We explore the equilibrium properties of a two-dimensional Ising spin model with short-range exchange and long-range dipolar interactions as a function of the applied magnetic field H. The model is studied through extensive Monte Carlo simulations that show the existence of many modulated phases with long range orientational order for a wide range of fields. These phases are characterized by different wave vectors that change discontinuously with the magnetic field. We provide numerical evidence supporting the existence of first order transitions between these phases. At higher fields our results suggest a Kosterliz-Thouless scenario for the transition from a bubble to a ferromagnetic phase.
The dipolar-random field Ising model (DRFIM) recently introduced displays a behaviour that can be connected to the magnetization of bidimensional magnetic media. Epitaxial magnetic garnet films seem to be the ideal test material for such a model. In this work the results of the measurements performed on garnet samples are presented, as well as the comparisons with simulation results obtained by the DRFIM. The results prove that a variety of hysteresis loops are well described by the DRFIM. This capability does not derive from the fine tuning of a great number of parameters, but by the interpla…
We describe a novel type of magnetic domain wall which, in contrast to Bloch or Neel walls, is non-localized and, in a certain temperature range, non-monotonic. The wall appears as the mean-field solution of the two-dimensional ferromagnetic Ising model frustrated by the long-ranged dipolar interaction. We provide experimental evidence of this wall delocalization in the stripe-domain phase of perpendicularly magnetized ultrathin magnetic films. In agreement with experimental results, we find that the stripe width decreases with increasing temperature and approaches a finite value at the Curie-…
Magnetic dipolar mode or magnetostatic (MS) oscillations in ferrite samples have the wavelength much smaller than the electromagnetic wavelength at the same frequency and, at the same time, much larger than the exchange interaction spin wavelength. This intermediate position between the electromagnetic and spin wave (exchange interaction) processes reveals very special behaviors of the geometrical effects. It was shown recently that magnetic dipolar mode oscillations in a normally magnetized ferromagnetic disk are characterized by discrete energy levels resulting from the structural confinemen…
We investigate the dynamics of a magnetic system consisting of two magnetic moments coupled by either exchange, dipole-dipole, or Dzyalozhinski-Moriya interaction. We compare the switching mechanisms and switching rates as induced by the three couplings. For each coupling and each configuration of the two anisotropy axes, we describe the switching modes and, using the kinetic theory of Langer, we provide (semi-)analytical expressions for the switching rate. We then compare the three interactions with regard to their efficiency in the reversal of the net magnetic moment of the dimer. We also in…
Magnetic domain structures are a fascinating area of study with interest deriving both from technological applications and fundamental scientific questions. The nature of the striped magnetic phases observed in ultra-thin films is one such intriguing system. The non-equilibrium dynamics of such systems as they evolve toward equilibrium has only recently become an area of interest and previous work on model systems showed evidence of complex, slow dynamics with glass-like properties as the stripes order mesoscopically. To aid in the characterization of the observed phases and the nature of the …
We derived the analytical forms of refractive index and Snell law for dipolar-exchange spin waves of reflection and refraction at a magnetically heterogeneous interface in a geometrically confined planer structure composed of different magnetic thin films from a microscopic scattering approach. A novel behavior, the optical total reflection, was demonstrated for spin waves with a specific interface between Yttrium iron garnet (Y3Fe5O12) and Permalloy (Ni80Fe20), by analytical and micromagnetic numerical calculations.
We investigate the effect of coupling (intensity and nature), applied field, and anisotropy on the spin dynamics of a multi-layer system composed of a hard magnetic slab coupled to a soft magnetic slab through a nonmagnetic spacer. The soft slab is modeled as a stack of several atomic layers while the hard layer, of a different material, is either considered as a pinned macroscopic magnetic moment or as an atomic multi-layer system. We compute the magnetization profile and hysteresis loop of the multi-layer system by solving the Landau-Lifshitz equations for the net magnetic moment of each (at…
The effect of dipolar and exchange interactions within pairs of paramagnetic electronic states on Pauli-blockade-controlled spin-dependent transport and recombination rates during magnetic resonant spin excitation is studied numerically using the superoperator Liouville-space formalism. The simulations reveal that spin-Rabi nutation induced by magnetic resonance can control transition rates which can be observed experimentally by pulsed electrically (pEDMR) and pulsed optically (pODMR) detected magnetic resonance spectroscopies. When the dipolar coupling exceeds the difference of the pair part…
In this paper we show that the vortex states can be created not only in magnetically soft "small" (with the dipolar and exchange energy competition) cylindrical dots, but also in magnetically saturated "big" (when the exchange is neglected) cylindrical dots. A property associated with a vortex structure becomes evident from an analysis of confinement phenomena of magnetic oscillations in a ferrite disk with a dominating role of magnetic-dipolar (non-exchange-interaction) spectra. In this case the scalar (magnetostatic-potential) wave functions may have a phase singularity in a center of a dot.…
We have studied the spin and exchange coupling of Ti atoms on a Cu$_2$N/Cu(100) surface using density functional theory. We find that individual Ti have a spin of 1.0 (i.e., 2 Bohr Magneton) on the Cu$_2$N/Cu(100) surface instead of spin-1/2 as found by Scanning Tunneling Microscope. We suggest an explanation for this difference, a two-stage Kondo effect, which can be verified by experiments. By calculating the exchange coupling for Ti dimers on the Cu$_2$N/Cu(100) surface, we find that the exchange coupling across a `void' of 3.6Å is antiferromagnetic, whereas indirect (superexchange) couplin…
We show that a crystal of mesoscopic Fe8 single molecule magnets is an experimental realization of the Quantum Ising Phase Transition (QIPT) model in a transverse field, with dipolar interactions. Quantum annealing has enabled us to explore the QIPT at thermodynamical equilibrium. The phase diagram and critical exponents we obtain are compared to expectations for the mean-field QIPT Universality class.
A property associated with a vortex structure becomes evident from an analysis of confinement phenomena of magnetic oscillations in a quasi-2D ferrite disk with a dominating role of magnetic-dipolar (non-exchange-interaction) spectra. The vortices are guaranteed by the chiral edge states of magnetic-dipolar modes which result in appearance of eigen electric moments oriented normally to the disk plane. Due to the eigen-electric-moment properties, a ferrite disk placed in a microwave cavity is strongly affected by the cavity RF electric field with a clear evidence for multi-resonance oscillation…
The nature of ordering in dilute dipolar interacting systems dates back to the work of Debye and is one of the most basic, oldest and as-of-yet unsettled problems in magnetism. While spin-glass order is readily observed in several RKKY-interacting systems, dipolar spin-glasses are subject of controversy and ongoing scrutiny, e.g., in ${{\rm LiHo_xY_{1-x}F_4}}$, a rare-earth randomly diluted uniaxial (Ising) dipolar system. In particular, it is unclear if the spin-glass phase in these paradigmatic materials persists in the limit of zero concentration or not. We study an effective model of ${{\r…
We study the effect of long range dipolar forces on the dynamics and morphology of domain walls in magnetic thin films by numerical simulations of the spin-1 random field Ising model. By studying the size distribution of avalanches of domain wall motion arising as a response to quasistatic external driving, we observe a cross-over from the case dominated by short range interactions to another universality class where the long range dipolar forces become important. This crossover is accompanied with a change of the domain wall morphology from a rough wall to walls with zigzag structure.
We study theoretically the spectrum, F(s), of spin-dependent transition rates within dipolar D and exchange J coupled pairs of two spins with S=1/2 undergoing Rabi oscillations due to a coherent magnetic resonant excitation. We show that the Rabi oscillation controlled rates exhibit a spectrum with three frequency components. When exchange is stronger than the Rabi frequency (J>>Ω_R), the frequency components of the Rabi oscillation do not depend on J, rather they are determined by the relation between Ω_R and D. We derive analytical expressions for the frequencies and the intensities of all t…
We study the critical properties of a two--dimensional Ising model with competing ferromagnetic exchange and dipolar interactions, which models an ultra-thin magnetic film with high out--of--plane anisotropy in the monolayer limit. We present numerical evidence showing that two different scenarios appear in the model for different values of the exchange to dipolar intensities ratio, namely, a single first order stripe - tetragonal phase transition or two phase transitions at different temperatures with an intermediate Ising nematic phase between the stripe and the tetragonal ones. Our results …
We present a simple model that allows hysteresis loops with exchange bias to be reproduced. The model is a modification of the T=0 random field Ising model driven by an external field and with synchronous local relaxation dynamics. The main novelty of the model is that a certain fraction f of the exchange constants between neighbouring spins is enhanced to a very large value J_E. The model allows the dependence of the exchange bias and other properties of the hysteresis loops to be analyzed as a function of the parameters of the model: the fraction f of enhanced bonds, the amount of the enhanc…
Spin ice, a peculiar thermal state of a frustrated ferromagnet on the pyrochlore lattice, has a finite entropy density and excitations carrying magnetic charge. By combining analytical arguments and Monte Carlo simulations, we show that spin ice on the two-dimensional kagome lattice orders in two stages. The intermediate phase has ordered magnetic charges and is separated from the paramagnetic phase by an Ising transition. The transition to the low-temperature phase is of the three-state Potts or Kosterlitz-Thouless type, depending on the presence of defects in charge order.
We analyze recent experiments on the dilute rare-earth compound LiHo_xY_(1-x)F_4 in the context of an effective Ising dipolar model. Using a Monte Carlo method we calculate the low-temperature behavior of the specific heat and linear susceptibility, and compare our results to measurements. In our model the susceptibility follows a Curie-Weiss law at high temperature, chi ~ 1/(T-T_cw), with a Curie-Weiss temperature that scales with dilution, T_cw ~ x, consistent with early experiments. We also find that the peak in the specific heat scales linearly with dilution, C_max(T) ~ x, in disagreement …
We report an interesting case where magnetic phenomena can transcend mesoscopic scales. Our system consists of tubes created by assembly of dipolar spheres. The cylindrical topology results in the breakup of degeneracy observed in the planar square and triangular packings. As far as the ground state is concerned, tubes switch from circular to axial magnetization with increasing tube length. All magnetostatic properties found in magnetic nanotubes, in which the dipolar interaction is comparable or dominate over the exchange interaction, are reproduced by the dipolar tubes including an intermedi…
We study the effect of antiferromagnetic interactions on the single spin-flip Glauber dynamics of two different one-dimensional (1D) Ising models with spin $\pm 1$. The first model is an Ising chain with antiferromagnetic exchange interaction limited to nearest neighbors and subject to an oscillating magnetic field. The system of master equations describing the time evolution of sublattice magnetizations can easily be solved within a linear field approximation and a long time limit. Resonant behavior of the magnetization as a function of temperature (stochastic resonance) is found, at low freq…
A phase transition is often accompanied by the appearance of an order parameter and symmetry breaking. Certain magnetic materials exhibit exotic hidden-order phases, in which the order parameters are not directly accessible to conventional magnetic measurements. Thus, experimental identification and theoretical understanding of a hidden order are difficult. Here we combine neutron scattering and thermodynamic probes to study the newly discovered rare-earth triangular-lattice magnet TmMgGaO$_4$. Clear magnetic Bragg peaks at K points are observed in the elastic neutron diffraction measurements.…
We present a comprehensive study of static and dynamic magnetic properties in the Ising-like dipolar antiferromagnet (AFM) DyScO$_3$\ by means of DC and AC magnetization measurements supported by classical Monte-Carlo calculations. Our AC-susceptibility data show that the magnetic dynamics exhibit a clear crossover from an Arrhenius-like regime to quantum tunneling of magnetization (QTM) at $T^* = 10$ K. Below $T_{\mathrm{N}} = 3.2$ K DyScO$_3$ orders in an antiferromagnetic $GxAy$-type magnetic structure and the magnetization dynamics slow down to the minute timescale. The low-temperature mag…
We have developed an efficient Monte Carlo algorithm, which accelerates slow Monte Carlo dynamics in quasi-one-dimensional Ising spin systems. The loop algorithm of the quantum Monte Carlo method is applied to the classical spin models with highly anisotropic exchange interactions. Both correlation time and real CPU time are reduced drastically. The algorithm is demonstrated in the layered triangular-lattice antiferromagnetic Ising model. We have obtained the relation between the transition temperature and the exchange interaction parameters, which modifies the result of the chain-mean-field t…
We present a muon spin relaxation study on the Ising pyrochlore Nd$_2$Zr$_2$O$_7$ which develops an "all-in-all-out" magnetic order below 0.4~K. At 20~mK far below the ordering transition temperature, the zero-field muon spin relaxation spectra show no static features and can be well described by a dynamical Gaussian-broadened Gaussian Kubo-Toyabe function indicating strong fluctuations of the ordered state. The spectra of the paramagnetic state (below 4.2~K) reveal anomalously slow paramagnetic spin dynamics and show only small difference with the spectra of the ordered state. We find that th…
Within the framework of mean field theory, we examine the phase transitions in Ising magnetic films and superlattices. By transfer matrix method, we derive two general nonlinear equations for phase transition temperatures of Ising magnetic films and superlattices, respectively. The equations can be applied to the films and superlattices with arbitrary exchange interaction constants and arbitrary layer number. Numerical results for phase transition temperatures as a function of exchange interaction constants are presented.
The results of extensive Monte Carlo simulations of classical spins on the two-dimensional kagome lattice with only dipolar interactions are presented. In addition to revealing the six-fold degenerate ground state, the nature of the finite-temperature phase transition to long-range magnetic order is discussed. Low temperature states consisting of mixtures of degenerate ground state configurations separated by domain walls can be explained as a result of competing exchange-like and shape anisotropy-like terms in the dipolar coupling. Fluctuations between pairs of degenerate spin configurations …
