An inverse transition of magnetic domain patterns in ultrathin films

Interlayer engineering of Fe3GeTe2: From 3D superlattice to 2D monolayer

The discoveries of ferromagnetism down to the atomically thin limit in van der Waals (vdW) crystals by mechanical exfoliation have enriched the family of magnetic thin films [C. Gong et al., Nature 546, 265-269 (2017) and B. Huang et al., Nature 546, 270-273 (2017)]. However, compared to the study of traditional magnetic thin films by physical deposition methods, the toolbox of the vdW crystals based on mechanical exfoliation and transfer suffers from low yield and ambient corrosion problem and now is facing new challenges to study magnetism. For example, the formation of magnetic superlattice is difficult in vdW crystals, which limits the study of the interlayer interaction in vdW crystals [M. Gibertini, M. Koperski, A. F. Morpurgo, K. S. Novoselov, Nat. Nanotechnol. 14, 408-419 (2019)]. Here, we report a strategy of interlayer engineering of the magnetic vdW crystal Fe3GeTe2 (FGT) by intercalating quaternary ammonium cations into the vdW spacing. Both three-dimensional (3D) vdW superlattice and two-dimensional (2D) vdW monolayer can be formed by using this method based on the amount of intercalant. On the one hand, the FGT superlattice shows a strong 3D critical behavior with a decreased coercivity and increased domain wall size, attributed to the co-engineering of the anisotropy, exchange interaction, and electron doping by intercalation. On the other hand, the 2D vdW few layers obtained by over-intercalation are capped with organic molecules from the bulk crystal, which not only enhances the ferromagnetic transition temperature (TC), but also substantially protects the thin samples from degradation, thus allowing the preparation of large-scale FGT ink in ambient environment.

Direct Observation of Magnetic Domain and Magnetization Reversal on Prussian Blue-Based Magnetic Films

Knowledge of the magnetic domain is indispensable for understanding the magnetostatic properties of magnets. However, to date, the magnetic domain has not yet been reported in the field of molecule-based magnets. Herein, we study the magnetic domains of molecule-based magnets. Two magnetic films of iron/chromium hexacyanidochromate FexCr1-x[Cr(CN)6]2/3·5H2O (x = 0; Film 1 and x = 0.2; Film 2) were prepared for investigation. The temperature evolution of surface magnetization was measured using magnetic force microscopy. Film 1 showed a magnetic domain below Curie temperature (TC) and its positive-magnetic polarization increased monotonously with decreasing temperature, while Film 2 showed positive magnetic polarization below TC and switches from positive to negative magnetization through a demagnetization state at 146 K. This study originally reports the temperature variation of the magnetization state at the magnetization reversal. The magnetic domains appeared as a maze pattern with an approximate domain size of one-to-several micrometers. This work shows that research on molecule-based magnets can be expanded from magnetochemistry to the magnetostatic engineering of bulk magnets, molecule-based magnetostatic engineering.

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.

Pattern Formation by Electric-Field Quench in a Mott Crystal

The control of the Mott phase is intertwined with the spatial reorganization of the electronic states. Out-of-equilibrium driving forces typically lead to electronic patterns that are absent at equilibrium, whose nature is however often elusive. Here, we unveil a nanoscale pattern formation in the Ca2RuO4 Mott insulator. We demonstrate how an applied electric field spatially reconstructs the insulating phase that, uniquely after switching off the electric field, exhibits nanoscale stripe domains. The stripe pattern has regions with inequivalent octahedral distortions that we directly observe through high-resolution scanning transmission electron microscopy. The nanotexture depends on the orientation of the electric field; it is nonvolatile and rewritable. We theoretically simulate the charge and orbital reconstruction induced by a quench dynamics of the applied electric field providing clear-cut mechanisms for the stripe phase formation. Our results open the path for the design of nonvolatile electronics based on voltage-controlled nanometric phases.

Tunable Magnetic Domain Patterns in Thickness-Gradient Nickel Films on Flexible PDMS Substrates

Flexible magnetoelectronic devices (based on magnetic films) have great application prospects in the fields of information storages, bionic robotics, and electronic skins. The intrinsic stress and external loading are very important to modulate the structures and properties of flexible magnetic films due to the magnetoelastic coupling effect. Here, we report on tunable magnetic domain patterns in thickness-gradient nickel (Ni) films deposited on flexible polydimethylsiloxane substrates. It is found that stripe magnetic domains spontaneously form in the Ni films and their sizes increase with the film thickness. The internal stress evolves from tensile to compressive states with decreasing film thickness, leading to the formation of cracks in thicker regions and wrinkles in thinner regions. Meanwhile, the orientations of stripe magnetic domains change from the gradient direction to the orthogonal direction. The structural features, evolution behaviors, and physical mechanisms of the cracks, wrinkles, and magnetic domains are analyzed based on the stress theory and magnetoelastic coupling. Periodic gradient Ni films with large-scale regulations of stripe magnetic domains are also realized by masking of copper grids. This study helps to better understand the magnetoelastic coupling effect in gradient flexible magnetic films and provides a technique to modulate anisotropic magnetic properties by designing specific film systems.

Strain-Driven Mixed-Phase Domain Architectures and Topological Transitions in Pb1- x Srx TiO3 Thin Films

The potential for creating hierarchical domain structures, or mixtures of energetically degenerate phases with distinct patterns that can be modified continually, in ferroelectric thin films offers a pathway to control their mesoscale structure beyond lattice-mismatch strain with a substrate. Here, it is demonstrated that varying the strontium content provides deterministic strain-driven control of hierarchical domain structures in Pb_{1- x} Sr_x TiO₃  solid-solution thin films wherein two types, c/a and a₁ /a₂ , of nanodomains can coexist. Combining phase-field simulations, epitaxial thin-film growth, detailed structural, domain, and physical-property characterization, it is observed that the system undergoes a gradual transformation (with increasing strontium content) from droplet-like a₁ /a₂  domains in a c/a domain matrix, to a connected-labyrinth geometry of c/a domains, to a disconnected labyrinth structure of the same, and, finally, to droplet-like c/a domains in an a₁ /a₂  domain matrix. A relationship between the different mixed-phase modulation patterns and its topological nature is established. Annealing the connected-labyrinth structure leads to domain coarsening forming distinctive regions of parallel c/a and a₁ /a₂  domain stripes, offering additional design flexibility. Finally, it is found that the connected-labyrinth domain patterns exhibit the highest dielectric permittivity.

Above-room-temperature strong intrinsic ferromagnetism in 2D van der Waals Fe3GaTe2 with large perpendicular magnetic anisotropy

The absence of two-dimensional (2D) van der Waals (vdW) ferromagnetic crystals with both above-room-temperature strong intrinsic ferromagnetism and large perpendicular magnetic anisotropy (PMA) severely hinders practical applications of 2D vdW crystals in next-generation low-power magnetoelectronic and spintronic devices. Here, we report a vdW intrinsic ferromagnetic crystal Fe₃GaTe₂ that exhibits record-high above-room-temperature Curie temperature (Tc, ~350-380 K) for known 2D vdW intrinsic ferromagnets, high saturation magnetic moment (40.11 emu/g), large PMA energy density (~4.79 × 10⁵J/m³), and large anomalous Hall angle (3%) at room temperature. Such large room-temperature PMA is better than conventional widely-used ferromagnetic films like CoFeB, and one order of magnitude larger than known 2D vdW intrinsic ferromagnets. Room-temperature thickness and angle-dependent anomalous Hall devices and direct magnetic domains imaging based on Fe₃GaTe₂ nanosheet have been realized. This work provides an avenue for room-temperature 2D ferromagnetism, electrical control of 2D ferromagnetism and promote the practical applications of 2D-vdW-integrated spintronic devices.

In isotropic two dimensional systems, long range ferromagnetic order is supressed by thermal fluctuations, and it is due to magnetic anisotropy that van der Waals magnetic materials can have ferromagnetic ordering at finite temperatures. Usually this magnetic anisotropy is relatively small, but in this manuscript Zhang et al make a two dimensional van der Waals material with exceptionally large perpendicular magnetic anisotropy and ferromagnetic ordering that exits up to 350 K.

Solution of disordered microphases in the Bethe approximation

The periodic microphases that self-assemble in systems with competing short-range attractive and long-range repulsive (SALR) interactions are structurally both rich and elegant. Significant theoretical and computational efforts have thus been dedicated to untangling their properties. By contrast, disordered microphases, which are structurally just as rich but nowhere near as elegant, have not been as carefully considered. Part of the difficulty is that simple mean-field descriptions make a homogeneity assumption that washes away all of their structural features. Here, we study disordered microphases by exactly solving a SALR model on the Bethe lattice. By sidestepping the homogenization assumption, this treatment recapitulates many of the key structural regimes of disordered microphases, including particle and void cluster fluids as well as gelation. This analysis also provides physical insight into the relationship between various structural and thermal observables, between criticality and physical percolation, and between glassiness and microphase ordering.

Thermally driven state in a spin-1 model with competing interactions

We study a recently proposed spin-1 model with competing antiferromagnetic first-neighbor interaction and a third-neighbor coupling mediated by nonmagnetic states, which reproduces topological features of the phase diagrams of high-T_{c} superconductors [S. A. Cannas and D. A. Stariolo, Phys. Rev. E 99, 042137 (2019)2470-004510.1103/PhysRevE.99.042137]. We employ a cluster mean-field approach to investigate effects of crystal field anisotropy on the phase transitions hosted by this model. At low temperatures, the temperature-crystal field phase diagram exhibits superantiferromagnetic (SAF), antiferromagnetic (AF), and paramagnetic (PM) phases. In addition, we found a thermally driven state between SAF and PM phases. This thermally driven state and the SAF phase appears in the phase diagram as a domelike structure. Our calculations indicate that only second-order phase transitions occur in the PM-AF phase boundary, as suggested by previous Monte Carlo simulations.

Imaging and control of critical fluctuations in two-dimensional magnets

Strong magnetization fluctuations are expected near the thermodynamic critical point of a continuous magnetic phase transition. Such critical fluctuations are highly correlated and in principle can occur at any time and length scales¹; they govern critical phenomena and potentially can drive new phases^2,3. Although critical phenomena in magnetic materials have been studied using neutron scattering, magnetic a.c. susceptibility and other techniques^4-6, direct real-time imaging of critical magnetization fluctuations remains elusive. Here we develop a fast and sensitive magneto-optical imaging microscope to achieve wide-field, real-time monitoring of critical magnetization fluctuations in single-layer ferromagnetic insulator CrBr₃. We track the critical phenomena directly from the fluctuation correlations and observe both slowing-down dynamics and enhanced correlation length. Through real-time feedback control of the critical fluctuations, we further achieve switching of magnetic states solely by electrostatic gating. The ability to directly image and control critical fluctuations in 2D magnets opens up exciting opportunities to explore critical phenomena and develop applications in nanoscale engines and information science.

Two Phases with Different Domain Wall Networks and a Reentrant Phase Transition in Bilayer Graphene under Strain

The analytical two-chain Frenkel-Kontorova model is used to describe domain wall networks in bilayer graphene upon biaxial stretching of one of the layers. We show that the commensurate-incommensurate phase transition leading to formation of a regular triangular domain wall network at the relative biaxial elongation of 3.0×10^{-3} is followed by the transition to another incommensurate phase with a striped network at the elongation of 3.7×10^{-3}. The reentrant transition to the phase with a triangular domain wall network is predicted for the elongation ∼10^{-2}.

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.

Evidence of Kosterlitz-Thouless phase transitions in the Ising model with dipolar interactions

The ferromagnetic bidimensional Ising model with dipolar interactions has been proposed to model ultrathin films with strong out-of-plane anisotropy. The phase diagram presents a rich phenomenology that includes low-temperature phases characterized by stripes of width n (h_{n}) and a high-temperature phase with domains of stripes with mutually perpendicular orientations, named tetragonal liquid (TL). The latter phase can be reached by two possible ways. One of them is the direct transition h_{n} to TL, and the other one is through an intermediate phase with orientational order but short-range positional disorder, named nematic phase (NM). The regions of the phase diagram where these transitions occur, as well as their character, remain an open question and are the object of the present work. In order to clarify this topic, intensive Monte Carlo simulations were performed by employing short-time dynamics as the main tool for studying the phase transition behavior. The dynamic evolution of the orientational order parameter and its moments are measured for selected values of the ratio between the ferromagnetic exchange and dipolar constants, called δ. The obtained results indicate that the intermediate NM phase is present for δ≥2 in narrow ranges of temperatures. Also, the results suggest that both transitions, i.e., h_{n}-NM and NM-TL, have a Kosterlitz-Thouless character. This type of topological transition is observed in continuous bidimensional models and have been proposed for discrete ones, as in the case of the present work.

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.

Patterning-Induced Ferromagnetism of Fe3GeTe2 van der Waals Materials beyond Room Temperature

Magnetic van der Waals (vdW) materials have emerged as promising candidates for spintronics applications, especially after the recent discovery of intrinsic ferromagnetism in monolayer vdW materials. There has been a critical need for tunable ferromagnetic vdW materials beyond room temperature. Here, we report a real-space imaging study of itinerant ferromagnet Fe₃GeTe₂ and the enhancement of its Curie temperature well above ambient temperature. We find that the magnetic long-range order in Fe₃GeTe₂ is characterized by an unconventional out-of-plane stripe-domain phase. In Fe₃GeTe₂ microstructures patterned by a focused ion beam, the out-of-plane stripe domain phase undergoes a surprising transition at 230 K to an in-plane vortex phase that persists beyond room temperature. The discovery of tunable ferromagnetism in Fe₃GeTe₂ materials opens up vast opportunities for utilizing vdW magnets in room-temperature spintronics devices.

Pathways to equilibrium orientation fluctuations in finite stripe-forming systems

Small-angle orientation fluctuations in ordered stripe-forming systems free of topological defects can exhibit aging and anisotropic growth of two length scales. In infinitely extended systems, the stripe orientation field develops a dominant modulation length λ_{∥}^{*}(t) in the direction parallel to the stripes, which increases with time t as λ_{∥}^{*}(t)∼t^{1/4}. Simultaneously, the orientation correlation length ξ_{⊥}(t) in the direction perpendicular to the stripes increases as ξ_{⊥}(t)∼t^{1/2} [Riesch et al., Interface Focus 7, 20160146 (2017)2042-889810.1098/rsfs.2016.0146]. Here we show that finite systems of size L_{⊥}×L_{∥} with periodic boundary conditions reach equilibrium when the dominant modulation length λ_{∥}^{*}(t) reaches the system size L_{∥} in the stripe direction. The equilibration time τ_{eq}^{∥} is solely determined by L_{∥}, with τ_{eq}^{∥}∼L_{∥}^{4}. In systems with L_{⊥}<L_{∥}^{2}/2πλ_{p}, where λ_{p} is the undulation penetration length, the initial aging and coarsening dynamics changes at the crossover time τ_{C}^{⊥}∼L_{⊥}^{2} to an aging and coarsening dynamics described by the one-dimensional Mullins-Herring equation, before reaching equilibrium at τ_{∥}^{eq}. Our work reveals the two pathways to equilibrium in stripe phases with periodic boundary conditions, the finite-size scaling behavior of equilibrium orientation fluctuations, and the characteristic exponents associated with the influence of a finite system size.

Motion and Interaction of Magnetic Dislocations in Alternating Magnetic Field

The behavior of magnetic dislocations (MDs) in an alternating harmonic magnetic field in iron garnets has been experimentally investigated. The results are presented for single-crystal plates in which the drift of domain walls is observed in fields of sound frequencies. It is found that MDs in a stripe domain structure are able to move not only along but also across domain walls. A pairwise interaction between magnetic dislocations when they approach each other to distances on the order of the sizes of the cores of MDs is revealed. The processes of the annihilation, mutual passing of magnetic dislocations through each other and overtaking are found. The features of the dynamic behavior of MDs are explained using a mechanism based on the presence of vertical Bloch lines in a structure of domain walls. MDs are formed at nucleation centers, and their nucleation field is lower than the drift-starting field, which corresponds to previously proposed dislocational mechanism of the drift. The dependencies of quantitative parameters of the drift and MDs on amplitude and frequency of the pumping field are determined. The behavior of MDs should be considered when analyzing the mechanisms for magnetization and temperature-dependent phase transitions in magnetic layers.

Scaling properties of ageing orientation fluctuations in stripe phases

We investigate the non-equilibrium dynamics of an ordered stripe-forming system free of topological defects. In particular, we study the ageing and the coarsening of orientation fluctuations parallel and perpendicular to the stripes via computer simulations based on a minimal phase-field model (model B with Coulomb interactions). Under the influence of noise, the stripe orientation field develops fluctuations parallel to the stripes, with the dominant modulation length λ*∥ increasing with time t as λ*∥ ∼ t1/4 and the correlation length perpendicular to the stripes ξ⊥θ increasing as ξ⊥θ ∼ t1/2. We explain these anisotropic coarsening dynamics with an analytic theory based on the linear elastic model for stripe displacements first introduced by Landau and Peierls. We thus obtain the scaling forms and the scaling exponents characterizing the correlation functions and the structure factor of the stripe orientation field. Our results reveal how the coarsening of orientation fluctuations prevents a periodically modulated phase free of topological defects from reaching equilibrium.

Programmable disorder in random DNA tilings

Scaling up the complexity and diversity of synthetic molecular structures will require strategies that exploit the inherent stochasticity of molecular systems in a controlled fashion. Here we demonstrate a framework for programming random DNA tilings and show how to control the properties of global patterns through simple, local rules. We constructed three general forms of planar network-random loops, mazes and trees-on the surface of self-assembled DNA origami arrays on the micrometre scale with nanometre resolution. Using simple molecular building blocks and robust experimental conditions, we demonstrate control of a wide range of properties of the random networks, including the branching rules, the growth directions, the proximity between adjacent networks and the size distribution. Much as combinatorial approaches for generating random one-dimensional chains of polymers have been used to revolutionize chemical synthesis and the selection of functional nucleic acids, our strategy extends these principles to random two-dimensional networks of molecules and creates new opportunities for fabricating more complex molecular devices that are organized by DNA nanostructures.

Phase transitions and multicritical behavior in the Ising model with dipolar interactions

In this work, the phase diagram of the ferromagnetic Ising model with dipole interactions is revisited with the aim of determining the nature of the phase transition between stripe-ordered phases with width n (h_{n}) and tetragonal liquid (TL) phases. Extensive Monte Carlo simulations are performed in order to study the short-time dynamic behavior of the observables for selected values of the ratio between the ferromagnetic exchange and dipolar constants δ. The obtained results indicate that the h_{1}-TL phase transition line is continuous up to δ=1.2585, while for the h_{2}-TL line a weak first-order character is found in the interval 1.2585≤δ≤1.36 and becomes continuous for 1.37≤δ≤1.9. This result suggests the existence of a tricritical point close to δ=1.37. When it is appropriate, the complete set of critical exponents is obtained, and in all the studied cases they depend on δ but do not belong to the Ising universality class. Furthermore, short-time dynamic studies reveal that at the point where the mentioned lines meet the h_{1}-h_{2} line, i.e., at δ=1.2585, the critical phase corresponding to the h_{1}-TL transition coexists with the h_{2} phase.

Phase transitions and critical phenomena in the two-dimensional Ising model with dipole interactions: A short-time dynamics study

The ferromagnetic Ising model with antiferromagnetic dipole interactions is investigated by means of Monte Carlo simulations, focusing on the characterization of the phase transitions between the tetragonal liquid and stripe of width h phases. The dynamic evolution of the physical observables is analyzed within the short-time regime for 0.5≤δ≤1.3, where δ is the ratio between the short-range exchange and the long-range dipole interaction constants. The obtained results for the interval 0.5≤δ≤1.2 indicate that the phase transition line between the h=1 stripe and tetragonal liquid phases is continuous. This finding contributes to clarifying the controversy about the order of this transition. This controversy arises from the difficulties introduced in the simulations due to the presence of long-range dipole interactions, such as an important increase in the simulation times that limits the system size used, strong finite size effects, as well as to the existence of multiple metastable states at low temperatures. The study of the short-time dynamics of the model allows us to avoid these hindrances. Moreover, due to the fact that the finite-size effects do not significantly affect the power-law behavior exhibited in the observables within the short-time regime, the results could be attributed to those corresponding to the thermodynamic limit. As a consequence of this, a careful characterization of the critical behavior for the whole transition line is performed by giving the complete set of critical exponents.

Tailoring the magnetic anisotropy of Py/Ni bilayer films using well aligned atomic steps on Cu(001)

Tailoring the spin orientation at the atomic scale has been a key task in spintronics technology. While controlling the out-of-plane to in-plane spin orientation has been achieved by a precise control of the perpendicular magnetic anisotropy at atomic layer thickness level, a design and control of the in-plane magnetic anisotropy has not yet been well developed. On well aligned atomic steps of a 6° vicinal Cu(001) surface with steps parallel to the [110] axis, we grow Py/Ni overlayer films epitaxially to permit a systematic exploration of the step-induced in-plane magnetic anisotropy as a function of both the Py and the Ni film thicknesses. We found that the atomic steps from the vicinal Cu(001) induce an in-plane uniaxial magnetic anisotropy that favors both Py and Ni magnetizations perpendicular to the steps, opposite to the behavior of Co on vicinal Cu(001). In addition, thickness-dependent study shows that the Ni films exhibit different magnetic anisotropy below and above ~6 ML Ni thickness.

Spin-stripe phase in a frustrated zigzag spin-1/2 chain

Motifs of periodic modulations are encountered in a variety of natural systems, where at least two rival states are present. In strongly correlated electron systems, such behaviour has typically been associated with competition between short- and long-range interactions, for example, between exchange and dipole-dipole interactions in the case of ferromagnetic thin films. Here we show that spin-stripe textures may develop also in antiferromagnets, where long-range dipole-dipole magnetic interactions are absent. A comprehensive analysis of magnetic susceptibility, high-field magnetization, specific heat and neutron diffraction measurements unveils β-TeVO4 as a nearly perfect realization of a frustrated (zigzag) ferromagnetic spin-1/2 chain. Notably, a narrow spin-stripe phase develops at elevated magnetic fields due to weak frustrated short-range interchain exchange interactions, possibly assisted by the symmetry-allowed electric polarization. This concept provides an alternative route for the stripe formation in strongly correlated electron systems and may help understanding of other widespread, yet still elusive, stripe-related phenomena.

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.

Magnetic inhomogeneity on a triangular lattice: the magnetic-exchange versus the elastic energy and the role of disorder

Inhomogeneity in the ground state is an intriguing, emergent phenomenon in magnetism. Recently, it has been observed in the magnetostructural channel of the geometrically frustrated α-NaMnO₂, for the first time in the absence of active charge degrees of freedom. Here we report an in-depth numerical and local-probe experimental study of the isostructural sister compound CuMnO₂ that emphasizes and provides an explanation for the crucial differences between the two systems. The experimentally verified, much more homogeneous, ground state of the stoichiometric CuMnO₂ is attributed to the reduced magnetoelastic competition between the counteracting magnetic-exchange and elastic-energy contributions. The comparison of the two systems additionally highlights the role of disorder and allows the understanding of the puzzling phenomenon of phase separation in uniform antiferromagnets.

Inverse transitions in a spin-glass model on a scale-free network

In this paper, we will investigate critical phenomena by considering a model spin glass on scale-free networks. For this purpose, we consider the Ghatak-Sherrington (GS) model, a spin-1 spin-glass model with a crystal field, instead of the usual Ising-type model. Scale-free networks on which the GS model is placed are constructed from the static model, in which the number of vertices is fixed from the beginning. On the basis of the replica-symmetric solution, we obtain the analytical solutions, i.e., free energy and order parameters, and we derive the various phase diagrams consisting of the paramagnetic, ferromagnetic, and spin-glass phases as functions of temperature T, the degree exponent λ, the mean degree K, and the fraction of the ferromagnetic interactions ρ. Since the present model is based on the GS model, which considers the three states (S = 0, ± 1), the S = 0 state plays a crucial role in the λ-dependent critical behavior: glass transition temperature T(g) has a finite value, even when 2 < λ < 3. In addition, when the crystal field becomes nonzero, the present model clearly exhibits three types of inverse transitions, which occur when an ordered phase is more entropic than a disordered one.

Spin-1 Hopfield model under a random field

The goal of the present work is to investigate the role of trivial disorder and nontrivial disorder in the three-state Hopfield model under a Gaussian random field. In order to control the nontrivial disorder, the Hebb interaction is used. This provides a way to control the system frustration by means of the parameter a=p/N, varying from trivial randomness to a highly frustrated regime, in the thermodynamic limit. We performed the thermodynamic analysis using the one-step replica-symmetry-breaking mean field theory to obtain the order parameters and phase diagrams for several strengths of a, the anisotropy constant, and the random field.

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.

Spin-glass splitting in the quantum Ghatak-Sherrington model

We propose an expanded spin-glass model, called the quantum Ghatak-Sherrington model, which considers spin-1 quantum spin operators in a crystal field and in a transverse field. The analytic solutions and phase diagrams of this model are obtained by using the one-step replica symmetry-breaking ansatz under the static approximation. Our results represent the splitting within one spin-glass (SG) phase depending on the values of crystal and transverse fields. The two separated SG phases, characterized by a density of filled states, show certain differences in their shapes and phase boundaries. Such SG splitting becomes more distinctive when the degeneracy of the empty states of spins is larger than one of their filled states.

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.

Inverse freezing in a cluster Ising spin-glass model with antiferromagnetic interactions

Inverse freezing is analyzed in a cluster spin-glass (SG) model that considers infinite-range disordered interactions between magnetic moments of different clusters (intercluster interaction) and short-range antiferromagnetic coupling J(1) between Ising spins of the same cluster (intracluster interaction). The intercluster disorder J is treated within a mean-field theory by using a framework of one-step replica symmetry breaking. The effective model obtained by this treatment is computed by means of an exact diagonalization method. With the results we build phase diagrams of temperature T/J versus J(1)/J for several sizes of clusters n(s) (number of spins in the cluster). The phase diagrams show a second-order transition from the paramagnetic phase to the SG order at the freezing temperature T(f) when J(1)/J is small. The increase in J(1)/J can then destroy the SG phase. It decreases T(f)/J and introduces a first-order transition. In addition, inverse freezing can arise at a certain range of J(1)/J and large enough n(s). Therefore, the nontrivial frustration generated by disorder and short-range antiferromagnetic coupling can introduce inverse freezing spontaneously.

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.

Stripe-tetragonal phase transition in the two-dimensional Ising model with dipole interactions: partition function zeros approach

We have performed multicanonical simulations to study the critical behavior of the two-dimensional Ising model with dipole interactions. This study concerns the thermodynamic phase transitions in the range of the interaction δ where the phase characterized by striped configurations of width h = 1 is observed. Controversial results obtained from local update algorithms have been reported for this region, including the claimed existence of a second-order phase transition line that becomes first order above a tricritical point located somewhere between δ = 0.85 and 1. Our analysis relies on the complex partition function zeros obtained with high statistics from multicanonical simulations. Finite size scaling relations for the leading partition function zeros yield critical exponents ν that are clearly consistent with a single second-order phase transition line, thus excluding such a tricritical point in that region of the phase diagram. This conclusion is further supported by analysis of the specific heat and susceptibility of the orientational order parameter.

Giant Skyrmions stabilized by dipole-dipole interactions in thin ferromagnetic films

Motivated by a recent magnetization reversal experiment on a TbFeCo thin film, we study a topological excitation in the anisotropic nonlinear sigma model together with the Zeeman and magnetic dipole-dipole interactions. Dipole-dipole interactions turn a ferromagnet into a frustrated spin system, which allows a nontrivial spin texture such as a giant Skyrmion. We derive an analytic formula for the Skyrmion radius. The radius is controllable by the external magnetic field. It is intriguing that a Skyrmion may have already been observed as a magnetic domain. A salient feature is that a single Skyrmion can be created or destroyed experimentally. An analysis is made also on Skyrmions in chiral magnets.

Thermodynamic first order transition and inverse freezing in a 3D spin glass

We present a numerical study of the random Blume-Capel model in three dimensions. The phase diagram is characterized by spin-glass-paramagnet phase transitions of both first and second order in the thermodynamic sense. Numerical simulations are performed using the exchange Monte Carlo algorithm, providing clear evidence for inverse freezing. The main features at criticality and in the phase coexistence region are investigated. We are not privy to other 3D short-range systems with quenched disorder undergoing inverse freezing.

Experimental phase diagram of perpendicularly magnetized ultrathin ferromagnetic films

We image the domain patterns in perpendicularly magnetized ultrathin Fe films on Cu(100) as a function of the temperature T and the applied magnetic field H. Between the low-field stripe phase and the high-field uniform phase we find a bubble phase, consisting of reversed circular domains in a homogeneous background. The curvature of the transition lines in the H-T parameter space is in contrast to the general expectations. The pattern transformations show yet undetected scaling properties.

Unusual polarization patterns in flat epitaxial ferroelectric nanoparticles

We investigate the effects of a lattice misfit strain on a ground state and polarization patterns in flat perovskite nanoparticles (nanoislands of BaTiO3 and PZT) with the use of an ab initio derived effective Hamiltonian. We show that the strain strongly controls the balance between the depolarizing field and the polarization anizotropy in determining the equilibrium polarization patterns. Compressive strain favors 180 degrees stripe or tweed domains while a tensile strain leads to in-plane vortex formation, with the unusual intermediate phase(s) where both ordering motifs coexist. The results may allow us to explain contradictions in recent experimental data for ferroelectric nanoparticles.

Phase diagram of a solution undergoing inverse melting

The phase diagram of alpha -cyclodextrin/water/4-methylpyridine solutions, a system undergoing inverse melting, has been studied by differential scanning calorimetry, rheological methods, and x-ray diffraction. Two different fluid phases separated by a solid region have been observed in the high alpha -cyclodextrin concentration range (c > or =150 mg/ml) . Decreasing c , the temperature interval where the solid phase exists decreases and eventually disappears, and a first-order phase transition is observed between the two different fluid phases.

Quantum mazes: luminescent labyrinthine semiconductor nanocrystals having a narrow emission spectrum

We exploit the polytypism of group II-VI semiconductors and the long-range dipolar interactions typical of CdSe nanoparticle formation to modulate the geometrical structure and the optical emission properties of novel branched CdSe nanocrystals through shape-dependent quantum confinement effects. X-ray diffraction confirms that these materials incorporate crystalline domains of cubic zinc-blende and hexagonal wurtzite within a polycrystalline growth form whose geometry can be controlled by varying thermodynamic conditions. In particular, labyrinthine-shaped nanoparticles of tunable dimensions are reproducibly synthesized based on a heterogeneous reaction between cadmium acetate in a solution in hexadecylamine and trioctylphosphine with Se as a solid precursor at a relatively low temperature (110 degrees C). The resulting highly branched CdSe structures resemble labyrinthine patterns observed in magnetic fluids and superconductors films in magnetic fields, and in lipid films and other materials where strong dipolar interactions "direct" large-scale pattern formation. Surprisingly, these novel maze-like structures emit light within a narrow bandwidth (full-width at half-maximum approximately equal to 33-42 nm) of the visible spectrum (508 nm < lambda < 563 nm), so the regular dimensions of the core regions of these branched structures govern their emission characteristics rather than overall nanoparticle size. This property should make these materials attractive for applications where luminescent materials having tunable emission characteristics and a narrow emission frequency range are required, along with the insensitivity of the particles' luminescent properties to environmental conditions.

Magnetic bubble domain phase at the spin reorientation transition of ultrathin Fe/Ni/Cu(001) film

Magnetic domain phases of ultrathin Fe/Ni/Cu(001) are studied using photoemission electron microscopy at the spin reorientation transition (SRT). We observe a new magnetic phase of bubble domains within a narrow SRT region after applying a nearly in-plane magnetic field pulse to the sample. By applying the magnetic field pulse along different directions, we find that the bubble domain phase exists only if the magnetic field direction is less than approximately 10 degrees relative to the sample surface. A temperature dependent measurement shows that the bubble domain phase becomes unstable above 370 K.

Ultrafast compact classical Mott polarimeter

An ultrafast compact classical Mott detector is described. The efficiency of the polarimeter is epsilon = 6 x 10(-4) and the maximum counting rate approximately 2000 kcps. The Mott polarimeter employs photomultipliers with scintillators as electron energy sensitive detectors with low dark noise. The photomultipliers and scintillators are placed in vacuum. With this choice of technology, it will be possible to build a classical Mott detector with a bulk size of cubic decimeter in the future.

Observation of stripe mobility in a dipolar frustrated ferromagnet

We have discovered two novel aspects of the stripe-domain to paramagnetic transition in perpendicularly magnetized Fe films on Cu(100). First, the width of the stripes carrying oppositely oriented spins decreases, close to the transition temperature, with a power law. Second, in a small temperature interval close to the transition temperature, the stripes--which form stationary patterns at low temperatures--become mobile. Various theoretical works have predicted stripe mobility in similar frustrated systems but no direct proof of this phenomenon has been reported so far.

Dynamic origin of stripe domains

We investigate stripe domain formation in nanometer sized Co bars. The magnetic equilibrium states and the magnetic spin wave frequencies are obtained from micromagnetic-like simulations. We find that the lowest frequency standing-wave mode has the same spatial structure as the stripe domains at remanence and it goes soft at the field where the stripe domains emerge. We show, therefore, that the final domain structure at remanence, which is not the configuration with lowest energy, is predicted from a high-field analysis of the frequencies of the standing spin waves.