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The Dzyaloshinskii-Moriya interaction (DMI) and perpendicular magnetic anisotropy (PMA) were measured on four series of Co films (1-2.2 nm thick) grown on Pt or Au and covered with h-BN or Cu. Clean h-BN/Co interfaces were obtained by exfoliating h-BN and transferring it onto the Co film in situ in the ultra-high-vacuum evaporation chamber. By comparing h-BN and Cu-covered samples, the DMI induced by the Co/h-BN interface was extracted and found to be comparable in strength to that of the Pt/Co interface, one of the largest known values. The strong observed DMI despite the weak spin-orbit interaction in h-BN supports a Rashba-like origin in agreement with recent theoretical results. Upon combination of it with Pt/Co in Pt/Co/h-BN heterostructures, even stronger PMA and DMI are found which stabilizes skyrmions at room temperature and a low magnetic field.

Magnetic skyrmions are swirling magnetic textures that can be efficiently driven with spin-orbit torques with a deflected trajectory. However, pinning slows skyrmions down and alters their trajectory, which prevents a quantitative comparison to analytical models. Here, we study skyrmions driven by spin-orbit torques at room temperature in ferrimagnetic GdCo thin films, an amorphous material with low pinning. Above a sharp current depinning threshold, we observe a clearly linear velocity increase with current that extrapolates to zero and a constant deflection angle, reaching high velocities up to 200 m/s. The mobility increases and the depinning threshold current decreases with the skyrmion diameter, which we vary using an external magnetic field. An analytical model based on the Thiele equation quantitatively reproduces these findings with a single fitting parameter. This validates the linear flow regime description and shows, in particular, the important role of skyrmion size in its dynamics., Comment: Supplemental information available from the final journal

We describe the dynamics of magnetic skyrmions in synthetic antiferromagnets (SAF), with a finite interlayer coupling. Due to the opposite gyrovector of the skyrmions in the two SAF layers, the coupled skyrmions reach a stationary regime with a spatial separation, in a direction orthogonal to their velocity. As a consequence, and contrary to the ferromagnetic situation, a transient regime necessarily occurs, with a finite acceleration, related to an inertia, and that limits its time response. The formalism developed here, based on two coupled Thiele equations, allows a quantitative description of this phenomenon. The time constant associated to the transient regime scales inversely with the antiferromagnetic coupling constant. We also show that the coupling force reaches a maximal value at a finite skyrmion separation. This sets a maximum velocity limit, beyond which the the coupling force cannot stabilize the bound state., 19 pages, 5 figures

The establishment of chiral coupling in thin magnetic films with inhomogeneous anisotropy has led to the development of artificial systems of fundamental and technological interest. The chiral coupling itself is enabled by the Dzyaloshinskii-Moriya interaction (DMI) enforced by the patterned noncollinear magnetization. Here, we create a domain wall track with out-of-plane magnetization coupled on each side to a narrow parallel strip with in-plane magnetization. With this we show that the chiral torques emerging from the DMI at the boundary between the regions of noncollinear magnetization in a single magnetic layer can be used to bias the domain wall velocity. To tune the chiral torques, the design of the magnetic racetracks can be modified by varying the width of the tracks or the width of the transition region between noncollinear magnetizations, reaching effective chiral magnetic fields of up to 7.8 mT. Furthermore, we show how the magnitude of the chiral torques can be estimated by measuring asymmetric domain wall velocities, and demonstrate spontaneous domain wall motion propelled by intrinsic torques even in the absence of any external driving force. ISSN:2331-7019

Magnetic skyrmions are topologically stable spin swirling particle like entities which are appealing for next generation spintronic devices. The expected low critical current density for the motion of skyrmions makes them potential candidates for future energy efficient electronic devices. Several heavy metal/ferromagnetic (HM/FM) systems have been explored in the past decade to achieve faster skyrmion velocity at low current densities. In this context, we have studied Pt/CoFeB/MgO heterostructures in which skyrmions have been stabilized at room temperature (RT). It has been observed that the shape of the skyrmions are perturbed even by the small stray field arising from low moment magnetic tips while performing the magnetic force microscopy (MFM), indicating presence of low pinning landscape in the samples. This hypothesis is indeed confirmed by the low threshold current density to drive the skyrmions in our sample, at velocities of few ∼10 m s−1.

International audience; This chapter explains what topology brings to the physics of magnetic textures in real space, from a physicist's point of view. The statics of magnetic textures is first discussed, and the distinction is made between a topological defect and a topologically stable-or protected-structure, also called topological soliton. The attention is then turned towards the physically observable consequences of topology, mainly in the dynamics of magnetic textures. Connection with experimental observations and applications is made, from early works at the beginnings of magnetic data storage up to the recent work on magnetic skyrmions, which triggered a revival of interest in topology as applied to magnetism.

An analytical model for the domain wall structure in ultrathin films with perpendicular easy axis and interfacial Dzyaloshinskii-Moriya interaction, submitted to an arbitrary in-plane magnetic field, is presented. Its solution is simplified to the numerical minimization of an analytic function of just one variable. The model predictions are compared to numerical micromagnetic simulations, using parameters of existing samples, revealing a very good agreement. Remaining differences are analyzed, and partly corrected. Differences with the predictions of the simplest model, usually found in the literature, in which only the domain wall moment's in-plane orientation can vary, are exemplified. The model allows accurate computations, as a function of in-plane field module and orientation, of the domain wall tension and width, quantities controlling the creep motion of domain walls in such films., Comment: 13 pages, 15 figures

The effect of damping-like spin-orbit torque (DL SOT) on magnetic domain walls (DWs) in in-plane magnetised soft tracks is studied analytically and with micromagnetic simulations. We find that DL SOT drives vortex DWs, whereas transverse DWs, the other typical DW structure in soft tracks, propagate only if the Dzyaloshinskii-Moriya interaction (DMI) is present. The SOT drive can add to, and be more efficient than, spin-transfer torque (STT), and so may greatly benefit applications that require in-plane DWs. Our analysis based on the Thiele equation shows that the driving force arises from a cycloidal distortion of the DW structure caused by geometrical confinement or DMI. This distortion is higher, and the SOT more efficient, in narrower, thinner tracks. These results show that the effects of SOT cannot be understood by simply considering the effective field at the center of the structure, an ill-founded but often-used estimation. We also show that the relative magnitude of STT and DL SOT can be determined by comparing the motion of different vortex DW structures in the same track., Accepted for publication in Physical Review B Rapid Communications

Topological magnetic textures, characterized by integer topological charge $S$, are potential candidates in future magnetic logic and memory devices, due to their smaller size and expected low threshold current density for their motion. An essential requirement to stabilize them is the Dzyaloshinskii-Moriya interaction (DMI) which promotes a particular chirality, leading to a unique value of $S$ in a given material. However, recently coexistence of skyrmions and antiskyrmions, with opposite topological charge, in frustrated ferromagnets has been predicted using $J_1$--$J_2$--$J_3$ classical Heisenberg model, which opens new perspectives, to use the topological charge as an additional degree of freedom. In this work, we propose another approach of using a synthetic antiferromagnetic (SAF) system, where one of the ferromagnetic (FM) layer has isotropic and the other FM layer has anisotropic DMI to promote the existence of skyrmions and antiskyrmions, respectively. A frustrated interaction arises due to the coupling between the magnetic textures in the FM layers, which enables the stabilization and coexistence of 6 novel elliptical topological textures., Comment: 11 pages

The mechanical manipulation of magnetic nanoparticles is a powerful approach to probing and actuating biological processes in living systems. Implementing this technique in high-throughput assays can be achieved using biocompatible micromagnet arrays. However, the magnetic properties of these arrays are usually indirectly inferred from simulations or Stokes drag measurements, leaving unresolved questions about the actual profile of the magnetic fields at the micrometer scale and the exact magnetic forces that are applied. Here, we exploit the magnetic field sensitivity of nitrogen-vacancy color centers in diamond to map the 3D stray magnetic field produced by a single soft ferromagnetic microstructure. By combining this wide-field optical magnetometry technique with magneto-optic Kerr effect microscopy, we fully analyze the properties of the micromagnets, including their magnetization saturation and their size-dependent magnetic susceptibility. We further show that the high magnetic field gradients produced by the micromagnets, greater than 10

International audience; Magnetization dynamics is of great interest in the aim of using spins in nanoscale information technology, which ultimately should reach the atomic size. In the present work, we explore magnetization and spin dynamics in atomic ferromagnetic contacts both experimentally and theoretically. We demonstrate that domain walls induce a giant rectification effect as the DC voltages measured across the contacts are greatly enhanced by the presence of a domain wall. This effect is understood using multiscale dynamic simulations showing that the atomic sized walls oscillate, both in position and size, when submitted to the radio-frequency excitation. This leads to an increase by three orders of magnitude due to the large atomic scale spin excursion at resonance in the presence of an atomic sized domain wall. Beside the interesting amplified rectification, this could also be used as a unique tool to measure dynamical properties at the atomic scale.

We demonstrate room-temperature stabilization of dipolar magnetic skyrmions with diameters in the range of $100$ nm in a single ultrathin layer of the Heusler alloy Co$_2$FeAl (CFA) under moderate magnetic fields. Current-induced skyrmion dynamics in microwires is studied with a scanning Nitrogen-Vacancy magnetometer operating in the photoluminescence quenching mode. We first demonstrate skyrmion nucleation by spin-orbit torque and show that its efficiency can be significantly improved using tilted magnetic fields, an effect which is not specific to Heusler alloys and could be advantageous for future skyrmion-based devices. We then show that current-induced skyrmion motion remains limited by strong pinning effects, even though CFA is a magnetic material with a low magnetic damping parameter., 5 pages, 4 figures

Extended numerical simulations enable to ascertain the diffusive behavior at finite temperatures of chiral walls and skyrmions in ultra-thin model Co layers exhibiting symmetric - Heisenberg - as well as antisymmetric - Dzyaloshinskii-Moriya - exchange interactions. The Brownian motion of walls and skyrmions is shown to obey markedly different diffusion laws as a function of the damping parameter. Topology related skyrmion diffusion suppression with vanishing damping parameter, albeit already documented, is shown to be restricted to ultra-small skyrmion sizes or, equivalently, to ultra-low damping coefficients, possibly hampering observation.

International audience; Magnetic domain walls are objects whose dynamics is inseparably connected to their structure. In this work we investigate magnetic bilayers, which are engineered such that a coupled pair of domain walls, one in each layer, is stabilized by a cooperation of Dzyaloshinskii-Moriya interaction and flux-closing mechanism. The dipolar field mediating the interaction between the two domain walls, links not only their position but also their structure. We show that this link has a direct impact on their magnetic field induced dynamics. We demonstrate that in such a system the coupling leads to an increased domain wall velocity with respect to single domain walls. Since the domain wall dynamics is observed in a precessional regime, the dynamics involves the synchronization between the two walls, to preserve the flux closure during motion. Properties of these coupled oscillating walls can be tuned by an additional in-plane magnetic field enabling a rich variety of states, from perfect synchronization to complete detuning.

We present a combined analytical and numerical micromagnetic study of the equilibrium energy, size and shape of anti-skyrmionic magnetic configurations. Anti-skyrmions can be stabilized when the Dzyaloshinskii-Moriya interaction has opposite signs along two orthogonal in-plane directions, breaking the magnetic circular symmetry. We compare the equilibrium energy, size and shape of anti-skyrmions and skyrmions that are stabilized respectively in environments with anisotropic and isotropic Dzyaloshinskii-Moriya interaction, but with the same strength of the magnetic interactions.When the dipolar interactions are neglected the skyrmion and the anti-skyrmion have the same energy, shape and size in their respective environment. However, when dipolar interactions are considered, the energy of the anti-skyrmion is strongly reduced and its equilibrium size increased with respect to the skyrmion. While the skyrmion configuration shows homochiral N\'{e}el magnetization rotations, anti-skyrmions show partly N\'{e}el and partly Bloch rotations. The latter do not produce magnetic charges and thus cost less dipolar energy. Both magnetic configurations are stable when the magnetic energies almost cancel each other, which means that a small variation of one parameter can drastically change their configuration, size and energy., Comment: Published as Physical Review B 97, 134404 (2018)

Nitrogen-vacancy magnetic microscopy is employed in quenching mode as a non-invasive, high resolution tool to investigate the morphology of isolated skyrmions in ultrathin magnetic films. The skyrmion size and shape are found to be strongly affected by local pinning effects and magnetic field history. Micromagnetic simulations including static disorder, based on a physical model of grain-to-grain thickness variations, reproduce all experimental observations and reveal the key role of disorder and magnetic history in the stabilization of skyrmions in ultrathin magnetic films. This work opens the way to an in-depth understanding of skyrmion dynamics in real, disordered media., 9 pages, 8 figures, including supplementary informations

We have used Brillouin Light Scattering spectroscopy to independently determine the in-plane Magneto-Crystalline Anisotropy and the Dzyaloshinskii-Moriya Interaction (DMI) in out-of-plane magnetized Au/Co/W(110). We found that the DMI strength is 2-3 times larger along the bcc$[\bar{1}10]$ than along the bcc$[001]$ direction. We use analytical considerations to illustrate the relationship between the crystal symmetry of the stack and the anisotropy of microscopic DMI. Such an anisotropic DMI is the first step to realize isolated elliptical skyrmions or anti-skyrmions in thin film systems with $C_{2v}$ symmetry., Revised and extended version

Brillouin light spectroscopy is a powerful and robust technique for measuring the interfacial Dzyaloshinskii-Moriya interaction in thin films with broken inversion symmetry. Here we show that the magnon visibility, i.e. the intensity of the inelastically scattered light, strongly depends on the thickness of the dielectric seed material - SiO$_2$. By using both, analytical thin-film optics and numerical calculations, we reproduce the experimental data. We therefore provide a guideline for the maximization of the signal by adapting the substrate properties to the geometry of the measurement. Such a boost-up of the signal eases the magnon visualization in ultrathin magnetic films, speeds-up the measurement and increases the reliability of the data.

Observing jumping domain walls Domain walls, which separate regions of opposite magnetization in a ferromagnet, have rich dynamics that are difficult to characterize in small samples. Tetienne et al. imaged the magnetization of a thin ferromagnetic wire and observed the jumping of a domain wall between different positions along the wire. They used a scanning magnetic microscope based on a defect in diamond. The laser light needed to operate the microscope also enabled the control of the domain wall motion by causing local heating, which made the illuminated position more likely to contain a domain wall. Science , this issue p. 1366

Magnetic skyrmions are topologically stable spin configurations, which usually originate from chiral interactions known as Dzyaloshinskii-Moriya interactions. Skyrmion lattices were initially observed in bulk non-centrosymmetric crystals, but have more recently been noted in ultrathin films, where their existence is explained by interfacial Dzyaloshinskii-Moriya interactions induced by the proximity to an adjacent layer with strong spin-orbit coupling. Skyrmions are promising candidates as information carriers for future information-processing devices due to their small size (down to a few nanometres) and to the very small current densities needed to displace skyrmion lattices. However, any practical application will probably require the creation, manipulation and detection of isolated skyrmions in magnetic thin-film nanostructures. Here, we demonstrate by numerical investigations that an isolated skyrmion can be a stable configuration in a nanostructure, can be locally nucleated by injection of spin-polarized current, and can be displaced by current-induced spin torques, even in the presence of large defects.

The Dzyaloshinskii-Moriya Interaction (DMI) has recently attracted considerable interest owing to its fundamental role in the stabilization of chiral spin textures in ultrathin ferromagnets, which are interesting candidates for novel spintronic technologies. Here, the authors present an experimental study of the DMI strength that is induced in nanometer-thick CoFeB ferromagnetic thin films in contact with different nonmagnetic metal underlayers. They use a novel technique for noninvasive high-sensitivity sensing of magnetic field: a scanning nanomagnetometer based on the magnetic response of a single nitrogen-vacancy defect in diamond. The magnetic domain walls are mapped, the spin structure and type of domain wall determined, and the DMI strength extracted. Importantly, the authors find local variation of the DMI constant, which clearly suggests that local field mapping techniques are extremely important to study this physics.

A path method is implemented in order to precisely and generally describe the collapse of isolated skyrmions in a Co/Pt(111) monolayer, on the basis of atomic scale simulations. Two collapse mechanisms with different energy barriers are found. The most obvious path, featuring a homogeneous shrinking gives the largest energy, whereas the lowest energy barrier is shown to comply with the outcome of Langevin dynamics under a destabilizing field of 0.25 T, with a lifetime of 20~ns at around 80~K. For this lowest energy barrier path, skyrmion destabilization occurs much before any topology change, suggesting that topology plays a minor role in the skyrmion stability. On the contrary, an important role appears devoted to the Dzyaloshinskii-Moriya interaction, establishing a route towards improved skyrmion stability., Comment: 9 pages, 6 figures

This paper reports on the voltage dependence of the magnetization reversal of a thin amorphous ferromagnetic TbFe film grown on a ferroelectric and piezoelectric BaTiO3 single crystal. Magneto-optical measurements, at macroscopic scale or in a microscope, demonstrate how the ferroelectric BaTiO3 polarisation history influences the properties of the perpendicularly magnetized TbFe film. Unpolarised and twinned regions are obtained when the sample is zero voltage cooled whereas flat and saturated regions are obtained when the sample is voltage cooled through the ferroelectric ordering temperature of the BaTiO3 crystal, as supported by atomic force microscopy experiments. The two steps involved in the TbFe magnetization reversal, namely nucleation and propagation of magnetic domain walls, depend on the polarisation history. Nucleation is associated to coupling through strains with the piezoelectric BaTiO3 crystal and propagation to pinning with the ferroelastic surface patterns visible in the BaTiO3 topography.

The dynamics of magnetic domain walls in ultrathin strip-patterned Pt/Co/AlOx samples with perpendicular easy axis has been studied experimentally under an easy-axis field, superposed to a hard-axis field oriented along the strip. The easy-axis field is large so that the domain walls move well beyond the creep regime. A chiral effect is observed where the domain wall velocity shows a monotonous and surprisingly large variation with an in-plane field. A micromagnetic analysis, combining analytic, one-dimensional, and two-dimensional simulations with structural disorder, shows that this behavior can be reproduced with a Dzyaloshinskii-Moriya interaction of the interfacial type, with due consideration of the dynamics of the tilt degree of freedom of the domain wall. The estimated effective value of this interaction ($D\ensuremath{\approx}\ensuremath{-}2.2\phantom{\rule{0.28em}{0ex}}\mathrm{mJ}/{\mathrm{m}}^{2}$ for a 0.6 nm Co thickness) is consistent with values obtained by other techniques. It is also shown, by micromagnetic analysis, that several modes and characteristic times occur in the dynamics of the tilt of such domain walls.

Various contributions to the magnetic anisotropy energy (MAE) dispersion for an assembly of CoPt nanoparticles are examined, using the empirical Neel anisotropy model. It is shown that, while small shape and composition variations have negligible effects, the statistical distribution of chemical arrangements can be the major source of MAE dispersion.

We study the magnetic anisotropy of CoPt clusters produced by condensation of a stoichiometric vapor with an inert gas (helium) and co-deposited with various matrices. From electron transmission microscopy we show that the clusters have a mean diameter of about 2 nm with a narrow size distribution and present the FCC A1 disordered phase. At high temperature, the clusters display a superparamagnetic behavior. The transition to the blocked state enables us to determine the clusters magnetic anisotropy energy (MAE). From a careful analysis, we show in the one hand that CoPt clusters present a higher volume and intrinsic surface MAE than pure Co ones. In the other hand, the presence of platinum at the interface in CoPt clusters decreases the strong interfacial exchange anisotropy observed for Co clusters embedded in MgO.

Magneto-optical microscopy and magnetometry have been used to study magnetization reversal in an ultrathin magnetically soft (Pt/Co)2 ferromagnetic film coupled to an array of magnetically harder (Co/Pt)4 nanodots via a predominantly dipolar interaction across a 3 nm Pt spacer. This interaction generates a spatially periodic pinning potential for domain walls propagating through the continuous magnetic film. When reversing the applied field with respect to the static nanodot array magnetization orientation, strong asymmetries in the wall velocity and switching fields are observed. Asymmetric switching fields mean that hysteresis of the film is characterized by a large bias field of dipolar origin which is linked to the wall velocity asymmetry. This latter asymmetry, though large at low fields, vanishes at high fields where the domains become round and compact. A field-polarity-controlled transition from dendritic to compact faceted domain structures is also seen at intermediate fields and a model is proposed to interpret the transition.

The Dzyaloshinskii-Moriya Interaction (DMI) between spins is induced by spin-orbit coupling in magnetic materials lacking inversion symmetry. DMI is recognized to play a crucial role at the interface between ferromagnetic (FM) and heavy nonmagnetic (NM) metals to create topological textures called magnetic skyrmions which are very attractive for ultra-dense information storage and spintronic devices. DMI also plays an essential role for fast domain wall (DW) dynamics driven by spin-orbit torques. Here, we present first principles calculations which clarify the main features and microscopic mechanisms of DMI in Co/Pt bilayers. DMI is found to be predominantly located at the interfacial Co layer, originating from spin-orbit energy provided by the adjacent NM layer. Furthermore, no direct correlation is found between DMI and proximity induced magnetism in Pt. These results clarify underlying mechanisms of DMI at FM/NM bilayers and should help optimizing material combinations for skyrmion- and DW-based storage and memory devices., 16 pages, 4 figures

International Workshop on Self-Organized Nanostructures, Cargese, FRANCE, JUL 17-23, 2005; International audience; We present both experimental and simulated results of ordered growth of cobalt nano-islands on a Au(111) vicinal template. Firstly, the temperature range for ordered growth and the islands size distributions are investigated by a rate equation model and kinetic Monte Carlo (KMC) simulations. Secondly, the incidence of the surface structure on the growth of cobalt is studied in detail by means of variable temperature scanning tunnelling microscopy experiments and KMC simulations. The underlying atomic processes responsible for the ordered growth are discussed.

A complete study of the link between growth conditions and cobalt nanodots morphology is performed on a Au(7 8 8) vicinal template using STM images at different temperatures. Once a good long-range order is established for the nanostructure superlattice, we elucidate how the substrate temperature during deposition influence the local order of the dots array. This work allows a full control of the local order of the nanostructure assembly and thus is an important step for the one who wants to perform physical properties measurements of nano-objects.

The nucleation of reversed magnetic domains in Pt/Co/AlO(x) microstructures with perpendicular anisotropy was studied experimentally in the presence of an in-plane magnetic field. For large enough in-plane field, nucleation was observed preferentially at an edge of the sample normal to this field. The position at which nucleation takes place was observed to depend in a chiral way on the initial magnetization and applied field directions. A quantitative explanation of these results is proposed, based on the existence of a sizable Dzyaloshinskii-Moriya interaction in this sample. Another consequence of this interaction is that the energy of domain walls can become negative for in-plane fields smaller than the effective anisotropy field.

We employ a scanning nitrogen-vacancy-center microscope to perform stray field imaging of bubble magnetic domains in a perpendicularly magnetized Pt/Co/AlOx trilayer with 6 A of Co. The stray field created by the domain walls is quantitatively mapped with few-nanometer spatial resolution, with a probe-sample distance of about 100 nm. As an example of application, we show that it should be possible to determine the Bloch or Neel nature of the domain walls, which is of crucial importance to the understanding of current-controlled domain wall motion.

The recent observation of current-induced domain wall (DW) motion with large velocity in ultrathin magnetic wires has opened new opportunities for spintronic devices. However, there is still no consensus on the underlying mechanisms of DW motion. Key to this debate is the DW structure, which can be of Bloch or N\'eel type, and dramatically affects the efficiency of the different proposed mechanisms. To date, most experiments aiming to address this question have relied on deducing the DW structure and chirality from its motion under additional in-plane applied fields, which is indirect and involves strong assumptions on its dynamics. Here we introduce a general method enabling direct, in situ, determination of the DW structure in ultrathin ferromagnets. It relies on local measurements of the stray field distribution above the DW using a scanning nanomagnetometer based on the Nitrogen-Vacancy defect in diamond. We first apply the method to a Ta/Co40Fe40B20(1 nm)/MgO magnetic wire and find clear signature of pure Bloch DWs. In contrast, we observe left-handed N\'eel DWs in a Pt/Co(0.6 nm)/AlOx wire, providing direct evidence for the presence of a sizable Dzyaloshinskii-Moriya interaction (DMI) at the Pt/Co interface. This method offers a new path for exploring interfacial DMI in ultrathin ferromagnets and elucidating the physics of DW motion under current., Comment: Main text and Supplementary Information, 33 pages and 12 figures

Thin-film ferromagnetic disks present a vortex spin structure whose dynamics, added to the small size (~10 nm) of their core, earned them intensive study. Here we use a scanning nitrogen-vacancy (NV) center microscope to quantitatively map the stray magnetic field above a 1 micron-diameter disk of permalloy, unambiguously revealing the vortex core. Analysis of both probe-to-sample distance and tip motion effects through stroboscopic measurements, allows us to compare directly our quantitative images to micromagnetic simulations of an ideal structure. Slight perturbations with respect to the perfect vortex structure are clearly detected either due to an applied in-plane magnetic field or imperfections of the magnetic structures. This work demonstrates the potential of scanning NV microscopy to map tiny stray field variations from nanostructures, providing a nanoscale, non-perturbative detection of their magnetic texture., 5 pages, 4 figures

We study the modification of micromagnetic configurations in nanostructures, due to the Dzyaloshinskii-Moriya interaction (DMI) that appear at the interface of an ultrathin film. We show that this interaction leads to new micromagnetic boundary conditions that bend the magnetization at the edges. We explore several cases of ultrathin film nanostructures that allow analytical calculations (1D systems, domain walls, cycloids and skyrmions), compare with fully numerical calculations, and show that a good physical understanding of this new type of micromagnetics can be reached. We particularly focus on skyrmions confined in circular nanodots and show that edges allow for the isolation of single skyrmions for a large range of the DMI parameter., Comment: Author adress: Laboratoire de Physique des Solides, Univ. Paris-Sud, CNRS UMR 8502, F-91405 Orsay Cedex, France

We show that the Dzyaloshinskii-Moriya interaction (DMI) can lead to a tilting of the domain wall (DW) surface in perpendicularly magnetized magnetic nanotracks when DW dynamics is driven by an easy axis magnetic field or a spin polarized current. The DW tilting affects the DW dynamics for large DMI and the tilting relaxation time can be very large as it scales with the square of the track width. The results are well explained by an analytical model based on a Lagrangian approach where the DMI and the DW tilting are included. We propose a simple way to estimate the DMI in a magnetic multilayers by measuring the dependence of the DW tilt angle on a transverse static magnetic field. Our results shed light on the current induced DW tilting observed recently in Co/Ni multilayers with inversion asymmetry, and further support the presence of DMI in these systems., 12 pages, 3 figures, 1 Supplementary Materials

Domain wall propagation has been measured in continuous, weakly disordered, quasi-two-dimensional, Ising-like magnetic layers that are subject to spatially periodic domain wall pinning potentials. The potentials are generated non-destructively using the stray magnetic field of ordered arrays of magnetically hard [Co/Pt]$_m$ nanoplatelets which are patterned above and are physically separated from the continuous magnetic layer. The effect of the periodic pinning potentials on thermally activated domain wall creep dynamics is shown to be equivalent, at first approximation, to that of a uniform, effective retardation field, $H_{ret}$, which acts against the applied field, $H$. We show that $H_{ret}$ depends not only on the array geometry but also on the relative orientation of $H$ and the magnetization of the nanoplatelets. A result of the latter dependence is that wall-mediated hysteresis loops obtained for a set nanoplatelet magnetization exhibit many properties that are normally associated with ferromagnet/antiferromagnet exchange bias systems. These include a switchable bias, coercivity enhancement and domain wall roughness that is dependent on the applied field polarity., Comment: 12 pages, 9 figures

Despite decades of advances in magnetic imaging, obtaining direct, quantitative information with nanometre scale spatial resolution remains an outstanding challenge. Recently, a technique has emerged that employs a single nitrogen-vacancy defect in diamond as an atomic-size magnetometer, which promises significant advances. However, the effectiveness of the technique when applied to magnetic nanostructures remains to be demonstrated. Here we use a scanning nitrogen-vacancy magnetometer to image a magnetic vortex, which is one of the most iconic objects of nanomagnetism, owing to the small size (~10 nm) of the vortex core. We report three-dimensional, vectorial and quantitative measurements of the stray magnetic field emitted by a vortex in a ferromagnetic square dot, including the detection of the vortex core. We find excellent agreement with micromagnetic simulations, both for regular vortex structures and for higher-order magnetization states. These experiments establish scanning nitrogen-vacancy magnetometry as a practical and unique tool for fundamental studies in nanomagnetism. Obtaining quantitative information on nanoscale magnetic structures is a challenge. Here, the authors apply scanning probe magnetometry based on a single nitrogen-vacancy defect in diamond to quantitatively map the stray magnetic field emitted by a vortex state in a ferromagnetic dot.

We explore a new type of domain wall structure in ultrathin films with perpendicular anisotropy, that is influenced by the Dzyaloshinskii-Moriya interaction due to the adjacent layers. This study is performed by numerical and analytical micromagnetics. We show that these walls can behave like Neel walls with very high stability, moving in stationary conditions at large velocities under large fields. We discuss the relevance of such walls, that we propose to call Dzyaloshinskii domain walls, for current-driven domain wall motion under the spin Hall effect., 7 pages, 3 figures. Accepted for publication in Europhysics Letters

Magnetization reversal dynamics in single perpendicular Pt/Co/Pt high aspect ratio nanodisks have been studied by polar magneto-optical Kerr effect microscopy. The He${}^{+}$ ion process used to pattern these nanodisks resulted in a soft/hard nanodisk structure. The energy barrier field dependence was determined from the simple exponential variation of the nonswitching probability with time. The standard coherent reversal scenario fails to account for it whereas a two-dimensional-confined droplet model supports the experimental observations. From a ring shaped metastable domain wall in the magnetically soft outer ring, the reversal progresses via the deformation of the domain wall and the expansion of a reversed confined droplet through the nanodisk hard core. This magnetic reversal, governed by domain wall propagation alone, ensures a magnetization reversal reproducibility from nanodisk to nanodisk and the very narrow energy barrier distribution observed.

We demonstrate quantitative magnetic field mapping with nanoscale resolution, by applying a lock-in technique on the electron spin resonance frequency of a single nitrogen-vacancy defect placed at the apex of an atomic force microscope tip. In addition, we report an all-optical magnetic imaging technique which is sensitive to large off-axis magnetic fields, thus extending the operation range of diamond-based magnetometry. Both techniques are illustrated by using a magnetic hard disk as a test sample. Owing to the non-perturbing and quantitative nature of the magnetic probe, this work should open up numerous perspectives in nanomagnetism and spintronics.

We have observed peculiar magnetization textures in Ni${}_{80}$Pd${}_{20}$ nanostrips using three different imaging techniques: magnetic force microscopy, photoemission electron microscopy under polarized x-ray absorption, and scanning electron microscopy with polarization analysis. The appearance of diamondlike domains with strong lateral charges and of weak-stripe structures reveals the presence of both a transverse and a perpendicular anisotropy in these nanostructures. The anisotropy is seen to reinforce as temperature decreases, as testified by observations performed at 150 K. A thermal stress model with relaxation is proposed to account for these observations. Elastic calculations coupled to micromagnetic simulations support qualitatively this model.

Standing spin-waves can be excited in artificial chains of magnetic atoms using inelastic electron tunnelling spectroscopy, thereby offering a route to speed up the switching of their magnetization.