<p>Skyrmions in chiral magnetic films exist either in the isolated phase, confined within the sample, or the condensed phase, occupying it entirely. The stability of magnetic structures in generic perpendicularly magnetized chiral magnetic films is fully determined by, <InlineEquation ID="IEq01"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42005_2025_1980_Article_IEq01.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\({\kappa }\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>κ</mi> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42005_2025_1980_Article_IEq1.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="16" /> </InlineMediaObject> <EquationSource Format="TEX">\({\kappa }^{{\prime} }\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi>κ</mi> </mrow> <mrow> <mo>′</mo> </mrow> </msup> </math></EquationSource> </InlineEquation>, measuring relative interaction strengths preferring curling and collinear structures, rather than individual material parameters. The phase diagram of skyrmion should span the isolated and condensed phases rather than skyrmion crystal and helical/conical states as in the conventional diagrams. Here, we provide a comprehensive skyrmion phase diagram between isolated and condensed phases in the <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42005_2025_1980_Article_IEq2.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="26" /> </InlineMediaObject> <EquationSource Format="TEX">\(\kappa {\kappa }^{{\prime} }\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>κ</mi> <msup> <mrow> <mi>κ</mi> </mrow> <mrow> <mo>′</mo> </mrow> </msup> </math></EquationSource> </InlineEquation>-plane. In the absence of magnetic crystalline anisotropy, perpendicular magnetic field is used to drive the transition from condensed to isolated skyrmions, where <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42005_2025_1980_Article_IEq3.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="16" /> </InlineMediaObject> <EquationSource Format="TEX">\({\kappa }^{{\prime} }\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi>κ</mi> </mrow> <mrow> <mo>′</mo> </mrow> </msup> </math></EquationSource> </InlineEquation> solely determines the (meta)stable structures and <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42005_2025_1980_Article_IEq4.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="56" /> </InlineMediaObject> <EquationSource Format="TEX">\(| {\kappa }^{{\prime} }| =4\)</EquationSource> <EquationSource Format="MATHML"><math> <mo>∣</mo> <msup> <mrow> <mi>κ</mi> </mrow> <mrow> <mo>′</mo> </mrow> </msup> <mo>∣</mo> <mo>=</mo> <mn>4</mn> </math></EquationSource> </InlineEquation> separates isolated skyrmions, including circular and polygonal skyrmions, from condensed skyrmions, including skyrmion crystal and helical states. <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42005_2025_1980_Article_IEq5.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="56" /> </InlineMediaObject> <EquationSource Format="TEX">\(| {\kappa }^{{\prime} }| =4\)</EquationSource> <EquationSource Format="MATHML"><math> <mo>∣</mo> <msup> <mrow> <mi>κ</mi> </mrow> <mrow> <mo>′</mo> </mrow> </msup> <mo>∣</mo> <mo>=</mo> <mn>4</mn> </math></EquationSource> </InlineEquation>, aligns with <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42005_2025_1980_Article_IEq6.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="41" /> </InlineMediaObject> <EquationSource Format="TEX">\(\kappa = 1\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>κ</mi> <mo>=</mo> <mn>1</mn> </math></EquationSource> </InlineEquation>, which separate these phases in the absence of a perpendicular magnetic field when <InlineEquation ID="IEq02"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42005_2025_1980_Article_IEq02.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\({\kappa }\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>κ</mi> </math></EquationSource> </InlineEquation> solely determines (meta)stable structures. Our phase diagram provides a versatile framework for exploring skyrmion behavior across different chiral magnetic films.</p>

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Phase-diagram of condensed and isolated skyrmions in chiral magnetic films

  • Moditha Viraj Wijethunga,
  • Xuchong Hu,
  • Xiangrong Wang

摘要

Skyrmions in chiral magnetic films exist either in the isolated phase, confined within the sample, or the condensed phase, occupying it entirely. The stability of magnetic structures in generic perpendicularly magnetized chiral magnetic films is fully determined by, \({\kappa }\) κ and \({\kappa }^{{\prime} }\) κ , measuring relative interaction strengths preferring curling and collinear structures, rather than individual material parameters. The phase diagram of skyrmion should span the isolated and condensed phases rather than skyrmion crystal and helical/conical states as in the conventional diagrams. Here, we provide a comprehensive skyrmion phase diagram between isolated and condensed phases in the \(\kappa {\kappa }^{{\prime} }\) κ κ -plane. In the absence of magnetic crystalline anisotropy, perpendicular magnetic field is used to drive the transition from condensed to isolated skyrmions, where \({\kappa }^{{\prime} }\) κ solely determines the (meta)stable structures and \(| {\kappa }^{{\prime} }| =4\) κ = 4 separates isolated skyrmions, including circular and polygonal skyrmions, from condensed skyrmions, including skyrmion crystal and helical states. \(| {\kappa }^{{\prime} }| =4\) κ = 4 , aligns with \(\kappa = 1\) κ = 1 , which separate these phases in the absence of a perpendicular magnetic field when \({\kappa }\) κ solely determines (meta)stable structures. Our phase diagram provides a versatile framework for exploring skyrmion behavior across different chiral magnetic films.