Abstract
The compensation behaviors and phase transitions of a new 3D fullerene-like polymer are explored by using Monte Carlo method. The ground-state phase diagrams and magnetization profiles are given, and the conditions for the occurrence of the compensation temperature Tcomp are obtained. As classified in Néel theory, N-type and P-type magnetization curves are found. To explore the changes in the transition temperature TC and the compensation temperature Tcomp induced by physical parameters, we also present the phase diagrams. Furthermore, the critical exponents of the system are calculated, and a good agreement can be achieved by comparing our results with others’. Finally, the triple hysteresis loops are discovered.
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References
Kroto HW, Allaf AW, Balm SP (1991) C60-Buckministerfullerene. Chem Rev 91:1213–1235
Haddon RC, Brus LE, Raghavachari K (1986) Rehybridization and π-orbital alignment: the key to the existence of spheroidal carbon clusters. Chem Phys Lett 131:165–169
Takabayashi Y, Prassides K (2016) Unconventional high-TC superconductivity in fullerides. Philos Trans R Soc A-Math Phys Eng Sci 374:20150320
Tutt LW, Kost A (1992) Optical limiting performance of C60 and C70 solutions. Nature 356:225–226
Wahlen J, De Vos DE, Jacobs PA, Alsters PL (2004) Solids materials as sources for synthetically useful singlet oxygen. Adv Synth Catal 346:152–164
Lai YL, Murugan P, Hwang K (2003) Fullerene derivative attenuates ischemia-reperfusion-induced lung injury. Life Sci 72:1271–1278
Dunsch L, Yang SF, Zhang L, Svitova A, Oswald S, Popov AA (2010) Metal sulfide in a C82 fullerene cage: a new form of endohedral clusterfullerenes. J Am Chem Soc 132:5413–5421
Chai Y, Guo T, Jin CM, Haufler RE, Felipe Chibante LP, Fure J, Wang LH, Michael Alford J, Smalley RE (1991) Fullerenes with metals inside. J Phys Chem 95:7564–7568
Amsharov K, Jansen M (2009) Synthesis of a higher fullerene precursor—an “unrolled” C84 fullerene. Chem Commun 19:2691–2693
Shinohara H (2000) Endohedral metallofullerenes. Rep Prog Phys 63:843–892
Kantar E (2019) The magnetic properties of the spin-1 ising fullerene cage with a core-shell structure. J Supercond Nov Magn 32:425–430
Kantar E (2017) Superconductivity-like phenomena in an ferrimagnetic endohedral fullerene with diluted magnetic surface. Solid State Commun 263:31–37
Kantar E (2019) Effective field study of the magnetism and superconductivity in idealised Ising-type X@Y-60 endohedral fullerene system. Philos Mag 99:1669–1693
Kantar E (2017) The thermal behaviors and phase diagrams of the Ising-type endohedral fullerene with magnetic core and diluted magnetic shell (Core@Shell(20)). Eur Phys J B 90:152
Wang L, Davids PS, Saxena A, Bishop AR (1992) Quasi-particle energy-spectra and magnetic response of certain curved graphitic geometries. Phys Rev B 46:7175–7178
Wang L, Davids PS, Saxena A, Bishop AR (1993) Magnetic response of certain curved graphitic geometries. Synth Met 56:3008–3013
Kantar E (2017) Dynamic calculations of the core/shell structured Ising-type endohedral fullerenes: The effect of core and core/shell interaction. Mod Phys Lett B 31:1750307
Benhouria Y, Essaoudi I, Ainane A, Ahuja R (2019) Dynamic magneto-caloric effect of a C70 fullerene: dynamic Monte Carlo. Physica E 108:191–196
Lin F, Sorensen ES, Kallin C, Berlinsky AJ (2007) Strong correlation effects in the fullerene C20 studied using a one-band Hubbard model. Phys Rev B 76:033414
Sabzevar M, Solaimani M, Ehsani MH, Tehrani DHT (2020) The effect of vacancy-defects on the magnetic properties of Ising fullerene-like nano-structures: a Monte Carlo study. J Magn Magn Mater 502:166573
Li Q, Wang W, Sun L, Li BC, Tian M (2021) Magnetic and thermodynamic properties of a diluted fullerene-like structure X-20 with embedded atom. Physica B 623:413362
Wang W, Li BC, Wang TL, Li Q, Wang F (2022) Thermodynamic and magnetocaloric properties of an A(n)B(60-n) fullerene-like structure under the applied magnetic field. J Magn Magn Mater 553:169292
Gao ZY, Lv D, Wang W, Yang LM, Sun L, Wang F (2021) Magnetic properties of a fullerene-like X-20 structure with embedded metal atom. Phys Scr 96:125858
Wang TL, Wang W, Li Q, Li BC (2022) Prediction of magnetic properties of a single-molecule magnetic metallofullerene cluster DySc2N@C80. Physica B 647:414377
Zhang ZD (2013) Mathematical structure of the three-dimensional (3D) Ising model. Chin Phys B 22:030513
Zhang ZD, Suzuki O, March NH (2019) Clifford algebra approach of 3D Ising model. Adv Appl Clifford Algebr 29:12
Zhang ZD (2020) Computational complexity of spin-glass three-dimensional (3D) Ising model. J Mater Sci Technol 44:116–120
Mhirech A, Aouini S, Alaoui-Ismaili A, Bahmad L (2017) Monte Carlo study of the magnetic properties in a fullerene-like Structure: X-20, X-60, or X-70. J Supercond Nov Magn 30:925–930
Aouini S, Mhirech A, Alaoui-Ismaili A, Bahmad L (2018) Magnetic properties in different fullerenes X-n nano-structures: Monte Carlo study. Chin J Phys 56:1640–1647
Sahdane T, Mhirech A, Bahmad L, Kabouchi B (2018) Magnetic properties of a bi-fullerene-like structure, X-60-Y-60, with RKKY interactions in the Blume-Capel model. Int J Mod Phys B 32:1850031
Aouini S, Mhirech A, Alaoui-Ismaili A, Bahmad L (2019) Phase diagrams and magnetic properties of a double fullerene structure with core/shell. Chin J Phys 59:346–356
El Maazouzi A, Masrour R, Jabar A (2022) Study of the magnetic properties of LiMn1.5Ni0.5O4 spinel: Ab initio calculation and Monte Carlo simulation. J Cryt Growth 584:126552
Belhamra S, Masrour R, Jabar A, Hlil EK (2022) Magnetic properties of B-site mixed of quantum spin liquid in the triangular ferromagnetic Sr3CuSb2O9 system. Indian J Phys 97:121–126
Jerrari M, Masrour R, Jabar A, Sahdane T (2023) Effect of defects on a nano-borophene structure consisting of mixed spins S=2 and sigma=5/2: Monte Carlo simulations. Indian J Phys 97:767–777
Brazhkin VV, Lyapin AG, Popova SV, Klyuev YA, Naletov AM (1998) Mechanical properties of the 3D polymerized, sp2-sp3 amorphous, and diamond-plus-graphite nanocomposite carbon phases prepared from C60 under high pressure. J Appl Phys 84:219–226
Marques L, Mezouar M, Hodeau JL, Núnez-Regueiro M, Serebryanaya N, Ivdenko V, Blank V, Dubitsky G (1999) “Debye-Scherrer ellipses” from 3D fullerene polymers: an anisotropic pressure memory signature. Science 283:1720–1723
Buga S, Blank V, Fransson A, Serebryanaya N, Sundqvist B (2002) DSC study of annealing and phase transformations of C60 and C70 polymerized under pressures in the range 9.5-13 GPa. J Phys Chem Solid 63:331–343
Yamanaka S, Kubo A, Inumaru K, Komaguchi K, Kini N, Inoue T, Irifune T (2006) Electron conductive three-dimensional polymer of cuboidal C60. Phys Rev Lett 96:076602
Yamanaka S, Kini N, Kubo A, Jida S, Kuramoto H (2008) Topochemical 3D polymerization of C60 under high pressure at elevated temperatures. J Am Chem Soc 30:4303–4309
Sato Y, Terauchi M, Yamanaka S (2015) Electronic structures of three-dimensional C60 polymers studied by high-energy-resolution electron energy-loss spectroscopy based on transmission electron microscopy. Chem Phys Lett 626:90–95
Laranjeira J, Marques L, Mezouar M, Melle-Franco M, Strutynski K (2017) Bonding frustration in the 9.5 GPa fcc polymeric C60. Phys Stat Sol-Rapid Res Lett 11:1700343
Mezouar M, Marques L, Hodeau JL, Pischedda V, Núnez-Regueiro M (2003) Equation of state of an anisotropic three-dimensional C60 polymer: the most stable form of fullerene. Phys Rev B 68:193414
Laranjeira J, Marques L, Fortunato NM, Melle-Franco M, Strutynski K, Barroso M (2018) Three-dimensional C60 polymers with ordered binary-alloy-type structures. Carbon 137:511–518
Mazin I, Liechtenstein A, Gunnarsson O, Andersen O, Antropov V, Burkov S (1993) Orientational order in A3C60: antiferromagnetic Ising model for the fcc lattice. Phys Rev Lett 70:4142–4145
Yildirim T, Hong S, Harris A, Mele E (1993) Orientational phases for M3C60. Phys Rev B 48:12262–12277
Li BC, Lv D, Wang W, Wang TL, Wang F (2022) Thermodynamic properties and magnetocaloric effect of a graphdiyne bilayer with RKKY interaction. J Magn Magn Mater 560:169607
Li BC, Wang W, Lv JQ, Yang M, Wang F (2022) Compensation and critical characteristics of the ferrimagnetic bilayer graphdiyne film with RKKY interaction. Appl Phys A-Mater Sci Process 128:445
Lv D, Li HY, Zhang DZ, Li BC (2023) Insights into magnetic behaviors of an Ising graphene ladder-type chain structure applied in an external magnetic field. Micro Nanostructures 180:207609
Li BC, Lv D, Wang W, Li HY (2023) Exploration of magnetic characteristics in perovskite LaCoO3 by particle swarm optimization combined with Monte Carlo method. Phys Lett A 464:128697
Li BC, Lv D, Wang W, Sun L, Hao ZM, Bao J (2023) Compensation temperature and hysteresis behaviors of a graphene-like bilayer: Monte Carlo Study. Commun Theor Phys 75:045702
Zhang XH, Wang W, Li BC, An Y (2023) Exploring magnetic properties of an edge-modified kekulene multilayer cluster in an external magnetic field. Eur Phys J Plus 138:333
Li NX, Wang W, Liu JY, Xu ZY, Xu C, Yang JL (2023) Monte Carlo study of magnetic properties of CrI3-like structure. Micro Nanostructures 181:207610
Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH, Teller E (1953) Equation of state calculations by fast computing machines. J Chem Phys 21:1087–1092
Tukey JW (1958) A problem of Berkson, and minimum variance orderly estimators. Ann Math Statist 29:588–592
Fisher ME, Barber MN (1972) Scaling theory for finite-size effects in the critical region. Phys Rev Lett 28:1516–1519
Landau P, Binder K (2005) A Guide to Monte Carlo Simulations in Statistical Physics. Cambridge University Press, New York, NY, USA
Stanley HE (1971) Introduction to Phase Transition and Critical Phenomena. Clarendon Press-Oxford, Oxford
Privman V (Ed.) (1990) Finite Size Scaling and Numerical Simulation of Statistical Systems. World Scientific.
Néel L (1948) Propriétés magnétiques des ferrites ferrimagnétisme et antiferromagnétisme. Ann Phys 3:137–198
An Y, Wang W, Xiao BW, Huang SY, Xu ZY (2023) Insight into the magnetic behavior and magnetocaloric effect of a borophene monolayer. Commu Theor Phys 75:115701
Yang Y, Wang W, Ma H, Li Q, Gao ZY, Huang T (2019) Magnetic and thermodynamic properties of a ferrimagnetic mixed-spin (1/2, 1, 3/2) Ising nanoisland: Monte Carlo study. Physica E 108:358–371
Le Guillou JC, Zinn-Justin J, Zinn-Justin J (1980) Critical exponents from field theory. Phys Rev B 21:3976–3998
Baker AG, Nickel BG, Meiron DI (1978) Critical indices from perturbation analysis of the Callan-Symanzik equation. Phys Rev B 17:1365
McKenzie S (1979) Self-Avioding Walks on the Face-centered cubic lattice. J Phys A 12:267
Huang K (1987) Statistical mechanics, 2nd edn. Wiley, New York
Kaul SN (1985) Static critical phenomena in ferromagnets with quenched disorder. J Magn Magn Mater 53:1
Banerjee BK (1964) On a generalised approach to first and second order magnetic transitions. Phys Lett 12:16
Fisher ME, Ma SK, Nickel BG (1972) Critical Exponents for Long-Range Interactions. Phys Rev Lett 29:917
Acknowledgements
This project was supported by Natural Science Foundation of Liaoning province (Grant No. 2023-MS-218), National Natural Science Foundation of China (Grant No. U22A20215, 52077141 and 52211540392).
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B-cL performed conceptualization, writing—original draft preparation, formal analysis, supervision, and visualization. WW provided funding acquisition, project administration, writing—reviewing, and editing. YA conducted data curation, software, investigation, and validation. Z-yX analyzed resources and methodology.
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Li, Bc., Wang, W., An, Y. et al. Compensation behaviors and phase transitions of a 3D fullerene-like polymer. J Mater Sci 59, 698–714 (2024). https://doi.org/10.1007/s10853-023-09238-0
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DOI: https://doi.org/10.1007/s10853-023-09238-0