<p>MgMn<InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="723_2025_1806_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="8" /> </InlineMediaObject> <EquationSource Format="TEX">\(_{6}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mn>6</mn> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation>Sn<InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="723_2025_1806_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="8" /> </InlineMediaObject> <EquationSource Format="TEX">\(_{6}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mn>6</mn> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation> is the itinerant ferromagnet on the kagome lattice with high ordering temperature featuring complex electronic properties due to the nontrivial topological electronic band structure where the spin–orbit coupling (SOC) plays a crucial role. Here, we report a detailed ferromagnetic resonance (FMR) spectroscopic study of MgMn<InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="723_2025_1806_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="8" /> </InlineMediaObject> <EquationSource Format="TEX">\(_{6}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mn>6</mn> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation>Sn<InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="723_2025_1806_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="8" /> </InlineMediaObject> <EquationSource Format="TEX">\(_{6}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mn>6</mn> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation> aimed to elucidate and quantify the intrinsic magnetocrystalline anisotropy that is responsible for the alignment of the Mn magnetic moments in the kagome plane. By analyzing the frequency, magnetic field, and temperature dependences of the FMR modes, we have quantified the magnetocrystalline anisotropy energy density that reaches the value of approximately <InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="723_2025_1806_Article_IEq9.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="56" /> </InlineMediaObject> <EquationSource Format="TEX">\(3.5\cdot 10^{6}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>3.5</mn> <mo>·</mo> <msup> <mn>10</mn> <mn>6</mn> </msup> </mrow> </math></EquationSource> </InlineEquation>&#xa0;erg/cm<InlineEquation ID="IEq10"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="723_2025_1806_Article_IEq10.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="8" /> </InlineMediaObject> <EquationSource Format="TEX">\(^{3}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mn>3</mn> </mmultiscripts> </math></EquationSource> </InlineEquation> at <InlineEquation ID="IEq11"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="723_2025_1806_Article_IEq11.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="44" /> </InlineMediaObject> <EquationSource Format="TEX">\(T = 3\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>T</mi> <mo>=</mo> <mn>3</mn> </mrow> </math></EquationSource> </InlineEquation>&#xa0;K and reduces to about <InlineEquation ID="IEq12"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="723_2025_1806_Article_IEq12.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="44" /> </InlineMediaObject> <EquationSource Format="TEX">\(1\cdot 10^{6}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1</mn> <mo>·</mo> <msup> <mn>10</mn> <mn>6</mn> </msup> </mrow> </math></EquationSource> </InlineEquation>&#xa0;erg/cm<InlineEquation ID="IEq13"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="723_2025_1806_Article_IEq10.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="8" /> </InlineMediaObject> <EquationSource Format="TEX">\(^{3}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mn>3</mn> </mmultiscripts> </math></EquationSource> </InlineEquation> at <InlineEquation ID="IEq14"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="723_2025_1806_Article_IEq14.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="60" /> </InlineMediaObject> <EquationSource Format="TEX">\(T = 300\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>T</mi> <mo>=</mo> <mn>300</mn> </mrow> </math></EquationSource> </InlineEquation>&#xa0;K. The revealed significantly strong magnetic anisotropy suggests a sizable contribution of the orbital&#xa0;magnetic moment to the spin&#xa0;magnetic moment of Mn, supporting the scenario of the essential role of SOC for the nontrivial electronic properties of MgMn<InlineEquation ID="IEq15"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="723_2025_1806_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="8" /> </InlineMediaObject> <EquationSource Format="TEX">\(_{6}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mn>6</mn> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation>Sn<InlineEquation ID="IEq16"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="723_2025_1806_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="8" /> </InlineMediaObject> <EquationSource Format="TEX">\(_{6}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mn>6</mn> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation>.</p>

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Ferromagnetic Resonance Spectroscopy on the Kagome Magnet MgMn\(_{6}\)Sn\(_{6}\)

  • Riju Pal,
  • Kakan Deb,
  • Nitesh Kumar,
  • Bernd Büchner,
  • Alexey Alfonsov,
  • Vladislav Kataev

摘要

MgMn \(_{6}\) 6 Sn \(_{6}\) 6 is the itinerant ferromagnet on the kagome lattice with high ordering temperature featuring complex electronic properties due to the nontrivial topological electronic band structure where the spin–orbit coupling (SOC) plays a crucial role. Here, we report a detailed ferromagnetic resonance (FMR) spectroscopic study of MgMn \(_{6}\) 6 Sn \(_{6}\) 6 aimed to elucidate and quantify the intrinsic magnetocrystalline anisotropy that is responsible for the alignment of the Mn magnetic moments in the kagome plane. By analyzing the frequency, magnetic field, and temperature dependences of the FMR modes, we have quantified the magnetocrystalline anisotropy energy density that reaches the value of approximately \(3.5\cdot 10^{6}\) 3.5 · 10 6  erg/cm \(^{3}\) 3 at \(T = 3\) T = 3  K and reduces to about \(1\cdot 10^{6}\) 1 · 10 6  erg/cm \(^{3}\) 3 at \(T = 300\) T = 300  K. The revealed significantly strong magnetic anisotropy suggests a sizable contribution of the orbital magnetic moment to the spin magnetic moment of Mn, supporting the scenario of the essential role of SOC for the nontrivial electronic properties of MgMn \(_{6}\) 6 Sn \(_{6}\) 6 .