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<p>Using Monte Carlo simulations (MCS), we investigated the magnetic properties and phase diagrams of a hexagonal ferrimagnetic Ising nanotube with a core–shell structure composed of spin-5/2 and spin-2 particles, taking surface dilution into account. Our results revealed several characteristic behaviors. Notably, the concentration of magnetic atoms has a significant influence on both the critical and compensation temperatures. For low values of the exchange interaction <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10909_2025_3305_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\({J}_{s}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>J</mi> <mi>s</mi> </msub> </math></EquationSource> </InlineEquation>​, dilution has no effect on the critical temperature. However, a compensation point appears beyond a dilution threshold, observed for <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10909_2025_3305_Article_IEq4.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="55" /> </InlineMediaObject> <EquationSource Format="TEX">\(x\ge 0.6\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>x</mi> <mo>≥</mo> <mn>0.6</mn> </mrow> </math></EquationSource> </InlineEquation>.We also identified critical thresholds for the crystal field anisotropies <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10909_2025_3305_Article_IEq5.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="TEX">\({D}_{s}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>D</mi> <mi>s</mi> </msub> </math></EquationSource> </InlineEquation>​ and <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10909_2025_3305_Article_IEq6.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">\({D}_{c}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>D</mi> <mi>c</mi> </msub> </math></EquationSource> </InlineEquation>​. Below these thresholds, the critical temperature remains nearly constant, then gradually increases and converges toward a saturation value once the thresholds are exceeded. Furthermore, the analysis of hysteresis loops shows that the system’s magnetic response is highly influenced by dilution: the remanent magnetization increases significantly in absolute value as the concentration of magnetic atoms rises from <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10909_2025_3305_Article_IEq7.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">\(0.6\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>0.6</mn> </mrow> </math></EquationSource> </InlineEquation> to<InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10909_2025_3305_Article_IEq8.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">\(1.0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1.0</mn> </mrow> </math></EquationSource> </InlineEquation>.</p>

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Surface Dilution Effects on Magnetic Properties and Compensation Phenomena of \({Fe}^{\text{II}}\), \({Fe}^{\text{III}})\) Core–Shell Ferrimagnetic Nanotubes: Monte Carlo Study

  • 期刊论文

  • 发表日期：

    2025年5月30日

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  • Z. Elmghabar,
  • A. Elidrysy,
  • L. B. Drissi,
  • S. Harir

摘要

Using Monte Carlo simulations (MCS), we investigated the magnetic properties and phase diagrams of a hexagonal ferrimagnetic Ising nanotube with a core–shell structure composed of spin-5/2 and spin-2 particles, taking surface dilution into account. Our results revealed several characteristic behaviors. Notably, the concentration of magnetic atoms has a significant influence on both the critical and compensation temperatures. For low values of the exchange interaction \({J}_{s}\) J s ​, dilution has no effect on the critical temperature. However, a compensation point appears beyond a dilution threshold, observed for \(x\ge 0.6\) x ≥ 0.6 .We also identified critical thresholds for the crystal field anisotropies \({D}_{s}\) D s ​ and \({D}_{c}\) D c ​. Below these thresholds, the critical temperature remains nearly constant, then gradually increases and converges toward a saturation value once the thresholds are exceeded. Furthermore, the analysis of hysteresis loops shows that the system’s magnetic response is highly influenced by dilution: the remanent magnetization increases significantly in absolute value as the concentration of magnetic atoms rises from \(0.6\) 0.6 to \(1.0\) 1.0 .