Theoretical Study of the Bilayer Honeycomb Spin Lattice in Transverse Field with Competing Ferromagnetic and Antiferromagnetic Interactions
Main Article Content
Abstract
In this work we studied theoretically the thermodynamics and magnetization process of this bilayer honeycomb spin lattice structure for the transverse field case using the transverse Ising model (TIM) [1] and mean field approximation (MFA). Theoretical investigations of the magnetization process in the AF bilayer honeycomb spin lattice with FM order in each layer using the Ising spin model in longitudinal and transverse fields have been shown. The obtained results show that the AF exchange interaction coupling has the effect of decreasing the critical fields and magnitude of the longitudinal susceptibility of the film.
Keywords:
Bilayer film, Transverse Ising model, dynamical susceptibility,
References
[1] B. T. Cong, N. T. Niem, B. H. Giang, Thermodynamic Properties of Ferroics Described by the Transverse Ising Model and Their Applications for CoNb2O6, Journal of Magnetism and Magnetic Materials, Vol. 483, 2019,
pp. 136-142, https://doi.org/10.1016/j.jmmm.2019.03.093.
[2] R. Xu, X. Zou, Electric Field-Modulated Magnetic Phase Transition in Van der Waals CrI3 Bilayers, Journal of Physical Chemistry Letters, Vol. 11, No. 8, 2020, pp. 3152-3158, https://doi.org/10.1021/acs.jpclett.0c00567.
[3] C. Gong, L. Li, Z. Li, H. Ji, A. Stern, Y. Xia, T. Cao, W. Bao, C. Wang, Y. Wang, Z. Q. Qiu, R. J. Cava, S. G. Louie, J. Xia, X. Zhang, Discovery of Intrinsic Ferromagnetism in Two-Dimensional Van der Waals Crystals, Nature, Vol. 546, No. 7657, 2017, pp. 265-269, https://doi.org/10.1038/nature22060.
[4] M. Gibertini, M. Koperski, A. F. Morpurgo, K. S. Novoselov, Magnetic 2D Materials and Heterostructures, Nature Nanotechnology, Vol. 14, No. 5, 2019, pp. 408-419, https://doi.org/10.1038/s41565-019-0438-6.
[5] B. Huang, G. Clark, E. Navarro-Moratalla, R. K. Dahlia, R. Cheng, L.S. Kyle, D. Zhong, E. Schmidgall, M. A. McGuire, D. H. Cobden, W. Yao, D. Xiao, P. Jarillo-Herrero, X. Xu, Layer-dependent Ferromagnetism in a Van der Waals Crystal Down to the Monolayer Limit, Nature, Vol. 546, No. 7657, 2017, pp. 270-273, https://doi.org/10.1038/nature22391.
[6] K. F. Mak, J. Shan, D. Ralph, Probing and Controlling Magnetic States in 2D Layered Magnetic Materials, Nature Reviews Physics, Vol. 1, No. 11, 2019, pp. 646-661, https://doi.org/10.1038/s42254-019-0110-y.
[7] S. Jiang, L. Li, Z. Wang, K. F. Mak, J. Shan, Controlling Magnetism in 2D CrI3 by Electrostatic Doping, Nature Nanotechnology, Vol. 13, No. 7, 2018, pp. 549-553, https://doi.org/10.1038/s41565-018-0135-x.
[8] N. T. K. Oanh, N. H. Phong, N. T. Niem, B. T. Cong, N. D. Huy, B. H. Giang, Monte Carlo Investigation for an Ising Model with Competitive Magnetic Interaction Regime, Communications in Physics, Vol. 33, No. 2, 2023, pp. 205-212, https://doi.org/10.15625/0868-3166/18109.
[9] N. T. Niem, B. H. Giang, P. H. Thao, N. D. Huy, N. T. K. Oanh, B. T. Cong, Magnetization Process in Bilayer Honeycomb Spin Lattice, Materials Transactions, Vol. 64, No. 9, 2023, pp. 2118-2123, https://doi.org/10.2320/matertrans.MT-MG2022025.
pp. 136-142, https://doi.org/10.1016/j.jmmm.2019.03.093.
[2] R. Xu, X. Zou, Electric Field-Modulated Magnetic Phase Transition in Van der Waals CrI3 Bilayers, Journal of Physical Chemistry Letters, Vol. 11, No. 8, 2020, pp. 3152-3158, https://doi.org/10.1021/acs.jpclett.0c00567.
[3] C. Gong, L. Li, Z. Li, H. Ji, A. Stern, Y. Xia, T. Cao, W. Bao, C. Wang, Y. Wang, Z. Q. Qiu, R. J. Cava, S. G. Louie, J. Xia, X. Zhang, Discovery of Intrinsic Ferromagnetism in Two-Dimensional Van der Waals Crystals, Nature, Vol. 546, No. 7657, 2017, pp. 265-269, https://doi.org/10.1038/nature22060.
[4] M. Gibertini, M. Koperski, A. F. Morpurgo, K. S. Novoselov, Magnetic 2D Materials and Heterostructures, Nature Nanotechnology, Vol. 14, No. 5, 2019, pp. 408-419, https://doi.org/10.1038/s41565-019-0438-6.
[5] B. Huang, G. Clark, E. Navarro-Moratalla, R. K. Dahlia, R. Cheng, L.S. Kyle, D. Zhong, E. Schmidgall, M. A. McGuire, D. H. Cobden, W. Yao, D. Xiao, P. Jarillo-Herrero, X. Xu, Layer-dependent Ferromagnetism in a Van der Waals Crystal Down to the Monolayer Limit, Nature, Vol. 546, No. 7657, 2017, pp. 270-273, https://doi.org/10.1038/nature22391.
[6] K. F. Mak, J. Shan, D. Ralph, Probing and Controlling Magnetic States in 2D Layered Magnetic Materials, Nature Reviews Physics, Vol. 1, No. 11, 2019, pp. 646-661, https://doi.org/10.1038/s42254-019-0110-y.
[7] S. Jiang, L. Li, Z. Wang, K. F. Mak, J. Shan, Controlling Magnetism in 2D CrI3 by Electrostatic Doping, Nature Nanotechnology, Vol. 13, No. 7, 2018, pp. 549-553, https://doi.org/10.1038/s41565-018-0135-x.
[8] N. T. K. Oanh, N. H. Phong, N. T. Niem, B. T. Cong, N. D. Huy, B. H. Giang, Monte Carlo Investigation for an Ising Model with Competitive Magnetic Interaction Regime, Communications in Physics, Vol. 33, No. 2, 2023, pp. 205-212, https://doi.org/10.15625/0868-3166/18109.
[9] N. T. Niem, B. H. Giang, P. H. Thao, N. D. Huy, N. T. K. Oanh, B. T. Cong, Magnetization Process in Bilayer Honeycomb Spin Lattice, Materials Transactions, Vol. 64, No. 9, 2023, pp. 2118-2123, https://doi.org/10.2320/matertrans.MT-MG2022025.