Abstract <p>The applicability of the values of the strength <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11972_2025_8816_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="28" /> </InlineMediaObject> <EquationSource Format="TEX">\(H_{\textrm{irr}}\)</EquationSource> <!--BPhysMGU2570066Fomina-m1--> </InlineEquation> of the irreversibility field and the strength <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11972_2025_8816_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="27" /> </InlineMediaObject> <EquationSource Format="TEX">\(H_{c2}\)</EquationSource> <!--BPhysMGU2570066Fomina-m2--> </InlineEquation> of the upper critical field in pinning mechanism determination in a sample of the family of iron pnictides of the class 111, NaFe<InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11972_2025_8816_Article_IEq3.gif" Format="GIF" Height="11" Rendition="HTML" Resolution="72" Type="Linedraw" Width="25" /> </InlineMediaObject> <EquationSource Format="TEX">\({}_{1-x}\)</EquationSource> <!--BPhysMGU2570066Fomina-m3--> </InlineEquation>Co<InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11972_2025_8816_Article_IEq4.gif" Format="GIF" Height="8" Rendition="HTML" Resolution="72" Type="Linedraw" Width="10" /> </InlineMediaObject> <EquationSource Format="TEX">\({}_{x}\)</EquationSource> <!--BPhysMGU2570066Fomina-m4--> </InlineEquation>As, was analyzed in this work. Methods for calculating <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11972_2025_8816_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="28" /> </InlineMediaObject> <EquationSource Format="TEX">\(H_{\textrm{irr}}\)</EquationSource> <!--BPhysMGU2570066Fomina-m5--> </InlineEquation> and <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11972_2025_8816_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="27" /> </InlineMediaObject> <EquationSource Format="TEX">\(H_{c2}\)</EquationSource> <!--BPhysMGU2570066Fomina-m6--> </InlineEquation> were also considered. The first method for determining the strength <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11972_2025_8816_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="28" /> </InlineMediaObject> <EquationSource Format="TEX">\(H_{\textrm{irr}}\)</EquationSource> <!--BPhysMGU2570066Fomina-m7--> </InlineEquation> of the irreversibility field is based on extrapolation of the zeros of the graph <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11972_2025_8816_Article_IEq8.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="44" /> </InlineMediaObject> <EquationSource Format="TEX">\(J_{c}(H)\)</EquationSource> <!--BPhysMGU2570066Fomina-m8--> </InlineEquation>. The second method, considered exclusively from a theoretical perspective, is Kramer’s method. It is based on extrapolation of the zeros of the graph <InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11972_2025_8816_Article_IEq9.gif" Format="GIF" Height="24" Rendition="HTML" Resolution="72" Type="Linedraw" Width="88" /> </InlineMediaObject> <EquationSource Format="TEX">\(J_{c}^{1/2}B^{1/4}(B)\)</EquationSource> <!--BPhysMGU2570066Fomina-m9--> </InlineEquation>. Each of the methods requires qualitative identification of the graph zeros in order to obtain the most accurate result. The strength of the upper critical field is determined by extrapolating the points obtained at the intersection of the graph <InlineEquation ID="IEq10"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11972_2025_8816_Article_IEq10.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="44" /> </InlineMediaObject> <EquationSource Format="TEX">\(M(T)\)</EquationSource> <!--BPhysMGU2570066Fomina-m10--> </InlineEquation> with the line at the level <InlineEquation ID="IEq11"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11972_2025_8816_Article_IEq11.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="50" /> </InlineMediaObject> <EquationSource Format="TEX">\(M=0\)</EquationSource> <!--BPhysMGU2570066Fomina-m11--> </InlineEquation>. Due to the limited operating range of the measuring device, the values of <InlineEquation ID="IEq12"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11972_2025_8816_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="28" /> </InlineMediaObject> <EquationSource Format="TEX">\(H_{\textrm{irr}}\)</EquationSource> <!--BPhysMGU2570066Fomina-m12--> </InlineEquation> for the NaFe<InlineEquation ID="IEq13"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11972_2025_8816_Article_IEq3.gif" Format="GIF" Height="11" Rendition="HTML" Resolution="72" Type="Linedraw" Width="25" /> </InlineMediaObject> <EquationSource Format="TEX">\({}_{1-x}\)</EquationSource> <!--BPhysMGU2570066Fomina-m13--> </InlineEquation>Co<InlineEquation ID="IEq14"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11972_2025_8816_Article_IEq4.gif" Format="GIF" Height="8" Rendition="HTML" Resolution="72" Type="Linedraw" Width="10" /> </InlineMediaObject> <EquationSource Format="TEX">\({}_{x}\)</EquationSource> <!--BPhysMGU2570066Fomina-m14--> </InlineEquation>As sample were obtained by approximating data from previously acquired results. When using <InlineEquation ID="IEq15"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11972_2025_8816_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="28" /> </InlineMediaObject> <EquationSource Format="TEX">\(H_{\textrm{irr}}\)</EquationSource> <!--BPhysMGU2570066Fomina-m15--> </InlineEquation>, a volume pinning type was identified. The values of <InlineEquation ID="IEq16"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11972_2025_8816_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="27" /> </InlineMediaObject> <EquationSource Format="TEX">\(H_{c2}\)</EquationSource> <!--BPhysMGU2570066Fomina-m16--> </InlineEquation> were also calculated based on already obtained data and allowed the surface pinning mechanism to be determined, which is consistent with earlier studies. This indicates that the pinning mechanism determined using <InlineEquation ID="IEq17"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11972_2025_8816_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="28" /> </InlineMediaObject> <EquationSource Format="TEX">\(H_{\textrm{irr}}\)</EquationSource> <!--BPhysMGU2570066Fomina-m17--> </InlineEquation> was established incorrectly. It was found that the use of irreversibility field strength values for the NaFe<InlineEquation ID="IEq18"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11972_2025_8816_Article_IEq3.gif" Format="GIF" Height="11" Rendition="HTML" Resolution="72" Type="Linedraw" Width="25" /> </InlineMediaObject> <EquationSource Format="TEX">\({}_{1-x}\)</EquationSource> <!--BPhysMGU2570066Fomina-m18--> </InlineEquation>Co<InlineEquation ID="IEq19"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11972_2025_8816_Article_IEq4.gif" Format="GIF" Height="8" Rendition="HTML" Resolution="72" Type="Linedraw" Width="10" /> </InlineMediaObject> <EquationSource Format="TEX">\({}_{x}\)</EquationSource> <!--BPhysMGU2570066Fomina-m19--> </InlineEquation>As sample may lead to incorrect identification of the pinning type.</p>

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Features of Pinning Mechanism Determination in Samples of the Class 111 Family of Iron Pnictides

  • E. M. Fomina,
  • A. I. Shilov,
  • E. O. Rakhmanov,
  • I. V. Zhuvagin

摘要

Abstract

The applicability of the values of the strength \(H_{\textrm{irr}}\) of the irreversibility field and the strength \(H_{c2}\) of the upper critical field in pinning mechanism determination in a sample of the family of iron pnictides of the class 111, NaFe \({}_{1-x}\) Co \({}_{x}\) As, was analyzed in this work. Methods for calculating \(H_{\textrm{irr}}\) and \(H_{c2}\) were also considered. The first method for determining the strength \(H_{\textrm{irr}}\) of the irreversibility field is based on extrapolation of the zeros of the graph \(J_{c}(H)\) . The second method, considered exclusively from a theoretical perspective, is Kramer’s method. It is based on extrapolation of the zeros of the graph \(J_{c}^{1/2}B^{1/4}(B)\) . Each of the methods requires qualitative identification of the graph zeros in order to obtain the most accurate result. The strength of the upper critical field is determined by extrapolating the points obtained at the intersection of the graph \(M(T)\) with the line at the level \(M=0\) . Due to the limited operating range of the measuring device, the values of \(H_{\textrm{irr}}\) for the NaFe \({}_{1-x}\) Co \({}_{x}\) As sample were obtained by approximating data from previously acquired results. When using \(H_{\textrm{irr}}\) , a volume pinning type was identified. The values of \(H_{c2}\) were also calculated based on already obtained data and allowed the surface pinning mechanism to be determined, which is consistent with earlier studies. This indicates that the pinning mechanism determined using \(H_{\textrm{irr}}\) was established incorrectly. It was found that the use of irreversibility field strength values for the NaFe \({}_{1-x}\) Co \({}_{x}\) As sample may lead to incorrect identification of the pinning type.