Abstract
With the Monte Carlo method, we simulate 3D alloys Heisenberg model of Cr-doped BiFeO\(_3\) with various proportions Cr-doped. This model includes external magnetic field h, DM interaction, and exchange coupling constant ratio R to reflect the properties of BiFe\(_{1-p}\)Cr\(_p\)O\(_3\). We neglect the influence of A site and oxygen atom, focus solely on the interaction of B site. The super-exchange interaction is approximated at B sites to the direct exchange interaction, for investigating the magnetic enhancement effect and the variation of transformation temperature with various Cr proportions. Finally, the formation conditions of V, N and P type BiFe\(_{1-p}\)Cr\(_p\)O\(_3\) ferrimagnetic configurations classified by the Néel classification standard.
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Sosnowska, I.M.: Neutron scattering studies of BiFeO\(_3\) multiferroics: a review for microscopists. J. Micro. (2009). https://doi.org/10.1111/j.1365-2818.2009.03227.x
Sosnowska, I., Peterlin-Neumaier, T., Steichele, E.: Spiral magnetic ordering in bismuth ferrite. J. Phys. C: Solid State Physics. (1982). https://doi.org/10.1088/0022-3719/15/23/020
Ramam, K., Diwakar, B.S., Varaprasad, K., et al.: Magnetic properties of nano-multiferroic materials. J. Magn. Magnetic. Mat. (2017). https://doi.org/10.1016/j.jmmm.2017.06.125
Mazumder, R., Devi P.S., Bhattacharya, D., et al.: Ferromagnetism in nanoscale BiFeO\(_3\). Appl. Phys. Lett. (2007). https://doi.org/10.1063/1.2768201
Chiang, Y.S., Tu, C.S., Chen, P.Y., et al.: Magnetic and phonon transitions in B-site Co doped BiFeO\(_3\) ceramics. Ceramics Int. (2016). https://doi.org/10.1016/j.ceramint.2016.05.097
Sharma, V., Ghosh, R.K., Kuanr, B.K.: Investigation of room temperature ferromagnetism in transition metal doped BiFeO\(_3\). J. Phys. Condens. Matter. (2019). https://doi.org/10.1088/1361-648X/ab29d1
Jacob, D., Haule, K., Kotliar, G.: Dynamical mean-field theory for molecular electronics: Electronic structure and transport properties. Phys. Rev. B. (2010). https://doi.org/10.1103/PhysRevB.82.195115
Yahyaoui, S., Khalfaoui, M., Kallel, S., et al.: Modeling the magnetic properties and magnetocaloric effect of La\(_{0.7}\)Sr\(_{0.3}\)Mn\(_{0.9}\)Ti\(_{0.1}\)O\(_3\). J. Alloys Compounds. (2016). https://doi.org/10.1016/j.jallcom.2016.05.318
Levin, M., Nave, C.P.: Tensor Renormalization Group Approach to Two-Dimensional Classical Lattice Models. Phys. Rev. Lett. (2007). https://doi.org/10.1103/PhysRevLett.99.120601
Ron, D., Swendsen, R.H., Brandt, A.: Inverse Monte Carlo Renormalization Group Transformations for Critical Phenomena. Phys. Rev. Lett. (2002). https://doi.org/10.1103/PhysRevLett.89.275701
Logemann, R., Rudenko, A.N., Katsnelson, M.I., et al.: Exchange interactions in transition metal oxides: The role of oxygen spin polarization. J. Phys. Condens. Matter. (2017). https://doi.org/10.1088/1361-648X/aa7b00
Korpinar, T., Demirkol, R.C., Korpinar, Z.: New fractional Heisenberg antiferromagnetic model and solitonic magnetic flux surfaces with normal direction. Int. J. Geo. Meth. Modern Phys. (2021). https://doi.org/10.1142/S021988782150136X
Kim, S.Y., Kwak, W.: Partition Function Zeros of the Ising Model on a Kagom Lattice in the Complex Magnetic-Field Plane. J. Korean Phys. Soc. (2018). https://doi.org/10.3938/jkps.73.547
Kim, S.Y.: Yang-Lee Edge Singularity of the Ising Model on a Honeycomb Lattice in an External Magnetic Field. J. Korean Phys. Soc. (2020). https://doi.org/10.3938/jkps.77.271
Apostolova, Wesselinowa, J.M.: Magnetic control of ferroelectric properties in multiferroic BiFeO\(_3\) nanoparticles. Solid State Communications. (2008). https://doi.org/10.1016/j.ssc.2008.05.003
Cao, X.S., Ji, G.F., Jiang, X.F.: Anomalous sound velocity in multiferroic BiFeO\(_3\). Solid State Communications. (2016). https://doi.org/10.1016/j.ssc.2016.07.022
Baettig, P., Ederer, C., Spaldin, N.A.: First principles study of the multiferroics BiFeO\(_3\), Bi\(_2\)FeCrO\(_6\), and BiCrO\(_3\): Structure, polarization, and magnetic ordering temperature. Phys. Rev. B. (2005). http://doi.org/10.1103/PhysRevB.72.214105
Wenzhe, S., Banggui, L.: Electronic structure and magnetic and optical properties of double perovskite Bi\(_2\)FeCrO\(_6\) from first-principles investigation. Chinese Physics B. (2013). http://doi.org/10.1088/1674-1056/22/4/047506
Metropolis, N.: Equation of State Calculations by Fast Computing Machines. J. Chem. Phys. (2004). http://doi.org/10.1063/1.1699114
Alzate-Cardona, J.D., et al.: Optimal phase space sampling for Monte Carlo simulations of Heisenberg spin systems. J. Phys. Condens. Matter. (2019). http://doi.org/10.1088/1361-648X/aaf852
Preis, T., et al.: GPU accelerated Monte Carlo simulation of the 2D and 3D Ising model. J. Comp. Phys. (2009). http://doi.org/10.1016/j.jcp.2009.03.018
Yksel, Y.: Monte Carlo simulation of Prussian blue analogs described by Heisenberg ternary alloy model. J. Phys. Chem. Solids. (2015). https://doi.org/10.1016/j.jpcs.2015.07.017
Acknowledgements
The research was supported partly by National Natural Science Foundation of China (grant number 12105137, 11447231), the Natural Science Foundation of Hunan Province, China (grant number 2020JJ4517), Research Foundation of Education Bureau of Hunan Province, China (grant number 19C1621, 19A434), the National Undergraduate Innovation and Entrepreneurship Training Program Support Projects of China (Grant No. 20200112).
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Mo, J., Zhang, Q., Chen, Y. et al. The Magnetic Properties of Different Proportions Cr-Doped Bifeo3 as Studied Using Heisenberg Model. J Supercond Nov Magn 35, 1207–1214 (2022). https://doi.org/10.1007/s10948-022-06151-6
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DOI: https://doi.org/10.1007/s10948-022-06151-6