;V/nm<InlineEquation ID="IEq17"> <EquationSource Format="TEX">\(.\)</EquationSource> </InlineEquation> Overall, our DFT calculations reveal that the crystal momentum offset (<InlineEquation ID="IEq18"> <EquationSource Format="TEX">\(k_\text{R}\)</EquationSource> </InlineEquation>) and Rashba energy (<InlineEquation ID="IEq19"> <EquationSource Format="TEX">\(E_\text{R}\)</EquationSource> </InlineEquation>) in SbSeI Janus layer are highly sensitive to external influences, namely mechanical strain and electric field. A detailed analysis establishes a strong correlation between these variations with the <InlineEquation ID="IEq20"> <EquationSource Format="TEX">\(p_z\)</EquationSource> </InlineEquation> orbital contribution of Sb atoms and the difference in Born effective charges between I and Se atoms, thereby providing a microscopic insights for the modulation of Rashba characteristics under external stimuli. Together, these findings advance the understanding of spin–orbit coupling at the atomic scale and highlight SbSeI Janus layer as a promising candidate for next-generation spin–orbitronic applications.</p>

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Electrically and mechanically tunable Rashba splitting in SbSeI Janus layer: a density functional theory study

  • Amrendra Kumar,
  • Anjana E. Sudheer,
  • G. Tejaswini,
  • Muthu Vallinayagam,
  • Matthias Zschornak,
  • D. Murali,
  • C. Kamal

摘要

Two-dimensional materials with Rashba-like spin splitting near the Fermi level hold significant potential for next-generation spintronic devices. Using density functional theory based calculations, we demonstrate that spin-orbit coupling along with broken out-of-plane mirror symmetry induces strong Rashba splitting in the lowest conduction states of SbSeI Janus layer. This allows the possibility of spin control via an external electric field. The Rashba spin split bands are isotropic around the \(\Gamma\) point due to the presence of three-fold rotational \(C_3\) symmetry. The values of Rashba splitting characteristics, namely Rashba energy \(E_\text{R}\) , crystal momentum offset \(k_\text{R}\) , and Rashba parameter \(\alpha _\text{R}\) , are found to be 39.3 meV, 0.05 Å \(\phantom{0}^{-1}\) , and 1.57 eV Å, respectively. The lowest conduction states around the \(\Gamma\) point possess a dominant contribution from the \(p_z\) orbital of Sb atoms. The spin-textures of the stronger \(S_x\) and \(S_y\) components show opposite phases while that of the weaker \(S_z\) component retains the \(C_3\) symmetry of the system. In addition, our calculations reveal that mechanical strain and external static electric field can effectively modulate the strength of spin-orbit coupling and thus, control the Rashba splitting. Rashba parameter \(\alpha _\text{R}\) remains robust under the biaxial strain and its value reduces less than 10% for strain ranging from -4% to +6%. Interestingly, uniaxial strain breaks the \(C_3\) symmetry which creates significant anisotropy in Rashba split bands around the \(\Gamma\) point. On the other hand, application of electric field leads to nearly linear variations of the above mentioned Rashba characteristics versus the field. The \(\alpha _R\) can be tuned from 1.45 to 1.70 eV Å for the field strength ranging from -1.12 to 1.12 V/nm \(.\) Overall, our DFT calculations reveal that the crystal momentum offset ( \(k_\text{R}\) ) and Rashba energy ( \(E_\text{R}\) ) in SbSeI Janus layer are highly sensitive to external influences, namely mechanical strain and electric field. A detailed analysis establishes a strong correlation between these variations with the \(p_z\) orbital contribution of Sb atoms and the difference in Born effective charges between I and Se atoms, thereby providing a microscopic insights for the modulation of Rashba characteristics under external stimuli. Together, these findings advance the understanding of spin–orbit coupling at the atomic scale and highlight SbSeI Janus layer as a promising candidate for next-generation spin–orbitronic applications.