The skyrmion-bubble transition in a ferromagnetic thin film

Magnetic skyrmions and bubbles, observed in ferromagnetic thin films with perpendicular magnetic anisotropy, are topological solitons which differ by their characteristic size and the balance in the energies at the origin of their stabilisation. However, these two spin textures have the same topology and a continuous transformation between them is allowed. In the present work, we derive an analytical model to explore the skyrmion-bubble transition. We evidence a region in the parameter space where both topological soliton solutions coexist and close to which transformations between skyrmion and bubbles are observed as a function of the magnetic field. Above a critical point, at which the energy barrier separating both solutions vanishes, only one topological soliton solution remains, which size can be continuously tuned from micrometer to nanometer with applied magnetic field

Resolving spin currents and spin densities generated by charge-spin interconversion in systems with reduced crystal symmetry

The ability to control the generation of spins in arbitrary directions is a long-sought goal in spintronics. Charge to spin interconversion (CSI) phenomena depend strongly on symmetry. Systems with reduced crystal symmetry allow anisotropic CSI with unconventional components, where charge and spin currents and the spin polarization are not mutually perpendicular to each other. Here, we demonstrate experimentally that the CSI in graphene-WTe induces spins with components in all three spatial directions. By performing multi-terminal nonlocal spin precession experiments, with specific magnetic fields orientations, we discuss how to disentangle the CSI from the spin Hall and inverse spin galvanic effects.We acknowledge support of the European Union's Horizon 2020 FET-PROACTIVE project TOCHA under Grant No. 824140 and of the Spanish Research Agency (AEI), Ministry of Science and Innovation, under Contracts No. PID2019-111773RB-I00/AEI/10.13039/501100011033, and SEV-2017-0706 Severo Ochoa. J F S acknowledges support from AEIunder contract RYC2019-028368-I/AEI/10.13039/50110001103, W S T and M V C from the European Union Horizon 2020 research and innovation program, Grant No. 881603 (Graphene Flagship), and I F A of a fellowship from 'la Caixa' Foundation (ID 100010434) with code LCF/BQ/DI18/11660030 and of H2020 Marie Skłodowska-Curie Grant No. 713673. J S acknowledges funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 754558

Toplogical magnetic solitons in thin epitaxial films with reduced symmetry

Dans cette thèse, j'ai étudié la relation entre la symétrie cristalline, la symétrie des interactions magnétiques et des soliton topologiques dans des couches minces magnétiques épitaxiées. Le cas particulier de couches avec une symétrie C2v a été considéré. Ces couches ont un intérêt particulier par leurs propriétés anisotropes qui permettent une stabilisation de solitons magnétiques avec différentes symétries et nombres topologiques. J'ai utilisé des approches théoriques et expérimentaux pour étudier ce phénomène :Approche micromagnétique :La relation entre les formulations atomistes et micromagnétiques des interactions magnétiques a été étudiée en fonction de la symétrie cristalline. Ceci a permis d'expliquer la présence des interactions anisotropes et d'étudier leur effet sur la configuration des solitons magnétiques 1D et 2D.La discussion commence par le plus simple soliton 1D, la paroi des domaines, et pas par pas des nouvelles interactions et symétries sont ajoutées afin de caractériser les conditions de stabilité et les propriétés des solitons 2D, les skyrmion et anti-skyrmions.Notre méthode a permis d'étudier les solitons topologiques 2D sur une large gamme de paramètres, et de construire un diagramme de phase en fonction de l'interaction Dzyaloshinskii-Moriya (DMI) et du champ magnétique appliqué. Trois types de solitons topologiques 2D ont été identifiées (skyrmions, bulles skyrmioniques et skyrmions supercritiques) en fonction de leur taille et leur réponse à un champ magnétique externe.On a aussi montré qu'une inversion du signe de la DMI selon deux directions perpendiculaires permet la stabilisation d'anti-skyrmions. Un modèle micromagnétique a été développé pour étudier la différence de configuration et d'énergie entre skyrmions et anti-skyrmions. On montre que l'interaction dipolaire rompt la symétrie circulaire de l'anti-skyrmion et le rend plus stable que le skyrmion.Approche expérimentale :J'ai préparé différentes couches magnétiques épitaxiées de symétrie C2v. Pour chaque système, je décris les paramètres de croissance et la symétrie cristalline, suivi par les résultats des caractérisations magnétiques et finalement les résultats de microscopie magnétique.J'ai étudié la symétrie et l'intensité de la DMI dans une tricouche Au/Co/W à aimantation perpendiculaire. La DMI dans ce système induit une chiralité horaire de la modulation de spin avec une forte anisotropie de l'intensité de la DMI, venant de la symétrie C2v. Des skyrmions dans ce système devraient avoir une forme elliptique. Nous avons stabilisé des skyrmions dans des films continus et dans des nanostructures. Leur configuration magnétique a été étudiée par XMCD-PEEM et MFM, mais sans observer des propriétés anisotropes.Pour augmenter l'effet des interactions anisotropes sur la configuration des skyrmions, j'ai développé le système W/Co/Au-Pt(solution solide). Des études par microscopie ont montré la stabilisation des bandes magnétiques parallèles à l'axe facile dans le plan dans ce système. Des études par microscopie Kerr ont montré que l'origine de cette configuration en bandes parallèles est une forte anisotropie de la dynamique du mouvement des parois.Des mesures MFM en champ magnétique statique ont été effectuées afin de confiner des bulles skyrmioniques elliptiques, mais la sensibilité de ces mesures à des couches ultrafines a été insuffisante pour caractériser leurs propriétés anisotropes.Des mesures XMCD-PEEM ont permis d'observer la structure interne de parois selon l'axe planaire difficile du système. Ces mesures mettent en évidence un composant Néel de la paroi.Finalement, j'ai préparé et étudié un système W/Fe/Co/Au avec le but de stabiliser des anti-skyrmions. Cependant, le système n'a pas montré l'aimantation hors-du-plan qui est nécessaire pour stabiliser ces solitons. Ce signifie que l'anisotropie planaire de l'interface W/Fe domine l'anisotropie perpendiculaire de l'interface Co/Au.In this thesis I studied the relationship between the crystal symmetry, the symmetry of the magnetic interactions and topological solitons in epitaxial magnetic thin films. The case of thin films with C2v symmetry has been considered. These systems are particularly interesting for the anisotropic properties that allow stabilising magnetic solitons with different symmetries and topology. I used theoretical and experimental approaches to investigate this phenomenon:Micromagnetic approach:The relationship between the atomistic and the micromagnetic formulations of magnetic interactions was studied as a function of the crystal symmetry.This allowed to explain the presence of anisotropicinteractions and study their effect on the configurations of 1D and 2D magnetic solitons. The discussion starts from the simplest 1D soliton, the domain wall, and step-by-step new interactions and symmetries are added in order to characterize the stability conditions and the properties of 2D solitons, skyrmions and anti-skyrmions. Our method allowed to study 2D topological solitons over a wide range of parameters and build a phase diagram as a function of the Dzyaloshinskii-Moriya interaction (DMI) strength and magnetic field intensity. This allowed us to distinguish three kinds of 2D topological solitons (skyrmions, skyrmionic bubbles and supercritical skyrmions) as a function of their size and response to an external magnetic field. We show that an inversion of DMI strength along perpendicular directions allows the stabilisation of anti-skyrmions. A micromagnetic model is developed to study the configuration and energy differences between skyrmions and anti-skyrmions. This shows that the dipolar interaction breaks the circular symmetry of the antiskyrmion and makes it more stable than the skyrmion.Experimental approach:Epitaxial magnetic systems with C2v symmetry have been grown. For each system I describe the growth parameters and crystal symmetry, followed by the results of the magnetic characterisation and finally the results from the magnetic microscopy measurements.I have investigated the DMI symmetry and strength in an out-of-plane magnetised epitaxial Au/Co/W trilayer. The DMI in this system promotes a clockwise chirality of the spin modulation with a strong anisotropy in the DMI strength. This anisotropy arises from the C2v symmetry of the Co/W stack.Skyrmions in this system should have an elliptical shape. We stabilised skyrmions in continuous films and in nanopatterned structures. Their magnetic configurations have been displayed with different microscopic techniques, XMCD-PEEM and MFM, without identifying anisotropic properties.We designed the W/Co/Au-Pt (solid solution) system to increase the effect of the anisotropic interactions on the skyrmion configuration. Microscopy studies in naturally demagnetised areas show that stripe domains parallel to the in-plane easy axis are stable in this system. The configuration with a larger periodicity has been found even for thinner Co layer after demagnetisation with a magnetic field. Kerr microscopy studies of the DW dynamics allowed to evidence the origin of this magnetic configuration, which arises from a strong anisotropy in the DW motion.MFM measurements with the application of a static magnetic field have been performed in order to confine elliptical skyrmionic bubbles but the reduced sensitivity of this technique to thin magnetic systems did not allow to display and characterise them. XMCD-PEEM measurements allowed to display the internal structure of the DWs along the in-plane hard axis of the system. They show the presence of a Néel DW component. Finally I have grown and studied a W/Fe/Co/Au system where anti-skyrmions may in principle be stabilised. However, the system did not show the out-of-plane magnetisation which is fundamental for the stabilisation of skyrmions. This means that the W/Fe in-plane anisotropy dominates the Co/Au out-of-plane anisotropy

Solitons magnétiques topologiques dans des couches minces epitaxiées à symétrie réduite

In this thesis I studied the relationship between the crystal symmetry, the symmetry of the magnetic interactions and topological solitons in epitaxial magnetic thin films. The case of thin films with C2v symmetry has been considered. These systems are particularly interesting for the anisotropic properties that allow stabilising magnetic solitons with different symmetries and topology. I used theoretical and experimental approaches to investigate this phenomenon:Micromagnetic approach:The relationship between the atomistic and the micromagnetic formulations of magnetic interactions was studied as a function of the crystal symmetry.This allowed to explain the presence of anisotropicinteractions and study their effect on the configurations of 1D and 2D magnetic solitons. The discussion starts from the simplest 1D soliton, the domain wall, and step-by-step new interactions and symmetries are added in order to characterize the stability conditions and the properties of 2D solitons, skyrmions and anti-skyrmions. Our method allowed to study 2D topological solitons over a wide range of parameters and build a phase diagram as a function of the Dzyaloshinskii-Moriya interaction (DMI) strength and magnetic field intensity. This allowed us to distinguish three kinds of 2D topological solitons (skyrmions, skyrmionic bubbles and supercritical skyrmions) as a function of their size and response to an external magnetic field. We show that an inversion of DMI strength along perpendicular directions allows the stabilisation of anti-skyrmions. A micromagnetic model is developed to study the configuration and energy differences between skyrmions and anti-skyrmions. This shows that the dipolar interaction breaks the circular symmetry of the antiskyrmion and makes it more stable than the skyrmion.Experimental approach:Epitaxial magnetic systems with C2v symmetry have been grown. For each system I describe the growth parameters and crystal symmetry, followed by the results of the magnetic characterisation and finally the results from the magnetic microscopy measurements.I have investigated the DMI symmetry and strength in an out-of-plane magnetised epitaxial Au/Co/W trilayer. The DMI in this system promotes a clockwise chirality of the spin modulation with a strong anisotropy in the DMI strength. This anisotropy arises from the C2v symmetry of the Co/W stack.Skyrmions in this system should have an elliptical shape. We stabilised skyrmions in continuous films and in nanopatterned structures. Their magnetic configurations have been displayed with different microscopic techniques, XMCD-PEEM and MFM, without identifying anisotropic properties.We designed the W/Co/Au-Pt (solid solution) system to increase the effect of the anisotropic interactions on the skyrmion configuration. Microscopy studies in naturally demagnetised areas show that stripe domains parallel to the in-plane easy axis are stable in this system. The configuration with a larger periodicity has been found even for thinner Co layer after demagnetisation with a magnetic field. Kerr microscopy studies of the DW dynamics allowed to evidence the origin of this magnetic configuration, which arises from a strong anisotropy in the DW motion.MFM measurements with the application of a static magnetic field have been performed in order to confine elliptical skyrmionic bubbles but the reduced sensitivity of this technique to thin magnetic systems did not allow to display and characterise them. XMCD-PEEM measurements allowed to display the internal structure of the DWs along the in-plane hard axis of the system. They show the presence of a Néel DW component. Finally I have grown and studied a W/Fe/Co/Au system where anti-skyrmions may in principle be stabilised. However, the system did not show the out-of-plane magnetisation which is fundamental for the stabilisation of skyrmions. This means that the W/Fe in-plane anisotropy dominates the Co/Au out-of-plane anisotropy.Dans cette thèse, j'ai étudié la relation entre la symétrie cristalline, la symétrie des interactions magnétiques et des soliton topologiques dans des couches minces magnétiques épitaxiées. Le cas particulier de couches avec une symétrie C2v a été considéré. Ces couches ont un intérêt particulier par leurs propriétés anisotropes qui permettent une stabilisation de solitons magnétiques avec différentes symétries et nombres topologiques. J'ai utilisé des approches théoriques et expérimentaux pour étudier ce phénomène :Approche micromagnétique :La relation entre les formulations atomistes et micromagnétiques des interactions magnétiques a été étudiée en fonction de la symétrie cristalline. Ceci a permis d'expliquer la présence des interactions anisotropes et d'étudier leur effet sur la configuration des solitons magnétiques 1D et 2D.La discussion commence par le plus simple soliton 1D, la paroi des domaines, et pas par pas des nouvelles interactions et symétries sont ajoutées afin de caractériser les conditions de stabilité et les propriétés des solitons 2D, les skyrmion et anti-skyrmions.Notre méthode a permis d'étudier les solitons topologiques 2D sur une large gamme de paramètres, et de construire un diagramme de phase en fonction de l'interaction Dzyaloshinskii-Moriya (DMI) et du champ magnétique appliqué. Trois types de solitons topologiques 2D ont été identifiées (skyrmions, bulles skyrmioniques et skyrmions supercritiques) en fonction de leur taille et leur réponse à un champ magnétique externe.On a aussi montré qu'une inversion du signe de la DMI selon deux directions perpendiculaires permet la stabilisation d'anti-skyrmions. Un modèle micromagnétique a été développé pour étudier la différence de configuration et d'énergie entre skyrmions et anti-skyrmions. On montre que l'interaction dipolaire rompt la symétrie circulaire de l'anti-skyrmion et le rend plus stable que le skyrmion.Approche expérimentale :J'ai préparé différentes couches magnétiques épitaxiées de symétrie C2v. Pour chaque système, je décris les paramètres de croissance et la symétrie cristalline, suivi par les résultats des caractérisations magnétiques et finalement les résultats de microscopie magnétique.J'ai étudié la symétrie et l'intensité de la DMI dans une tricouche Au/Co/W à aimantation perpendiculaire. La DMI dans ce système induit une chiralité horaire de la modulation de spin avec une forte anisotropie de l'intensité de la DMI, venant de la symétrie C2v. Des skyrmions dans ce système devraient avoir une forme elliptique. Nous avons stabilisé des skyrmions dans des films continus et dans des nanostructures. Leur configuration magnétique a été étudiée par XMCD-PEEM et MFM, mais sans observer des propriétés anisotropes.Pour augmenter l'effet des interactions anisotropes sur la configuration des skyrmions, j'ai développé le système W/Co/Au-Pt(solution solide). Des études par microscopie ont montré la stabilisation des bandes magnétiques parallèles à l'axe facile dans le plan dans ce système. Des études par microscopie Kerr ont montré que l'origine de cette configuration en bandes parallèles est une forte anisotropie de la dynamique du mouvement des parois.Des mesures MFM en champ magnétique statique ont été effectuées afin de confiner des bulles skyrmioniques elliptiques, mais la sensibilité de ces mesures à des couches ultrafines a été insuffisante pour caractériser leurs propriétés anisotropes.Des mesures XMCD-PEEM ont permis d'observer la structure interne de parois selon l'axe planaire difficile du système. Ces mesures mettent en évidence un composant Néel de la paroi.Finalement, j'ai préparé et étudié un système W/Fe/Co/Au avec le but de stabiliser des anti-skyrmions. Cependant, le système n'a pas montré l'aimantation hors-du-plan qui est nécessaire pour stabiliser ces solitons. Ce signifie que l'anisotropie planaire de l'interface W/Fe domine l'anisotropie perpendiculaire de l'interface Co/Au

Micromagnetics of anti-skyrmions in ultrathin films

International audienceWe 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

The skyrmion-bubble transition in a ferromagnetic thin film

Magnetic skyrmions and bubbles, observed in ferromagnetic thin films with perpendicular magnetic anisotropy, are topological solitons which differ by their characteristic size and the balance in the energies at the origin of their stabilisation. However, these two spin textures have the same topology and a continuous transformation between them is allowed. In the present work, we derive an analytical model to explore the skyrmion-bubble transition. We evidence a region in the parameter space where both topological soliton solutions coexist and close to which transformations between skyrmion and bubbles are observed as a function of the magnetic field. Above a critical point, at which the energy barrier separating both solutions vanishes, only one topological soliton solution remains, which size can be continuously tuned from micrometer to nanometer with applied magnetic field

Self-organised stripe domains and elliptical skyrmion bubbles in ultra-thin epitaxial Au{0.67}Pt{0.33}/Co/W(110) films

International audienceWe studied the symmetry of magnetic properties and the resulting magnetic textures in ultra-thin epitaxial Au$_{0.67}$Pt$_{0.33}$/Co/W, a model system exhibiting perpendicular magnetic anisotropy and interface Dzyaloshinskii-Moriya interaction (DMI). As a peculiar feature, the C$_\mathrm{2v}$ crystal symmetry induced by the Co/W interface results in an additional uniaxial in-plane magnetic anisotropy in the cobalt layer. Photoemission electron microscopy with magnetic sensitivity reveals the formation of self-organized magnetic stripe domains oriented parallel to the hard in-plane magnetization axis. We attribute this behavior to the lower domain wall energy when oriented along this axis, where both the DMI and the in-plane magnetic anisotropy favor a N\'{e}el domain wall configuration. The anisotropic domain wall energy also leads to the formation of elliptical skyrmion bubbles in a weak out-of-plane magnetic field

Passivation of Bi2_2Te3_3 topological insulator by transferred CVD‐graphene: toward intermixing‐free interfaces

International audienceThe investigation, and ultimate application, of topological insulators, typically involve exposure to ambient conditions or their integration with metals, which lead to surface oxidation or material intermixing. X-ray photoelectron spectroscopy (XPS) measurements that demonstrate passivated and intermixing-free interfaces in the topological insulator Bi2Te3 by means of dry-transferred CVD graphene are reported. After air exposure, no traces of Bi2Te3 oxidation are found. Furthermore, it is demonstrated that graphene acts as a very efficient metal and chalcogen diffusion barrier in Bi2Te3/graphene/permalloy (Py) heterostructures, which are relevant for spintronics. Such results are in stark contrast with the significant surface degradation observed in bare Bi2Te3 under ambient conditions and the deep Bi-Te bonding disruption that occurs in Bi2Te3/Py heterostructures. These findings provide a new approach to control and engineer topological insulator interfaces for spintronic applications and a new platform to investigate the combined use of graphene and topological insulator Dirac states

Anisotropic Dzyaloshinskii-Moriya Interaction in ultra-thin epitaxial Au/Co/W(110)

Revised and extended versionInternational audienceWe 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 \textit{bcc}$[001]$ than along the \textit{bcc}$[\overline{1}10]$ 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