- Access by Xinjiang University
Suppression of local magnetic moment formation and paramagnetic exchange interactions in monolayer
Phys. Rev. B 114, 165119 – Published 14 September, 2026
DOI: https://doi.org/10.1103/h8ws-g38m
Abstract
We study the electronic and magnetic properties of monolayer within the density-functional plus dynamical mean-field theory approach in the paramagnetic phase. We argue that this compound is sufficiently far from the local magnetic moment limit, demonstrating nonlinear temperature dependencies of the partial inverse local and uniform magnetic susceptibilities in a broad temperature range. We find that in the regime of moderate Coulomb interactions (), the iron atoms located above and below the Ge plane carry a substantial local magnetic moment (), while the iron atom located within the Ge plane does not exhibit any pronounced magnetic moment. At the same time, the exchange interaction between these two symmetry-nonequivalent types of atoms turns out to be crucial for stabilizing long-range ferromagnetic order in . The estimated spin-wave stiffness and Curie temperature are in good agreement with the experimental data, indicating that a dynamical treatment of electron correlations in is essential to properly describe its partially itinerant magnetic behavior.
Physics Subject Headings (PhySH)
Article Text
References (63)
- S. Jiang, J. Shan, and K. F. Mak, Electric-field switching of two-dimensional van der Waals magnets, Nat. Mater. 17, 406 (2018).
- M. Bonilla, S. Kolekar, Y. Ma, H. C. Diaz, V. Kalappattil, R. Das, T. Eggers, H. R. Gutierrez, M.-H. Phan, and M. Batzill, Strong room-temperature ferromagnetism in monolayers on van der Waals substrates, Nat. Nanotechnol. 13, 289 (2018).
- K.-Z. Du, X.-Z. Wang, Y. Liu, P. Hu, M. I. B. Utama, C. K. Gan, Q. Xiong, and C. Kloc, Weak van der Waals stacking, wide-range band gap, and Raman study on ultrathin layers of metal phosphorus trichalcogenides, ACS Nano 10, 1738 (2016).
- B. Huang, G. Clark, E. Navarro-Moratalla, D. R. Klein, R. Cheng, K. L. Seyler, D. Zhong, E. Schmidgall, M. A. McGuire, D. H. Cobden, W. Yao, D. Xiao, P. Jarillo-Herrero, and X. Xu, Layer-dependent ferromagnetism in a van der Waals crystal down to the monolayer limit, Nature (London) 546, 270 (2017).
- M. Gibertini, M. Koperski, A. F. Morpurgo, and K. S. Novoselov, Magnetic 2D materials and heterostructures, Nat. Nanotechnol. 14, 408 (2019).
- D. Soriano, M. I. Katsnelson, and J. Fernández-Rossier, Magnetic two-dimensional chromium trihalides: A theoretical perspective, Nano Lett. 20, 6225 (2020).
- Y. Deng, Y. Yu, Y. Song, J. Zhang, N. Z. Wang, Z. Sun, Y. Yi, Y. Z. Wu, S. Wu, J. Zhu, J. Wang, X. H. Chen, and Y. Zhang, Gate-tunable room-temperature ferromagnetism in two-dimensional , Nature (London) 563, 94 (2018).
- Z. Fei, B. Huang, P. Malinowski, W. Wang, T. Song, J. Sanchez, W. Yao, D. Xiao, X. Zhu, A. F. May, W. Wu, D. H. Cobden, J.-H. Chu, and X. Xu, Two-dimensional itinerant ferromagnetism in atomically thin , Nat. Mater. 17, 778 (2018).
- K. Kim, J. Seo, E. Lee, K.-T. Ko, B. S. Kim, B. G. Jang, J. M. Ok, J. Lee, Y. J. Jo, W. Kang, et al., Large anomalous Hall current induced by topological nodal lines in a ferromagnetic van der Waals semimetal, Nat. Mater. 17, 794 (2018).
- J. Xu, W. A. Phelan, and C.-L. Chien, Large anomalous Nernst effect in a van der Waals ferromagnet , Nano Lett. 19, 8250 (2019).
- R. Roemer, C. Liu, and K. Zou, Robust ferromagnetism in wafer-scale monolayer and multilayer , npj 2D Mater. Appl. 4, 33 (2020).
- Y. Zhang et al., Emergence of Kondo lattice behavior in a van der Waals itinerant ferromagnet , Sci. Adv. 4, eaao6791 (2018).
- M. Zhao et al., Kondo holes in the two-dimensional itinerant Ising ferromagnet , Nano Lett. 21, 6117 (2021).
- D. I. Badrtdinov, G. V. Pushkarev, M. I. Katsnelson, and A. N. Rudenko, Electron transport and scattering mechanisms in ferromagnetic monolayer , npj 2D Mater. Appl. 7, 52 (2023).
- V. I. Anisimov, A. I. Poteryaev, M. A. Korotin, A. O. Anokhin, and G. Kotliar, First-principles calculations of the electronic structure and spectra of strongly correlated systems: Dynamical mean-field theory, J. Phys.: Condens. Matter 9, 7359 (1997).
- A. I. Lichtenstein and M. I. Katsnelson, Ab initio calculations of quasiparticle band structure in correlated systems: approach, Phys. Rev. B 57, 6884 (1998).
- G. Kotliar, S. Y. Savrasov, K. Haule, V. S. Oudovenko, O. Parcollet, and C. A. Marianetti, Electronic structure calculations with dynamical mean-field theory, Rev. Mod. Phys. 78, 865 (2006).
- J.-X. Zhu, M. Janoschek, D. S. Chaves, J. C. Cezar, T. Durakiewicz, F. Ronning, Y. Sassa, M. Mansson, B. L. Scott, N. Wakeham, E. D. Bauer, and J. D. Thompson, Electronic correlation and magnetism in the ferromagnetic metal , Phys. Rev. B 93, 144404 (2016).
- T. J. Kim, S. Ryee, and M. J. Han, : A site-differentiated Hund metal, npj Comput. Mater. 8, 245 (2022).
- S. Ghosh, S. Ershadrad, V. Borisov, and B. Sanyal, Unraveling effects of electron correlation in two-dimensional () by dynamical mean field theory, npj Comput. Mater. 9, 86 (2023).
- D. Sharma, A. Ali, N. Bhatt, R. R. Chowdhury, C. Patra, R. P. Singh, and R. S. Singh, Manifestation of incoherent-coherent crossover and non‐Stoner magnetism in the electronic structure of , Phys. Rev. B 110, 125119 (2024).
- M. I. Katsnelson and A. I. Lichtenstein, First-principles calculations of magnetic interactions in correlated systems, Phys. Rev. B 61, 8906 (2000).
- Y. O. Kvashnin, O. Grånäs, I. Di Marco, M. I. Katsnelson, A. I. Lichtenstein, and O. Eriksson, Exchange parameters of strongly correlated materials: Extraction from spin-polarized density functional theory plus dynamical mean-field theory, Phys. Rev. B 91, 125133 (2015).
- A. Szilva, Y. Kvashnin, E. A. Stepanov, L. Nordström, O. Eriksson, A. I. Lichtenstein, and M. I. Katsnelson, Quantitative theory of magnetic interactions in solids, Rev. Mod. Phys. 95, 035004 (2023).
- B. Chen, J. Yang, H. Wang, M. Imai, H. Ohta, C. Michioka, K. Yoshimura, and M. Fang, Magnetic properties of layered itinerant electron ferromagnet , J. Phys. Soc. Jpn. 82, 124711 (2013).
- P. Rhodes and E. P. Wohlfarth, The effective Curie–Weiss constant of ferromagnetic metals and alloys, Proc. R. Soc. London, Ser. A 273, 247 (1963).
- T. Moriya, Spin Fluctuations in Itinerant Electron Magnetism, Springer Series in Solid-State Sciences Vol. 56 (Springer, Berlin, 1985).
- J. M. Santiago, C.-L. Huang, and E. Morosan, Itinerant magnetic metals, J. Phys.: Condens. Matter 29, 373002 (2017).
- M. I. Katsnelson and A. I. Lichtenstein, Electronic structure and magnetic properties of correlated metals, Eur. Phys. J. B 30, 9 (2002).
- L. V. Pourovskii, M. I. Katsnelson, and A. I. Lichtenstein, Correlation effects in electronic structure of actinide monochalcogenides, Phys. Rev. B 72, 115106 (2005).
- J. Braun, J. Minár, H. Ebert, M. I. Katsnelson, and A. I. Lichtenstein, Spectral function of ferromagnetic metals: A self-consistent approach combined with the one-step model of photoemission, Phys. Rev. Lett. 97, 227601 (2006).
- I. Di Marco, J. Minár, S. Chadov, M. I. Katsnelson, H. Ebert, and A. I. Lichtenstein, Correlation effects in the total energy, the bulk modulus, and the lattice constant of a transition metal: Combined local-density approximation and dynamical mean-field theory applied to Ni and Mn, Phys. Rev. B 79, 115111 (2009).
- J. Sánchez-Barriga, J. Minár, J. Braun, A. Varykhalov, V. Boni, I. Di Marco, O. Rader, V. Bellini, F. Manghi, H. Ebert, M. I. Katsnelson, A. I. Lichtenstein, O. Eriksson, W. Eberhardt, H. A. Dürr, and J. Fink, Quantitative determination of spin-dependent quasiparticle lifetimes and electronic correlations in hcp cobalt, Phys. Rev. B 82, 104414 (2010).
- A. Kutepov, K. Haule, S. Y. Savrasov, and G. Kotliar, Self-consistent determination of the interaction strength: Application to the iron arsenide superconductors, Phys. Rev. B 82, 045105 (2010).
- P. Werner, M. Casula, T. Miyake, F. Aryasetiawan, A. J. Millis, and S. Biermann, Satellites and large doping and temperature dependence of electronic properties in hole-doped , Nat. Phys. 8, 331 (2012).
- M. I. Katsnelson and A. I. Lichtenstein, Magnetic susceptibility, exchange interactions and spin-wave spectra in the local spin density approximation, J. Phys.: Condens. Matter 16, 7439 (2004).
- I. V. Solovyev, Exchange interactions and magnetic force theorem, Phys. Rev. B 103, 104428 (2021).
- I. V. Solovyev, Linear response theories for interatomic exchange interactions, J. Phys.: Condens. Matter 36, 223001 (2024).
- A. A. Katanin, A. S. Belozerov, A. I. Lichtenstein, and M. I. Katsnelson, Exchange interactions in iron and nickel: DFT+DMFT study in paramagnetic phase, Phys. Rev. B 107, 235118 (2023).
- A. A. Katanin, Exchange interactions in itinerant magnets: The effects of local particle-hole irreducible vertex corrections and SU(2) symmetry of Hund interaction, Phys. Rev. B 112, 085141 (2025).
- A. A. Katanin, DFT+DMFT study of exchange interactions in cobalt and their implications for the competition of hcp and fcc phases, Phys. Rev. B 108, 235170 (2023).
- A. A. Katanin, Magnetic properties of half metal from the paramagnetic phase: DFT+DMFT study of exchange interactions in , Phys. Rev. B 110, 155115 (2024).
- A. A. Katanin and E. M. Agapov, Magnetic properties of monolayer, multilayer, and bulk , Phys. Rev. B 111, 035118 (2025).
- A. A. Katanin and E. M. Agapov, Erratum: Magnetic properties of monolayer, multilayer, and bulk , Phys. Rev. B 113, 119901(E) (2026).
- J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
- G. Kresse and J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54, 11169 (1996).
- G. Kresse and J. Hafner, Ab initio molecular dynamics for liquid metals, Phys. Rev. B 47, 558 (1993).
- H.-J. Deiseroth, K. Aleksandrov, C. Reiner, L. Kienle, and R. K. Kremer, and – two new layered transition-metal compounds: Crystal structures, hrtem investigations, and magnetic and electrical properties, Eur. J. Inorg. Chem. 2006, 1561 (2006).
- N. Marzari and D. Vanderbilt, Maximally localized generalized Wannier functions for composite energy bands, Phys. Rev. B 56, 12847 (1997).
- G. Pizzi, V. Vitale, R. Arita, S. Blügel, F. Freimuth, G. Géranton, M. Gibertini, D. Gresch, C. Johnson, T. Koretsune, J. Ibañez-Azpiroz, H. Lee, J.-M. Lihm, D. Marchand, A. Marrazzo, Y. Mokrousov, J. I. Mustafa, Y. Nohara, Y. Nomura, L. Paulatto, et al., Wannier90 as a community code: New features and applications, J. Phys.: Condens. Matter 32, 165902 (2020).
- V. I. Anisimov, F. Aryasetiawan, and A. I. Lichtenstein, First-principles calculations of the electronic structure and spectra of strongly correlated systems: The LDA+ method, J. Phys.: Condens. Matter 9, 767 (1997).
- M. T. Czyżyk and G. A. Sawatzky, Local-density functional and on-site correlations: The electronic structure of and , Phys. Rev. B 49, 14211 (1994).
- G. Rohringer, H. Hafermann, A. Toschi, A. A. Katanin, A. E. Antipov, M. I. Katsnelson, A. I. Lichtenstein, A. N. Rubtsov, and K. Held, Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory, Rev. Mod. Phys. 90, 025003 (2018).
- A. A. Katanin, Hubb_DMFT and Wan2mb_DMFT continuous-time quantum Monte Carlo solvers for single- and multi-Orbital Hubbard model, arXiv:2608.18540.
- P. Werner, A. Comanac, L. de' Medici, M. Troyer, and A. J. Millis, Continuous-time solver for quantum impurity models, Phys. Rev. Lett. 97, 076405 (2006).
- L. Huang, Y. Wang, Z. Y. Meng, L. Du, P. Werner, and X. Dai, iQIST: An open source continuous-time quantum Monte Carlo impurity solver toolkit, Comput. Phys. Commun. 195, 140 (2015).
- A. A. Katanin, A. I. Poteryaev, A. V. Efremov, A. O. Shorikov, S. L. Skornyakov, M. A. Korotin, and V. I. Anisimov, Orbital-selective formation of local moments in -iron: First-principles route to an effective model, Phys. Rev. B 81, 045117 (2010).
- S. V. Tyablikov, Methods in the Quantum Theory of Magnetism (Plenum Press, New York, 1967).
- A. F. May, S. Calder, C. Cantoni, H. Cao, and M. A. McGuire, Magnetic structure and phase stability of the van der Waals bonded ferromagnet , Phys. Rev. B 93, 014411 (2016).
- C. R. Trainer, O. R. Armitage, H. Lane, L. C. Rhodes, E. Chan, I. Benedičič, J. A. Rodriguez-Rivera, O. Fabelo, C. Stock, and P. Wahl, Relating spin-polarized STM imaging and inelastic neutron scattering in the van der Waals ferromagnet , Phys. Rev. B 106, L081405 (2022).
- G. V. Pushkarev, D. I. Badrtdinov, I. A. Iakovlev, V. V. Mazurenko, and A. N. Rudenko, An effective spin model on the honeycomb lattice for the description of magnetic properties in two-dimensional , J. Magn. Magn. Mater. 588, 171456 (2023).
- V. Y. Irkhin and A. A. Katanin, Thermodynamics of isotropic and anisotropic layered magnets: Renormalization group approach and 1/ expansion, Phys. Rev. B 57, 379 (1998).
- V. Y. Irkhin, A. A. Katanin, and M. I. Katsnelson, Self-consistent spin-wave theory of layered Heisenberg magnets, Phys. Rev. B 60, 1082 (1999).