Ising Ferromagnet Research Articles

Topological phase diagrams of the frustrated Ising ferromagnet

The emergence of complex modulated structures in the magnetization pattern of thin films is a well-established experimental phenomenology caused by the frustrating effects of competing interactions. Using a coarse-grained version of the Ising ferromagnet with dipolar interactions, we develop a method that uses the information from the microscopic Hamiltonian to predict the specific topological phases present in the temperature-external magnetic field phase diagram. This is done by the combination of mean-field variational calculations and the renormalization group equations from the classical theory of two-dimensional melting. In this framework, we are able to distinguish when the orientational and translational symmetries are broken, discriminating between the ordered and disordered states of the system for all temperatures and fields. We observe that the reentrance developed by the $H$-$T$ phase diagrams in the regime of weak dipolar interactions is directly related with the appearance of anomalous topological transitions. These results motivate the realization of new experiments on magnetic thin films in order to explore the topological properties of the magnetic textures, allowing to identify new exotic phases in these materials.

Effects of random fields on the reversal of magnetisation of Ising ferromagnet

We have studied the reversal time of the magnetisation in two dimensional Ising ferromagnet in the presence of externally applied uniform magnetic field using Monte Carlo simulation based on Metropolis single spin flip algorithm. Then we have investigated the change in reversal time due to the presence of quenched random field in addition to the uniform magnetic field. We report the results of statistical distribution of reversal times in the presence of three different types of the distributions (namely, uniform, bimodal and normal) of random fields and compared the results with those obtained for uniform field only. We have observed that the reversal time decreases due to the presence of any kind (of distribution) of the random fields. The metastable volume fraction is observed to follow the Avrami’s law. Dependence of reversal times on temperature and different widths of the distributions of random fields are also reported. We have also checked whether the system obeyed Becker–Döring theory of classical nucleation in presence of additional random field and tried to investigate the range of the width of the distribution of random field. For larger width of the distribution of random field, the system fails to show the reversal via the nucleation of a single droplet (for small values of uniform field only). The possible reason is analysed.

VI3 : A two-dimensional Ising ferromagnet

Two-dimensional (2D) magnetic materials are of great current interest for their promising applications in spintronics. Here we propose the van der Waals (vdW) material VI3 to be a 2D Ising ferromagnet (FM), using density functional calculations, crystal field level diagrams, superexchange model analyses, and Monte Carlo simulations. The $a_{1g}$$^1$$e'_{-}$$^1$ ground state in the trigonal crystal field gives rise to the 2D Ising FM due to a significant single ion anisotropy (SIA) and enhanced FM superexchange both associated with the $S_z$=1 and $L_z$=--1 state of V3+ ions. We find that a tensile strain on the VI3 monolayer further stabilizes the $a_{1g}$$^1$$e'_{-}$$^1$ ground state, and its Curie temperature ($T_{\rm C}$) would increase from 70 K to 90-110 K under a 2.5-5\% tensile strain. Moreover, we suggest a group of spin-orbital states with a strong SIA which may help to search more 2D Ising magnets.

Area-law-like systems with entangled states can preserve ergodicity

We study the ground entangled state of the one-dimensional spin-1/2 Ising ferromagnet at its transverse-field critical point. When this problem is expressed in terms of independent fermions, we show that the usual thermostatistical sums emerging within Fermi-Dirac statistics can, for an L-sized subsystem, be indistinctively taken up to L terms or up to lnL terms, providing a neat understanding of the origin of the logarithmic scaling of the entanglement entropy in the system. This is interpreted as a compact occupancy of the phase-space of the L-subsystem, hence standard Boltzmann-Gibbs thermodynamics quantities with an effective system size V ∝ lnL are appropriate and are explicitly calculated. The calculations are then to be done in a Hilbert space whose effective dimension is 2ln L instead of 2L. In this we can assume ergodicity. Our analysis suggests a scenario where the physical systems are essentially grouped into three classes, in terms of their phase-space occupancy, ergodicity and Lebesgue measure.

Loop expansion around the Bethe solution for the random magnetic field Ising ferromagnets at zero temperature

We apply to the random-field Ising model at zero temperature ([Formula: see text]) the perturbative loop expansion around the Bethe solution. A comparison with the standard ϵ expansion is made, highlighting the key differences that make the expansion around the Bethe solution much more appropriate to correctly describe strongly disordered systems, especially those controlled by a [Formula: see text] renormalization group (RG) fixed point. The latter loop expansion produces an effective theory with cubic vertices. We compute the one-loop corrections due to cubic vertices, finding additional terms that are absent in the ϵ expansion. However, these additional terms are subdominant with respect to the standard, supersymmetric ones; therefore, dimensional reduction is still valid at this order of the loop expansion.

From early nucleation past the percolation threshold: Status of the Kolmogorov-Avrami theory on a cold Ising lattice.

A high-precision test of the Kolmogorov-Avrami (KA) model of "geometric" interactions between growing nuclei is performed for an Ising ferromagnet driven by Metropolis dynamics. As long as the interface boundaries of interacting nuclei are rough, the KA model is adequate for arbitrary large densities of the new phase, well beyond the percolation transition, as in the case of homogeneous nucleation. For a prenucleated system the KA description breaks down at sufficiently low temperature, when the length of a kinetically smooth interface exceeds the distance between seeds.

Ground states and hyperuniformity of the hierarchical Coulomb gas in all dimensions

Stochastic point processes with Coulomb interactions arise in various natural examples of statistical mechanics, random matrices and optimization problems. Often such systems due to their natural repulsion exhibit remarkable hyperuniformity properties, that is, the number of points landing in any given region fluctuates at a much smaller scale compared to that of a set of i.i.d. random points. A well known conjecture from physics appearing in the works of Jancovici, Lebowitz, Manificat, Martin, and Yalcin (see Jancovici et al. in J Stat Phys 72(3–4):773–787, 1993, Lebowitz in Phys Rev A 27:1491–1494, 1983, Martin and Yalcin in J Stat Phys 22(4):435–463, 1980), states that the variance of the number of points landing in a set should grow like the surface area instead of the volume unlike i.i.d. random points. In a recent beautiful work (Chatterjee in Rigidity of the three-dimensional hierarchical Coulomb gas, 2017. arXiv preprint. arXiv:1708.01965 , To appear in Probability Theory and Related Fields), Chatterjee gave the first proof of such a result in dimension three for a Coulomb type system, known as the hierarchical Coulomb gas, inspired by Dyson’s hierarchical model of the Ising ferromagnet (Dyson in Phys Rev 92:1331–1338, 1953, Dyson in Commun Math Phys 12(2):91–107, 1969). However the case of dimensions greater than three had remained open. In this paper, we establish the correct fluctuation behavior up to logarithmic factors in all dimensions greater than three, for the hierarchical model. Using similar methods, we also prove sharp variance bounds for smooth linear statistics which were unknown in any dimension bigger than two. A key intermediate step is to obtain precise results about the ground states of such models whose behavior can be interpreted as hierarchical analogues of various crystalline conjectures predicted for energy minimizing systems, and could be of independent interest.

Magnetic domain dynamics in an insulating quantum ferromagnet

The statistics and form of avalanches in a driven system reveal the nature of the underlying energy landscape and dynamics. In conventional metallic ferromagnets, eddy-current back action can dominate the dynamics. Here, we study Barkhausen noise in Li(Ho,Y)F4, an insulating Ising ferromagnet that cannot sustain eddy currents. For large avalanches at temperatures approaching the Curie point, we find a symmetric response free of drag effects. In the low temperature limit, drag effects contribute to the dynamics, which we link to enhanced pinning from local random fields that are enabled by the microscopic dipole-coupled Hamiltonian (the Ising model in transverse field).

Non-self-averaging in the Critical Point of a Random Ising Ferromagnet

In this paper, we review recent results on sample-to-sample fluctuations in a critical Ising model with quenched random ferromagnetic couplings. In particular, in terms of the renormalized replica Ginzburg–Landau Hamiltonian in dimensions D < 4 an explicit expression for the probability distribution function (PDF) of the critical free energy fluctuations is derived. Next, using known fixed-point values for the renormalized coupling parameters the universal curve for such PDF in the dimension D = 3 is obtained. For the specific case of the two-dimensional Ising model, using replica calculations in the renormalization group framework, we derive explicit expressions for the PDF of the critical internal energy and for the specific heat fluctuations. It is shown that the disorder distribution of internal energy is Gaussian, and its typical sample-to-sample fluctuations as well as its average value scale with the system size L like ~ Llnln(L). In contrast, the specific heat is shown to be self-averaging with a distribution function that tends to a δ-peak in the thermodynamic limit L → ∞.

Probing predictions due to the nonlocal interface Hamiltonian: Monte Carlo simulations of interfacial fluctuations in Ising films.

Extensive Monte Carlo simulations have been performed on an Ising ferromagnet under conditions that would lead to complete wetting in a semi-infinite system. We studied an L×L×D slab geometry with oppositely directed surface fields so that a single interface is formed and can undergo a localization-delocalization transition. Under the chosen conditions the interface position is, on average, in the middle of the slab, and its fluctuations allow a sensitive test of predictions that the effective interactions between the interface and the confining surfaces are nonlocal. The decay of distance dependent correlation functions are measured within the surface, in the middle of the slab, and between middle and the surface for slabs of varying thickness D. From Fourier transforms of these correlation functions a nonlinear correlation length is extracted, and its behavior is found to confirm theoretical predictions for D>6 lattice spacings.

Compact susceptometer for studies under transverse field geometries at very low temperatures.

We present the design of a compact AC susceptometer for studies under arbitrarily oriented static magnetic fields, in particular magnetic fields oriented transverse to the AC excitation field. The small size of the susceptometer permits versatile use in conventional cryostats with superconducting magnet systems. The design of the susceptometer minimizes parasitic signal contributions while providing excellent thermal anchoring suitable for measurements in a wide range down to very low temperatures. The performance is illustrated by means of measurements of the transverse susceptibility at the magnetic field tuned quantum phase transition of the dipolar-coupled Ising ferromagnet LiHoF4.

Non-coplanar Model States in Quantum Magnetism Applications of the High-Order Coupled Cluster Method

Coplanar model states for applications of the coupled cluster method (CCM) to problems in quantum magnetism are those in which all spins lie in a plane, whereas three-dimensional (3D) model states are, by contrast, non-coplanar ones in which all the spins do not lie in any single plane. A crucial first step in applying the CCM to any such lattice quantum spin system is to perform a passive rotation of the local spin axes so that all spins in the model state appear mathematically to point in the same (say, downwards z-)direction. Whereas this process leads to terms with only real coefficients in the rotated Hamiltonian for coplanar model states, an additional complication arises for 3D model states where the corresponding coefficients can become complex-valued. We show here for the first time how high-order implementations of the CCM can be performed for such Hamiltonians. We explain in detail why the extension of the computational implementation of the CCM when going from coplanar to 3D model states is a non-trivial task that has not hitherto been undertaken. To illustrate these new developments, we present results for three cases: (a) the spin-half one-dimensional Ising ferromagnet in an applied transverse magnetic field (as an exactly solvable test model to use as a yardstick for the viability and accuracy of our new methodology); (b) the spin-half triangular-lattice Heisenberg antiferromagnet in the presence of an external magnetic field; and (c) the spin-S triangular-lattice XXZ antiferromagnet in the presence of an external magnetic field, for the cases frac{1}{2} le S le 5 . For 3D model states the sets of algebraic CCM equations for the ket- and bra-state correlation coefficients become complex-valued, but ground-state expectation values of all physical observables are manifestly real numbers, as required, and as we explicitly demonstrate in all three applications. Indeed, excellent correspondence is seen with the results of other methods, where they exist, for these systems. In particular, our CCM results demonstrate explicitly that coplanar ordering is favoured over non-coplanar ordering for the triangular-lattice spin-half Heisenberg antiferromagnet at all values of the applied external magnetic field, whereas for the anisotropic XXZ model non-coplanar ordering can be favoured in some regions of the parameter space. Specifically, we present a precise determination of the boundary (i.e., the critical value of the XXZ anisotropy parameter Delta ) between a 3D ground state and a coplanar ground state for the XXZ model for values for the external magnetic field near to saturation, for values of the spin quantum number S le 5. Although the CCM calculations are computationally intensive for this frustrated model, especially for high spin quantum numbers, our accurate new results certainly improve our understanding of it.

Finite-field phase transitions and criticality in a generalized kagomé Ising ferromagnet: Exact solutions

The standard two-parameter (nearest-neighbor pair-interaction J2 and magnetic field h) planar Ising model ferromagnet only has phase transitions in zero field. We generalize a standard kagomé Ising model ferromagnet by adding localized triplet Ising interactions J3. Exact solutions are obtained for the phase diagrams of the three-parameter model, demonstrating finite-field phase transitions and criticality. Necessary conditions for the latter findings include the pair-interaction parameter being ferromagnetic (J2>0), the applied field parameter competing against the intrinsic triplet-interaction parameter, the ratio of the triplet- and pair-interaction parameters residing within a determined finite symmetrical interval, and the field parameter being properly tuned, viz., tracing the pertinent field vs temperature phase boundary curve. The curvilinear shape of the phase boundary facilitates the relative strength |J3|∕J2 of the triplet interaction to be experimentally accessible. Employing generalized fluid–magnet correspondence relations, it is mathematically convenient and informative to affiliate the above magnetic phase diagrams with the corresponding fluid phase diagrams of the associated generalized kagomé lattice-gas model.

Thermodynamic geometry of Ising ferromagnet in an external magnetic field: A self-consistent field theory calculation

We present a complete geometrical description for the ferromagnetic Ising model in the pair approximation as introduced by Balcerzak (2003) using self-consistent field theory. A metric is defined in a two-dimensional phase space of magnetization (M) and nearest-neighbour correlation function (C). Based on the metric elements an expression for the thermodynamic Ricci scalar (R) is derived in terms of the lattice coordination number q. We study R as the temperature (T), magnetic field (h) and exchange energy coupling (J) are varied and show that there are T and h dependent critical properties for q=6. By direct comparison, we demonstrate that the special case q=2 provides a consistent behaviour with the already known exact formula in Janyszek and Mrugała work (1989) for the one-dimensional Ising model.

Magnetic field driven critical behavior in bulk Gd

Gadolinium (Gd) has been proven to be such a complex magnetic system that its static universality class varies as a function of the reduced temperature (|ɛ| = |T−TC|/TC). Though many works have been done, physical mechanisms of this phenomenon have not been fully elucidated. In this work, we analyzed the static magnetization data, M(H), around the ferromagnetic-paramagnetic phase transition temperature (TC) based on Banerjee's criteria, the modified Arrott plot and Kouvel–Fisher techniques, the critical isotherm analysis, and the scaling hypothesis to reconsider the phase transition, magnetic order, and isotropic and uniaxial behaviors of a polycrystalline Gd bulk. The M(H) data analyses with H variations up to 140 kOe indicated that Gd still keeps the nature of a second-order phase transition and short-range magnetic order. In the critical region of |ɛ| = 3.4 × 10−3–6.9 × 10−2, we observed the critical-behavior transition from a mixed isotropic and uniaxial ferromagnet for H = 3–10 kOe through an isotropic 3D Heisenberg ferromagnet for H = 10–100 kOe to a uniaxial 3D Ising ferromagnet for H = 100–140 kOe. The results demonstrate the possibility of using high fields to identify the universality class of Gd. The fluctuations and preferred reorientation of spins in the hexagonal close-packed lattice at temperatures T &amp;gt; 230 K are thought to cause these interesting phenomena.

Rigidity of the three-dimensional hierarchical Coulomb gas

A random set of points in Euclidean space is called ‘rigid’ or ‘hyperuniform’ if the number of points falling inside any given region has significantly smaller fluctuations than the corresponding number for a set of i.i.d. random points. This phenomenon has received considerable attention in recent years, due to its appearance in random matrix theory, the theory of Coulomb gases and zeros of random analytic functions. However, most of the published results are in dimensions one and two. This paper gives the first proof of hyperuniformity in a Coulomb type system in dimension three, known as the hierarchical Coulomb gas. This is a simplified version of the actual 3D Coulomb gas. The interaction potential in this model, inspired by Dyson’s hierarchical model of the Ising ferromagnet, has a hierarchical structure and is locally an approximation of the Coulomb potential. Hyperuniformity is proved at both macroscopic and microscopic scales, with upper and lower bounds for the order of fluctuations that match up to logarithmic factors. The fluctuations have cube-root behavior, in agreement with a well-known prediction for the 3D Coulomb gas. For completeness, analogous results are also proved for the 2D hierarchical Coulomb gas and the 1D hierarchical log gas.

Thermodynamic properties of ferroics described by the transverse Ising model and their applications for CoNb2O6

The temperature and transverse field dependence of the entropy and the specific heat of ferroics in the quantum paramagnetic (QPa) state is investigated using the transverse Ising model (TIM) with different spin values within mean field and Gaussian spin fluctuation approximations. A maximum peak of the temperature dependence of the specific heat curves is enhanced in the QPa state due to spin fluctuations. This peak shifts to higher temperature region and its magnitude reduces with increasing transverse field. In addition, the temperature corresponding to this maximum depends linearly on the deviation of the transverse field from its critical value. The obtained specific heat qualitatively agrees with the experimental observation for the quasi-one-dimensional (1D) Ising ferromagnet CoNb2O6 in the QPa phase. It is also shown that the spin-1/2 three dimensional (3D) TIM clearly describes the specific heat of CoNb2O6 in the QPa states near the critical temperature. However, the spin-3/2 3D-TIM is more adequate than the spin-1/2 3D-TIM for describing the thermal behavior of CoNb2O6 in the QPa states at high fields and at elevated temperatures.

Determining Interaction Enhanced Valley Susceptibility in Spin-Valley-Locked MoS2.

Two-dimensional transition metal dichalcogenides (TMDCs) are recently emerged electronic systems with various novel properties, such as spin-valley locking, circular dichroism, valley Hall effect, and superconductivity. The reduced dimensionality and large effective masses further produce unconventional many-body interaction effects. Here we reveal strong interaction effects in the conduction band of MoS2 by transport experiment. We study the massive Dirac electron Landau levels (LL) in high-quality MoS2 samples with field-effect mobilities of 24 000 cm2/(V·s) at 1.2 K. We identify the valley-resolved LLs and low-lying polarized LLs using the Lifshitz-Kosevitch formula. By further tracing the LL crossings in the Landau fan diagram, we unambiguously determine the density-dependent valley susceptibility and the interaction enhanced g-factor from 12.7 to 23.6. Near integer ratios of Zeeman-to-cyclotron energies, we discover LL anticrossings due to the formation of quantum Hall Ising ferromagnets, the valley polarizations of which appear to be reversible by tuning the density or an in-plane magnetic field. Our results provide evidence for many-body interaction effects in the conduction band of MoS2 and establish a fertile ground for exploring strongly correlated phenomena of massive Dirac electrons.

Surface-Engineered MXenes: Electric Field Control of Magnetism and Enhanced Magnetic Anisotropy.

Controlling magnetism in two-dimensional (2D) materials via electric fields and doping enables robust long-range order by providing an external mechanism to modulate magnetic exchange interactions and anisotropy. In this report, we predict that transition metal carbide and nitride MXenes are promising candidates for controllable magnetic 2D materials. The surface terminations introduced during synthesis act as chemical dopants that influence the electronic structure, enabling controllable magnetic order. We show ground-state magnetic ordering in Janus M2XO xF2- x (M is an early transition metal, X is carbon or nitrogen, and x = 0.5, 1, or 1.5) with asymmetric surface functionalization, where local structural and chemical disorder induces magnetic ordering in some systems that are nonmagnetic or weakly magnetic in their pristine form. The resulting magnetic states of these noncentrosymmetric structures can be robustly switched and stabilized by tuning the interlayer exchange couplings with small applied electric fields. Furthermore, bond directionality is enhanced by Janus functionalization, resulting in improved magnetic anisotropy, which is essential to stable 2D magnetic ordering. The mixed termination-induced anisotropy leads to robust Ising ferromagnetism with an out-of-plane easy axis over the full range of relevant termination compositions for Janus Mn2N. Janus Cr2C, V2C, and Ti2C were found to be robustly antiferromagnetic. Our results provide a strategy for exploiting asymmetric surface functionalization to achieve room-temperature nanoscale magnetism under ambient conditions in MXenes with currently available synthesis techniques.

Universality Class of the Nonequilibrium Phase Transition in Two-Dimensional Ising Ferromagnet Driven by Propagating Magnetic Field Wave

The finite size analysis of the nonequilibrium phase transition, in two dimensional Ising ferromagnet driven by plane propagating magneticwave, is studied by Monte Carlo simulation. It is observed that the system undergoes a nonequilibrium dynamicphase transition from a high temperature dynamically symmetric ({\it propagating}) phase to a low temperature dynamically symmetry-broken ({\it pinned}) phase as the system is cooled below the transition temperature. This transition temperature is determined precisely by studying the fourth order Binder Cumulant of the dynamic order parameter as a function of temperature for different system sizes ($L$). From the finite size analysis of dynamic order parameter ($Q_L \sim L^{-{{\beta} \over {\nu}}}$) and the dynamic susceptibility ($\chi^{Q}_{L} \sim L^{{\gamma} \over {\nu}}$), we have estimated the critical exponents $\beta/\nu=0.146\pm0.025$ and $\gamma/\nu=1.869\pm0.135$ (measured from the data read at the critical temperature obtained from Binder cumulant), and $\gamma/\nu=1.746\pm0.017$ (measured from the peak positions of dynamic susceptibility). Our results indicate that such driven Ising ferromagnet belongs to the same universality class of the two-dimensional equilibrium Ising ferromagnet (where $\beta/\nu=1/8$ and $\gamma/\nu=7/4$), within the limits of statistical errors.