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arXiv · 2104.10371

Trends of higher-order exchange interactions in transition-metal trilayers

Mara Gutzeit·Soumyajyoti Haldar·Sebastian Meyer·Stefan Heinze
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Abstract

We present a systematic study of higher-order exchange interactions beyond the pair-wise Heisenberg exchange in transition-metal trilayers based on density functional theory calculations. We show that these terms can play an important role in magnetic trilayers composed of a single hexagonal Fe or Co atomic layer sandwiched between $4d$ and $5d$ transition-metal layers. We study the dependence of the biquadratic and the three-site and four-site four spin interaction on the band filling of the $4d$ and $5d$ layers as well as the stacking sequence, i.e. fcc vs. hcp stacking. Our calculations reveal relatively small higher-order interactions for Co based trilayers. For Fe based trilayers with a Rh or Ir layer the higher-order terms can be on the same order of magnitude as pair-wise Heisenberg exchange. The trends obtained for freestanding trilayers are used to understand the higher-order interactions in ultrathin film systems on surfaces that are experimentally accessible. It is shown that hcp Rh/Fe/Ir(111) and hcp-Rh/Fe/Rh(111) exhibit the largest values for the biquadratic and the three-site four spin interaction of all systems under study. We further demonstrate that the three-site four spin interaction is responsible for the experimentally observed change of the magnetic ground state of Rh/Fe/Ir(111) from a spin spiral (single-Q) for fcc-Rh to a 2Q state for hcp-Rh. We find similar trends for Rh/Fe/Rh(111), i.e. replacing the Ir surface by the isoelectronic Rh surface. For Rh/Co/Ir(111), we obtain a negative value for the four-site four spin interaction which will lead to a reduced stability of magnetic skyrmions which are metastable in this film at zero magnetic field. In contrast, for Pd/Fe/Ir(111), the four-site four spin interaction is positive which leads to an enhanced stability of skyrmions.

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Mara Gutzeit, Soumyajyoti Haldar, Sebastian Meyer, Stefan Heinze. 2021-04-21. Trends of higher-order exchange interactions in transition-metal trilayers. https://doi.org/10.1103/physrevb.104.024420

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