Experimental phase diagram of perpendicularly magnetized ultrathin ferromagnetic films

Inverse transitions and disappearance of the λ-line in the asymmetric random-field Ising and Blume-Capel models

We report on reentrance in the random-field Ising and Blume-Capel models, induced by an asymmetric bimodal random-field distribution. The conventional continuous line of transitions between the paramagnetic and ferromagnetic phases, the λ-line, is wiped away by the asymmetry. The phase diagram, then, consists of only first-order transition lines that always end at ordered critical points. We find that, while for symmetric random-field distributions there is no reentrance, the asymmetry in the random-field results in a range of temperatures for which magnetization shows reentrance. While this does not give rise to an inverse transition in the Ising model, for the Blume-Capel model, however, there is a line of first-order inverse phase transitions that ends at an inverse-ordered critical point. We show that the location of the inverse transitions can be inferred from the ground-state phase diagram of the model.

Magnetic Field Magnitudes Needed for Skyrmion Generation in a General Perpendicularly Magnetized Film

Due to its topological protection, the magnetic skyrmion has been intensively studied for both fundamental aspects and spintronics applications. However, despite recent advancements in skyrmion research, the deterministic creation of isolated skyrmions in a generic perpendicularly magnetized film is still one of the most essential and challenging techniques. Here, we present a method to create magnetic skyrmions in typical perpendicular magnetic anisotropy (PMA) films by applying a magnetic field pulse and a method to determine the magnitude of the required external magnetic fields. Furthermore, to demonstrate the usefulness of this result for future skyrmion research, we also experimentally study the PMA dependence on the minimum size of skyrmions. Although field-driven skyrmion generation is unsuitable for device application, this result can provide an easier approach for obtaining isolated skyrmions, making skyrmion-based research more accessible.

Magnetic reversal in perpendicularly magnetized antidot arrays with intrinsic and extrinsic defects

Defects can significantly affect performance of nanopatterned magnetic devices, therefore their influence on the material properties has to be understood well before the material is used in technological applications. However, this is experimentally challenging due to the inability of the control of defect characteristics in a reproducible manner. Here, we construct a micromagnetic model, which accounts for intrinsic and extrinsic defects associated with the polycrystalline nature of the material and with corrugated edges of nanostructures. The predictions of the model are corroborated by the measurements obtained for highly ordered arrays of circular Co/Pd antidots with perpendicular magnetic anisotropy. We found that magnetic properties, magnetic reversal and the evolution of the domain pattern are strongly determined by density of defects, heterogeneity of nanostructures, and edge corrugations. In particular, an increase in the Néel domain walls, as compared to Bloch walls, was observed with a increase of the antidot diameters, suggesting that a neck between two antidots can behave like a nanowire with a width determined by the array period and antidot size. Furthermore, the presence of edge corrugations can lead to the formation of a network of magnetic bubbles, which are unstable in non-patterned flat films.

Three-state model with competing antiferromagnetic and pairing interactions

Motivated by the rich phase diagram of the high-temperature superconductors, we introduce a pseudospin model with three state variables which can be interpreted as two states (spin ±1/2) particles and holes. The Hamiltonian has a term which favors antiferromagnetism and an additional competing interaction which favors bonding between pairs of antiparallel spins mediated by holes. For low concentration of holes the dominant interaction between particles has antiferromagnetic character, leading to an antiferromagnetic phase in the temperature-hole concentration phase diagram, qualitatively similar to the antiferromagnetic phase of doped Mott insulators. For growing concentration of holes antiferromagnetic order is weakened and a phase with a different kind of order mediated by holes appears. This last phase has the form of a dome in the T-hole concentration plane. The whole phase diagram resembles those of some families of high-T_{c} superconductors. We compute the phase diagram in the mean-field approximation and characterize the different phase transitions through Monte Carlo simulations.

On the mechanism behind the inverse melting in systems with competing interactions

The competition between a short range attractive interaction and a nonlocal repulsive interaction promote the appearance of modulated phases. In this work we present the microscopic mechanisms leading to the emergence of inverse transitions in such systems by considering a thorough mean-field analysis of a variety of minimal models with different competing interactions. We identify the specific connections between the characteristic energy of the homogeneous and modulated phases and the observed reentrant behaviors in the phase diagram. In particular, we find that reentrance is appreciable when the characteristic energy cost of the homogeneous and modulated phases are comparable to each other, and for systems in which the local order parameter is limited. In the asymptotic limit of high energy cost of the homogeneous phase we observe that the degree of reentrance decreases exponentially with the ratio of the characteristic energy cost of homogeneous and modulated phases. These mean-field results are confronted with Langevin simulations of an effective coarse grained model, confirming the expected extension of the reentrance in the phase diagram. These results shed new light on many systems undergoing inverse melting transitions by qualitatively improving the understanding of the interplay of entropy and energy around the inverse melting points.

Straight motion of half-integer topological defects in thin Fe-N magnetic films with stripe domains

In thin magnetic films with perpendicular magnetic anisotropy, a periodic “up-down” stripe-domain structure can be originated at remanence, on a mesoscopic scale (~100 nm) comparable with film thickness, by the competition between short-range exchange coupling and long-range dipolar interaction. However, translational order is perturbed because magnetic edge dislocations are spontaneously nucleated. Such topological defects play an important role in magnetic films since they promote the in-plane magnetization reversal of stripes and, in superconductor/ferromagnet hybrids, the creation of superconducting vortex clusters. Combining magnetic force microscopy experiments and micromagnetic simulations, we investigated the motion of two classes of magnetic edge dislocations, randomly distributed in an \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\rm{N}}}_{2}^{+}$$\end{document}N2+-implanted Fe film. They were found to move in opposite directions along straight trajectories parallel to the stripes axis, when driven by a moderate dc magnetic field. Using the approximate Thiele equation, analytical expressions for the forces acting on such magnetic defects and a microscopic explanation for the direction of their motion could be obtained. Straight trajectories are related to the presence of a periodic stripe domain pattern, which imposes the gyrotropic force to vanish even if a nonzero, half-integer topological charge is carried by the defects in some layers across the film thickness.

Orientational ordering of lamellar structures on closed surfaces

Self-assembly of particles with short-range attraction and long-range repulsion interactions on a flat and on a spherical surface is compared. Molecular dynamics simulations are performed for the two systems having the same area and the density optimal for formation of stripes of particles. Structural characteristics, e.g., a cluster size distribution, a number of defects, and an orientational order parameter (OP), as well as the specific heat, are obtained for a range of temperatures. In both cases, the cluster size distribution becomes bimodal and elongated clusters appear at the temperature corresponding to the maximum of the specific heat. When the temperature decreases, orientational ordering of the stripes takes place and the number of particles per cluster or stripe increases in both cases. However, only on the flat surface, the specific heat has another maximum at the temperature corresponding to a rapid change of the OP. On the sphere, the crossover between the isotropic and anisotropic structures occur in a much broader temperature interval; the orientational order is weaker and occurs at significantly lower temperature. At low temperature, the stripes on the sphere form spirals and the defects resemble defects in the nematic phase of rods adsorbed at a sphere.

Nucleation and annihilation of skyrmions in Mn2CoAl observed through the topological Hall effect

Magnetic skyrmions are topologically protected spin textures with great technological potential. These topologically non-trivial non-coplanar spin textures give rise to a topological Hall effect, enabling the purely electronic detection of magnetic skyrmions. We report a clear topological Hall effect in thin films of the the Heusler alloy Mn₂CoAl, a ferromagnetic spin-gapless semiconductor, capped by a thin layer of Pd. We exploit the strong thickness- and temperature-dependence of the anomalous Hall effect in this system, tuning it to zero to enable the unambiguous measurement of the topological Hall effect, which is observed for temperatures between 3 K and 280 K. The topological Hall effect is evidence of skyrmions, and we demonstrate the simultaneous coexistence of opposite polarity skyrmions using a novel method involving minor field loops of the Hall effect.

Critical exponents and scaling invariance in the absence of a critical point

The paramagnetic-to-ferromagnetic phase transition is classified as a critical phenomenon due to the power-law behaviour shown by thermodynamic observables when the Curie point is approached. Here we report the observation of such a behaviour over extraordinarily many decades of suitable scaling variables in ultrathin Fe films, for certain ranges of temperature T and applied field B. This despite the fact that the underlying critical point is practically unreachable because protected by a phase with a modulated domain structure, induced by the dipole–dipole interaction. The modulated structure has a well-defined spatial period and is realized in a portion of the (T, B) plane that extends above the putative critical temperature, where thermodynamic quantities do not display any singularity. Our results imply that scaling behaviour of macroscopic observables is compatible with an avoided critical point.

Thermodynamic observables develop power laws and singularities when approaching the Curie point of a ferromagnetic phase transition. Here, Saratz et al. demonstrate that topological excitations (that is, magnetic domains in Fe/Cu(100) films that even persist above the Curie point) remove those singularities compatibly with an avoided critical point.

Modeling magnetization curves in magnetic thin films with striped patterns

In this work, we study magnetic thin films presenting magnetic stripe patterns. A fingerprint of such domains is a linear behavior of the in-plane magnetization curves below a given saturation field. We present free energy models for the in-plane magnetization curves which permit us to extract key geometrical information about the stripe patterns, such as the maximum canted angle of the magnetization and the domain wall width. As an example, we discuss in this work magnetization curves for Fe(1-x)Ga(x) magnetic films which present a stripe pattern with a period of 160 nm and we found a typical maximum canted angle of 85° and a domain wall width around 30 nm.

Room-Temperature Creation and Spin-Orbit Torque Manipulation of Skyrmions in Thin Films with Engineered Asymmetry

Magnetic skyrmions, which are topologically protected spin textures, are promising candidates for ultralow-energy and ultrahigh-density magnetic data storage and computing applications. To date, most experiments on skyrmions have been carried out at low temperatures. The choice of available materials is limited, and there is a lack of electrical means to control skyrmions in devices. In this work, we demonstrate a new method for creating a stable skyrmion bubble phase in the CoFeB-MgO material system at room temperature, by engineering the interfacial perpendicular magnetic anisotropy of the ferromagnetic layer. Importantly, we also demonstrate that artificially engineered symmetry breaking gives rise to a force acting on the skyrmions, in addition to the current-induced spin-orbit torque, which can be used to drive their motion. This room-temperature creation and manipulation of skyrmions offers new possibilities to engineer skyrmionic devices. The results bring skyrmionic memory and logic concepts closer to realization in industrially relevant and manufacturable thin film material systems.

Nematic phase in the J(1)-J(2) square-lattice Ising model in an external field

The J(1)-J(2) Ising model in the square lattice in the presence of an external field is studied by two approaches: the cluster variation method (CVM) and Monte Carlo simulations. The use of the CVM in the square approximation leads to the presence of a new equilibrium phase, not previously reported for this model: an Ising-nematic phase, which shows orientational order but not positional order, between the known stripes and disordered phases. Suitable order parameters are defined, and the phase diagram of the model is obtained. Monte Carlo simulations are in qualitative agreement with the CVM results, giving support to the presence of the new Ising-nematic phase. Phase diagrams in the temperature-external field plane are obtained for selected values of the parameter κ=J(2)/|J(1)| which measures the relative strength of the competing interactions. From the CVM in the square approximation we obtain a line of second order transitions between the disordered and nematic phases, while the nematic-stripes phase transitions are found to be of first order. The Monte Carlo results suggest a line of second order nematic-disordered phase transitions in agreement with the CVM results. Regarding the stripes-nematic transitions, the present Monte Carlo results are not precise enough to reach definite conclusions about the nature of the transitions.

Real-time observation of domain fluctuations in a two-dimensional magnetic model system

Domain patterns of perpendicularly magnetized ultra-thin ferromagnetic films are often determined by the competition of the short range but strong exchange interaction favouring ferromagnetic alignment of magnetic moments and the long range but weak antiferromagnetic dipolar interaction. Detailed phase diagrams of the resulting stripe domain patterns have been evaluated in recent years; however, the domain fluctuations in these pattern forming systems have not been studied in great detail so far. Here we show that domain fluctuations can be observed in ultra-thin two-dimensional ferromagnetic Fe/Ni/Cu(001) films with perpendicular magnetization in the stripe domain phase. Non-stroboscopic time-resolved threshold photoemission electron microscopy with high temporal resolution allows analysing the dynamic fingerprint of the topological excitations in the nematic domain phase. Furthermore, proliferation of domain ending defects in the vicinity of the spin reorientation transition is witnessed.

Nematic phase in stripe-forming systems within the self-consistent screening approximation

We show that in order to describe the isotropic-nematic transition in stripe-forming systems with isotropic competing interactions of the Brazovskii class it is necessary to consider the next to leading order in a 1/N approximation for the effective Hamiltonian. This can be conveniently accomplished within the self-consistent screening approximation. We solve the relevant equations and show that the self-energy in this approximation is able to generate the essential wave vector dependence to account for the anisotropic character of a two-point correlation function characteristic of a nematic phase.

Dipolar-energy-activated magnetic domain pattern transformation driven by thermal fluctuations

Two-dimensional ferromagnetic layers can serve as a playground for the study of basic physical properties of various pattern forming systems by virtue of their tuneable magnetic properties. Here we use threshold photoemission magnetic circular dichroism in combination with photoemission electron microscopy to investigate ultra-thin ferromagnetic Fe/Ni/Cu(001) films in the stripe domain phase near the spin reorientation transition as a function of film thickness, temperature and effective anisotropy. Here we report a metastable domain state with domain width larger than the thermodynamically stable one as a result of a rapid reduction of the anisotropy. The transformation into the equilibrium state takes place via the propagation of a transition front, which originates from defined steps in the film thickness.

Nematic phase in two-dimensional frustrated systems with power-law decaying interactions

We address the problem of orientational order in frustrated interaction systems as a function of the relative range of the competing interactions. We study a spin model Hamiltonian with short-range ferromagnetic interaction competing with an antiferromagnetic component that decays as a power law of the distance between spins, 1/r(α). These systems may develop a nematic phase between the isotropic disordered and stripe phases. We evaluate the nematic order parameter using a self-consistent mean-field calculation. Our main result indicates that the nematic phase exists, at mean-field level, provided 0<α<4. We analytically compute the nematic critical temperature and show that it increases with the range of the interaction, reaching its maximum near α~0.5. We also compute a coarse-grained effective Hamiltonian for long wavelength fluctuations. For 0<α<4 the inverse susceptibility develops a set of continuous minima at wave vectors |k[over arrow]|=k(0)(α) which dictate the long-distance physics of the system. For α→4, k(0)→0, making the competition between interactions ineffective for greater values of α.

Coarse-grained models of stripe forming systems: phase diagrams, anomalies, and scaling hypothesis

Two coarse-grained models which capture some universal characteristics of stripe forming systems are studied. At high temperatures, the structure factors of both models attain their maxima on a circle in reciprocal space, as a consequence of generic isotropic competing interactions. Although this is known to lead to some universal properties, we show that the phase diagrams have important differences, which are a consequence of the particular k dependence of the fluctuation spectrum in each model. The phase diagrams are computed in a mean field approximation and also after inclusion of small fluctuations, which are shown to modify drastically the mean field behavior. Observables like the modulation length and magnetization profiles are computed for the whole temperature range accessible to both models and some important differences in behavior are observed. A stripe compression modulus is computed, showing an anomalous behavior with temperature as recently reported in related models. Also, a recently proposed scaling hypothesis for modulated systems is tested and found to be valid for both models studied.

Finite-temperature phase diagram of ultrathin magnetic films without external fields

We analyze the finite-temperature phase diagram of ultrathin magnetic films by introducing a mean-field theory, valid in the low-anisotropy regime, i.e., close to the spin reorientation transition. The theoretical results are compared with Monte Carlo simulations carried out on a microscopic Heisenberg model. Connections between the finite-temperature behavior and the ground-state properties of the system are established. Several properties of the stripe pattern, such as the presence of canted states, the stripe width variation phenomenon, and the associated magnetization profiles, are also analyzed.

Topological defects and misfit strain in magnetic stripe domains of lateral multilayers with perpendicular magnetic anisotropy

Stripe domains are studied in perpendicular magnetic anisotropy films nanostructured with a periodic thickness modulation that induces the lateral modulation of both stripe periods and in-plane magnetization. The resulting system is the 2D equivalent of a strained superlattice with properties controlled by interfacial misfit strain within the magnetic stripe structure and shape anisotropy. This allows us to observe, experimentally for the first time, the continuous structural transformation of a grain boundary in this 2D magnetic crystal in the whole angular range. The magnetization reversal process can be tailored through the effect of misfit strain due to the coupling between disclinations in the magnetic stripe pattern and domain walls in the in-plane magnetization configuration.