Littérature scientifique sur le sujet « Helimagnetism »

2015 - 2016
This work is focused on two helimagnetic materials: Ba2CuGe2O7 and Cu3Nb2O8. Recent studies report a number of interesting anisotropic proper- ties [1, 2, 3]. Ba2CuGe2O7 melilite oxide shows a complex magnetic behaviour, indeed it is known that at low temperature the system undergoes a transition from a paramagnetic phase to an incommensurate antiferromagnetic cycloid spin structure. Applying a magnetic field, additional magnetic transitions take place, as for example a spin-cone phase [3]. Moreover, Ba2CuGe2O7 shows also multiferroic properties [1]. Several works report that the physical properties of melilite oxides mainly depend on the nature of the transition metal ion, thus interesting proper- ties could emerge in mixed melilite oxides. In this work Ba2MGe2O7 with M=Cu,Ni and Mn have been studied. Cu3Nb2O8 is an unusual helimagnetic compound that undergoes a series of magnetic ordering at low temperature. Development of electric polarization P has been reported at TN=25K corresponding to emergence of a non-collinear helicoidal ordering. P is oriented perpendicularly to the common plane of rotation of the spins. This observation cannot be reconciled with the conven- tional theory developed for cycloidal multiferroics [2]. The study of all these complex anisotropic phenomena requires the availability of good single crystals. In this thesis, an investigation on crystal growth conditions of Ba2MGe2O7 and of Cu3Nb2O8 will be presented [4, 5]. Single crystal samples are vital to study the physical properties exhibited by compounds which have high magnetic/ferroelectric anisotropy where significantly different behaviour is seen along different crystallographic directions. Preliminarily, high quality polycrystalline powders have been prepared for all compounds, indeed this is a critical point to grow pure crystalline samples. 1 Abstract 2 In this work the procedure to synthesize polycrystalline powders with high purity is reported. Moreover, by using powder X-ray diffraction and energy dispersive spectroscopy (EDS), the composition of the starting polycrystalline powder is checked. Successfully, the growth conditions to realize large and pure single crystals suitable for low temperature magnetometry and lattice dynamic studies are described. The chemical composition and the morphology of the crystals are investigated by X-ray diffraction and by scanning electron microscopy (SEM), with wave- length dispersive spectrometry (WDS). Furthermore, the excellent quality of the crystals is confirmed by rocking curve measurements. The X-ray Laue back reflection and electron backscattered diffraction (EBSD) techniques are used to orient single crystals specifically for selected experi- ments. To study the magnetic phase diagrams of grown crystals, magnetization measurement vs temperature is performed in the range 1.5 KQuesto lavoro si concentra su due materiali elimagnetici: Ba2CuGe2O7 e Cu3Nb2O8. Recenti studi riportano una serie di interessanti propriet`a aniso- trope [1, 2, 3]. L’ossido melilite Ba2CuGe2O7 mostra un comportamento magnetico com- plesso, infatti a bassa temperatura il sistema attraversa una transizione di magnetica dalla fase paramegnetica a quella di cicloide di spin antiferroma- gnetica. Applicando un campo magnetico esterno, sono state rivelate ulteriori transizioni magnetiche, come ad esempio la fase di coni di spin [3]. Inoltre, il Ba2CuGe2O7 mostra anche propriet`a multiferroiche [1]. Numerosi lavori riportano che le propriet`a degli ossidi meliliti dipendono dalla natura del metallo di transizione, perci`o propriet`a interessanti potrebbero emergere nel caso di meliliti misti. In questo lavoro vengono studiati i sistemi Ba2MGe2O7 with M=Cu,Ni e Mn. Il Cu3Nb2O8 `e un composto elimagnetico che attraversa una serie di transizio- ni magnetiche a bassa temperatura. In letteratura `e riportato lo sviluppo di una polarizzazione elettrica P a TN=25K in corrispondenza dell’ordinamento magnetico elicoidale. Il vettore polarizzazione elettrica P `e perpendicolare al piano di rotazione degli spin. Questo rende il Cu3Nb2O8 un sistema non convenzionale, perch`e questa osservazione non pu`o essere spiegata attraverso la teoria convenzionale sviluppata per i sistemi multiferroici con ordinamento magnetico cicloidale [2]. Lo studio di tutti questi fenomeni complessi e anisotropi richiede la disponibi- lit`a di campioni di cristallo singolo di buona qualit`a. Nell’ambito di questa tesi si mostra uno studio delle condizioni di crescista di cristalli di Ba2MGe2O7 e di Cu3Nb2O8 [4, 5]. I campioni di cristalli singoli sono essenziali per lo studio delle propriet`a fisiche dei composti che mostrano anisotropie magnetiche ed elettriche dove un comportamento diverso si osserva lungo differenti direzioni cristallografiche. 1 Abstract 2 In modo preliminare, sono state preparate polveri policristalline di elevata qualit`a, infatti questa sintesi `e un fattore critico per la realizzazione di cam- pioni cristallini puri. Inoltre, si riporta lo studio della composizione chimica e della struttura dei campioni illustrando i risultati dell’analisi mediante diffrazione X e mediante spettroscopia Energy Dispersive X-ray Analysise (EDS). Successivamente, si descrivono le condizioni di crescita per realizzare campioni di cristallo singolo di dimensioni centimetriche con elevata purezza disponibili per misure magnetiche a bassa temperatura e misure ottiche. La composizione chimica e la morfologia dei cristalli `e stata studiata attra- verso diffrazione X e microscopia elettronica a scansione (SEM), combinata alla spettroscopia Wavelength Dispersive System (WDS). Inoltre, l’eccellente qualit`a dei cristalli `e confermata dalle misure di rocking curve. Le tecniche Laue ed Electron Backscattered Diffraction (EBSD) sono state utilizzate per orientare i campioni di cristallo singolo lungo precise direzioni cristallografiche. Lo studio dei diagrammi di fase magnetici dei sistemi Ba2CuGe2O7 e Cu3Nb2O8 attraverso misure della magnetizzazione in funzione della temperatura sono stati realizzati nel range 1.5 KXV n.s. (XXIX )

Magnetic skyrmions have the potential to provide solutions for low-power, high-density data storage and processing. One of the major challenges in developing skyrmion-based devices is the skyrmions' magnetic stability in confined helimagnetic nanostructures. Through a systematic study of equilibrium states, using a full three-dimensional micromagnetic model, we demonstrate that skyrmionic states are the lowest energy states in confined helimagnetic nanostructures at zero external magnetic field and in absence of magnetocrystalline anisotropy. We show that bistable skyrmionic states undergo hysteretic behaviour between two energetically equivalent skyrmionic configurations with different core orientation, even in the absence of both magnetocrystalline and demagnetisation-based shape anisotropies, suggesting the existence of novel Dzyaloshinskii-Moriya-based shape anisotropy. We show that the skyrmionic state core reversal is facilitated by the Bloch point occurrence and propagation. In this work, we also study the dynamic properties (resonance frequencies and corresponding eigenmodes) of these skyrmionic states in confined helimagnetic nanostructures. The eigenvalue method allows us to identify all resonance frequencies and corresponding eigenmodes that can exist in the simulated system. However, using a particular experimentally feasible excitation can excite only a limited set of eigenmodes. Because of that, we perform and report ringdown simulations that resemble the experimental setup using both an in-plane and an out-of-plane excitations. In addition, we report the nonlinear dependence of resonance frequencies on the external magnetic bias field and disk sample diameter and report the possible reversal mode of skyrmionic states. Finally, we show that neglecting the demagnetisation energy contribution or ignoring the magnetisation variation in the out-of-film direction in either static or dynamic simulations is not always justified.

This thesis describes high quality magnetisation measurements made on single crystals of MnSi, FeGe and ZrZn(_2) using a vibrating sample magnetometer. The measurements on MnSi have also been complemented with neutron scattering experiments. MnSi is a heavily investigated itinerant helimagnet which exhibits a variety of interesting phenomena associated with formation of a helical spin density wave propagating along < 111 > directions. Magnetisation measurements were performed as a function of magnetic field at fixed temperatures stepping through the magnetic transition observed at 29.1 ± 0.05K. These were found to be highly anisotropic and included observation of the so-called 'Phase A' consistent with measurements using other techniques and providing explanation of apparent anomalies in previous magnetisation data (Kadowaki et al. (1981)). Further investigation of 'Phase A' using small angle neutron scattering (SANS) was successful in determining the magnetic state of MnSi within this regime in terms of helix reorientation which is shown to be broadly consistent with the expression for the free energy derived by Bak and Jensen (1980) and Plumer and Walker (1981). Reorientation of the helical spin density wave as a function of magnetic field was also studied using SANS to complement the magnetisation measurements. The second order process observed is similar to that predicted by Plumer and Walker (1981) and the form of their model for the magnetisation of is compared with the experimental results. Finally, anomalous magnetisation measurements close to the magnetic transition were further explored through neutron scattering. The results suggest a possible isotropic phase pre-empting the helical spin density wave formation. Cubic FeGe is also capable of supporting a static helical spin density wave and has a critical temperature of 278.7K with helix propagating along < 100 > directions above 211K and along < 111 > directions below 211K (for decreasing temperatures). Magnetisation measurements were made on cubic FeGe with magnetic field applied parallel to the < 100 > direction and the magnetic phase diagram determined. Coupled with the SANS data of Lebech et al. (1989) it shows similar processes in terms of helix reorientation in an applied magnetic field occur for both FeGe and MnSi. The magnetic phase diagram is in good agreement with that predicted by Plumer (1990) for magnetic field applied parallel to the < 100 >

Axisymmetric magnetic strings with a fixed sense of rotation and nanometer sizes (chiral magnetic vortices or Skyrmions) have been predicted to exist in a large group of non-centrosymmetric crystals more than two decades ago. Recently these extraordinary magnetic states have been directly observed in thin layers of cubic helimagnet (Fe,Co)Si. In this thesis we apply our earlier theoretical findings and recent results to review main properties of chiral Skyrmions, to elucidate their physical nature, and to analyse these recent experimental results on magnetic-field-driven evolution of Skyrmions and helicoids in chiral helimagnets. Concentrating on the physical side of the problem rather than on mathematical details we give an elementary introduction into the properties of chiral Skyrmions in magnetism.

Dans cette thèse nous étudions les transitions de phase et leurs propriétés thermodynamiques au sein de couches minces en se basant sur des simulations Monte-Carlo et sur le formalisme de la fonction de Green .Dans le premier chapitre, nous étudions le modèle de Blume-Emery-Griffith pour un film mince sur réseaux triangulaires empilés. Le spin $S_i$ dans ce modèle prend trois valeurs (+/-1,0). Notre travail a été motivé par le désir de vérifier si a nature de la transition de phase se conserve quand on réduit l'épaisseur du film. En utilisant la simulation Monte Carlo, nous montrons qu'il existe une valeur critique d'anisotropie D où la transition change de nature. Nous montrons ainsi que la nature premier ordre ne disparaît pas lorsque nous réduisons l'épaisseur du film contrairement à d'autres systèmes.Dans le deuxième chapitre, nous étudions les propriétés quantiques des couches mince hélimagnétiques. Nous montrons qu'il existe des modes de surface qui affectent la magnétisation de surface, nous montrons également que les fluctuations quantiques provoquent la contraction des spins à T=0 et donnent lieu à un croisement entre les magnétisations des couches à basse température. Nous nous intéressons ensuite à l'effet d'un champ magnétique appliqué perpendiculairement à la surface du film. Nous montrons que les spins réagissent en créant une configuration particulière. En utilisant la simulation Monte Carlo nous étudions la transition de phase en fonction de l'intensité du champ appliqué. Nous montrons que le système subit une transition de phase déclenchée par la destruction des composantes transversales xy des spins de certaines couches. À basse température, nous étudions les effets des fluctuations quantiques en utilisant la méthode des fonctions de Green. Les résultats montrent que la contraction des spins à T=0 est différente d'une couche à l'autre, et que la croisement des magnétisations de couche dépend de l'ampleur des angles hélicoïdaux.Dans le troisième chapitre, nous introduisons l'interaction de Dzyaloshinskii-Moriya. Il a été montré dans divers travaux que l'interaction DM est à l'origine de formation des skyrmions et de nouveau genre de domaines Walls. Nous nous intéressons aux propriétés quantiques d'un système de spins qui interagissent les uns avec les autres via une interaction DM et une interaction ferromagnétique. En utilisant la méthode "steepest descend", nous avons trouvé un état fondamental non-colinéaire qui est dû à la compétition entre l'interaction ferromagnétique et l'interaction asymétrique DM. Utilisant la théorie des fonctions de Green pour calculer le spectre des ondes de spin et la magnétisation des couches à température finie en deux et trois dimensions ainsi que dans un film mince avec des effets de surface. Nous avons constaté que l'excitation des ondes de spin dans les cristaux 2D et 3D est stable à T=0 sans nécessiter d'anisotropie, mais dans le cas d'un film mince nous avons besoin d'une faible anisotropie pour stabiliser le spectre en raison du manque de voisins à la surface. On trouve aussi que l'énergie des ondes de spin est proportionnelle à $K^2$ pour les faibles valeurs de DM et une proportionnalité en $K$ pour les interactions fortes.Dans le quatrième chapitre, nous nous intéressons aux cristaux de skyrmion crées grâce à la compétition entre l'interaction ferromagnétique, le DM et le champ magnétique appliqué. Ces skyrmions s'organisent dans une structure périodique, ils ont été observés expérimentalement dans les composés MnSi, FeCoSi et dans les semiconducteurs dopés. En utilisant la simulation Monte Carlo, nous montrons que les cristaux de skyrmions sont stable à des températures finies et jusqu'à la transition où la structure topologique de chaque skyrmion et la structure périodique sont détruites. Nous étudions également la relaxation des skyrmions dans la phase cristalline et nous constatons que le temps de relaxation suit une loi exponentielle étirée
In this thesis, we study the phase transition and thermodynamic properties of classical and quantum spin models in thin films using both Green's function and standard Monte Carlo simulation.In chapter 1, we study the Blume-Emery-Griffith model. This model has been introduced to describe the mixing phase of superfluid He$^4$ ($S_i=pm$ 1) and normal fluid He$^3$ ($S_i$= 0) at low temperatures, such system undergoes two kinds of phase transition, first and second-order ones. Using Monte Carlo simulation, we show that there exists a critical value of anisotopy D$below (above) which the transition is of second (first) order, and that the first order nature of transition does not disappear when we reduce the film thickness unlike in other systems where the bulk first-order transition becomes second order with small thickness. In the Helium vocabulary, we show that the film surfaces have a deficit of He$^4$ with respect to interior layers of the film.In chapter 2 we first study quantum properties of a helimagnetic thin film. We show that there exist surface acoustic and optical modes which affect the surface magnetization. We also show that quantum fluctuations cause the spin contraction at $T$=0 and give rise to a cross-over between layer magnetizations at low temperatures. In the second part of chapter 2, we are interested in the effect of an external magnetic field applied. We show that spins react to a moderate applied magnetic field by creating a particular spin configuration along the $c$-axis. Using Monte Carlo simulation we study the phase transition as functions of the magnetic field strength. We show that the system undergoes a phase transition triggered by the destruction of the transverse xy spin-components. At low temperatures, we investigate effects of quantum fluctuations using Green's function method. The results show that the zero-point spin contraction is different from layer to layer. We also find a crossover of layer magnetizations which depends on the magnitude of helical angles.In the third chapter, we introduce the in-plane Dzyaloshinskii-Moriya interaction (DM). It has been showed in various works that the DM interaction is at the origin of topological skyrmions and a new kind of magnetic domain walls. In this chapter, we are interested in the spin-wave properties of a system of spins interacting with each other via a DM interaction. Using the steepest descend method we found a non-collinear ground state which is due to the competition between the ferromagnetic and the asymmetric DM interaction. We use the Green's function theory to calculate the spin-wave spectrum and the layer magnetization at finite temperatures in two and three dimensions as well as in a thin film with surface effects. We found that the spin-wave excitation in 2D and 3D crystals is stable at $T$=0 without the need of an anisotropy, but in the case of a thin film we need a small anisotropy to stabilize the spin-wave spectrum because of the lack of neighbors at the surface. We find also that the spin-wave energy is proportional to $k^2$ for a small DM interaction and is linear in $k$ for a strong one.Finally, in the fourth chapter we are interested in skyrmion crystals created by the competition between the ferromagnetic interaction and the DM interaction under an applied magnetic field. They arrange themselves in a periodic structure. These skyrmion crystals have been experimentally observed in MnSi compounds and in doped semiconductors. Using Monte Carlo simulation, we show that skyrmion crystals are stable at finite temperatures up to a transition temperature where the topological structure of each skyrmion and the periodic structure of skyrmions are destroyed. We also investigate the relaxation of the skyrmions in the crystalline phase and find that the relaxation time follows a stretched exponential law which is a characteristic of slowly-relaxed systems such as spin glasses

This chapter delves into the physics of multiferroics, the recent developments of which are discussed here from the viewpoint of the spin current and “emergent electromagnetism” for constrained systems. It presents the three sources of U(1) gauge fields, namely, the Berry phase associated with the noncollinear spin structure, the spin-orbit interaction (SOI), and the usual electromagnetic field. The chapter reviews multiferroic phenomena in noncollinear magnets from this viewpoint and discusses theories of multiferroic behavior of cycloidal helimagnets in terms of the spin current or vector spin chirality. Relativistic SOI leads to a coupling between the spin current and the electric polarization, and hence the ferroelectric and dielectric responses are a new and important probe for the spin states and their dynamical properties. Microscopic theories of the ground state polarization for various electronic configurations, collective modes including the electromagnon, and some predictions including photoinduced chirality switching are discussed with comparison to experimental results.