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

Abstract Multiferroic materials, particularly rare-earth orthochromates (RECrO $$_3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mn>3</mml:mn> <mml:mrow/> </mml:mmultiscripts> </mml:math> ), 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 $$\acute{\mathrm{e}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>e</mml:mi> <mml:mo>´</mml:mo> </mml:mover> </mml:math> el temperature, $$T_\mathrm{N}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>N</mml:mi> </mml:msub> </mml:math> ), 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 $$_3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mn>3</mml:mn> <mml:mrow/> </mml:mmultiscripts> </mml:math> compounds under various doping scenarios. Experimental and literature data were integrated to train machine learning models, enabling accurate predictions of $$T_\mathrm{N}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>N</mml:mi> </mml:msub> </mml:math> , besides remanent polarization ( $$P_\mathrm{r}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>P</mml:mi> <mml:mi>r</mml:mi> </mml:msub> </mml:math> ) and piezoelectric coefficients ( $$d_{33}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>d</mml:mi> <mml:mn>33</mml:mn> </mml:msub> </mml:math> ). The results indicate that doping with specific RE elements significantly impacts $$T_\mathrm{N}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>N</mml:mi> </mml:msub> </mml:math> , with optimal doping levels identified for enhanced performance. Furthermore, high-entropy RECrO $$_3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mn>3</mml:mn> <mml:mrow/> </mml:mmultiscripts> </mml:math> 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 $$_3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mn>3</mml:mn> <mml:mrow/> </mml:mmultiscripts> </mml:math> materials, offering valuable insights into their potential applications in energy storage and sensor technologies. Graphical Abstract