Abstract
Our aim of this work is to study the magnetic properties of a bi-layer borophene structure, using Monte Carlo simulations under the Metropolis algorithm. Such a system is formed by two layers. The first one contains 126 atoms with spin σ = ± 3/2, ± 1/2 and 84 atoms with spins S = ± 1, 0 while the second one contains 84 atoms with spin σ = ± 3/2, ± 1/2 and 126 atoms with spins S = ± 1, 0. We establish, in various planes, the ground-state phase diagrams. Furthermore, we present the thermal variation of the total magnetization and total susceptibility for several values of exchange coupling interactions and crystal field. It is found that the increase in both exchange coupling interactions leads to an almost linear increase in transition temperature in one hand and, on the other hand, to a decrease in the corresponding crystal field transition.
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N. Maaouni, M. Qajjour, A. Mhirech, B. Kabouchi, L. Bahmad, W. Ousi Benomar, J. Magn. Magn. Mater. 468, 175–180 (2018)
S. Naskar, A.K. Chakraborty, J. Persp. Sci. 8, 273–275 (2016)
J. Liu, H. Chen, B. Guan, K. Liu, J. Wen, Z. Sun, J. Constr. Build. Mater. 190, 287–293 (2018)
K. Ramam, B.S. Diwakar, K. Varaprasad, V. Swaminadham, V. Reddy, J. Magn. Magn. Mater. 442, 453–459 (2017)
R.E. Christiansen, J. Vester-Petersen, S.P. Madsen, O. Sigmund, J. Comput. Methods Appl. Mech. Eng. 343, 23–39 (2019)
W. Liu, P.K.J. Wong, Y. Xu, J. Prog. Mater. Sci. 99, 27–105 (2019)
W. Jiang, Y.N. Wang, A.-B. Guo, Y.Y. Yang, K.-L. Shi, Carbon 110, 41–47 (2016)
S. Aouini, S. Ziti, H. Labrim, L. Bahmad, Solid State Commun. 267, 57–62 (2017)
W. Ming, Z. Zhang, S. Wang, Y. Zhang, F. Shen, G. Zhang, J. Clean. Prod. 214, 12–28 (2019)
N. Zhang, W. Liu, D. Deng, Z. Tang, X. Liu, Z. Yan, H. Zhang, J. Opt. Laser Tech. 108, 247–254 (2018)
A. Mhirech, S. Aouini, A. Alaoui-Ismaili, L. Bahmad, J. Low. Temp. Phys. 117, 382–391 (2018)
T. Sahdane, A. Mhirech, L. Bahmad, B. Kabouchi, J. Supercond. Nov. Magn. 31, 1089–1093 (2018)
R. Masrour, A. Jabar, Phys. Lett. A 491, 843–851 (2018)
E. Jurčišinová, M. Jurčišin, J. Phys. A 514, 644–657 (2019)
J.P. Santos, F.C. Sá Barreto, J. Magn. Magn. Mater. 439, 114–119 (2017)
M.B. Einhorn, J. Wudka, Nuc. Phys. B 876, 556–574 (2013)
R.K. Qiu, F.F. Guo, Z.D. Zhang, J. Magn. Magn. Mater. 399, 228–235 (2016)
N.G. Diamantis, E. Manousakis, J. Phys. Proc. 68, 85–89 (2015)
M.I. Bin-Zhou, Phys. B 497, 23–30 (2016)
G. Mert, Phys. A 404, 217–223 (2014)
V.S. Leite, W. Figueiredo, Phys. A 350, 379–392 (2005)
T. Kaneyoshi, J. Magn. Magn. Mater. 321, 3430–3435 (2009)
H. Magoussi, A. Zaim, M. Kerouad, J. Super. Micro. 89, 188–203 (2016)
R.G.B. Mendes, F.C. Sá Barreto, J.P. Santos, J. Magn. Magn. Mater. 471, 365–369 (2019)
E. Albayrak, Chin. J. Phys. 5, 2291–2296 (2018)
A. Oubelkacem, Y. Benhouria, I. Essaoudi, A. Ainane, R. Ahuja, Cond. Mater. 549, 82–86 (2018)
M. Mouhib, N. Benayad, M. Azhari, J. Magn. Magn. Mater. 419, 325–337 (2016)
S.S. Ahmed, L. Bahmad, A. El Yousfi, A. Benyoussef, A.G. El Hachimi, J. Sup. Micro. 123, 1–11 (2018)
W. Wang, D. Lv, Y. Liu, Y. Yang, X. Zhao, J. Sup. Micro. 112, 688–696 (2017)
J.R.V. Pereira, T.M. Tunes, A.S. de Arruda, M. Godoy, J. Phys. A 500, 265–272 (2018)
B. Deviren, Y. Şener, J. Magn. Magn. Mater. 386, 12–19 (2015)
I.J.L. Diaz, N.S. Branco, Phys. Lett. A 468, 158–170 (2017)
I.J.L. Diaz, N.S. Branco, Phys. Lett. A 490, 904–917 (2018)
R. Masrour, A. Jabar, A. Benyoussef, M. Hamedoun, Phys. Lett. A 491, 1028–1039 (2018)
N. Tahiri, A. Jabar, L. Bahmad, J. Phys. Lett. A 381, 189–193 (2017)
C.L. Zou, D.Q. Guo, F. Zhang, J. Meng, H.L. Miao, W. Jiang, Phys. E 104, 138–145 (2018)
Z.A. Piazza, Hu. Han-Shi, W.-L. Li, Y.-F. Zhao, J. Li, L.-S. Wang, Nat. Commun. 5, 3113–3119 (2014)
H.R. Jiang, Z. Lu, M.C. Wu, F. Ciucci, T.S. Zhao, Nano Energy 23, 97–104 (2016)
B. Feng, J. Zhang, Q. Zhong, W. Li, S. Li, H. Li, P. Cheng, S. Meng, L. Chen, K. Wu, Nat. Chem. 8, 563–568 (2016)
A.J. Mannix, X.F. Zhou, B. Kiraly, J.D. Wood, D. Alducin, B.D. Myers, L. Xiaolong, Science 350, 1513–1516 (2015)
W. Li, L. Kong, C. Chen, J. Gou, S. Sheng, W. Zhang, H. Li, L. Chen, P. Cheng, K. Wu, Sci. Bull. 63, 282–286 (2018)
R. Bhuvaneswari, R. Chandiramouli, Chem. Phys. Lett. 701, 34–42 (2018)
Z. Zhang, Y. Yang, E.S. Penev, B.I. Yakobson, Adv. Funct. Mater. 27, 1605059 (2017)
P. Mathé, E. Novak, J. Compl. 23, 673–696 (2007)
M. Qajjour, N. Maaouni, Z. Fadil, A. Mhirech, B. Kabouchi, W. Ousi Benomar, L. Bahmad, Chin. J. Phys. 63, 36 (2020)
Z. Fadil, M. Qajjour, A. Mhirech, B. Kabouchi, L. Bahmad, W.O. Benomar, J. Magn. Magn. Mater. 491, 165559 (2019)
Z. Fadil, M. Qajjour, A. Mhirech, B. Kabouchi, L. Bahmad, W.O. Benomar, Phys. B Condens. Matter 564, 104–113 (2019)
X.S. Wang, F. Zhang, N. Si, J. Meng, Y.L. Zhang, W. Jiang, Phys. A Stat. Mech. Appl. 527, 121356 (2019)
Z. Fadil, A. Mhirech, B. Kabouchi, L. Bahmad, W.O. Benomar, Superlatt. Microstruct. 135, 106285 (2019)
K.L. Shi, W. Jiang, Phys. E 101, 94–102 (2018)
Z. Fadil, M. Qajjour, A. Mhirech, B. Kabouchi, L. Bahmad, W.O. Benomar, Phys. B Condens. Matter 578, 411852 (2020)
Z. Fadil, A. Mhirech, B. Kabouchi, L. Bahmad, W.O. Benomar, Superlatt. Microstruct. 134, 106224 (2019)
N. Si, F. Zhang, W. Jiang, Y.L. Zhang, Phys. A 510, 641–648 (2018)
Z. Fadil, A. Mhirech, B. Kabouchi, L. Bahmad, W.O. Benomar, Chin. J. Phys. 64, 295–304 (2020)
S.A. Deviren, Solid State Commun. 251, 73–78 (2017)
S. Chen, D. Haziza, Comput. Stat. Data Anal. 127, 258–268 (2018)
Y. Yang, W. Wang, H. Ma, Q. Li, Z.Y. Gao, T. Huang, Phys. E 108, 358–371 (2019)
K. Shi, W. Jiang, A. Guo, K. Wang, C. Wu, Phys. A 500, 11–22 (2018)
W. Wang, R. Liu, D. Lv, X. Luo, Superlatt. Micro. 98, 458–472 (2016)
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Qajjour, M., Fadil, Z., Mhirech, A. et al. Magnetic Properties of a Bi-Layer Borophene Structure with Mixed Spins: Monte Carlo Study. J Low Temp Phys 202, 231–246 (2021). https://doi.org/10.1007/s10909-020-02543-x
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DOI: https://doi.org/10.1007/s10909-020-02543-x