<p>Multiferroic materials, particularly rare-earth orthochromates (RECrO<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43673_2025_175_Article_IEq1.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 /> <mn>3</mn> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation>), have garnered significant interest due to their unique magnetic and electric-polar properties, making them promising candidates for multifunctional devices. Although extensive research has been conducted on their antiferromagnetic (AFM) transition temperature (N<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43673_2025_175_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="10" /> </InlineMediaObject> <EquationSource Format="TEX">\(\acute{\mathrm{e}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mover accent="true"> <mi mathvariant="normal">e</mi> <mo>´</mo> </mover> </math></EquationSource> </InlineEquation>el temperature, <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43673_2025_175_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(T_\mathrm{N}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>T</mi> <mi mathvariant="normal">N</mi> </msub> </math></EquationSource> </InlineEquation>), ferroelectricity, and piezoelectricity, the effects of doping and substitution of rare-earth (RE) elements on these properties remain insufficiently explored. In this study, convolutional neural networks (CNNs) were employed to predict and analyze the physical properties of RECrO<InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43673_2025_175_Article_IEq1.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 /> <mn>3</mn> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation> compounds under various doping scenarios. Experimental and literature data were integrated to train machine learning models, enabling accurate predictions of <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43673_2025_175_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(T_\mathrm{N}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>T</mi> <mi mathvariant="normal">N</mi> </msub> </math></EquationSource> </InlineEquation>, besides remanent polarization (<InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43673_2025_175_Article_IEq6.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(P_\mathrm{r}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>P</mi> <mi mathvariant="normal">r</mi> </msub> </math></EquationSource> </InlineEquation>) and piezoelectric coefficients (<InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43673_2025_175_Article_IEq7.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">\(d_{33}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>d</mi> <mn>33</mn> </msub> </math></EquationSource> </InlineEquation>). The results indicate that doping with specific RE elements significantly impacts <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43673_2025_175_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(T_\mathrm{N}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>T</mi> <mi mathvariant="normal">N</mi> </msub> </math></EquationSource> </InlineEquation>, with optimal doping levels identified for enhanced performance. Furthermore, high-entropy RECrO<InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43673_2025_175_Article_IEq1.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 /> <mn>3</mn> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation> compounds were systematically analyzed, demonstrating how the inclusion of multiple RE elements influences magnetic properties. This work establishes a robust framework for predicting and optimizing the properties of RECrO<InlineEquation ID="IEq10"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43673_2025_175_Article_IEq1.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 /> <mn>3</mn> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation> materials, offering valuable insights into their potential applications in energy storage and sensor technologies.</p> Graphical Abstract <p></p>

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Synergistic effects of rare-earth doping on the magnetic properties of orthochromates: a machine learning approach

  • Guanping Xu,
  • Zirui Zhao,
  • Muqing Su,
  • Hai-Feng Li

摘要

Multiferroic materials, particularly rare-earth orthochromates (RECrO \(_3\) 3 ), have garnered significant interest due to their unique magnetic and electric-polar properties, making them promising candidates for multifunctional devices. Although extensive research has been conducted on their antiferromagnetic (AFM) transition temperature (N \(\acute{\mathrm{e}}\) e ´ el temperature, \(T_\mathrm{N}\) T N ), ferroelectricity, and piezoelectricity, the effects of doping and substitution of rare-earth (RE) elements on these properties remain insufficiently explored. In this study, convolutional neural networks (CNNs) were employed to predict and analyze the physical properties of RECrO \(_3\) 3 compounds under various doping scenarios. Experimental and literature data were integrated to train machine learning models, enabling accurate predictions of \(T_\mathrm{N}\) T N , besides remanent polarization ( \(P_\mathrm{r}\) P r ) and piezoelectric coefficients ( \(d_{33}\) d 33 ). The results indicate that doping with specific RE elements significantly impacts \(T_\mathrm{N}\) T N , with optimal doping levels identified for enhanced performance. Furthermore, high-entropy RECrO \(_3\) 3 compounds were systematically analyzed, demonstrating how the inclusion of multiple RE elements influences magnetic properties. This work establishes a robust framework for predicting and optimizing the properties of RECrO \(_3\) 3 materials, offering valuable insights into their potential applications in energy storage and sensor technologies.

Graphical Abstract