Session S11: Thin Film Skyrmions

Synthesizing Skyrmion Molecules in Fe-Gd Thin Films

Controlled creation of tunable skyrmion phases at room temperature holds the promise of advanced spintronics applications using these topological entities. By varying the composition and thickness of an amorphous Fe-Gd thin film and optimizing the applied field protocol, we produced at room temperature an ordered, achiral phase of skyrmion molecules, that is, bound pairs of magnetic skyrmions having the same polarity but opposite helicity. This phase appears between stripe and uniform magnetization phase and its origin lies in the existence of mirror planes in the stripe domain structure. Dipolar, exchange, and anisotropy forces are the dominant interactions in these materials, while the role of bulk and surface chiral exchange interactions is small.   

Chirality evaluation of spin spiral in Mn thin film on W(110)

In crystal fields with broken inversion symmetry such as surfaces or interfaces, the Dzyaloshinskii-Moriya interaction (DMI), which is induced by the spin orbit interaction, may have a significant contribution to the formation of spin structures. Because of DMI, magnetic thin films formed on a heavy-elemental substrate such as W often exhibit peculiar spin spiral structures whose chirality is fixed and determined by the polarity of DMI. Investigating the chirality of spin structures is thus important to reveal the formation mechanism of spin structures and, more specifically, to determine whether DMI plays a decisive role on it. Monolayer (ML) Mn thin films formed on W(110), the first surface spin spiral structures, show a cycloidal spin spiral structure propagating along to [1-10] axis. Spin-polarized scanning tunneling microscopy (SP-STM) and theoretical analysis based on density functional calculation revealed left-handed chirality of the structure and concluded that it is driven by DMI. A SP-STM recent study revealed that double layer (DL) Mn thin films on W(110) show a conical spin spiral structure whose propagation direction is along [001]. The chirality and its driving interaction, however, have not been revealed yet. Here in this study, we have investigated the chirality of DL Mn by SP-STM. Our experimental results revealed that the spin spiral structure of DL Mn is homochiral but right-handed, which is opposite to that of ML Mn. In the presentation we will discuss different roles of DMI exerted on the two Mn thin films.   

Determination of interfacial Dzyaloshinskii-Moriya exchange interaction from static domain size imaging

Dzyaloshinskii-Moriya interaction (DMI) has been identified [1-2] as a necessary ingredient for the formation of chiral spin structures such as skyrmions and N\'{e}el domain walls in perpendicularly magnetized thin films. Various simulation and experimental studies have tried to quantify DMI from domain wall [2] and skyrmion [3-4] motion with applied currents and magnetic fields. Here, a means to quantify DMI in multilayer films using only static magnetic characterizations is proposed. Static domain structure is observed using magnetic force microscopy (MFM) in multilayer stacks of [Pt(2.5-7.5nm)/CoFeB(0.8nm)/MgO(1.5nm)]$_{15}$ where the thickness $t_{pt}$ of the Pt layer is systematically varied from 2.5 nm to 7.5 nm. A variation of domain size from \textasciitilde 300 nm to \textasciitilde 70 nm is seen in the labyrinthine demagnetized state as $t_{pt}$ is decreased. It is shown that the domain size as a function of $t_{pt}$ can be well-fitted analytically by a model in which the domain wall energy is the sole free parameter. Additional measurements of magnetic anisotropy of the film reveal the significant contribution of interfacial DMI (\textasciitilde 1.4 mJ/m$^{2})$ to the domain wall energy. Ref: 1.Fert et al., \textit{Nat. Nanotech}., 8, 152-156 (2013); 2. S. Emori et al., \textit{Nature Materials} 12,611--616 (2013); 3. S. Woo et al., arXiv:1502.07376;~4.W. Jiang et al., arXiv:1502.08028v1   

Interface-induced skyrmions in magnetic films and multilayers

The talk is on individual skyrmions induced by interface Dzyaloshinskii-Moriya Interactions (DMI) in thin magnetic films or multilayers. I will present: \begin{enumerate} \item Ab-initio calculations of the characteristic features of interface DMI [1]: extension of the DMI away from the interface in the magnetic film, thickness dependence, influence of the existence of proximity-induced magnetism in neighbor layers, influence of interface roughness, perspective with new materials\textellipsis \item Experimental results on small skyrmions at room temperature in (Ir/Co/Pt)x10 multilayers [2]. \item Towards applied devices: micromagnetic simulations of the nucleation and current-induced motion of skyrmions [3]. \end{enumerate} [1] H. Yang et al, arXiv:1501.055112. [2] C. Moreau-Luchaire et al, arXiv: 1502.07853. [3] J. Sampaio et al. Nat. Nanotech$.$ 8, 839-844 (2013).   

Observation of sub-100 nm N\'{e}el skyrmions at room temperature

Magnetic skyrmions are topologically stable spin textures that have attracted tremendous attention in the field of spintronics. As compared to Bloch skyrmions, which are typical for only few bulk chiral magnets, N\'{e}el skyrmions in magnetic multilayers [1, 2, 3] may be more ubiquitous and have the advantage that included layers of heavy metals provide efficient current induced spin-orbit torques. By optimizing the stacking structure, we present an experimental strategy towards nanometer-scale skyrmions at room temperature in the absence of a magnetic field. Furthermore, we discuss the experimental challenge of identifying the chiral nature of N\'{e}el skyrmions by using Lorentz transmission electron microscopy. Our results constitute an important step for enabling skyrmion based ultra-high density data storage, and for probing topological physics at room temperature. [1] W. Jiang, et al., Science, 349, 283 (2015). [2] S. Woo, et al., arXiv:1502.07376 (2015). [3] C. Moreau-Luchaire, et al., arXiv:1502.07853 (2015).   

Skyrmions in thin-film multilayers with interfacially-induced Dzyaloshinskii-Moriya interaction observed by MFM

By proper selection of interfaces in thin-film multilayers one can separately engineer the anisotropy, magnetization and Dzyaloshinskii-Moriya interaction (DMI), which is useful in the design of skyrmion materials. We use high-sensitivity, high-resolution magnetic force microscopy (MFM) in various applied magnetic fields to image the micromagnetic structures in multilayers based on symmetric-interface stacks of Pt/Co/Pt and asymmetric ones of Pt/Co/Ir. The former have domain sizes of several microns, whereas the latter show considerably smaller domain sizes. These are (246$\pm $40) nm independently of the demagnetization process used. We attribute the lower domain size to a net DMI. The calculated DMI in the asymmetric case is too small to support a skyrmion phase, but isolated skyrmions can exist. MFM experiments reveal skyrmions with a diameter below 50 nm, when the field is reduced from positive saturation. In negative fields these skyrmions are either incorporated into expanding domains or burst into a larger domain. Local DMI constants estimated from the bursting fields agree well with the average DMI constant. Our work demonstrates that MFM can detect skyrmions in thin films, and can help accelerate research in this field.   

Engineering of the anisotropy and Dzyaloshinskii-Moriya interaction energies in Pt-Co and Pt-Co-Cu heterostructures

It has previously been shown that perpendicular magnetic anisotropy is increased in Pt-Co-Pt structures by placing a Cu spacer between the top, diffuse Co-Pt interface.\footnote{S. Bandiera et al, \textbf{Appl. Phys. Lett.} 100, 142410 (2012)} However, including a spacer layer increases interfacial asymmetry in the system: a prerequisite for a strong Dzyaloshinskii-Moriya interaction (DMI) which governs helical spin structures such as skyrmions and chiral domain walls.\footnote{S. Emori et al, \textbf{Nature Mater.} 12, 611-616 (2013)} We show that the increased asymmetry significantly enhances DMI strength in Pt-Co-Cu-Pt heterostructures as compared to corresponding Pt-Co-Pt systems. We further show that one can control the characteristic length scales governing domain width by engineering the magnetostatic, anisotropy, and DMI energies in heavy-metal/ferromagnet heterostructures. These structures may provide insight into engineering the size of skyrmions in spintronic devices.   

Skyrmion bubble stability in thin films with strong Dzyaloshinskii-Moriya interaction

The Dzyaloshinskii-Moriya interaction (DMI) at heavy-metal/FM interfaces stabilizes chiral spin textures, such as magnetic skyrmions [1]. Magnetic skyrmions are applicable to energy efficient spintronics [2,3]. However, room temperature stability of skyrmion bubbles (SBs) has not been quantified experimentally. We show when the ratio of the DMI effective field to the perpendicular anisotropy field is large, expanding bubble domains leave behind fine-scale dendritic structure, consisting of coupled 360 degree domain walls (DW). Dendritic structures are manipulated to form stable SBs. We imaged SBs in Pt(3nm)/Co(0.9nm)/Gd(1nm)/GdOx(30nm) films using Kerr microscopy to characterize the stability of SBs. We show that the field stability of SBs is a strong function of the applied in-plane field. Increasing in-plane field reduces the annihilation threshold of the skyrmions. The SB annihilation field becomes deterministic at in-plane fields near the DMI effective field. Simulations show Bloch points are formed in the SB DW at high in-plane fields, leading to the deterministic collapse of the bubbles.[1] A. Fert et al., Nat. Nano., 8, 152-156 (2013) [2] S. Woo et al., arXiv:1502.07376 (2015) [3] A. Fert et al., arXiv:1502.07853 (2015)   

Skyrmion-induced bound states on the surface of 3D Topological Insulators

In this work, we study the interaction between the surface state of a 3D Topological Insulator and a skyrmion magnetic texture. The skyrmion texture couples to the spin of the surface state electron with strength $\Delta_S$. Vortex and hedgehog skyrmion and anti-skyrmion structures are considered and their interaction is compared. Due to the vortex structure, the interaction of the in-plane components can be neglected and a step function is used to describe the skyrmion magnetization profile. In the hedgehog case, it is shown that the in-plane components cannot be disregarded and thus a realistic description for the skyrmion is required. Working in the micromagnetic framework, we derive a macrospin description for the skyrmion using the variational principle and then numerically solve for the bound states. It is shown that the existense and properties of these states as a function of skyrmion size, strongly depend on the skyrmion type. Both vortex and hedgehog skyrmions or anti-skyrmions can induce bound states with energies $|E|<\Delta_S$. For the hedgehog skyrmion case however, bound state appearance depends on the chirality. Finally, the probability densities in these states are computed and it is demonstrated that the electrons are localized throughout the skyrmion region.   

Skyrmion-induced bound states in a superconductor

We consider a superconductor proximity coupled to a two-dimensional ferromagnetic film with a skyrmion texture. We predict the skyrmion bound states (SBS) that are induced in the superconductor, similar to the well-known Yu-Shiba-Rusinov (YSR) states. Using the T-matrix calculations and numerical modeling we calculate the spin-polarized local density of states in the superconductor in the vicinity of the skyrmion. The SBS wavefunctions have spatial power-law decay. Presence of the SBS suggests the mechanism by which superconductivity could facilitate an effective long-range interaction between skyrmions when their SBS wavefunctions overlap. \\ \\ arXiv:1511.01842   

Stability of skyrmion lattices and symmetries of Dzyaloshinskii-Moriya magnets

Recently, there has been substantial interest in realizations of skyrmions, in particular in 2D systems due to increased stability resulting from reduced dimensionality. A stable skyrmion, representing the smallest realizable magnetic texture, could be an ideal element for ultra-dense magnetic memories. Here, we use the most general form of the 2D free energy with Dzyaloshinskii-Moriya interactions constructed from general symmetry considerations reflecting the underlying system. We predict that skyrmion phase is robust and it is present even when the system lacks the in-plane rotational symmetry. In fact, the lowered symmetry leads to increased stability of vortex-antivortex lattices with four-fold symmetry and in-plane spirals, in some instances even in the absence of an external magnetic field. Our results relate different hexagonal and square cell phases to the symmetries of materials used for realizations of skyrmions. This will give clear directions for experimental rea lizations of hexagonal and square cell phases, and will allow engineering of skyrmions with unusual properties. We also predict striking differences in gyro-dynamics induced by spin currents for isolated skyrmions and for crystals where spin currents can be induced by charge carriers or by thermal magnons.   

Increasing skyrmion lattice stability: theory and experiment

Magnetic skyrmions are vortices of spins, considered to be topologically protected against perturbations, and envisaged as very possible next-generation information carriers due to their nanoscale size. In chiral ferromagnets they form a two-dimensional hexagonal array - the skyrmion lattice. A key challenge is that bulk skyrmions have been restricted so far to a tiny region in the temperature-field phase diagram. In this work we address theoretically the stability of the skyrmion lattice. We demonstrate that tuning anisotropy can lead to dramatic (20 times) enhancement of the skyrmion phase volume, which has been recently revealed in our experiment.   

Enhanced stability of skyrmions in magnets with broken mirror symmetry

Most previous work on skyrmion phases in chiral magnets with Dzyaloshinkii Moriya interactions (DMI) focuses on the case of broken bulk inversion symmetry. The skyrmion crystal is then stable only in a limited range of parameter space with easy-axis anisotropy. In this talk I will describe the effects [1] of including broken mirror or surface inversion symmetry which leads to a Rashba DMI, in addition to the Dresselhaus DMI arising from broken bulk inversion. I will show that increasing Rashba DMI leads to a progressively larger domain of stability for skyrmions, especially in the easy-plane anisotropy regime. In the latter regime the topological charge density shows an unusual internal structure, and isolated skyrmions cannot be embedded in a ferromagnetic background. Thus the homotopy group $\pi_2(S^2)$ method of classifying skyrmions fails. I will discuss a Chern number classification of these non-trivial skyrmions using maps from the 2-torus (the unit cell for skyrmion crystals) to the 2-sphere in spin space. Finally, I will discuss the elliptic cone phase, a new state that emerges for easy-axis anisotropy and broken mirror symmetry. [1] J. Rowland, S. Banerjee, and M. Randeria, arXiv:1509.07508v2.