Non-Majorana modes in diluted spin chains proximitized to a superconductor.

Spin chains proximitized with superconducting condensates have emerged as one of the most promising platforms for the realization of Majorana modes. Here, we craft diluted spin chains atom by atom following a seminal theoretical proposal suggesting indirect coupling mechanisms as a viable route to trigger topological superconductivity. Starting from single adatoms hosting deep Shiba states, we use the highly anisotropic Fermi surface of the substrate to create spin chains characterized by different magnetic configurations along distinct crystallographic directions. By scrutinizing a large set of parameters we reveal the ubiquitous emergence of boundary modes. Although mimicking signatures of Majorana modes, the end modes are identified as topologically trivial Shiba states. Our work demonstrates that zero-energy modes in spin chains proximitized to superconductors are not necessarily a link to Majorana modes while simultaneously identifying other experimental platforms, driving mechanisms, and test protocols for the determination of topologically nontrivial superconducting phases.

Manipulating the Spin Orientation of Co Atoms Using Monatomic Cu Chains.

Harnessing the spin of single atoms is at the heart of quantum information nanotechnology based on magnetic concepts. By attaching single Co atoms to monatomic Cu chains, we demonstrate the ability to control the spin orientation by the atomic environment. Due to spin-orbit coupling (SOC), the spin is tilted by ≈58° from the surface normal toward the chain as evidenced by inelastic tunneling spectroscopy. These findings are reproduced by density functional theory calculations and have implications for Co atoms on pristine Cu(111), which are believed to be Kondo systems. Our quantum Monte Carlo calculations suggest that SOC suppresses the Kondo effect of Co atoms at chains and on the flat surface. Our work impacts the fundamental understanding of low-energy excitations in nanostructures on surfaces and demonstrates the ability to manipulate atomic-scale magnetic moments, which can have tremendous implications for quantum devices.

Transverse Transport in Two-Dimensional Relativistic Systems with Nontrivial Spin Textures.

Using multiple scattering theory, we show that the generally accepted expression of transverse resistivity in magnetic systems that host skyrmions, given by the linear superposition of the ordinary, the anomalous, and the topological Hall effect, is incomplete and must be amended by an additional term, the "noncollinear" Hall effect (NHE). Its angular form is determined by the magnetic texture, the spin-orbit field of the electrons, and the underlying crystal structure, allowing us to disentangle the NHE from the various other Hall contributions. Its magnitude is proportional to the spin-orbit interaction strength. The NHE is an essential term required for decoding two- and three-dimensional spin textures from transport experiments.

Brain palpation from physiological vibrations using MRI.

We present a magnetic resonance elastography approach for tissue characterization that is inspired by seismic noise correlation and time reversal. The idea consists of extracting the elasticity from the natural shear waves in living tissues that are caused by cardiac motion, blood pulsatility, and any muscle activity. In contrast to other magnetic resonance elastography techniques, this noise-based approach is, thus, passive and broadband and does not need any synchronization with sources. The experimental demonstration is conducted in a calibrated phantom and in vivo in the brain of two healthy volunteers. Potential applications of this "brain palpation" approach for characterizing brain anomalies and diseases are foreseen.

Tuning Paramagnetic Spin Excitations of Single Adatoms.

We predict the existence of paramagnetic spin excitations (PSE) in nonmagnetic single adatoms. Our calculations demonstrate that PSE develop a well-defined structure in the meV region when the adatom's Stoner criterion for magnetism is close to the critical point. We further reveal a subtle tunability and enhancement of PSE by external magnetic fields. Finally, we show how PSE can be detected as moving steps in the dI/dV signal of inelastic scanning tunneling spectroscopy, opening a potential route for experimentally accessing electronic properties of nonmagnetic adatoms, such as the Stoner parameter.

Zero-Point Spin-Fluctuations of Single Adatoms.

Stabilizing the magnetic signal of single adatoms is a crucial step toward their successful usage in widespread technological applications such as high-density magnetic data storage devices. The quantum mechanical nature of these tiny objects, however, introduces intrinsic zero-point spin-fluctuations that tend to destabilize the local magnetic moment of interest by dwindling the magnetic anisotropy potential barrier even at absolute zero temperature. Here, we elucidate the origins and quantify the effect of the fundamental ingredients determining the magnitude of the fluctuations, namely, the (i) local magnetic moment, (ii) spin-orbit coupling, and (iii) electron-hole Stoner excitations. Based on a systematic first-principles study of 3d and 4d adatoms, we demonstrate that the transverse contribution of the fluctuations is comparable in size to the magnetic moment itself, leading to a remarkable ≳50% reduction of the magnetic anisotropy energy. Our analysis gives rise to a comprehensible diagram relating the fluctuation magnitude to characteristic features of adatoms, providing practical guidelines for designing magnetically stable nanomagnets with minimal quantum fluctuations.

Superconductivity in Nb: Impact of Temperature, Dimensionality and Cooper-Pairing.

The ability to realistically simulate the electronic structure of superconducting materials is important to understand and predict various properties emerging in both the superconducting topological and spintronics realms. We introduce a tight-binding implementation of the Bogoliubov-de Gennes method, parameterized from density functional theory, which we utilize to explore the bulk and thin films of Nb, known to host a significant superconducting gap. The latter is useful for various applications such as the exploration of trivial and topological in-gap states. Here, we focus on the simulation's aspects of superconductivity and study the impact of temperature, Cooper-pair coupling and dimensionality on the value of the superconducting pairing interactions and gaps.

Kagomerization of transition metal monolayers induced by two-dimensional hexagonal boron nitride.

The kagome lattice is an exciting solid state physics platform for the emergence of nontrivial quantum states driven by electronic correlations: topological effects, unconventional superconductivity, charge and spin density waves, and unusual magnetic states such as quantum spin liquids. While kagome lattices have been realized in complex multi-atomic bulk compounds, here we demonstrate from first-principles a process that we dub kagomerization, in which we fabricate a two-dimensional kagome lattice in monolayers of transition metals utilizing an hexagonal boron nitride (h-BN) overlayer. Surprisingly, h-BN induces a large rearrangement of the transition metal atoms supported on a fcc(111) heavy-metal surface. This reconstruction is found to be rather generic for this type of heterostructures and has a profound impact on the underlying magnetic properties, ultimately stabilizing various topological magnetic solitons such as skyrmions and bimerons. Our findings call for a reconsideration of h-BN as merely a passive capping layer, showing its potential for not only reconstructing the atomic structure of the underlying material, e.g. through the kagomerization of magnetic films, but also enabling electronic and magnetic phases that are highly sought for the next generation of device technologies.

Magnetic exchange interactions at the proximity of a superconductor.

Interfacing magnetism with superconductivity gives rise to a wonderful playground for intertwining key degrees of freedom: Cooper pairs, spin, charge, and spin-orbit interaction, from which emerge a wealth of exciting phenomena, fundamental in the nascent field of superconducting spinorbitronics and topological quantum technologies. Magnetic exchange interactions (MEIs), being isotropic or chiral such as the Dzyaloshinskii-Moriya interactions, are vital in establishing the magnetic behavior at these interfaces as well as in dictating not only complex transport phenomena, but also the manifestation of topologically trivial or non-trivial objects. Here, we propose a methodology enabling the extraction of the tensor of MEI from electronic structure simulations accounting for superconductivity. We apply our scheme to the case of a Mn layer deposited on Nb(110) surface and explore proximity-induced impact on the MEI. The latter are weakly modified by a realistic electron-phonon coupling. However, tuning the superconducting order parameter, we unveil potential change of the magnetic order accompanied with chirality switching, as induced by the interplay of spin-orbit interaction and Cooper pairing. Owing to its simple formulation, our methodology can be readily implemented in state-of-the-art frameworks capable of tackling superconductivity and magnetism. We thus foresee implications in the simulations and prediction of topological superconducting bits as well as of cryogenic superconducting hybrid devices involving magnetic units.

Parity effect in the ground state localization of antiferromagnetic chains coupled to a ferromagnet.

We investigate the ground states of antiferromagnetic Mn nanochains on Ni(110) by spin-polarized scanning tunneling microscopy in combination with theory. While the ferrimagnetic linear trimer experimentally shows the predicted collinear classical ground state, no magnetic contrast was observed for dimers and tetramers where noncollinear structures were expected based on ab initio theory. This striking observation can be explained by zero-point energy motion for even-numbered chains derived within a classical equation of motion leading to nonclassical ground states. Thus, depending on the parity of the chain length, the system shows a classical or a quantum behavior.

Intrinsic Néel Antiferromagnetic Multimeronic Spin Textures in Ultrathin Films.

Topological antiferromagnetism is a vibrant and captivating research field, generating considerable enthusiasm with the aim of identifying topologically protected magnetic states of key importance in the hybrid realm of topology, magnetism, and spintronics. While topological antiferromagnetic (AFM) solitons bear various advantages with respect to their ferromagnetic cousins, their observation is scarce. Utilizing first-principles simulations, here we predict new chiral particles in the realm of AFM topological magnetism, exchange-frustrated multimeronic spin textures hosted by a Néel magnetic state, arising universally in single Mn layers directly grown on an Ir(111) surface or interfaced with Pd-based films. These nanoscale topological structures are intrinsic; i.e. they form in a single AFM material, can carry distinct topological charges, and can combine in various multimeronic sequences with enhanced stability against external magnetic fields. We envision the frustrated Néel AFM multimerons as exciting highly sought after AFM solitons having the potential to be utilized in novel spintronic devices hinging on nonsynthetic AFM quantum materials, further advancing the frontiers of nanotechnology and nanophysics.

Magnetic adatom induced Skyrmion-like spin texture in surface electron waves.

When a foreign atom is placed on a surface of a metal, the surrounding sea of electrons responds by screening the additional charge leading to oscillations or ripples. On surfaces, those electrons are sometimes confined to two-dimensional surface states, whose spin-degeneracy is lifted due to the Rashba effect arising from the spin-orbit interaction of electrons and the inversion asymmetric environment. It is believed that at least for a single adatom scanning tunneling microscopy measurements are insensitive to the Rashba splitting; i.e., no signatures in the charge oscillations will be observed. Resting on scattering theory, we demonstrate that, if magnetic, one single adatom is enough to visualize the presence of the Rashba effect in terms of an induced spin magnetization of the surrounding electrons exhibiting a twisted spin texture described as superposition of two Skyrmionic waves of opposite chirality.

Generalization of the Landau-Lifshitz-Gilbert equation by multi-body contributions to Gilbert damping for non-collinear magnets.

We propose a systematic and sequential expansion of the Landau-Lifshitz-Gilbert equation utilizing the dependence of the Gilbert damping tensor on the angle between magnetic moments, which arises from multi-body scattering processes. The tensor consists of a damping-like term and a correction to the gyromagnetic ratio. Based on electronic structure theory, both terms are shown to depend on e.g. the scalar, anisotropic, vector-chiral and scalar-chiral products of magnetic moments:ei⋅ej, (nij⋅ei)(nij⋅ej),nij⋅ (ei×ej),(ei⋅ej)2,ei⋅ (ej×ek) …, where some terms are subjected to the spin-orbit fieldnijin first and second order. We explore the magnitude of the different contributions using both the Alexander-Anderson model and time-dependent density functional theory in magnetic adatoms and dimers deposited on Au(111) surface.

Spin-orbit enabled all-electrical readout of chiral spin-textures.

Chirality and topology are intimately related fundamental concepts, which are heavily explored to establish spin-textures as potential magnetic bits in information technology. However, this ambition is inhibited since the electrical reading of chiral attributes is highly non-trivial with conventional current perpendicular-to-plane (CPP) sensing devices. Here we demonstrate from extensive first-principles simulations and multiple scattering expansion the emergence of the chiral spin-mixing magnetoresistance (C-XMR) enabling highly efficient all-electrical readout of the chirality and helicity of respectively one- and two-dimensional magnetic states of matter. It is linear with spin-orbit coupling in contrast to the quadratic dependence associated with the unveiled non-local spin-mixing anisotropic MR (X-AMR). Such transport effects are systematized on various non-collinear magnetic states - spin-spirals and skyrmions - and compared to the uncovered spin-orbit-independent multi-site magnetoresistances. Owing to their simple implementation in readily available reading devices, the proposed magnetoresistances offer exciting and decisive ingredients to explore with all-electrical means the rich physics of topological and chiral magnetic objects.

Interplay of magnetic states and hyperfine fields of iron dimers on MgO(001).

Individual nuclear spin states can have very long lifetimes and could be useful as qubits. Progress in this direction was achieved on MgO/Ag(001) via detection of the hyperfine interaction (HFI) of Fe, Ti and Cu adatoms using scanning tunneling microscopy. Previously, we systematically quantified from first-principles the HFI for the whole series of 3d transition adatoms (Sc-Cu) deposited on various ultra-thin insulators, establishing the trends of the computed HFI with respect to the filling of the magnetic s- and d-orbitals of the adatoms and on the bonding with the substrate. Here we explore the case of dimers by investigating the correlation between the HFI and the magnetic state of free standing Fe dimers, single Fe adatoms and dimers deposited on a bilayer of MgO(001). We find that the magnitude of the HFI can be controlled by switching the magnetic state of the dimers. For short Fe-Fe distances, the antiferromagnetic state enhances the HFI with respect to that of the ferromagnetic state. By increasing the distance between the magnetic atoms, a transition toward the opposite behavior is observed. Furthermore, we demonstrate the ability to substantially modify the HFI by atomic control of the location of the adatoms on the substrate. Our results establish the limits of applicability of the usual hyperfine hamiltonian and we propose an extension based on multiple scattering processes.

Noncollinear magnetism in two-dimensional CrTe2.

The discovery of two-dimensional (2D) van der Waals magnets opened unprecedented opportunities for the fundamental exploration of magnetism in quantum materials and the realization of next generation spintronic devices. Here, based on a multiscale modelling approach that combines first-principles calculations and a Heisenberg model supplied with ab-initio parameters, we report a strong magnetoelastic coupling in a free-standing monolayer of CrTe2. We demonstrate that different crystal structures of a single CrTe2give rise to non-collinear magnetism through magnetic frustration and emergence of the Dzyaloshinskii-Moriya interaction. Utilizing atomistic spin dynamics, we perform a detailed investigation of the complex magnetic properties pertaining to this 2D material impacted by the presence of various types of structural distortions akin to charge density waves.

Anomalous excitations of atomically crafted quantum magnets.

High-energy resolution spectroscopic studies of quantum magnets proved extremely valuable in accessing magnetodynamics quantities, such as energy barriers, magnetic interactions, and lifetime of excited states. Here, we investigate a previously unexplored flavor of low-energy spin excitations for quantum spins coupled to an electron bath. In sharp contrast to the usual tunneling signature of two steps symmetrically centered around the Fermi level, we find a single step in the conductance. Combining time-dependent and many-body perturbation theories, magnetic field-dependent tunneling spectra are explained as the result of an interplay between weak magnetic anisotropy energy, magnetic interactions, and Stoner-like electron-hole excitations that are strongly dependent on the magnetic states of the nanostructures. The results are rationalized in terms of a noncollinear magnetic ground state and the dominance of ferro- and antiferromagnetic interactions. The atomically crafted nanomagnets offer an appealing model for the exploration of electrically pumped spin systems.

Emergence of zero-field non-synthetic single and interchained antiferromagnetic skyrmions in thin films.

Antiferromagnetic (AFM) skyrmions are envisioned as ideal localized topological magnetic bits in future information technologies. In contrast to ferromagnetic (FM) skyrmions, they are immune to the skyrmion Hall effect, might offer potential terahertz dynamics while being insensitive to external magnetic fields and dipolar interactions. Although observed in synthetic AFM structures and as complex meronic textures in intrinsic AFM bulk materials, their realization in non-synthetic AFM films, of crucial importance in racetrack concepts, has been elusive. Here, we unveil their presence in a row-wise AFM Cr film deposited on PdFe bilayer grown on fcc Ir(111) surface. Using first principles, we demonstrate the emergence of single and strikingly interpenetrating chains of AFM skyrmions, which can co-exist with the rich inhomogeneous exchange field, including that of FM skyrmions, hosted by PdFe. Besides the identification of an ideal platform of materials for intrinsic AFM skyrmions, we anticipate the uncovered knotted solitons to be promising building blocks in AFM spintronics.

Friedel Oscillations Induced by Magnetic Skyrmions: From Scattering Properties to All-Electrical Detection.

Magnetic skyrmions are spin swirling solitonic defects that can play a major role in information technology. Their future in applications and devices hinges on their efficient manipulation and detection. Here, we explore from ab-initio their nature as magnetic inhomongeities in an otherwise unperturbed magnetic material, Fe layer covered by a thin Pd film and deposited on top of Ir(111) surface. The presence of skyrmions triggers scattering processes, from which Friedel oscillations emerge. The latter mediate interactions among skyrmions or between skyrmions and other potential surrounding defects. In contrast to their wavelengths, the amplitude of the oscillations depends strongly on the size of the skyrmion. The analogy with the scattering-off atomic defects enables the assignment of an effective scattering potential and a phase shift to the skyrmionic particles, which can be useful to predict their behavior on the basis of simple scattering frameworks. The induced charge ripples can be utilized for a noninvasive all-electrical detection of skyrmions located on a surface or even if buried a few nanometers away from the detecting electrode.

Multiple magnetic states of CoPc molecule on a two-dimensional layer of NbSe2.

Molecular spintronics hinges on the detailed understanding of electronic and magnetic properties of molecules interfaced with various materials. Here we demonstrate withab initiosimulations that the prototypical Co-phthalocyanine (CoPc) molecule can surprisingly develop multi-spin states once deposited on the two-dimensional 2H-NbSe2layer. Conventional calculations based on density functional theory (DFT) show the existence of low, regular and high spin states, which reduce to regular and high spins states once correlations are incorporated with a DFT +Uapproach. Depending onU, the ground state is either the low spin or high spin state with energy differences affected by the molecular orientation on top of the substrate. Our results are compared to recent scanning probe measurements and motivate further theoretical and experimental studies on the unveiled rich multi-magnetic behavior of CoPc molecule.