镧系单分子磁体的自旋-晶格弛豫的高效模拟

doi:10.1016/j.actphy.2026.100392

摘要/Abstract

摘要： 单分子磁体(SMMs)因其在下一代自旋电子器件中的广阔应用前景而备受关注。然而,其磁双稳态的稳定性受到自旋-晶格弛豫过程的限制;在这一过程中,分子自旋的能量会耗散至晶格声子。由于弛豫动力学取决于自旋所处的化学环境,因此,尽管其内在机制十分复杂,建立分子结构与弛豫行为之间的直接理论联系仍对理性分子设计至关重要。在本工作中,我们采用均匀化方法对主方程进行约化,以探究Orbach过程的作用机制,并揭示静态有效哈密顿量如何影响弛豫能垒。为降低计算数千个非平衡结构所需的高昂成本,我们提出了一种新方法,通过洛伦兹分布抽样生成自旋-声子耦合参数。该简化方案的有效性在七个具有代表性的镧系单分子磁体中得到了验证。本工作不仅深化了对Orbach弛豫基本机制的理解,还为快速模拟单分子磁体的弛豫行为提供了一套高效框架,从而有助于实现更具针对性的分子设计。

关键词: 单分子磁体, 自旋声子耦合, 弛豫时间, 主方程, 第一性原理计算

Abstract: Single-molecule magnets (SMMs) have attracted considerable attention as promising candidates for next-generation spintronic devices. Their magnetic bi-stability, however, is limited by spinlattice relaxation, a process in which molecular spins dissipate energy to lattice phonons. Since the relaxation dynamics are dictated by the spin’s chemical environment, establishing a direct theoretical connection between molecular structure and relaxation behavior is essential for rational molecular design, despite the inherent complexity of the underlying mechanisms. Here, we explore the mechanism of the Orbach process by reducing the master equation with uniformization method, revealing how the static effective Hamiltonian governs the relaxation energy barrier. To alleviate the heavy cost of calculating thousands of non-equilibrium structures, we propose a new approach that introduces a spin-phonon coupling parameters drawn from a Lorentz distribution. The validity of this simplified protocol is confirmed using seven representative lanthanide SMMs. This work not only deepens the fundamental understanding of Orbach relaxation but also provides an efficient framework for quickly simulating the relaxation behavior of SMMs, thereby facilitating faster targeted molecular design.

Key words: Single-molecule magnets, Spin-phonon coupling, Relaxation time, Master equation, Ab initio calculation

邓意凡, 孙荣, 孙政, 邹子龙, 孙怀洋, 蒋鸿, 王炳武, 高松. 镧系单分子磁体的自旋-晶格弛豫的高效模拟[J]. 物理化学学报 2026, (), 100392. doi: 10.1016/j.actphy.2026.100392

Yifan Deng, Rong Sun, Zheng Sun, Zilong Zou, Huaiyang Sun, Hong Jiang, Bing-Wu Wang, Song Gao. High-efficiency simulation of spin-lattice relaxation in lanthanide single-molecule magnets[J]. Acta Phys. -Chim. Sin. 2026, (), 100392. doi: 10.1016/j.actphy.2026.100392

链接本文: https://www.whxb.pku.edu.cn/CN/10.1016/j.actphy.2026.100392

https://www.whxb.pku.edu.cn/CN/Y2026/V/I/100392

参考文献

[1] L. Escalera-Moreno, J.J. Baldoví, A. Gaita-Ariño, E. Coronado, Chem. Sci. 9 (2018) 3265, https://doi.org/10.1039/c7sc05464e.
[2] A. Lunghi, Appl. Magn. Reson. 51 (2020) 1343, https://doi.org/10.1007/s00723-020-01255-5.
[3] M.S. Albert, G.D. Cates, B. Driehuys, W. Happer, B. Saam, C.S. Springer Jr, A. Wishnia, Nature 370 (1994) 199, https://doi.org/10.1038/370199a0.
[4] M.R. Wasielewski, M.D.E. Forbes, N.L. Frank, K. Kowalski, G.D. Scholes, J. Yuen-Zhou, M.A. Baldo, D.E. Freedman, R.H. Goldsmith, T. Goodson III, M.L. Kirk, et al., Nat. Rev. Chem. 4 (2020) 490, https://doi.org/10.1038/s41570-020-0200-5.
[5] F. Dalitz, M. Cudaj, M. Maiwald, G. Guthausen, Prog. Nucl. Magn. Reson. Spectrosc. 60 (2012) 52, https://doi.org/10.1016/j.pnmrs.2011.11.003.
[6] S.H. Koenig, R.D. Brown III, Magn. Reson. Med. 1 (1984) 478, https://doi.org/10.1002/mrm.1910010407.
[7] A.M. Nolan, Y. Zhu, X. He, Q. Bai, Y. Mo, Joule 2 (2018) 2016, https://doi.org/10.1016/j.joule.2018.08.017.
[8] K.T. Butler, J.M. Frost, J.M. Skelton, K.L. Svane, A. Walsh, Chem. Soc. Rev. 45 (2016) 6138, https://doi.org/10.1039/c5cs00841g.
[9] S.S. Eaton, G.R. Eaton, Relaxation times of organic radicals and transition metal ions, In Distance Measurements in Biological Systems by EPR, Springer:Boston, MA, USA, 2002, pp 29-154.
[10] G. Christou, D. Gatteschi, D.N. Hendrickson, R. Sessoli, MRS Bull. 25 (2000) 66, https://doi.org/10.1557/mrs2000.226.
[11] S.F. Maehrlein, I. Radu, P. Maldonado, A. Paarmann, M. Gensch, A.M. Kalashnikova, R.V. Pisarev, M. Wolf, P.M. Oppeneer, J. Barker, et al., Sci. Adv. 4 (2018) eaar5164, https://doi.org/10.1126/sciadv.aar5164.
[12] I. uti, J. Fabian, S.D. Sarma, Rev. Mod. Phys. 76 (2004) 323, https://doi.org/10.1103/RevModPhys.76.323.
[13] G. Wolfowicz, F.J. Heremans, C.P. Anderson, S. Kanai, H. Seo, A. Gali, G. Galli, D.D. Awschalom, Nat. Rev. Mater. 6 (2021) 906, https://doi.org/10.1038/s41578-021-00306-y.
[14] M. Atzori, R. Sessoli, J. Am. Chem. Soc. 141 (2019) 11339, https://doi.org/10.1021/jacs.9b00984.
[15] A. Zabala-Lekuona, J.M. Seco, E. Colacio, Coord. Chem. Rev. 441 (2021) 213984, https://doi.org/10.1016/j.ccr.2021.213984.
[16] D. Gatteschi, R. Sessoli, Angew. Chem.-Int. Ed. 42 (2003) 268, https://doi.org/10.1002/anie.200390099.
[17] J.G.C. Kragskow, A. Mattioni, J.K. Staab, D. Reta, J.M. Skelton, N.F. Chilton, Chem. Soc. Rev. 52 (2023) 4567, https://doi.org/10.1039/d2cs00705c.
[18] R. Orbach, Proc. R. Soc. London Ser. A-Math. Phys. Eng. Sci. 264 (1961) 458, https://doi.org/10.1098/rspa.1961.0211.
[19] D.N. Woodruff, R.E.P. Winpenny, R.A. Layfield, Chem. Rev. 113 (2013) 5110, https://doi.org/10.1021/cr400018q.
[20] R. Sessoli, D. Gatteschi, A. Caneschi, M.A. Novak, Nature 365 (1993) 141, https://doi.org/10.1038/365141a0.
[21] S. Accorsi, A.-L. Barra, A. Caneschi, G. Chastanet, A. Cornia, A.C. Fabretti, D. Gatteschi, C. Mortalo, E. Olivieri, F. Parenti, et al., J. Am. Chem. Soc. 128 (2006) 4742, https://doi.org/10.1021/ja0576381.
[22] J.H. Van Vleck, Phys. Rev. 57 (1940) 426, https://doi.org/10.1103/PhysRev.57.426.
[23] K.N. Shrivastava, Phys. Status Solidi B-Basic Res. 117 (1983) 437, https://doi.org/10.1002/pssb.2221170202.
[24] A. Castro-Alvarez, Y. Gil, L. Llanos, D. Aravena, Inorg. Chem. Front. 7 (2020) 2478, https://doi.org/10.1039/d0qi00487a.
[25] A. Lunghi, F. Totti, S. Sanvito, R. Sessoli, Chem. Sci. 8 (2017) 6051, https://doi.org/10.1039/c7sc02832f.
[26] A. Lunghi, F. Totti, R. Sessoli, S. Sanvito, Nat. Commun. 8 (2017) 1, https://doi.org/10.1038/ncomms14620.
[27] C.A.P. Goodwin, F. Ortu, D. Reta, N.F. Chilton, D.P. Mills, Nature 548 (2017) 439, https://doi.org/10.1038/nature23447.
[28] P. Evans, D. Reta, G.F.S. Whitehead, N.F. Chilton, D.P. Mills, J. Am. Chem. Soc. 141 (2019) 19935, https://doi.org/10.1021/jacs.9b11515.
[29] K.-X. Yu, J.G.C. Kragskow, Y.-S. Ding, Y.-Q. Zhai, D. Reta, N.F. Chilton, Y.-Z. Zheng, Chem 6 (2020) 1777, https://doi.org/10.1016/j.chempr.2020.04.024.
[30] D. Reta, J.G.C. Kragskow, N.F. Chilton, J. Am. Chem. Soc. 143 (2021) 5943, https://doi.org/10.1021/jacs.1c01410.
[31] S. Mondal, A. Lunghi, J. Am. Chem. Soc. 144 (2022) 22965, https://doi.org/10.1021/jacs.2c08876.
[32] M. Briganti, F. Santanni, L. Tesi, F. Totti, R. Sessoli, A. Lunghi, J. Am. Chem. Soc. 143 (2021) 13633, https://doi.org/10.1021/jacs.1c05068.
[33] A. Lunghi, Sci. Adv. 8 (2022) eabn7880, https://doi.org/10.1126/sciadv.abn7880.
[34] N.F. Chilton, Chem. Soc. Rev. 54 (2025) 11468, https://doi.org/10.1039/d5cs00493d.
[35] M. Atanasov, S.V. Rao, F. Neese, Chem. Sci. 16 (2025) 18985, https://doi.org/10.1039/d5sc90219c.
[36] X. Wu, J.-F. Li, B. Yin, Dalton Trans. 51 (2022) 14793, https://doi.org/10.1039/d2dt01507b.
[37] E. Garlatti, A. Chiesa, P. Bonfà, E. Macaluso, I.J. Onuorah, V.S. Parmar, Y.-S. Ding, Y.-Z. Zheng, M.J. Giansiracusa, D. Reta, et al., J. Phys. Chem. Lett. 12 (2021) 8826, https://doi.org/10.1021/acs.jpclett.1c02367.
[38] J.K. Staab, N.F. Chilton, J. Chem. Theory Comput. 18 (2022) 6588, https://doi.org/10.1021/acs.jctc.2c00611.
[39] R. Nabi, J.K. Staab, A. Mattioni, J.G.C. Kragskow, D. Reta, J.M. Skelton, N.F. Chilton, J. Am. Chem. Soc. 145 (2023) 24558, https://doi.org/10.1021/jacs.3c06015.
[40] A. Lunghi, S. Sanvito, J. Phys. Chem. Lett. 11 (2020) 6273, https://doi.org/10.1021/acs.jpclett.0c01681.
[41] A. Lunghi, S. Sanvito, J. Chem. Phys. 153 (2020) 174113, https://doi.org/10.1063/5.0017118.
[42] A. Lunghi, S. Sanvito, J. Phys. Chem. C 124 (2020) 5802, https://doi.org/10.1021/acs.jpcc.0c01187.
[43] V. Zaverkin, J. Netz, F. Zills, A. Khn, J. Kästner, J. Chem. Theory Comput. 18 (2022) 1, https://doi.org/10.1021/acs.jctc.1c00853.
[44] V.H.A. Nguyen, A. Lunghi, Phys. Rev. B 105 (2022) 165131, https://doi.org/10.1103/PhysRevB.105.165131.
[45] V. Briganti, A. Lunghi, npj Comput. Mater. 11 (2025) 62, https://doi.org/10.1038/s41524-025-01547-z.
[46] H.-P. Breuer, F. Petruccione, The theory of open quantum systems, Oxford University Press:New York, NY, USA, 2002.
[47] V. May, O. Khn, Charge and Energy Transfer Dynamics in Molecular Systems, Wiley-VCH:Berlin, Germany, 2011.
[48] A. Nitzan. Chemical Dynamics in Condensed Phases:Relaxation, Transfer and Reactions in Condensed Molecular Systems, Oxford University Press:New York, NY, USA, 2006.
[49] L.F. Chibotaru, Adv. Chem. Phys. 153 (2013) 397, https://doi.org/10.1002/9781118571767.ch6.
[50] L.F. Chibotaru, Ab initio investigation of anisotropic magnetism and magnetization blockingin metal complexes, In Computational Modelling of Molecular Nanomagnets, Rajaraman, G. Ed., Springer:Cham, Switzerland, 2023, pp 1-62.
[51] N.F. Chilton, R.P. Anderson, L.D. Turner, A. Soncini, K.S. Murray, J. Comput. Chem. 34 (2013) 1164, https://doi.org/10.1002/jcc.23234.
[52] C. Rudowicz, M. Karbowiak, Coord. Chem. Rev. 287 (2015) 28, https://doi.org/10.1016/j.ccr.2014.12.006.
[53] D. Gatteschi, R. Sessoli, J. Villain, Molecular Nanomagnets, Oxford University Press:New York, NY, USA, 2006.
[54] N.G. Van Kampen, Stochastic Processes in Physics and Chemistry, Elsevier:Boston, MA, USA, 2007.
[55] A. Lunghi, Spin-phonon relaxation in magnetic molecules:theory, predictionsand insights, In Computational Modelling of Molecular Nanomagnets, Rajaraman, G. Ed., Springer:Cham, Switzerland, 2023.
[56] S.-D. Jiang, B.-W. Wang, G. Su, Z.-M. Wang, S. Gao, Angew. Chem. Int. Ed. 41 (2010) 7610, https://doi.org/10.1002/ange.201004027.
[57] C. Wang, R. Sun, Y. Chen, B.-W. Wang, Z.-M. Wang, S. Gao, CCS Chem. 2 (2020) 362, https://doi.org/10.31635/ccschem.020.202000138.
[58] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865, https://doi.org/10.1103/PhysRevLett.77.3865.
[59] G. Kresse, J. Furthmller, Comput. Mater. Sci. 6 (1996) 15, https://doi.org/10.1016/0927-0256(96)00008-0.
[60] P.E. Blöchl, Phys. Rev. B 50 (1994) 17953, https://doi.org/10.1103/PhysRevB.50.17953.
[61] F. Aquilante, J. Autschbach, R.K. Carlson, L.F. Chibotaru, M.G. Delcey, L. De Vico, I. Fdez. Galván, N. Ferré, L.M. Frutos, L. Gagliardi, et al., J. Comput. Chem. 37 (2016) 506, https://doi.org/10.1002/jcc.24221.
[62] L. Ungur, L.F. Chibotaru, Computational modelling of the magnetic properties of lanthanide compounds, In Lanthanides and Actinides in Molecular Magnetism, Layfield, R. A., Murugesu, M. Eds., Wiley-VCH:Berlin, Germany, 2015, pp. 153-184.
[63] L. Ungur, L.F. Chibotaru, Chem.-Eur. J. 23 (2017) 3708, https://doi.org/10.1002/chem.201605102.
[64] M. Douglas, N.M. Kroll, Ann. Phys. 82 (1974) 89, https://doi.org/10.1016/0003-4916(74)90333-9.
[65] B.A. Hess, Phys. Rev. A 33 (1986) 3742, https://doi.org/10.1103/PhysRevA.33.3742.
[66] B.A. He, C.M. Marian, U. Wahlgren, O. Gropen, Chem. Phys. Lett. 251 (1996) 365, https://doi.org/10.1016/0009-2614(96)00119-4.
[67] B.O. Roos, R. Lindh, P.-. Malmqvist, V. Veryazov, P.-O. Widmark, J. Phys. Chem. A 108 (2004) 2851, https://doi.org/10.1021/jp031064+.
[68] B.O. Roos, R. Lindh, P.-. Malmqvist, V. Veryazov, P.-O. Widmark, A.C. Borin, J. Phys. Chem. A 112 (2008) 11431, https://doi.org/10.1021/jp803213j.
[69] A. Jensen, Scand. Actuar. J. 1953 (1953) 87, https://doi.org/10.1080/03461238.1953.10419459.
[70] P.C. Bressloff, J.M. Newby, Phys. Rev. E 89 (2014) 042701, https://doi.org/10.1103/PhysRevE.89.042701.
[71] C. Gardiner, Stochastic Methods, Springer:Berlin, Germany, 2009.
[72] P.G. Hufton, Y.T. Lin, T. Galla, Phys. Rev. E 99 (2019) 032121, https://doi.org/10.1103/PhysRevE.99.032121.
[73] G. Latouche, V. Ramaswami, Introduction to Matrix Analytic Methods in Stochastic Modeling, SIAM:Philadelphia, PA, USA, 1999.
[74] N.M. van Dijk, S.P.J. van Brummelen, R.J. Boucherie, Perform. Eval. 118 (2018) 8, https://doi.org/10.1016/j.peva.2017.09.008.
[75] G.-J. Chen, Y.-N. Guo, J.-L. Tian, J. Tang, W. Gu, X. Liu, S.-P. Yan, P. Cheng, D.-Z. Liao, Chem.-Eur. J. 18 (2012) 2484, https://doi.org/10.1002/chem.201103816.
[76] J. Liu, Y.-C. Chen, J.-L. Liu, V. Vieru, L. Ungur, J.-H. Jia, L.F. Chibotaru, Y. Lan, W. Wernsdorfer, S. Gao, et al., J. Am. Chem. Soc. 138 (2016) 5441, https://doi.org/10.1021/jacs.6b02638.
[77] Y.-S. Ding, N.F. Chilton, R.E.P. Winpenny, Y.-Z. Zheng, Angew. Chem.-Int. Edit. 55 (2016) 16071, https://doi.org/10.1002/ange.201609685.
[78] B. Yin, C.-C. Li, Phys. Chem. Chem. Phys. 22 (2020) 9923, https://doi.org/10.1039/d0cp00933d.
[79] G. Rajaraman, Computational Modelling of Molecular Nanomagnets, Springer:Cham, Switzerland, 2023.
[80] M.A. Palafox, Phys. Sci. Rev. 3 (2018) 20170184, https://doi.org/10.1515/psr-2017-0184.