Diluted Ising Antiferromagnet Research Articles

Random fields and apparent exchange bias in the dilute Ising antiferromagnet Fe0.6Zn0.4F2

Random field induced spontaneous excess moments appear in field cooled single crystals of diluted Ising antiferromagnets. Here we report results from low temperature measurements of field cooled (including zero field) magnetic hysteresis loops parallel and perpendicular to the c-axis of a single crystal of composition Fe0.6Zn0.4F2. We find that weak static ferromagnetic excess moments attained on field cooling give rise to an apparent exchange bias of the magnetic hysteresis loops, whose magnitude is controlled by temperature and the strength and direction of the cooling field. Random field induced temporal excess moments only become observable in cooling fields larger than 1 T applied along the c-axis direction of the Fe0.6Zn0.4F2 single crystal.

Magnetism of the Diluted Ising Antiferromagnet in a Magnetic Field on the Kagome Lattice: Single-Spin Cluster Approximation

An effective-field theory based on the single-spin cluster has been used to study of a diluted spin-$1/2$ Ising antiferromagnet on the Kagome lattice with nearest-neighbor interactions. We observe five plateaus in the magnetization curve of the diluted antiferromagnet when a magnetic field is applied which is in agreement with Monte Carlo calculation. The effect of the site-dilution on the magnetic susceptibility is also investigated and discussed. In particular, we have found that the frustrated Kagome lattice inverse susceptibility fall to zero at $0$K.

Ferrimagnetism of dilute Ising antiferromagnets

It is shown that nearest-neighbor antiferromagnetic interactions of identical Ising spins on unbalanced bipartite lattice and imbalanced bipartite hierarchical fractal result in ferrimagnetic order instead of anti-ferromagnetic one. On some crystal lattices dilute Ising antiferromagnets may also become ferrimagnets due to the imbalanced nature of the magnetic percolation cluster when it coexists with the percolation cluster of vacancies. As evidenced by the existing experiments on FepZn1−pF2, such ferrimagnetism is inherent property of bcc lattice so thermodynamics of these compounds at low p can be similar to that of antiferromagnet on imbalanced hierarchical fractal.

Effects of selective dilution on phase diagram and ground-state magnetizations of an Ising antiferromagnet on triangular and honeycomb lattices

We employ an effective-field theory with correlations in order to study the phase diagram and ground-state magnetizations of a selectively diluted Ising antiferromagnet on triangular and honeycomb lattices. Dilution of different sublattices with generally unequal probabilities results in a rather intricate phase diagram in the sublattice dilution parameters space. In the case of the frustrated triangular lattice antiferromagnet the selective dilution affects the degree of frustration which can lead to some peculiar phenomena, such as reentrant behavior of long-range order or unsaturated sublattice magnetizations at zero temperature. The selectively diluted Ising antiferromagnet on the honeycomb lattice is obtained as a special case when one sublattice of the triangular lattice is completely removed by dilution.

Local entropy and structure in a two-dimensional frustrated system

We calculate the local contributions to the Shannon entropy and excess entropy and use these information theoretic measures as quantitative probes of the order arising from quenched disorder in the diluted Ising antiferromagnet on a triangular lattice. When one sublattice is sufficiently diluted, the system undergoes a temperature-driven phase transition, with the other two sublattices developing magnetizations of equal magnitude and opposite sign as the system is cooled.(1) The diluted sublattice has no net magnetization but exhibits spin glass ordering. The distribution of local entropies shows a dramatic broadening at low temperatures; this indicates that the system's total entropy is not shared equally across the lattice. The entropy contributions from some regions exhibit local reentrance, although the entropy of the system decreases monotonically as expected. The average excess entropy shows a sharp peak at the critical temperature, showing that the excess entropy is sensitive to the structural changes that occur as a result of the spin glass ordering.

Monte Carlo simulation of a random-field Ising antiferromagnet

Phase transitions in the three-dimensional diluted Ising antiferromagnet in an applied magnetic field are analyzed numerically. It is found that random magnetic field in a system with spin concentration below a certain threshold induces a crossover from second-order phase transition to first-order transition to a new phase characterized by a spin-glass ground state and metastable energy states at finite temperatures.

Magnetic Phase Diagram of Three-Dimensional Diluted Ising Antiferromagnet Ni0.8Mg0.2(OH)2

$H$-$T$ diagram of 3D diluted Ising antiferromagnet Ni$_{c}$Mg$_{1-c}$(OH)$_{2}$ with $c$ = 0.8 has been determined from measurements of SQUID DC magnetization and AC magnetic susceptibility. At $H$ = 0, this compound undergoes two magnetic phase transitions: an antiferromagnetic (AF) transition at the N\'{e}el temperature $T_{N}$ (= 20.7 K) and a reentrant spin glass (RSG) transition at $T_{RSG}$ ($\approx$ 6 K). The $H$-$T$ diagram consists of the RSG, spin glass (SG), and AF phases. These phases meet a multicritical point $P_{m}$ ($H_{m}$ = 42 kOe, $T_{m}$ = 5.6 K). The irreversibility of susceptibility defined by $\delta$ (= $\chi_{FC} - \chi_{ZFC}$) shows a negative local minimum for 10 $\leq H \leq$ 35 kOe, suggesting the existence of possible glassy phase in the AF phase. A broad peak in $\delta$ and $\chi^{\prime \prime}$ at $H \geq$ 20 kOe for $T_{N}(c=0.8,H) \leq T \leq T_{N}(c=1,H=0)$ (= 26.4 K) suggests the existence of the Griffiths phase.

Low-temperature magnetization in dilute Ising antiferromagnets

The dynamics of the remanent magnetization \ensuremath{\mu} and the excess magnetization $\ensuremath{\Delta}M$ of a dilute Ising antiferromagnet has been investigated by measurements on ${\mathrm{Fe}}_{0.6}{\mathrm{Zn}}_{0.4}{\mathrm{F}}_{2}$ and by deriving the corresponding behavior from a continuum version of the random-field Ising model. It is found that $\ensuremath{\Delta}M,$ due to domain wall magnetization, at low temperatures follows a $\ensuremath{\Delta}M\ensuremath{\propto}{H}^{m}$ dependence, where $m>{\ensuremath{\nu}}_{H}; {\ensuremath{\nu}}_{H}$ determines the size of the random-field domains, $R\ensuremath{\propto}{H}^{{\ensuremath{\nu}}_{H}}.$ The low-temperature dynamics of \ensuremath{\mu} is found to obey $\ensuremath{\mu}(H,T,t)\ensuremath{\propto}{H}^{m}{1\ensuremath{-}c[T\mathrm{ln}(t/{\ensuremath{\tau}}_{0}){]}^{a}},$ where $m=2.9\ifmmode\pm\else\textpm\fi{}0.1$ and $a=0.70\ifmmode\pm\else\textpm\fi{}0.05.$

Universality in three dimensional random-field ground states

We investigate the critical behavior of three-dimensional random-field Ising systems with both Gauss and bimodal distribution of random fields and additional the three-dimensional diluted Ising antiferromagnet in an external field. These models are expected to be in the same universality class. We use exact ground-state calculations with an integer optimization algorithm and by a finite-size scaling analysis we calculate the critical exponents nu, beta, and gamma-bar. While the random-field model with Gauss distribution of random fields and the diluted antiferromagnet appear to be in same universality class, the critical exponents of the random-field model with bimodal distribution of random fields seem to be significantly different.

Degeneracy algorithm for random magnets

It has been known for a long time that the ground-state problem of random magnets, e.g., the random field Ising model, can be mapped onto the maximum flow, minimum cut problem of transportation networks. We build on this approach, relying on the concept of residual graph, and design an algorithm that we prove to be exact for finding all the minimum cuts, i.e., the ground-state degeneracy of these systems. We demonstrate that this algorithm is also relevant for the study of the ground-state properties of the dilute Ising antiferromagnet in a constant field and interfaces in random bond magnets.

Non-exponential relaxation in dilute antiferromagnets

Dilute Ising antiferromagnets in a homogenous magnetic field have a disordered phase for sufficiently large values of the field and for low temperatures. Here, the system is in a domain state with a broad size-distribution of fractal domains. We study the relaxation dynamics of this domain state after removing the external field for two and three dimensions. Using Monte Carlo simulation techniques, we measure the decay of the remanent magnetization. Its temperature dependence can be understood as thermal activation. All data can be described by a unique generalized power law for a wide range of temperatures in two-and three-dimensions. The question of whether the exponent of the generalized power-law is universal remains open.

Ground-state structure of diluted antiferromagnets and random field systems

A method is presented for the calculation of all exact ground states of diluted Ising antiferromagnets and random field Ising systems in an arbitrary range of magnetic fields B ϵ [ B start , B end ] resp. Δ ϵ [ Δ start , Δ end ]. It works by calculating all jump-fields B, Δ where the system changes its ground state. For each field value, all degenerated ground states are represented by a set of (anti-) ferromagnetic clusters and a relation between the clusters. So a complete description of the ground-state structure of these systems is possible. Systems are investigated up to size 48 3 on the whole field-range and up to 160 3 for some particular fields. The behavior of order parameters is investigated, the number of jumps is analyzed and the degree of degeneracy as functions of size and fields is calculated.

On the relaxation dynamics of diluted antiferromagnets

The phase diagram of a diluted Ising antiferromagnet in an external magnetic field has a disordered phase for sufficiently large values of this field and for low temperatures, in which the system's equilibrium state is a domain state. We study the relaxation dynamics out of this state after switching off the magnetic field, for two- and three-dimensional diluted antiferromagnets using Monte Carlo Simulation techniques. We measure the decay of the initial magnetization carried by the domain state. The data can be described by a unique law for a wide range of temperatures, magnetic fields and dilutions in two and three dimensions.

Dynamics of the antiferromagnetic random-exchange Ising systemFexZn1−xF2near the percolation threshold

Dynamic magnetic properties of the diluted Ising antiferromagnet, ${\mathrm{Fe}}_{0.25}{\mathrm{Zn}}_{0.75}{\mathrm{F}}_{2},$ have been investigated by dc-magnetic relaxation and ac-susceptibility measurements. In similarity with spin glasses, a strongly frequency-dependent cusp in the dynamic susceptibility appears at low temperature. The corresponding slowing down of the relaxation times is however found to follow an Arrhenius law, i.e., critical dynamics indicating a phase transition is not observed. Also, there are no indications of an equilibrium Almeida-Thouless line in the $H\ensuremath{-}T$ plane and the field dependence of the equilibrium susceptibility behaves noncritically. However, an ageing behavior, a common feature of frustrated disordered magnetic systems, is observed at low temperatures.

A synchrotron X-ray study of the phases and phase transitions in the mixed Ising-XY magnet FexCo1−x TiO3

We report a detailed synchrotron x-ray scattering study of the phases and phase transitions in the mixed Ising-XY magnetic system with quenched randomness: FexCo1−x TiO3 (x=0.35, 0.50, 0.65 and 0.75). For concentrations x=0.35, 0.50 and 0.65, we observe at high resolution a breakup of both the magnetic and the atomic structures of the crystal into domains, as well as a uniform lattice distortion following the ordering of the XY spin components. We argue that this breakup into domains in the XY phases results from random anisotropy, random field and magnetoelastic effects in FexCo1−x TiO3. In particular, we find that in random anisotropy XY magnets, there exists a novel phase transition which is critical, but involves no long-range ordered phase. In addition to the XY behavior, the Ising spin component in the mixed phase (x=0.65) is found to break into domains following the (short range) ordering of the XY spin components. Specifically, the scattering profiles of the low temperature mixed states are well described by a Lorentzian squared cross-section, which in three dimensions corresponds to exponential decay of the real space spin-spin correlations. This loss of the long-range order of the Ising order due to the ordering of the XY spin components after initial establishment of the Ising order on cooling is difficult to understand within our current picture of the random field Ising model. We have also carried out a detailed study of the magnetic field effects on phase transitions in the mixed Ising random magnet Fe0.75Co0.25TiO3, for fields up to 2.9T. It is found, as in the diluted Ising antiferromagnets MnxZn1−x F2 and FexZn1−x F2, that when the sample is cooled in the presence of a field, it evolves from the high temperature paramagnetic phase to a low temperature domain state. The low temperature scattering profiles are well described by a Lorentzian squared cross-section. However, if the sample is cooled below the Neel temperature T N in the absence of a field, and a magnetic field is subsequently applied, the long range magnetic order persists on warming, up to a well defined field-dependent metastability temperature, T M(H). The shedding of this LRO in the metastable region is consistent with the “trompe l’oeil critical behavior” description, with a β ZFC∼0.17. The depression of the metastability temperature in magnetic fields can be well described by the form T M(H)=T N(0)−bH 2−aH 2/φ, with the best fit value for the crossover exponent φ=1.2(1). This smaller value (than the theoretical value φ=1.4) for φ probably arises from the close proximity of a multicritical point at higher fields. At the superlattice reciprocal lattice point (1, 1,–1.5), we observe a drastic field-dependence of the x-ray, but not the neutron, scattering intensity. This additional x-ray intensity is believed to arise from an induced staggered charge density. In particular, the quadratic magnetic field dependence of the additional intensity is consistent with a lattice and magnetism coupling of the form, ρ s M s M, where ρ ss is a staggered charge density, M s the staggered magnetization and M the uniform magnetization.

Spin-glass and antiferromagnet critical behavior in a diluted fcc antiferromagnet.

We report on a Monte Carlo study of a diluted Ising antiferromagnet on a fcc lattice. This is a typical model example of a highly frustrated antiferromagnet, and we ask whether sufficient random dilution of spins does produce a spin-glass phase. Our data strongly indicate the existence of a spin-glass transition for spin concentration p0.75: We find a divergent spin-glass susceptibility and a divergent spin-glass correlation length, whereas the antiferromagnetic correlation length saturates in this regime. Furthermore, we find a first-order phase transition to an antiferromagnet for 1\ensuremath{\ge}p\ensuremath{\gtrsim}0.85, which becomes continuous in the range 0.85\ensuremath{\gtrsim}p\ensuremath{\gtrsim}0.75. Finite-size scaling is employed to obtain critical exponents. We compare our results with experimental systems as diluted frustrated antiferromagnets as ${\mathrm{Zn}}_{1\mathrm{\ensuremath{-}}\mathit{p}}$${\mathrm{Mn}}_{\mathit{p}}$Te. \textcopyright{} 1996 The American Physical Society.

Spin dynamics in the two-dimensional percolating Ising antiferromagnet

Using neutron scattering techniques, we investigated the magnetic correlations in diluted antiferromagnets close to the percolation threshold, in which the magnetic connectivity takes the form of a fractal. Recent experimental results concerning the self-similarity of the magnetic order, ordering kinetics, and magnetic excitations in a two-dimensional diluted Ising antiferromagnet, Rb 2Co c Mg 1− c F 4, are presented.

RELAXATION OF THE FRACTAL DOMAIN STATE OF DILUTED ANTIFERROMAGNETS

The diluted Ising antiferromagnet in an external magnetic field is an ideal system to study random field behavior theoretically as well as experimentally. When the system is cooled in an external field, a frozen domain state develops. The domains have been shown to be fractal. In this paper, I want to focus on the relaxation dynamics of this frozen domain state after removal of the external field. Using Monte Carlo methods, I investigated the nature of the relaxation of the fractal domains numerically as well as by graphical representation. The antiferromagnetic correlation length is shown to grow during the relaxation. The corresponding relaxation mechanism is investigated and analogies to SOC are discussed.

Self-Similarity of Magnetic Order in Two-Dimensional Percolating Antiferromagnets

The intensity distribution of the magnetic elastic scattering of neutrons near the superlattice position in two-dimensional diluted Ising antiferromagnets, Rb 2 Co c Mg 1- c F 4 ( c =0.60, 0.65 and 0.70), reveals direct experimental evidence of the self-similarity of the magnetic order in a percolating magnetic system. The observed fractal dimension is 1.95±0.07, which is in accord with a numerically estimated value of 1.896. Evidence for a crossover from a self-similar fractal structure to a homogeneous structure is also presented.

Low-temperature dynamics of a diluted Ising antiferromagnet.

We report the low-temperature dynamics of a diluted Ising antiferromagnet (${\mathrm{Fe}}_{0.46}$${\mathrm{Zn}}_{0.54}$${\mathrm{F}}_{2}$) over a wide range of magnetic fields. By measuring the magnetization through a number of cooling protocols, we deduce the density of antiferromagnetic domain walls, which can be compared with predictions of the random-field Ising model (RFIM). In both magnetization-relaxation and field-cycling experiments, we find a region of the (H,T) phase diagram in which the dynamic behavior is consistent with the RFIM, as well as a theoretically unexpected region of frozen dynamics.