On structural invariants of energy spectrum of S=1 Heisenberg antiferromagnets with single-ion anisotropy

doi:10.26565/2220-637X-2024-42-06

Victor Tokariev V. N. Karazin Kharkiv National University, 4 Svobody sq., Kharkiv, 61022, Ukraine https://orcid.org/0000-0002-8874-0032
Mariia Fedorenko V. N. Karazin Kharkiv National University, 4 Svobody sq., Kharkiv, 61022, Ukraine https://orcid.org/0009-0001-4077-4444

DOI: https://doi.org/10.26565/2220-637X-2024-42-06

Keywords: molecular nanomagnet, Heisenberg model, Ising model, single-ion anisotropy, spin wave theory

Abstract

We study the relationship of the energy spectrum of finite S=1 Heisenberg antiferromagnets with their structure in the presence of single-ion anisotropy. We show that in the limit of strong easy-plane anisotropy magnets with the structure of adjacency cospectral graphs have equal ground state energies with magnetization M=0. We derive additional necessary condition for equality of lowest energy levels with M=±1. For strong easy-axis anisotropy we found that bipartite S=1 magnets with structures, for which S=1/2 Ising models have equal spectra for arbitrary longitudinal magnetic field, have close energy spectra of S=1 antiferromagnets for arbitrary parameter of single-ion anisotropy. For moderate easy-axis anisotropy bipartite S=1 antiferromagnets with equal energies of spin waves in linear approximation are also approximately isoenergetic. Overall, this explains the remarkable similarity of energy spectra in M=0 subspace for S=1 antiferromagnetic Heisenberg model on bipartite cospectral regular graphs.

Downloads

Download data is not yet available.

References

Chilton, N. F. Molecular Magnetism. Annu. Rev. Mater. Res. 2022, 52, 79-101. https://doi.org/10.1146/annurev-matsci-081420-042553.

Chiesa, A., Santini, P., Garlatti, E., Luis, F. and Carretta, S. Rep. Prog. Phys. 2024, 87, 034501. https://doi.org/10.1088/1361-6633/ad1f81.

Forment-Aliaga, A., Gaita-Ariño, A. Chiral, magnetic, molecule-based materials: A chemical path toward spintronics and quantum nanodevices. J. Appl. Phys., 2022, 132(18). https://doi.org/10.1063/5.0118582.

Hu, J. J., Peng, Y., Liu, S. J., and Wen, H. R. Recent advances in lanthanide coordination polymers and clusters with magnetocaloric effect or single-molecule magnet behavior. Dalton Trans., 2021, 50(43), 15473-15487. https://doi.org/10.1039/D1DT02797B.

Wang, J. H., Li, Z. Y., Yamashita, M., and Bu, X. H. Recent progress on cyano-bridged transition-metal-based single-molecule magnets and single-chain magnets. Coord. Chem. Rev., 2021, 428, 213617. https://doi.org/10.1016/j.ccr.2020.213617.

Gu, L., Li, J., and Wu, R. Reconsidering spin-phonon relaxation in magnetic molecules. J. Magn. Magn. Mater., 2022, 170138. https://doi.org/10.1016/j.jmmm.2022.170138.

Neese, F., Pantazis, D. A. What is not required to make a single molecule magnet. Farad. Disc., 2011, 148, 229-238. https://doi.org/10.1039/C005256F.

Garlatti, E., Carretta, S., Schnack, J., Amoretti, G., and Santini, P. Theoretical design of molecular nanomagnets for magnetic refrigeration. Appl. Phys. Lett., 2013, 103(20). https://doi.org/10.1063/1.4830002.

Evangelisti, M., Lorusso, G., and Palacios, E. Comment on “Theoretical design of molecular nanomagnets for magnetic refrigeration” [Appl. Phys. Lett., 2013, 103, 202410]. Appl. Phys. Lett., 2014, 105(4). https://doi.org/10.1063/1.4891336.

Inui, K., Motome, Y. Inverse Hamiltonian design by automatic differentiation. Commun. Phys. 2023, 6, 37. https://doi.org/10.1038/s42005-023-01132-0.

Quintanilla, J. Relationship between the wave function of a magnet and its static structure factor. Phys. Rev. B, 2022, 106(10), 104435. https://doi.org/10.1103/PhysRevB.106.104435.

Albertini, F., D’Alessandro, D. Model identification for spin networks. Linear Algebra Appl., 2005, 394, 237-256. https://doi.org/10.1016/j.laa.2004.07.007.

Barghi, A. R., Ponomarenko, I. Non-isomorphic graphs with cospectral symmetric powers. Electron. J. Comb., 2009, R120-R120. https://doi.org/10.37236/209.

Audenaert, K., Godsil, C., Royle, G., and Rudolph, T. Symmetric squares of graphs. J. Combin. Theory, Ser. B, 2007, 97(1), 74-90. https://doi.org/10.1016/j.jctb.2006.04.002.

Schmidt, H. J., Luban, M. Continuous families of isospectral Heisenberg spin systems and the limits of inference from measurements. J. Phys. A, 2001, 34(13), 2839. https://doi.org/10.1088/0305-4470/34/13/313.

Tokarev, V. V. Quantum magnets with equal spin-wave ground state energies, VIII International Conference for Professionals & Young Scientists ”Low Temperature Physics”, Kharkiv, 2017, p 88.

Tokarev, V. V. Invariant transformations for spin wave models of ferrimagnets, 6th International Conference on Superconductivity and Magnetism, Antalya, Turkey, 2018, p 552.

Brouwer, A. E., Haemers, W. H. Spectra of graphs. Springer New York; New York, 2011. ISBN: 978-1-4614-1938-9.

Bauer, B. et al. The ALPS project release 2.0: open source software for strongly correlated systems. J. Stat. Mech.: Theory Exp., 2011, 05, P05001. https://doi.org/10.1088/1742-5468/2011/05/P05001.

McKay, B. D., Piperno, A. Practical graph isomorphism, II. J. Symb. Comput., 2014, 60, 94-112. https://doi.org/10.1016/j.jsc.2013.09.003.

Colpa, J. H. P. Diagonalization of the quadratic boson Hamiltonian. Phys. A: Stat. Mech. Appl., 1978, 93(3-4), 327-353. https://doi.org/10.1016/0378-4371(78)90160-7.

Toth, S., Lake, B. Linear spin wave theory for single-Q incommensurate magnetic structures. J. Condens. Matter Phys., 2015, 27(16), 166002. https://doi.org/10.1088/0953-8984/27/16/166002.

Maurice, R. Magnetic anisotropy in a cubane-like Ni4 complex: an ab initio perspective. Inorg. Chem., 2021, 60(9), 6306-6318. https://doi.org/10.1021/acs.inorgchem.1c00047.

Jamie L. Manson, Paul A. Goddard, John Singleton et al., Enhancing easy-plane anisotropy in bespoke Ni(II) quantum magnets, Polyhedron, 180, 2020, 114379, https://doi.org/10.1016/j.poly.2020.114379.

Antkowiak, M., Brzostowski, B., Florek, W., Kamieniarz, G. Metallic core [Ni6IICrIII] as an example of centered heterometallic rings displaying quantum effects, J. Magn. Magn. Mater., 2022, 544, 168701, https://doi.org/10.1016/j.jmmm.2021.168701.

Lewin, M. On the coefficients of the characteristic polynomial of a matrix, Discrete Math., 1994, 125(1–3), 255-262. https://doi.org/10.1016/0012-365X(94)90166-X.

Chiesa, A., Whitehead, G., Carretta, S. et al. Molecular nanomagnets with switchable coupling for quantum simulation. Sci. Rep., 2014, 4, 7423. https://doi.org/10.1038/srep07423

Smolko, R., Dušek, M., Kuchár, J., Čižmár, E., Černák, J., Syntheses, characterizations and crystal structures of two Ni(II) complexes [Ni2(neoc)4(H2O)(CO3)](NO3)2·3H2O and [Ni(bapa)2](NO3)2·H2O and magnetic properties of the carbonato complex, Polyhedron, 2024, 255, 116953. https://doi.org/10.1016/j.poly.2024.116953.

Beaudin, L., Ellis-Monaghan, J., Pangborn, G., and Shrock, R. A little statistical mechanics for the graph theorist. Discrete Math., 2010, 310(13-14), 2037-2053. https://doi.org/10.1016/j.disc.2010.03.011.

Ellis-Monaghan, J. A., Moffatt, I. The Tutte–Potts connection in the presence of an external magnetic field, Adv. Appl. Math., 2011, 47(4), 772-782. https://doi.org/10.1016/j.aam.2011.02.004.

Vinci, W., Markström, K., Boixo, S., Roy, A., Spedalieri, F. M., Warburton, P. A., and Severini, S. Hearing the shape of the Ising model with a programmable superconducting-flux annealer. Sci. Rep., 2014, 4(1), 5703. https://doi.org/10.1038/srep05703.

Brylawski, T. Intersection theory for graphs, J. Combin. Theory, Ser. B, 1981, 30(2), 233-246, https://doi.org/10.1016/0095-8956(81)90068-X.

Godsil, C. D., McKay, B. D., Constructing cospectral graphs, Aequ. Math., 1982, 25(1), 257-268. https://doi.org/10.1007/BF02189621.