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Magnons and plasmons are different collective modes, involving the spin and charge degrees of freedom, respectively. Formation of hybrid plasmon–magnon polaritons in heterostructures of plasmonic and magnetic systems faces two challenges, the small interaction of the electromagnetic field of the plasmon with the spins, and the energy mismatch, as in most systems plasmons have energies orders of magnitude larger than those of magnons. We show that graphene plasmons form polaritons with the magnons of two-dimensional ferromagnetic insulators, placed up to to half a micrometer apart, with Rabi splittings in the range of 100 GHz (dramatically larger than cavity magnonics). This is facilitated both by the small energy of graphene plasmons and the cooperative super-radiant nature of the plasmon–magnon coupling afforded by phase matching. We show that the coupling can be modulated both electrically and mechanically, and we propose a ferromagnetic resonance experiment implemented with a two-dimensional ferromagnet driven by graphene plasmons. We acknowledge financial support from the Fundação Para a Ciência e a Tecnologia, Portugal Grant No. PTDC/FIS-MAC/2045/2021) and from the European Union (Grant FUNLAYERS - 101079184). J.F.-R. and A.T.C. acknowledge financial support from the Swiss National Science Foundation Sinergia (Grant Pimag), MICIIN – Spain (Grant No. PID2019-109539GB-41), Generalitat Valenciana (Grant Nos. Prometeo2021/017 and MFA/2022/045), FEDER/Junta de Andalucía-Consejera de Transformación Económica, Industria, Conocimiento y Universidades (Grant No. P18-FR-4834). N.M.R.P. and M.I.V. acknowledge support by the Portuguese Foundation for Science and Technology (FCT) in the framework of the Strategic Funding UIDB/04650/2020, COMPETE 2020, PORTUGAL 2020, FEDER, and FCT through projects POCI-01-0145-FEDER-028114, POCI-01-0145-FEDER-02888 and PTDC/NANOPT/29265/2017, PTDC/FIS-MAC/2045/2021, and EXPL/FIS-MAC/0953/2021, and from the European Commission through the project Graphene Driven Revolutions in ICT and Beyond (Ref. No. 881603, CORE 3).

Two computational methods — one physics-based, and the other one deep-learning based — are proposed to enable the systematic investigation of magnetic order in moiré magnets from first principles.

We designed and built a compact device capable of measuring electronic transport in atomic-sized contacts. This experimental setup is based on the break-junction (BJ) approach. According to the samples used as electrodes, we named the instrument a Surface-Tip Break Junction. Our instrument, like a scanning tunnelling microscope in the BJ configuration, can measure the quantum transport in atoms captured by electrodes. In our case, to measure this transport, we included a homemade I–V converter, a low-cost oscilloscope, and a mobile phone that functions as a data acquisition system. Moreover, we developed a protocol to analyse the digitized data obtained from the oscilloscope. This low-cost pedagogical setup offers the possibility of implementation in undergraduate and graduate laboratories. C S thanks for the financial support to Generalitat Valenciana through CIDEXG/2022/45, CDEIGENT/2018/028, and Banco Santander through the MOVSANTANDER 2020 program. Becas Iberoamérica Santander Investigación—Santander Universidades 2020.

Quantum state preparation is a key step in all digital quantum simulation algorithms. Here we propose methods to initialize on a gate-based quantum computer a general class of quantum spin wave functions, the so-called Valence-Bond-Solid (VBS) states, that are important for two reasons. First, VBS states are the exact ground states of a class of interacting quantum spin models introduced by Affleck, Kennedy, Lieb and Tasaki (AKLT). Second, the two-dimensional VBS states are universal resource states for measurement-based quantum computing. We find that schemes to prepare VBS states based on their tensor-network representations yield quantum circuits that are too deep to be within reach of noisy intermediate-scale quantum (NISQ) computers. We then apply the general non-deterministic method herein proposed to the preparation of the spin-1 and spin-3/2 VBS states, the ground states of the AKLT models defined in one dimension and in the honeycomb lattice, respectively. Shallow quantum circuits of depth independent of the lattice size are explicitly derived for both cases, making use of optimization schemes that outperform standard basis gate decomposition methods. Given the probabilistic nature of the proposed routine, two strategies that achieve a quadratic reduction of the repetition overhead for any VBS state defined on a bipartite lattice are devised. Our approach should permit to use NISQ processors to explore the AKLT model and variants thereof, outperforming conventional numerical methods in the near future., Comment: Main text: 17 pages, 7 figures. Appendices: 10 pages, 5 figures. QASM files to be added in next version of preprint

We studied by means of an atomistic model based on molecular dynamics the thermal evolution of surface atoms in amorphous silica under high electronic excitation produced by irradiation with swift heavy ions. The model was validated with the total and differential yields measured in sputtering experiments with different ions and ion energies showing a very good quantitative prediction capability. Three mechanisms are behind the evolution of the surface region: (1) an ejection mechanism of atoms and clusters with kinetic energy exceeding their binding energy to the sample surface, which explains the experimentally observed angular distributions of emitted atoms, and the correlation of the total sputtering yield with the electronic stopping power and the incidence angle. (2) A collective mechanism of the atoms in the ion track originated by the initial atom motion outwards the track region subsequently followed by the return to the resulting low-density region in the track center. The collective mechanism describes the energy dissipation of bulk atoms and the changes in density, residual stress, defect formation and optical properties. (3) A flow mechanism resulting from the accumulation and subsequent evolution of surface atoms unable to escape. This mechanism is responsible for the crater rim formation. Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. This work was funded by the projects Radiafus-5 (PID2019-105325RB-C32) of Spanish Ministry of Science, Technofusion (S2018/EMT-4437) of Madrid Regional Government and Eurofusion (EH150531176). The authors acknowledge the computer resources and technical assistance provided by the Centro de Supercomputación y Visualización de Madrid (CeSViMa) CESVIMA-MAGERIT. AP acknowledges the support of FONDECYT under grants 3190123. EMB thanks support from grant ANPCyT PICTO-UUMM-2019-00048. JK was supported by the Beatriz Galindo Program (BEAGAL18/00130) from the Ministerio de Educación y Formación Profesional of Spain.

Magnetic 2D materials hold promise to change the miniaturization paradigm of unidirectional photonic components. However, the integration of these materials in devices hinges on the accurate determination of the optical properties down to the monolayer limit, which is still missing. By using hyperspectral wide-field imaging at room temperature, we reveal a nonmonotonic thickness dependence of the complex optical dielectric function in the archetypal magnetic 2D material CrI3 extending across different length scales: onsetting at the mesoscale, peaking at the nanoscale, and decreasing again down to the single layer. These results portray a modification of the electronic properties of the material and align with the layer-dependent magnetism in CrI3, shedding light on the long-standing structural conundrum in this material. The unique modulation of the complex dielectric function from the monolayer up to more than 100 layers will be instrumental for understanding mesoscopic effects in layered materials and tuning light-matter interactions in magnetic 2D materials. The project that gave rise to these results received the financial support of a fellowship from the “la Caixa” Foundation (ID No. 100010434, fellowship codes LCF/BQ/PR21/11840011 and LCF/BQ/DI22/11940022) and Grant No. PID2020-118938GA-100 from the Spanish Ministerio de Ciencia e Innovación (MICINN). E. N. M. acknowledges the European Research Council (ERC) under the Horizon 2020 research and innovation program (ERC StG, Grant Agreement No. 803092). E. N. M. and M. G. acknowledge the MICINN and the European Union NextGenerationEU for financial support from the Ramon y Cajal program (Grants No. RYC2018-024736-I and No. RYC2021-034609-I). F. C. P. also acknowledges the MICINN for the FPU program (Grant No. FPU17/01587). F. R. M. acknowledges the MICINN for financial support (Grant No. PID2021-123163OB-I00). This work was also supported by the Spanish Unidad de Excelencia “María de Maeztu” (Grant No. CEX2019-000919-M) and is part of the Advanced Materials program supported by MICINN with funding from European Union NextGenerationEU (PRTR-C17.I1) and by Generalitat Valenciana. D. S. and A.C. acknowledge Generalitat Valenciana for financial support (from the CIDEGENT program Grant No. CIDEGENT/2021/052 and PROMETEO2020-016 respectively) and computational resources at University of Pisa.

Electron-spin resonance carried out with scanning tunneling microscopes (ESR-STM) is a recently developed experimental technique that is attracting enormous interest on account of its potential to carry out single-spin on-surface resonance with subatomic resolution. Here we carry out a theoretical study of the role of tip-adatom interactions and provide guidelines for choosing the experimental parameters in order to optimize spin resonance measurements. We consider the case of the Fe adatom on a MgO surface and its interaction with the spin-polarized STM tip. We address three problems: first, how to optimize the tip-sample distance to cancel the effective magnetic field created by the tip on the surface spin, in order to carry out proper magnetic field sensing. Second, how to reduce the voltage dependence of the surface-spin resonant frequency, in order to minimize tip-induced decoherence due to voltage noise. Third, we propose an experimental protocol to infer the detuning angle between the applied field and the tip magnetization, which plays a crucial role in the modeling of the experimental results., 10 pages, 5 Figures

Spin-orbit coupling gives rise to a range of spin-charge interconversion phenomena in non-magnetic systems where certain spatial symmetries are reduced or absent. Chirality-induced spin selectivity (CISS), a term that generically refers to a spin-dependent electron transfer in non-magnetic chiral systems, is one such case, appearing in a variety of seemingly unrelated situations ranging from inorganic materials to molecular devices. In particular, the origin of CISS in molecular junctions is a matter of an intense current debate. Here we derive a set of geometrical conditions for this effect to appear, hinting at the fundamental role of symmetries beyond otherwise relevant quantitative issues. Our approach, which draws on the use of point-group symmetries within the scattering formalism for transport, shows that electrode symmetries are as important as those of the molecule when it comes to the emergence of a spin-polarization and, by extension, to the possible appearance of CISS. It turns out that standalone metallic nanocontacts can exhibit spin-polarization when relative rotations which reduce the symmetry are introduced. As a corollary, molecular junctions with $\textbf{achiral}$ molecules can also exhibit spin-polarization along the direction of transport, provided that the whole junction is chiral in a specific way. This formalism also allows the prediction of qualitative changes of the spin-polarization upon substitution of a chiral molecule in the junction with its enantiomeric partner. Quantum transport calculations based on density functional theory corroborate all of our predictions and provide further quantitative insight within the single-particle framework., 34 pages, 4 figures, 1 table

Low-temperature scanning tunneling microscopy is used here to study the dynamic bonding of gold atoms on surfaces under low coordination conditions. In the experiments, using an atomically sharp gold tip, a gold adatom is deposited onto a gold surface with atomic precision either on the first hollow site near a step edge or far away from it. Classical molecular dynamics simulations at 4.2 K and density-functional theory calculations serve to elucidate the difference in the bonding behavior between these two different placements, while also providing information on the crystalline classification of the STM tips based on their experimental performance. This work was supported by the Generalitat Valenciana through Grants No. CDEIGENT/2018/028, No. PROMETEO/2017/139, and No. PROMETEO/2021/017. The authors also acknowledge financial support from Spanish MICIN through Grant No. PID2019-109539 GB-C43, the María de Maeztu Program for Units of Excellence in R&D (Grant No. CEX2018-000805-M), the Comunidad Autónoma de Madrid through the Nanomag COST-CM Program (Grant No. S2018/NMT-4321). The theoretical modeling was performed on the high-performance computing facilities of the University of South Africa and the University of Alicante. Netherlands Organization for Scientific Research (NWO/OCW) supported the experiments.

We have carried out the synthesis of two dithia[9]helicenes by means of a LED-based double photocyclization. The compounds have sulfur atoms placed at the terminal rings of the helicene, and they display two alternative C2-symmetrical arrangements named exo (1) and endo (2). Separation of enantiomers of opposite helicity allowed the complete characterization of their chiroptical properties in solution, in silico, by X-ray crystallography, and adsorbed on gold. The theoretical analysis confirms the unexpected finding that endo-dithia[9]helicene displays an experimental dissymmetry factor in CPL (glum) larger than its isomer, exo-dithia[9]helicene. This enhanced glum factor ranks among the largest for a helicene-type molecule. Comparison with smaller analogues, namely exo and endo-dithia[7]helicenes (10 and 11, respectively), is also presented. AG and CU thank the financial support by the Spanish MICIIN (PID2019-109539GB-C41), the Generalitat Valenciana (PROMETEO/2021/017), and the University of Alicante (VIGROB-285). CS thanks for the financial support by the Generalitat Valenciana through CDEIGENT2018/028. The computational resources provided by the Department of Applied Physics of the University of Alicante are greatly appreciated. JA and PM thank the National Science Foundation, grant CHE-1855470, for support of the theoretical component of this study, and the Center for Computational Research (CCR) at UB for providing computational resources. J.C. thanks the the Ministère de l’Education Nationale, de la Recherche et de la Technologie and the Centre National de la Recherche Scientifique (CNRS).

After evaporation of the organic solvents, benzene, toluene, and cyclohexane on gold substrates, Scanning Tunneling Microscope (STM) shows the presence of a remaining adsorbed layer. The different solvent molecules were individually observed at ambient conditions, and their electronic transport properties characterized through the STM in the Break Junction approach. The combination of both techniques reveals, on one hand, that solvents are not fully evaporated over the gold electrode and, secondly, characterize the electronic transport of the solvents in molecular electronics. This work was supported by the Spanish Government (MAT2016-78625-C2 and PID2019-109539 GB-C41) and the Generalitat Valenciana through PROMETEO/2017/139 and program CDEIGENT/2018/028.

The spin and lattice dynamics of a ferromagnetic nanoparticle are studied via molecular dynamics and with semi-classical spin dynamics simulations where spin and lattice degrees of freedom are coupled via a dynamic uniaxial anisotropy term. We show that this model conserves total angular momentum, whereas spin and lattice angular momentum are not conserved. We carry out simulations of the Einstein–de Haas effect for a Fe nanocluster with more than 500 atoms that is free to rotate, using a modified version of the open-source spin-lattice dynamics code (SPILADY). We show that the rate of angular momentum transfer between spin and lattice is proportional to the strength of the magnetic anisotropy interaction. The addition of the anisotropy allows full spin-lattice relaxation to be achieved on previously reported timescales of ∼ 100 ps and for tight-binding magnetic anisotropy energies comparable to those of small Fe nanoclusters. We acknowledge financial support from the Ministry of Science and Innovation of Spain (grant No. PID2019-109539GB-4). This work was supported by the Generalitat Valenciana, Spain through PROMETEO2017/139 and PROMETEO/2021/017. C. S. gratefully acknowledges financial supports from Generalitat Valenciana with (CDEIGENT2018/028). JFR acknowledges funding from FCT, Portugal grant PTDC/FIS-MAC/2045/2021. The SLD calculations in this paper were performed on the high-performance computing facilities of the University of South Africa.

In order to investigate the long-term evolution of radiation-induced defects in the fission- and fusion-relevant material iron, we introduce cascade overlap effects into Object Kinetic Monte Carlo simulations. In addition to cascade overlap, we study the effect of introducing discrete C15 Laves phase clusters into the simulations. By applying either, none, or both of these effects we identify how they influence the evolution of the system. We find that both cascade overlap and C15 clusters affect the evolution of the radiation damage in different ways and on different time scales. Cascade overlap is found to reduce the number of Frenkel pairs. On the other hand, the explicit consideration of C15 Laves phase clusters increases the accumulation of defects at low dose. The results are compared to Molecular Dynamics simulation results under similar conditions. This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014–2018 and 2019–2020 under grant agreement no. 633053.

We study the emergence of magnetism and its interplay with structural properties in a two-dimensional molecular crystal of cyclacenes, using density functional theory (DFT). Isolated cyclacenes with an even number of fused benzenes host two unpaired electrons in two topological protected zero modes, at the top and bottom carbon rings that form the molecule. We show that, in the gas phase, electron repulsion promotes an open-shell singlet with strong intramolecular antiferromagnetic exchange. We consider a closed packing triangular lattice crystal phase and we find a strong dependence of the band structure and magnetic interactions on the rotation angle of the cyclacenes with respect to the crystal lattice vectors. The orientational ground state maximizes the intermolecular hybridization, yet local moments survive. Intermolecular exchange is computed to be antiferromagnetic, and DFT predicts a broken symmetry 120∘ spin phase reflecting the frustration of the intermolecular spin coupling. Thus, the cyclacene crystal realizes a bilayer of two antiferromagnetically coupled S = 1/2 triangular lattices. Our results provide a bottom-up route towards carbon based strongly correlated platforms in two dimensions. We acknowledge funding support from Ministry of Science and Innovation of Spain (Grants No. PID2019-106114GB-I00 and No. PID2019-109539GB), Generalitat Valenciana and Fondo Social Europeo (Grant No. ACIF/2018/175), Generalitat Valenciana (Grant No. Prometeo2017/139), and FEDER/Junta de Andalucía Consejería de Transformación Económica, Industria, Conocimiento y Universidades, Grant No. PY18-4834.

The Haldane phase for antiferromagnetic spin-1 chains is a celebrated topological state of matter, featuring gapped excitations and fractional spin-1/2 edge states. Here, we provide numerical evidence that this phase can be realized with a Hubbard model at half filling, where each $s=1$ spin is stored in a four-site fermionic structure. We find that the noninteracting limit of our proposed model describes a one-dimensional topological insulator, and we conjecture it to be adiabatically connected to the Haldane phase. Our work suggests a route to build spin-1 networks using Hubbard model quantum simulators., Revised version, including Supplemental Material

La presente experiencia educativa tiene por objetivo fomentar el aprendizaje de materiales porosos en asignaturas de Ciencia de Materiales de grados de ciencia e ingeniería a través de la transformación de una tecnología TIC como la impresión 3D en tecnologías propias de la sociedad del conocimiento (TACs - Tecnologías para el Aprendizaje y el Conocimiento) para favorecer nuevas posibilidades educativas de aprendizaje y formación. Los autores presentan una metodología para implementar la herramienta de impresión 3D con el objetivo de fabricar de forma rápida y con bajo coste diversos materiales porosos para su estudio en modalidades organizativas de clases prácticas. La evaluación de la experiencia se realizó mediante encuestas de satisfacción utilizando tres instrumentos: i) cuestionarios anónimos realizados al alumnado mediante la plataforma Kahoot; ii) cuestionarios al profesorado implicado; y iii) cuestionarios a personal externo. La experiencia, desarrollada con un total de 22 estudiantes voluntarios y organizada por 3 profesores y una investigadora posdoctoral, ha resultado motivadora para todos los participantes y representa un avance docente ya que no existe actualmente ningún trabajo en la literatura internacional sobre la caracterización fluidodinámica de materiales macroporosos en prácticas de laboratorio para cursos de universidad. El profesorado externo consultado apunta consideraciones a tener en cuenta sobre la facilidad de implementación de los resultados de esta experiencia educativa.

Paramagnons are the collective modes that govern the spin response of nearly magnetic conductors. In some cases they mediate electron pairing leading to superconductivity. This scenario may occur in 2H-NbSe$_2$ monolayers, that feature spin-valley coupling on account of spin-orbit interactions and their lack of inversion symmetry. Here we explore spin anisotropy of paramagnons both for non-centrosymmetric Kane-Mele-Hubbard models for 2H-NbSe$_2$ monolayers described with a DFT-derived tight-binding model. In the infinite wavelength limit we find spatially uniform paramagnons with energies around $1$~meV that feature a colossal off-plane uniaxial magnetic anisotropy, with quenched transversal spin response. At finite wave vectors, longitudinal and transverse channels reverse roles: XY fluctuations dominate within a significant portion of the Brillouin zone. Our results show that 2H-NbSe$_2$ is close to a Coulomb-driven in-plane (XY) spin density wave instability., Comment: 10 pages (6 main text, 4 supplementary material), 10 figures (4 in the main text, 6 in the SM)

Detection is most often the main impediment to reduce the number of spins in paramagnetic resonance experiments. Here we propose a new route to carry out electrically-detected spin resonance of an individual spin, placed at the edge of a quantum spin Hall insulator (QSHI). The edges of a QSHI host a one dimensional electron gas with perfect spin-momentum locking. Therefore, the spin relaxation induced by emission of an electron-hole pair at the edge state of the QSHI can generate current. Here we demonstrate that driving the system with an $AC$ signal, a nonequilibrium occupation can be induced in the absence of applied bias voltage, resulting in a $DC$ measurable current. We compute the $DC$ current as a function of the Rabi frequency $\Omega$, the spin relaxation and decoherence times, $T_1$ and we discuss the feasibility of this experiment with state-of-the-art instrumentation., Comment: 5 pages, 1 figure

A theorem that establishes a one-to-one relation between zero-temperature static spin-spin correlators and coupling constants for a general class of quantum spin Hamiltonians bilinear in the spin operators has been recently established by J. Quintanilla, using an argument in the spirit of the Hohenberg-Kohn theorem in density functional theory. Quintanilla's theorem gives a firm theoretical foundation to quantum spin Hamiltonian learning using spin structure factors as input data. Here we extend the validity of the theorem in two directions. First, following the same approach as Mermin, the proof is extended to the case of finite-temperature spin structure factors, thus ensuring that the application of this theorem to experimental data is sound. Second, we note that this theorem applies to all types of Hamiltonians expressed as sums of bilinear operators, so that it can also relate the density-density correlators to the Coulomb matrix elements for interacting electrons in the lowest Landau level., Comment: 4 pages

The M4F project brings together the fusion and fission materials communities working on the prediction of radiation damage production and evolution and their effects on the mechanical behaviour of irradiated ferritic/martensitic (F/M) steels. It is a multidisciplinary project in which several different experimental and computational materials science tools are integrated to understand and model the complex phenomena associated with the formation and evolution of irradiation induced defects and their effects on the macroscopic behaviour of the target materials. In particular the project focuses on two specific aspects: (1) To develop physical understanding and predictive models of the origin and consequences of localised deformation under irradiation in F/M steels; (2) To develop good practices and possibly advance towards the definition of protocols for the use of ion irradiation as a tool to evaluate radiation effects on materials. Nineteen modelling codes across different scales are being used and developed and an experimental validation programme based on the examination of materials irradiated with neutrons and ions is being carried out. The project enters now its 4th year and is close to delivering high-quality results. This paper overviews the work performed so far within the project, highlighting its impact for fission and fusion materials science. Peer Reviewed L. Malerba a,*, M.J. Caturla b, E. Gaganidze c, C. Kaden d, M.J. Konstantinovi´c e, P. Olsson f, C. Robertson g, D. Rodney h, A.M. Ruiz-Moreno i, M. Serrano a, J. Aktaa c, N. Anento j, S. Austin i, A. Bakaev e, J.P. Balbuena b, F. Bergner d, F. Boioli k, M. Boleininger l, G. Bonny e, N. Castin e, J.B. J. Chapman l, P. Chekhonin d, M. Clozel m, B. Devincre k, L. Dupuy g, G. Diego a, S.L. Dudarev l, C.-C. Fu g, R. Gatti k, L. G´el´ebart g, B. G´omez-Ferrer n, D. Gonçalves g, C. Guerrero a, P.M. Gueye n, P. H¨ahner i, S.P. Hannula o, Q. Hayat p, M. Hern´andez-Mayoral a, J. Jagielski m, N. Jennett p, F. Jim´enez a, G. Kapoor d, A. Kraych h, T. Khvan e,q, L. Kurpaska m, A. Kuronen r, N. Kvashin j, O. Libera s, P.-W. Ma l, T. Manninen o, M.-C. Marinica g, S. Merino a, E. Meslin g, F. Mompiou t, F. Mota a, H. Namburi s, C.J. Ortiz a, C. Pareige n, M. Prester u, R.R. Rajakrishnan t, M. Sauzay g, A. Serra j, I. Simonovski i, F. Soisson g, P. Sp¨atig v, D. Tanguy h, D. Terentyev e, M. Trebala o, M. Trochet g, A. Ulbricht d, M.Vallet g, K. Vogel d, T. Yalcinkaya w, J. Zhao r a Centro de Investigaciones Energ´eticas, Medioambientales y Tecnol´ogicas (CIEMAT), Madrid, Spain b Universidad de Alicante, San Vicente del Raspeig, Spain c Karlsruher Institut für Technologie (KIT), Karlsruhe, Germany d Helmholtz-Zentrum Dresden-Rossendorf Ev (HZDR), Rossendorf, Germany e Studiecentrum voor Kernenergie / Centre d’´Etude de l’´Energie Nucl´eaire (SCK CEN), Mol, Belgium f KTH Royal Institute of Technology, Stockholm, Sweden g Universit´e Paris-Saclay, Commissariat `a l’´Energie Atomique et aux ´Energies Alternatives (CEA), Gif-sur-Yvette, France h Institut Lumi`ere Mati`ere (ILM), Centre National de la Recherche Scientifique, Lyon, France i Joint Research Centre (JRC)- European Commission, Petten, the Netherlands j Universitat Polit`ecnica de Catalunya, Barcelona, Spain k Laboratoire d’Etude des Microstructures (LEM), Centre National de la Recherche Scientifique, Chˆatillon, France l United Kingdom Atomic Energy Authority (UKAEA), Culham, UK m Narodowe Centrum Badan Jadrowych (NCBJ), Swierk, Poland n Normandie Univ, UNIROUEN, INSA Rouen, CNRS, Groupe de Physique des Mat´eriaux, 76000 Rouen, France o Aalto University, Espoo, Finland p Coventry University, UK q Universit´e de Li`ege, Belgium r Helsingin Yliopisto, Helsinki, Finland s Centrum Vyzkumu ˇReˇz S.R.O. (CVR), ˇReˇz, Czech Republic t Centre pour l’´Elaboration Elaboration de Mat´eriaux et pour l’´Etude des Structures (CEMES), Centre National de la Recherche Scientifique, Toulouse, France u Institut za Fiziku, Zagreb, Croatia v Paul Scherrer Institut (PSI), Villingen, Switzerland w Middle East Technical University (METU), Ankara, Turkey

The interactions of the spins of single atoms with a substrate can be controlled via the moiré lattice created by depositing a 2D material on top of the substrate.