<p>In this study, we investigate the effect of structural disorder on structural, elastic, and magnetic properties of Fe<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10948_2025_6979_Article_IEq1.gif" Format="GIF" Height="11" Rendition="HTML" Resolution="72" Type="Linedraw" Width="37" /> </InlineMediaObject> <EquationSource Format="TEX">\(_{100-x}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow> <mn>100</mn> <mo>-</mo> <mi>x</mi> </mrow> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation>Ga<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10948_2025_6979_Article_IEq2.gif" Format="GIF" Height="8" Rendition="HTML" Resolution="72" Type="Linedraw" Width="10" /> </InlineMediaObject> <EquationSource Format="TEX">\(_x\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mi>x</mi> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation> (<InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10948_2025_6979_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="110" /> </InlineMediaObject> <EquationSource Format="TEX">\(x = 3.7, 5.5, 9.3\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>x</mi> <mo>=</mo> <mn>3.7</mn> <mo>,</mo> <mn>5.5</mn> <mo>,</mo> <mn>9.3</mn> </mrow> </math></EquationSource> </InlineEquation>&#xa0;at.%) alloys in the <i>A</i>2 phase by means of the density functional theory and Monte Carlo simulations. For each composition of Ga, ten configurations with a random arrangement of non-magnetic atoms in the <i>A</i>2 structure were generated. Calculations performed using the density functional theory have shown that, depending on the localization of atoms in the calculation cell, the calculated equilibrium volume of the unit cell per atom can either increase or decrease, which affects the magnitude of the magnetic moment per Fe atom. The elastic moduli, obtained in this work, has the same trend as observed in experiment. The magnetic exchange interaction between nearest neighbor Fe pair is ferromagnetic and about 22–25&#xa0;meV. By using the long-range exchange interactions between magnetic atoms in the classical Heisenberg Hamiltonian, we have simulated the temperature dependencies of magnetization for Fe<InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10948_2025_6979_Article_IEq1.gif" Format="GIF" Height="11" Rendition="HTML" Resolution="72" Type="Linedraw" Width="37" /> </InlineMediaObject> <EquationSource Format="TEX">\(_{100-x}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow> <mn>100</mn> <mo>-</mo> <mi>x</mi> </mrow> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation>Ga<InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10948_2025_6979_Article_IEq2.gif" Format="GIF" Height="8" Rendition="HTML" Resolution="72" Type="Linedraw" Width="10" /> </InlineMediaObject> <EquationSource Format="TEX">\(_x\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mi>x</mi> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation> alloys at zero magnetic field and estimated Curie temperatures. By using the long-range exchange interactions between magnetic atoms in the classical Heisenberg Hamiltonian, we have simulated the temperature dependencies of magnetization for Fe<InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10948_2025_6979_Article_IEq1.gif" Format="GIF" Height="11" Rendition="HTML" Resolution="72" Type="Linedraw" Width="37" /> </InlineMediaObject> <EquationSource Format="TEX">\(_{100-x}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow> <mn>100</mn> <mo>-</mo> <mi>x</mi> </mrow> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation>Ga<InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10948_2025_6979_Article_IEq2.gif" Format="GIF" Height="8" Rendition="HTML" Resolution="72" Type="Linedraw" Width="10" /> </InlineMediaObject> <EquationSource Format="TEX">\(_x\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mi>x</mi> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation> alloys at zero magnetic field. It was shown that the Curie temperature is directly related to the values of the magnetic exchange parameter and demonstrates an increasing dependence. The following results were obtained for the studied compounds: 1138 K for Fe<InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10948_2025_6979_Article_IEq8.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="TEX">\(_{96.3}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow> <mn>96.3</mn> </mrow> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation>Ga<InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10948_2025_6979_Article_IEq9.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(_{3.7}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow> <mn>3.7</mn> </mrow> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation>, 1185 K for Fe<InlineEquation ID="IEq10"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10948_2025_6979_Article_IEq10.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="TEX">\(_{94.5}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow> <mn>94.5</mn> </mrow> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation>Ga<InlineEquation ID="IEq11"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10948_2025_6979_Article_IEq11.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(_{5.5}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow> <mn>5.5</mn> </mrow> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation>, and 1267 K for Fe<InlineEquation ID="IEq12"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10948_2025_6979_Article_IEq12.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="TEX">\(_{90.7}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow> <mn>90.7</mn> </mrow> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation>Ga<InlineEquation ID="IEq13"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10948_2025_6979_Article_IEq13.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(_{9.3}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow> <mn>9.3</mn> </mrow> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation>.</p>

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The Effect of Structural Disorder on Magnetic Properties of Fe-Ga Alloys: Insights from Ab Initio and Monte Carlo Calculations

  • M. A. Zagrebin,
  • M. V. Matyunina,
  • Yu. S. Tarasova,
  • V. V. Sokolovskiy,
  • V. D. Buchelnikov

摘要

In this study, we investigate the effect of structural disorder on structural, elastic, and magnetic properties of Fe \(_{100-x}\) 100 - x Ga \(_x\) x ( \(x = 3.7, 5.5, 9.3\) x = 3.7 , 5.5 , 9.3  at.%) alloys in the A2 phase by means of the density functional theory and Monte Carlo simulations. For each composition of Ga, ten configurations with a random arrangement of non-magnetic atoms in the A2 structure were generated. Calculations performed using the density functional theory have shown that, depending on the localization of atoms in the calculation cell, the calculated equilibrium volume of the unit cell per atom can either increase or decrease, which affects the magnitude of the magnetic moment per Fe atom. The elastic moduli, obtained in this work, has the same trend as observed in experiment. The magnetic exchange interaction between nearest neighbor Fe pair is ferromagnetic and about 22–25 meV. By using the long-range exchange interactions between magnetic atoms in the classical Heisenberg Hamiltonian, we have simulated the temperature dependencies of magnetization for Fe \(_{100-x}\) 100 - x Ga \(_x\) x alloys at zero magnetic field and estimated Curie temperatures. By using the long-range exchange interactions between magnetic atoms in the classical Heisenberg Hamiltonian, we have simulated the temperature dependencies of magnetization for Fe \(_{100-x}\) 100 - x Ga \(_x\) x alloys at zero magnetic field. It was shown that the Curie temperature is directly related to the values of the magnetic exchange parameter and demonstrates an increasing dependence. The following results were obtained for the studied compounds: 1138 K for Fe \(_{96.3}\) 96.3 Ga \(_{3.7}\) 3.7 , 1185 K for Fe \(_{94.5}\) 94.5 Ga \(_{5.5}\) 5.5 , and 1267 K for Fe \(_{90.7}\) 90.7 Ga \(_{9.3}\) 9.3 .