@article{heisenberg_zur_1928,
	title = {Zur {Theorie} des {Ferromagnetismus}},
	volume = {49},
	issn = {0044-3328},
	url = {https://doi.org/10.1007/BF01328601},
	doi = {10.1007/BF01328601},
	abstract = {Die Weissschen Molekularkräfte werden zurückgeführt auf ein quantenmechanisches Austauschphänomen; und zwar handelt es sich um diejenigen Austauschvorgänge, die in letzter Zeit von Heitier und London mit Erfolg zur Deutung der homöopolaren Valenzkräfte herangezogen worden sind.},
	language = {de},
	number = {9},
	urldate = {2024-10-07},
	journal = {Zeitschrift für Physik},
	author = {Heisenberg, W.},
	month = sep,
	year = {1928},
	pages = {619--636},
}

@article{metropolis_equation_1953,
	title = {Equation of {State} {Calculations} by {Fast} {Computing} {Machines}},
	volume = {21},
	issn = {0021-9606, 1089-7690},
	url = {https://pubs.aip.org/jcp/article/21/6/1087/202680/Equation-of-State-Calculations-by-Fast-Computing},
	doi = {10.1063/1.1699114},
	abstract = {A general method, suitable for fast computing machines, for investigating such properties as equations of state for substances consisting of interacting individual molecules is described. The method consists of a modified Monte Carlo integration over configuration space. Results for the two-dimensional rigid-sphere system have been obtained on the Los Alamos MANIAC and are presented here. These results are compared to the free volume equation of state and to a four-term virial coefficient expansion.},
	language = {en},
	number = {6},
	urldate = {2024-10-07},
	journal = {The Journal of Chemical Physics},
	author = {Metropolis, Nicholas and Rosenbluth, Arianna W. and Rosenbluth, Marshall N. and Teller, Augusta H. and Teller, Edward},
	month = jun,
	year = {1953},
	pages = {1087--1092},
}

@article{torelli_calculating_2018,
	title = {Calculating critical temperatures for ferromagnetic order in two-dimensional materials},
	volume = {6},
	issn = {2053-1583},
	url = {https://iopscience.iop.org/article/10.1088/2053-1583/aaf06d},
	doi = {10.1088/2053-1583/aaf06d},
	number = {1},
	urldate = {2024-10-07},
	journal = {2D Materials},
	author = {Torelli, Daniele and Olsen, Thomas},
	month = dec,
	year = {2018},
	pages = {015028},
}

@article{luo_skyrmion_2021,
	title = {Skyrmion devices for memory and logic applications},
	volume = {9},
	issn = {2166-532X},
	url = {https://pubs.aip.org/apm/article/9/5/050901/43554/Skyrmion-devices-for-memory-and-logic-applications},
	doi = {10.1063/5.0042917},
	abstract = {Skyrmions have received considerable attention in various studies since the experimental observation in magnetic materials in 2009. Skyrmions, which are topological, particle-like localized structures, show significant fundamental research value in the field of physics and materials and are also regarded as novel information carriers that have the potential for use in developing high-density, low-power, and multi-functional spintronic devices. In this Perspective, we first overview the development, structure, and materials of skyrmions. Subsequently, we focus on the recent progress in skyrmion devices for memory and logic applications and discuss their challenges and prospects.},
	language = {en},
	number = {5},
	urldate = {2024-10-07},
	journal = {APL Materials},
	author = {Luo, Shijiang and You, Long},
	month = may,
	year = {2021},
	pages = {050901},
}


@article{muller_spirit_2019,
	title = {\textit{{Spirit}} : {Multifunctional} framework for atomistic spin simulations},
	volume = {99},
	issn = {2469-9950, 2469-9969},
	shorttitle = {\textit{{Spirit}}},
	url = {https://link.aps.org/doi/10.1103/PhysRevB.99.224414},
	doi = {10.1103/PhysRevB.99.224414},
	language = {en},
	number = {22},
	urldate = {2024-10-08},
	journal = {Physical Review B},
	author = {Müller, Gideon P. and Hoffmann, Markus and Dißelkamp, Constantin and Schürhoff, Daniel and Mavros, Stefanos and Sallermann, Moritz and Kiselev, Nikolai S. and Jónsson, Hannes and Blügel, Stefan},
	month = jun,
	year = {2019},
	pages = {224414},
}

@article{augustin_properties_2021,
	title = {Properties and dynamics of meron topological spin textures in the two-dimensional magnet {CrCl3}},
	volume = {12},
	copyright = {2021 The Author(s)},
	issn = {2041-1723},
	url = {https://www.nature.com/articles/s41467-020-20497-2},
	doi = {10.1038/s41467-020-20497-2},
	abstract = {Merons are nontrivial topological spin textures highly relevant for many phenomena in solid state physics. Despite their importance, direct observation of such vortex quasiparticles is scarce and has been limited to a few complex materials. Here, we show the emergence of merons and antimerons in recently discovered two-dimensional (2D) CrCl3 at zero magnetic field. We show their entire evolution from pair creation, their diffusion over metastable domain walls, and collision leading to large magnetic monodomains. Both quasiparticles are stabilized spontaneously during cooling at regions where in-plane magnetic frustration takes place. Their dynamics is determined by the interplay between the strong in-plane dipolar interactions and the weak out-of-plane magnetic anisotropy stabilising a vortex core within a radius of 8–10 nm. Our results push the boundary to what is currently known about non-trivial spin structures in 2D magnets and open exciting opportunities to control magnetic domains via topological quasiparticles.},
	language = {en},
	number = {1},
	urldate = {2024-10-08},
	journal = {Nature Communications},
	author = {Augustin, Mathias and Jenkins, Sarah and Evans, Richard F. L. and Novoselov, Kostya S. and Santos, Elton J. G.},
	month = jan,
	year = {2021},
	keywords = {Graphene, Materials science, Nanoscale materials},
	pages = {185},
}

@article{kabiraj_realizing_2023,
	title = {Realizing unipolar and bipolar intrinsic skyrmions in {MXenes} from high-fidelity first-principles calculations},
	volume = {9},
	copyright = {2023 The Author(s)},
	issn = {2057-3960},
	url = {https://www.nature.com/articles/s41524-023-01129-x},
	doi = {10.1038/s41524-023-01129-x},
	abstract = {Magnetic skyrmions, which are topologically protected tiny spin textures, have emerged as information carriers in energy-efficient logic and memory devices. Skyrmions are commonly realized by inducing large Dzyaloshinskii–Moriya interaction (DMI) in the interface of heavy metal heterolayers. With the advent of two-dimensional magnetism, it is being envisioned to host intrinsic skyrmions in a monolayer, which will be free from any interfacial defect and stacking order. Here using high-fidelity exchange-correlation functional-based first-principles calculations, we investigate such a possibility in methodically designed non-centrosymmetric MXene structures. From a search space of about 3000 materials, our customized high-throughput computational pipeline systematically harnesses out-of-the-plane and in-plane magnetism along with strong DMI to realize typical ‘unipolar’ skyrmions in 78 materials and exotic ‘bipolar’ skyrmions in 13 materials. Micromagnetic and atomistic Monte Carlo simulations further reveal that skyrmions in some of these materials may be stable at room temperature without any external magnetic field. Our study may pave the way for the practical realization of skyrmions-based information technology.},
	language = {en},
	number = {1},
	urldate = {2024-10-08},
	journal = {npj Computational Materials},
	author = {Kabiraj, Arnab and Mahapatra, Santanu},
	month = sep,
	year = {2023},
	keywords = {Electronic structure, Magnetic properties and materials, Two-dimensional materials},
	pages = {1--12},
}

@article{liang_very_2020,
	title = {Very large {Dzyaloshinskii}-{Moriya} interaction in two-dimensional {Janus} manganese dichalcogenides and its application to realize skyrmion states},
	volume = {101},
	issn = {2469-9950, 2469-9969},
	url = {https://link.aps.org/doi/10.1103/PhysRevB.101.184401},
	doi = {10.1103/PhysRevB.101.184401},
	language = {en},
	number = {18},
	urldate = {2024-10-08},
	journal = {Physical Review B},
	author = {Liang, Jinghua and Wang, Weiwei and Du, Haifeng and Hallal, Ali and Garcia, Karin and Chshiev, Mairbek and Fert, Albert and Yang, Hongxin},
	month = may,
	year = {2020},
	pages = {184401},
}

@article{kabiraj_massive_2022,
	title = {Massive {Monte} {Carlo} simulations-guided interpretable learning of two-dimensional {Curie} temperature},
	volume = {3},
	issn = {2666-3899},
	url = {https://www.sciencedirect.com/science/article/pii/S2666389922002574},
	doi = {10.1016/j.patter.2022.100625},
	abstract = {Monte Carlo (MC) simulation of the classical Heisenberg model has become the de facto tool to estimate the Curie temperature (TC) of two-dimensional (2D) magnets. As an alternative, here we develop data-driven models for the five most common crystal types, considering the isotropic and anisotropic exchange of up to four nearest neighbors and the single-ion anisotropy. We sample the 20-dimensional Heisenberg spin Hamiltonian and conceive a bisection-based MC technique to simulate a quarter of a million materials for training deep neural networks, which yield testing R2 scores of nearly 0.99. Since 2D magnetism has a natural tendency toward low TC, learning-from-data is combined with data-from-learning to ensure a nearly uniform final data distribution over a wide range of TC (10–1,000 K). Global and local analysis of the features confirms the models’ interpretability. We also demonstrate that the TC can be accurately estimated by a purely first-principles-based approach, free from any empirical corrections.},
	number = {12},
	urldate = {2024-10-08},
	journal = {Patterns},
	author = {Kabiraj, Arnab and Jain, Tripti and Mahapatra, Santanu},
	month = dec,
	year = {2022},
	keywords = {machine learning, Monte Carlo simulation, 2D materials, magnetism, Curie temperature, density functional theory, Shapley score, AutoML, deep learning, anisotropic Heisenberg model},
	pages = {100625},
}

@article{PhysRevB.99.224414,
  title = {Spirit: Multifunctional framework for atomistic spin simulations},
  author = {M\"uller, Gideon P. and Hoffmann, Markus and Di\ss{}elkamp, Constantin and Sch\"urhoff, Daniel and Mavros, Stefanos and Sallermann, Moritz and Kiselev, Nikolai S. and J\'onsson, Hannes and Bl\"ugel, Stefan},
  journal = {Phys. Rev. B},
  volume = {99},
  issue = {22},
  pages = {224414},
  numpages = {16},
  year = {2019},
  month = {Jun},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevB.99.224414},
  url = {https://link.aps.org/doi/10.1103/PhysRevB.99.224414}
}
@article{evans_atomistic_2014,
	title = {Atomistic spin model simulations of magnetic nanomaterials},
	volume = {26},
	copyright = {http://iopscience.iop.org/info/page/text-and-data-mining},
	issn = {0953-8984, 1361-648X},
	url = {https://iopscience.iop.org/article/10.1088/0953-8984/26/10/103202},
	doi = {10.1088/0953-8984/26/10/103202},
	number = {10},
	urldate = {2024-10-10},
	journal = {Journal of Physics: Condensed Matter},
	author = {Evans, R F L and Fan, W J and Chureemart, P and Ostler, T A and Ellis, M O A and Chantrell, R W},
	month = mar,
	year = {2014},
	pages = {103202},
}

@article{psaroudaki_skyrmion_2021,
	title = {Skyrmion {Qubits}: {A} {New} {Class} of {Quantum} {Logic} {Elements} {Based} on {Nanoscale} {Magnetization}},
	copyright = {arXiv.org perpetual, non-exclusive license},
	shorttitle = {Skyrmion {Qubits}},
	url = {https://arxiv.org/abs/2108.02219},
	doi = {10.48550/ARXIV.2108.02219},
	abstract = {We introduce a new class of primitive building blocks for realizing quantum logic elements based on nanoscale magnetization textures called skyrmions. In a skyrmion qubit, information is stored in the quantum degree of helicity, and the logical states can be adjusted by electric and magnetic fields, offering a rich operation regime with high anharmonicity. By exploring a large parameter space, we propose two skyrmion qubit variants depending on their quantized state. We discuss appropriate microwave pulses required to generate single-qubit gates for quantum computing, and skyrmion multiqubit schemes for a scalable architecture with tailored couplings. Scalability, controllability by microwave fields, operation time scales, and readout by nonvolatile techniques converge to make the skyrmion qubit highly attractive as a logical element of a quantum processor.},
	urldate = {2024-10-10},
	author = {Psaroudaki, Christina and Panagopoulos, Christos},
	year = {2021},
	keywords = {Mesoscale and Nanoscale Physics (cond-mat.mes-hall), Strongly Correlated Electrons (cond-mat.str-el), Quantum Physics (quant-ph), FOS: Physical sciences, FOS: Physical sciences},
}

@article{bessarab_lifetime_2018,
	title = {Lifetime of racetrack skyrmions},
	volume = {8},
	issn = {2045-2322},
	url = {https://www.nature.com/articles/s41598-018-21623-3},
	doi = {10.1038/s41598-018-21623-3},
	abstract = {Abstract
            The skyrmion racetrack is a promising concept for future information technology. There, binary bits are carried by nanoscale spin swirls–skyrmions–driven along magnetic strips. Stability of the skyrmions is a critical issue for realising this technology. Here we demonstrate that the racetrack skyrmion lifetime can be calculated from first principles as a function of temperature, magnetic field and track width. Our method combines harmonic transition state theory extended to include Goldstone modes, with an atomistic spin Hamiltonian parametrized from density functional theory calculations. We demonstrate that two annihilation mechanisms contribute to the skyrmion stability: At low external magnetic field, escape through the track boundary prevails, but a crossover field exists, above which the collapse in the interior becomes dominant. Considering a Pd/Fe bilayer on an Ir(111) substrate as a well-established model system, the calculated skyrmion lifetime is found to be consistent with reported experimental measurements. Our simulations also show that the Arrhenius pre-exponential factor of escape depends only weakly on the external magnetic field, whereas the pre-exponential factor for collapse is strongly field dependent. Our results open the door for predictive simulations, free from empirical parameters, to aid the design of skyrmion-based information technology.},
	language = {en},
	number = {1},
	urldate = {2024-10-10},
	journal = {Scientific Reports},
	author = {Bessarab, Pavel F. and Müller, Gideon P. and Lobanov, Igor S. and Rybakov, Filipp N. and Kiselev, Nikolai S. and Jónsson, Hannes and Uzdin, Valery M. and Blügel, Stefan and Bergqvist, Lars and Delin, Anna},
	month = feb,
	year = {2018},
	pages = {3433},
}

@article{acs_nanolett,
author = {Cui, Qirui and Zhu, Yingmei and Ga, Yonglong and Liang, Jinghua and Li, Peng and Yu, Dongxing and Cui, Ping and Yang, Hongxin},
title = {Anisotropic Dzyaloshinskii–Moriya Interaction and Topological Magnetism in Two-Dimensional Magnets Protected by P4m2 Crystal Symmetry},
journal = {Nano Letters},
volume = {22},
number = {6},
pages = {2334-2341},
year = {2022},
doi = {10.1021/acs.nanolett.1c04803},
    note ={PMID: 35266723},
URL = {https://doi.org/10.1021/acs.nanolett.1c04803},
eprint = {https://doi.org/10.1021/acs.nanolett.1c04803}
}

@article{gilbert_classics_2004,
	title = {Classics in {Magnetics} {A} {Phenomenological} {Theory} of {Damping} in {Ferromagnetic} {Materials}},
	volume = {40},
	copyright = {https://ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html},
	issn = {0018-9464},
	url = {http://ieeexplore.ieee.org/document/1353448/},
	doi = {10.1109/TMAG.2004.836740},
	language = {en},
	number = {6},
	urldate = {2024-10-10},
	journal = {IEEE Transactions on Magnetics},
	author = {Gilbert, T.L.},
	month = nov,
	year = {2004},
	pages = {3443--3449},
}

@article{du_spontaneous_2022,
	title = {Spontaneous Magnetic Skyrmions in Single-Layer $CrInX_3$ ({X} = {Te}, {Se})},
	volume = {22},
	copyright = {https://doi.org/10.15223/policy-029},
	issn = {1530-6984, 1530-6992},
	url = {https://pubs.acs.org/doi/10.1021/acs.nanolett.2c00836},
	doi = {10.1021/acs.nanolett.2c00836},
	language = {en},
	number = {8},
	urldate = {2024-10-10},
	journal = {Nano Letters},
	author = {Du, Wenhui and Dou, Kaiying and He, Zhonglin and Dai, Ying and Huang, Baibiao and Ma, Yandong},
	month = apr,
	year = {2022},
	pages = {3440--3446},
}

@article{PhysRevLett.17.1133,
  title = {Absence of Ferromagnetism or Antiferromagnetism in One- or Two-Dimensional Isotropic Heisenberg Models},
  author = {Mermin, N. D. and Wagner, H.},
  journal = {Phys. Rev. Lett.},
  volume = {17},
  issue = {22},
  pages = {1133--1136},
  numpages = {0},
  year = {1966},
  month = {Nov},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.17.1133},
  url = {https://link.aps.org/doi/10.1103/PhysRevLett.17.1133}
}

@article{Huang2017,
  title = {Layer-dependent ferromagnetism in a van der Waals crystal down to the monolayer limit},
  volume = {546},
  ISSN = {1476-4687},
  url = {http://dx.doi.org/10.1038/nature22391},
  DOI = {10.1038/nature22391},
  number = {7657},
  journal = {Nature},
  publisher = {Springer Science and Business Media LLC},
  author = {Huang,  Bevin and Clark,  Genevieve and Navarro-Moratalla,  Efrén and Klein,  Dahlia R. and Cheng,  Ran and Seyler,  Kyle L. and Zhong,  Ding and Schmidgall,  Emma and McGuire,  Michael A. and Cobden,  David H. and Yao,  Wang and Xiao,  Di and Jarillo-Herrero,  Pablo and Xu,  Xiaodong},
  year = {2017},
  month = jun,
  pages = {270–273}
}

@article{Lakshmanan2011-hm,
  title        = "The fascinating world of {Landau-Lifshitz-Gilbert} equation:
                  An overview",
  author       = "Lakshmanan, M",
  abstract     = "The Landau-Lifshitz-Gilbert (LLG) equation is a fascinating
                  nonlinear evolution equation both from mathematical and
                  physical points of view. It is related to the dynamics of
                  several important physical systems such as ferromagnets,
                  vortex filaments, moving space curves, etc. and has intimate
                  connections with many of the well known integrable soliton
                  equations, including nonlinear Schr{\"o}dinger and
                  sine-Gordon equations. It can admit very many dynamical
                  structures including spin waves, elliptic function waves,
                  solitons, dromions, vortices, spatio-temporal patterns,
                  chaos, etc. depending on the physical and spin dimensions and
                  the nature of interactions. An exciting recent development is
                  that the spin torque effect in nanoferromagnets is described
                  by a generalization of the LLG equation which forms a basic
                  dynamical equation in the field of spintronics. This article
                  will briefly review these developments as a tribute to Robin
                  Bullough who was a great admirer of the LLG equation.",
  journal      = "arXiv [nlin.PS]",
  publisher    = "arXiv",
  year         =  2011,
  primaryClass = "nlin.PS"
}

@article{Kartsev2020,
  title = {Biquadratic exchange interactions in two-dimensional magnets},
  volume = {6},
  ISSN = {2057-3960},
  url = {http://dx.doi.org/10.1038/s41524-020-00416-1},
  DOI = {10.1038/s41524-020-00416-1},
  number = {1},
  journal = {npj Computational Materials},
  publisher = {Springer Science and Business Media LLC},
  author = {Kartsev,  Alexey and Augustin,  Mathias and Evans,  Richard F. L. and Novoselov,  Kostya S. and Santos,  Elton J. G.},
  year = {2020},
  month = oct 
}

@article{Koziol2020-cp,
  title     = "Number of equidistant neighbors on honeycomb lattice",
  author    = "Koziol, Zbigniew",
  abstract  = "Abstract A convenient scheme is presented for calculating
               potential energy of van der Waals interacting bilayer graphene
               and other similar 2D compounds. It is based on the notion of the
               existence of two types of local symmetry of carbon atoms
               ordering, a 3- and 6-fold one. Potential energy of an atom is
               expressed as a sum of contributions from rings of equidistant
               atoms on neighboring layer. Methods are described to compute the
               radius of rings of equidistant atoms and number of atoms they
               contain. Exact positions of atoms are found as well, allowing to
               apply the introduced method in modelling of anisotropic
               potentials and to be used when twisting between layers is
               present.",
  DOI	  = {10.1088/2399-6528/aba035},
  journal   = "J. Phys. Commun.",
  publisher = "IOP Publishing",
  volume    =  4,
  number    =  7,
  pages     = "075003",
  month     =  jul,
  year      =  2020,
  copyright = "http://creativecommons.org/licenses/by/4.0/"
}
