Multiple-scattering approach for multi-spin chiral magnetic interactions: application to the one- and two-dimensional Rashba electron gas
Various multi-spin magnetic exchange interactions (MEI) of chiral nature have been recently unveiled. Owing to their potential impact on the realisation of twisted spin-textures, their future implication in spintronics or quantum computing is very promising. Here, I address the long-range behavior o...
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| Format: | Article |
| Language: | English |
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IOP Publishing
2020-01-01
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| Series: | New Journal of Physics |
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| Online Access: | https://doi.org/10.1088/1367-2630/abb514 |
| _version_ | 1797750318467907584 |
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| author | Samir Lounis |
| author_facet | Samir Lounis |
| author_sort | Samir Lounis |
| collection | DOAJ |
| description | Various multi-spin magnetic exchange interactions (MEI) of chiral nature have been recently unveiled. Owing to their potential impact on the realisation of twisted spin-textures, their future implication in spintronics or quantum computing is very promising. Here, I address the long-range behavior of multi-spin MEI on the basis of a multiple-scattering formalism implementable in Green functions based methods such as the Korringa–Kohn–Rostoker (KKR) Green function framework. I consider the impact of spin–orbit coupling (SOC) as described in the one- (1D) and two-dimensional (2D) Rashba model, from which the analytical forms of the four- and six-spin interactions are extracted and compared to the well known bilinear isotropic, anisotropic and Dzyaloshinskii–Moriya interactions (DMI). Similarly to the DMI between two sites i and j , there is a four-spin chiral vector perpendicular to the bond connecting the two sites. The oscillatory behavior of the MEI and their decay as function of interatomic distances are analysed and quantified for the Rashba surfaces states characterizing Au surfaces. The interplay of beating effects and strength of SOC gives rise to a wide parameter space where chiral MEI are more prominent than the isotropic ones. The multi-spin interactions for a plaquette of N magnetic moments decay like ${\left\{{q}_{\mathrm{F}}^{N-d}{P}^{\frac{1}{2}\left(d-1\right)}L\right\}}^{-1}$ simplifying to ${\left\{{q}_{\mathrm{F}}^{N-d}{R}^{\left[1+\frac{N}{2}\left(d-1\right)\right]}N\right\}}^{-1}$ for equidistant atoms, where d is the dimension of the mediating electrons, q _F the Fermi wave vector, L the perimeter of the plaquette while P is the product of interatomic distances. This recovers the behavior of the bilinear MEI, ${\left\{{q}_{\mathrm{F}}^{2-d}{R}^{d}\right\}}^{-1}$ , and shows that increasing the perimeter of the plaquette weakens the MEI. More important, the power-law pertaining to the distance-dependent 1D MEI is insensitive to the number of atoms in the plaquette in contrast to the linear dependence associated with the 2D MEI. Furthermore, the N -dependence of q _F offers the possibility of tuning the interactions amplitude by engineering the electronic occupation. |
| first_indexed | 2024-03-12T16:30:59Z |
| format | Article |
| id | doaj.art-f200316b2120422fbb9eaf744413fee1 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:30:59Z |
| publishDate | 2020-01-01 |
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| series | New Journal of Physics |
| spelling | doaj.art-f200316b2120422fbb9eaf744413fee12023-08-08T15:30:07ZengIOP PublishingNew Journal of Physics1367-26302020-01-01221010300310.1088/1367-2630/abb514Multiple-scattering approach for multi-spin chiral magnetic interactions: application to the one- and two-dimensional Rashba electron gasSamir Lounis0https://orcid.org/0000-0003-2573-2841Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszetrum Jülich and JARA, 52425 Jülich, GermanyVarious multi-spin magnetic exchange interactions (MEI) of chiral nature have been recently unveiled. Owing to their potential impact on the realisation of twisted spin-textures, their future implication in spintronics or quantum computing is very promising. Here, I address the long-range behavior of multi-spin MEI on the basis of a multiple-scattering formalism implementable in Green functions based methods such as the Korringa–Kohn–Rostoker (KKR) Green function framework. I consider the impact of spin–orbit coupling (SOC) as described in the one- (1D) and two-dimensional (2D) Rashba model, from which the analytical forms of the four- and six-spin interactions are extracted and compared to the well known bilinear isotropic, anisotropic and Dzyaloshinskii–Moriya interactions (DMI). Similarly to the DMI between two sites i and j , there is a four-spin chiral vector perpendicular to the bond connecting the two sites. The oscillatory behavior of the MEI and their decay as function of interatomic distances are analysed and quantified for the Rashba surfaces states characterizing Au surfaces. The interplay of beating effects and strength of SOC gives rise to a wide parameter space where chiral MEI are more prominent than the isotropic ones. The multi-spin interactions for a plaquette of N magnetic moments decay like ${\left\{{q}_{\mathrm{F}}^{N-d}{P}^{\frac{1}{2}\left(d-1\right)}L\right\}}^{-1}$ simplifying to ${\left\{{q}_{\mathrm{F}}^{N-d}{R}^{\left[1+\frac{N}{2}\left(d-1\right)\right]}N\right\}}^{-1}$ for equidistant atoms, where d is the dimension of the mediating electrons, q _F the Fermi wave vector, L the perimeter of the plaquette while P is the product of interatomic distances. This recovers the behavior of the bilinear MEI, ${\left\{{q}_{\mathrm{F}}^{2-d}{R}^{d}\right\}}^{-1}$ , and shows that increasing the perimeter of the plaquette weakens the MEI. More important, the power-law pertaining to the distance-dependent 1D MEI is insensitive to the number of atoms in the plaquette in contrast to the linear dependence associated with the 2D MEI. Furthermore, the N -dependence of q _F offers the possibility of tuning the interactions amplitude by engineering the electronic occupation.https://doi.org/10.1088/1367-2630/abb514chiral magnetismmulti-spin interactionslong-range magnetic interactionsRashba model |
| spellingShingle | Samir Lounis Multiple-scattering approach for multi-spin chiral magnetic interactions: application to the one- and two-dimensional Rashba electron gas New Journal of Physics chiral magnetism multi-spin interactions long-range magnetic interactions Rashba model |
| title | Multiple-scattering approach for multi-spin chiral magnetic interactions: application to the one- and two-dimensional Rashba electron gas |
| title_full | Multiple-scattering approach for multi-spin chiral magnetic interactions: application to the one- and two-dimensional Rashba electron gas |
| title_fullStr | Multiple-scattering approach for multi-spin chiral magnetic interactions: application to the one- and two-dimensional Rashba electron gas |
| title_full_unstemmed | Multiple-scattering approach for multi-spin chiral magnetic interactions: application to the one- and two-dimensional Rashba electron gas |
| title_short | Multiple-scattering approach for multi-spin chiral magnetic interactions: application to the one- and two-dimensional Rashba electron gas |
| title_sort | multiple scattering approach for multi spin chiral magnetic interactions application to the one and two dimensional rashba electron gas |
| topic | chiral magnetism multi-spin interactions long-range magnetic interactions Rashba model |
| url | https://doi.org/10.1088/1367-2630/abb514 |
| work_keys_str_mv | AT samirlounis multiplescatteringapproachformultispinchiralmagneticinteractionsapplicationtotheoneandtwodimensionalrashbaelectrongas |