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<p>In this work, we investigate the magnetic properties and hysteresis behavior of a mixed spin-1 and spin-7/2 Blume–Capel (BC) Ising model via the mean field approximation (MFA) method, which is based on the Gibbs–Bogoliubov inequality for free energy. We study the system both in the presence and absence of an external magnetic field (<i>h</i>) and explore the appearance of compensation critical points for different crystal field <i>D</i> values when <i>h</i> = 0. The results indicate that there is a critical point of <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10948_2025_6985_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="27" /> </InlineMediaObject> <EquationSource Format="TEX">\(D_B\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>D</mi> <mi>B</mi> </msub> </math></EquationSource> </InlineEquation>&#xa0;= − 2.0, which promotes the appearance of compensation points, whereas <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10948_2025_6985_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="27" /> </InlineMediaObject> <EquationSource Format="TEX">\(D_A\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>D</mi> <mi>A</mi> </msub> </math></EquationSource> </InlineEquation> influences the value of the compensation points. The thermal behavior of the order parameters is analyzed across various crystal field values under multiple external field strengths at specific temperatures. Our results indicate that the system undergoes a second-order phase transition at <i>h</i> = 0, whereas first-order phase transitions occur for <i>h</i> &gt; − 0.5. Only a single hysteresis loop exists for <i>D</i> = 0 and T &lt; 8; however, triple and double hysteresis loops are observed when the crystal field conditions change, along with the emergence of a superparamagnetic phase at higher temperatures and at lower values of <i>D</i>.</p>

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Critical Magnetic Hysteresis Behaviors in a Mixed Spin-1 and Spin-7/2 Blume-Capel Ising System

  • 期刊论文

  • 发表日期：

    2025年6月6日

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  • Ali Ismael Al-Brihy,
  • Hasan F. Alturki

摘要

In this work, we investigate the magnetic properties and hysteresis behavior of a mixed spin-1 and spin-7/2 Blume–Capel (BC) Ising model via the mean field approximation (MFA) method, which is based on the Gibbs–Bogoliubov inequality for free energy. We study the system both in the presence and absence of an external magnetic field (h) and explore the appearance of compensation critical points for different crystal field D values when h = 0. The results indicate that there is a critical point of \(D_B\) D B  = − 2.0, which promotes the appearance of compensation points, whereas \(D_A\) D A influences the value of the compensation points. The thermal behavior of the order parameters is analyzed across various crystal field values under multiple external field strengths at specific temperatures. Our results indicate that the system undergoes a second-order phase transition at h = 0, whereas first-order phase transitions occur for h > − 0.5. Only a single hysteresis loop exists for D = 0 and T < 8; however, triple and double hysteresis loops are observed when the crystal field conditions change, along with the emergence of a superparamagnetic phase at higher temperatures and at lower values of D.