<p>The low-temperature phase MnBi has been a focus of rare-earth free permanent magnet research because of its atypical behavior of magnetic anisotropy and coercivity enhancements at an elevated temperature. Using systematic density functional theory, density functional perturbation theory, and Monte Carlo simulations, we investigate the structural stability and intrinsic magnetic properties of MnBi with metal and metalloid substitute elements. We theoretically demonstrate that the low magnetocrystalline anisotropy in the MnBi plane can reorient to a large uniaxial magnetocrystalline anisotropy (<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_20764_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">\(K_u\)</EquationSource> </InlineEquation>), which is associated with Mn relocation at an interstitial site and lattice expansion under thermal conditions. Furthermore, we predict that among 11 substitute elements, only the Bi-site Ge can preserve the MnBi phase stability and simultaneously improve intrinsic permanent magnetism. More specifically, we predict a large <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_20764_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">\(K_u\)</EquationSource> </InlineEquation> value of 3.6 MJ/<InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_20764_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(\hbox {m}^3\)</EquationSource> </InlineEquation> and Curie temperature <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_20764_Article_IEq4.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(T_c\)</EquationSource> </InlineEquation> up to 780 K for <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_20764_Article_IEq5.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="84" /> </InlineMediaObject> <EquationSource Format="TEX">\(\hbox {MnBi}_\mathrm{{1\text {-}x}}\hbox {Ge}_\mathrm{{x}}\)</EquationSource> </InlineEquation> with x&lt;0.2, which are significantly higher than the corresponding values of <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_20764_Article_IEq6.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(-\)</EquationSource> </InlineEquation>0.3 MJ/<InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_20764_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(\hbox {m}^3\)</EquationSource> </InlineEquation> and 750 K for the MnBi phase. The underlying mechanism for magnetization reversal and large <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_20764_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">\(K_u\)</EquationSource> </InlineEquation> is illustrated by an energy-level shift in the strong spin-orbit-coupled Bi 6<i>p</i> orbital states. These results demonstrate the feasibility of a possible enhancement of the intrinsic magnetic performance of the MnBi phase through substitutional doping with nonmagnetic metalloid elements.</p>

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Atomic engineering of intrinsic permanent magnetism in MnBi

  • Uranbaigal Enkhtur,
  • Dorj Odkhuu

摘要

The low-temperature phase MnBi has been a focus of rare-earth free permanent magnet research because of its atypical behavior of magnetic anisotropy and coercivity enhancements at an elevated temperature. Using systematic density functional theory, density functional perturbation theory, and Monte Carlo simulations, we investigate the structural stability and intrinsic magnetic properties of MnBi with metal and metalloid substitute elements. We theoretically demonstrate that the low magnetocrystalline anisotropy in the MnBi plane can reorient to a large uniaxial magnetocrystalline anisotropy ( \(K_u\) ), which is associated with Mn relocation at an interstitial site and lattice expansion under thermal conditions. Furthermore, we predict that among 11 substitute elements, only the Bi-site Ge can preserve the MnBi phase stability and simultaneously improve intrinsic permanent magnetism. More specifically, we predict a large \(K_u\) value of 3.6 MJ/ \(\hbox {m}^3\) and Curie temperature \(T_c\) up to 780 K for \(\hbox {MnBi}_\mathrm{{1\text {-}x}}\hbox {Ge}_\mathrm{{x}}\) with x<0.2, which are significantly higher than the corresponding values of \(-\) 0.3 MJ/ \(\hbox {m}^3\) and 750 K for the MnBi phase. The underlying mechanism for magnetization reversal and large \(K_u\) is illustrated by an energy-level shift in the strong spin-orbit-coupled Bi 6p orbital states. These results demonstrate the feasibility of a possible enhancement of the intrinsic magnetic performance of the MnBi phase through substitutional doping with nonmagnetic metalloid elements.