Dilute Antiferromagnets Research Articles

Scaling properties ofthe critical behaviour of the dilute antiferromagnetFe0.93Zn0.07F2

Critical scattering analyses for dilute antiferromagnets are madedifficult by the lack of predicted theoretical line shapes beyondmean-field models. Nevertheless, with the use of some generalscaling assumptions we have developed a procedure by means of which we cananalyse the equilibrium critical scattering in these systems forH = 0, the random-exchange Ising model, and, more importantly, forH>0, the random-field Ising model. Our new fitting approach, unlikethe more conventional techniques, allows us to obtain theuniversal critical behaviour exponents and amplitude ratios as wellas the critical line shapes. We discuss the technique as applied toFe0.93Zn0.07F2. The general technique, however, shouldbe applicable to other problems where the scattering line shapes arenot well understood but scaling is expected to hold.

Equilibrium Random-Field Ising Critical Scattering in the AntiferromagnetFe0.93Zn0.07F2

It has long been believed that equilibrium random-field Ising model (RFIM) critical scattering studies are not feasible in dilute antiferromagnets close to and below Tc(H) because of severe non-equilibrium effects. The high magnetic concentration Ising antiferromagnet Fe(0.93)Zn(0.07)F2, however, does provide equilibrium behavior. We have employed scaling techniques to extract the universal equilibrium scattering line shape, critical exponents nu = 0.87 +- 0.07 and eta = 0.20 +- 0.05, and amplitude ratios of this RFIM system.

Ground state structure of random magnets

Using exact optimization methods, we find all of the ground states of +/- h random-field Ising magnets (RFIM) and of dilute antiferromagnets in a field (DAFF). The degenerate ground states are usually composed of isolated clusters (two-level systems) embedded in a frozen background. We calculate the paramagnetic response (sublattice response) and the ground state entropy for the RFIM (DAFF) due to these clusters. In both two and three dimensions there is a broad regime in which these quantities are strictly positive, even at irrational values of h/J (J is the exchange constant).

Broken symmetry and strangeness of the semiconductor impurity band metal-insulator transition.

The filamentary model of the metal-insulator transition in randomly doped semiconductor impurity bands is geometrically equivalent to similar models for continuous transitions in dilute antiferromagnets and even to the lambda transition in liquid He, but the critical behaviors are different. The origin of these differences lies in two factors: quantum statistics and the presence of long range Coulomb forces on both sides of the transition in the electrical case. In the latter case, in addition to the main transition, there are two satellite transitions associated with disappearance of the filamentary structure in both insulating and metallic phases. These two satellite transitions were first identified by Fritzsche in 1958, and their physical origin is explained here in geometrical and topological terms that facilitate calculation of critical exponents.

Hysteresis and relaxation behavior in dilutedA2Fe1−xInxCl5⋅H2O(A=K,Rb)

Low-anisotropy antiferromagnetic compounds of the general formula ${A}_{2}$Fe${}_{1\ensuremath{-}x}$In${}_{x}$Cl${}_{5}\ensuremath{\cdot}$H${}_{2}$O $(A=$K,Rb) exhibit a net spontaneous magnetization below their transition temperature ${(T}_{N})$ when they are cooled in very small applied magnetic fields. This magnetization is observed when the easy axis of the system is aligned parallel to the field and is found to saturate at fields of a few Oe. Hysteresis loops $M$ vs $H$ have been obtained at several temperatures for single crystals of samples with different concentrations $x$. For low values of $x$ the loops are not symmetric and show a series of well-defined jumps. This behavior suggests that a structure of domains is present, the jumps being associated with avalanche-type movements of the antiferromagnetic domain walls. The coercive fields are of the order of a few hundreds of Oe and for similar $x$ are lower in the Rb-based samples than in the K ones. When the applied field is removed below ${T}_{N}$ some of the samples of the dilute rubidium derivative show relaxation effects. The drop in $M$ after the field is removed is two orders of magnitude larger than the drop expected from the susceptibility term $({\ensuremath{\chi}}_{\ensuremath{\Vert}}H)$. The origin of the net magnetization in this and in other dilute antiferromagnets has not yet been established but net domain wall magnetization of antiferromagnetic domains is suggested as the most consistent mechanism.

Influence of quantum fluctuations on the Néel temperature of a dilute two-dimensional anisotropic antiferromagnet

A quantum Monte Carlo procedure is used to calculate the energy, sublattice magnetization, Neel temperature, and the slopes of the S=[1/TN(x=0)]dTN(x)/dx curves as functions of the hole concentration and the exchange anisotropy Δ=1−Jx,y/Jz in the Heisenberg model with anisotropic negative interactions between nearest neighbors in a square lattice with dilution among the lattice sites. The slope diverges in the limit Δ→0: S∼ln(6.5/Δ).

Logarithmic frequency dependence of the piezoelectric effect due to pinning of ferroelectric-ferroelastic domain walls

Pinning of the ferroelastic-ferroelectric domain walls on randomly distributed defects in ferroelectric ceramics leads to a field dependence of the piezoelectric coefficient that is analogous to the Rayleigh law for magnetic susceptibility. It is shown in this paper that the piezoelectric coefficient of a lead zirconate titanate ferroelastic-ferroelectric system depends linearly on the logarithm of the frequency of the field. Both the reversible and irreversible components of the piezoelectric coefficient are found to be frequency dependent. A similar type of frequency dependence due to domain-wall pinning has been predicted for the magnetic susceptibility in disordered ferromagnets and dilute antiferromagnets. The presented results offer experimental evidence that the theoretical approach developed for domain-wall pinning effects in magnetic materials is generally valid for pinning processes in all ferroic systems, ferromagnetics, ferroelectrics, and ferroelastics.

Spin waves in dilute antiferromagnets

Spin wave approximation is used to study magnetic properties of a dilute antiferromagnet (DAF). The ground state of these systems is found to be the same as of an AF for B an ⪢ B E, while in the case B an ⪡ B E this state departs from the completely ordered. This could be due to the more critical exchange interactions in a DAF. In the long wavelength, low temperature and zero field limits, the system behaves like an ordinary semiconductor. In the very dilute limit the spin mean deviations and heat capacity are rational fractions of the concentration.

Spin correlations in percolating networks with fractal geometry

Using neutron-scattering techniques, we have investigated the magnetic correlations in dilute antiferromagnets close to the percolation threshold, in which the magnetic connectivity takes a fractal form. Recent experimental results concerning the self-similarity of the magnetic order, and magnetic excitations in two-dimensional Ising and threedimensional Heisenberg antiferromagnets are presented.

Domain growth in the three-dimensional random-field Ising magnetFe0.5Zn0.5F2

Complementary neutron-scattering and superconducting quantum interference device (SQUID) magnetometry measurements have been carried out to study the time dependence of the field-cooled metastable domains in ${\mathrm{Fe}}_{0.5}$${\mathrm{Zn}}_{0.5}$${\mathrm{F}}_{2}$. These neutron-scattering data provide direct evidence of a logarithmic increase in the correlation length upon quenching the system to T\ensuremath{\le}${\mathit{T}}_{\mathit{c}}$ at H=5.5 T. At low temperatures the magnetic domains are frozen on experimental time scales. SQUID measurements performed at a series of fields and temperatures confirm the evolution of the excess magnetization ${\mathit{M}}_{\mathrm{ex}}$ arising from domain surfaces and allow quantitative analysis of its time dependence. Specifically, we found that ${\mathit{M}}_{\mathrm{ex}}$\ensuremath{\sim}${\mathit{H}}_{\mathit{M}}^{\ensuremath{\nu}}$[ln(t/\ensuremath{\tau})${]}^{\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\psi}}}$, where ${\ensuremath{\nu}}_{\mathit{M}}$=2.7\ifmmode\pm\else\textpm\fi{}0.1 and \ensuremath{\psi}=1.1\ifmmode\pm\else\textpm\fi{}0.3 for H\ensuremath{\ge}3.45 T; \ensuremath{\psi} is much less than 1 for lower fields. In particular, \ensuremath{\psi}=0.42\ifmmode\pm\else\textpm\fi{}0.14 at H=1.5 T, in agreement with a prediction by Nattermann and Vilfan. At H=5.5 T, ${\mathit{M}}_{\mathrm{ex}}$(T) and the inverse correlation length \ensuremath{\kappa}(T) exhibit identical time dependences. Overall, these measurements reveal the varied time dependence of a field-cooled, strongly anisotropic dilute antiferromagnet in different applied fields, and shed light on the mechanisms of domain evolution.

Effect of fractons on the exciton dynamics in dilute magnets.

The effect of fractons on the exciton dynamics in dilute magnets is investigated theoretically. It is predicted that the total intensity of the hot exciton-fracton absorption band varies with temperature as ${\mathit{T}}^{\mathit{d}\mathrm{\ifmmode\bar\else\textasciimacron\fi{}}+2\mathit{d}\mathrm{\ifmmode\bar\else\textasciimacron\fi{}}/\mathit{D}}$, where d\ifmmode\bar\else\textasciimacron\fi{} is the fracton dimension and D the fractal dimension. Also, the fracton-exciton interaction results in a quadratic temperature dependence of the exciton intersublattice relaxation rate in dilute antiferromagnets, substantially different from that (cubic temperature dependence) of magnon-exciton scattering. Implication of the results for experimental study of the magnon-fracton crossover in dilute magnets is demonstrated.

Dilute antiferromagnets: Imry-Ma argument, hierarchical model, and equivalence to random field Ising models

We discuss some aspects of the problem of the equivalence of dilute antiferromagnets and random field Ising models. We first investigate for dilute antiferromagnets the validity of the arguments of Imry and Ma. It turns out that they are applicable, but some care is required concerning the role played by the so-called internal Peierls contours. Next we consider a hierarchical version of a dilute antiferromagnetic Ising model in the presence of a uniform magnetic field and show that a renormalization group transformation maps it exactly into a hierarchical version of the random field Ising model, thus proving their equivalence as far as the critical behavior is concerned. In particular this implies that phase transition with spontaneous magnetization occurs only for dimensiond>2. Finally we show that in the absence of internal Peierls contours both models, in their hierarchical versions, exhibit phase transition already in dimensiond=2.

Remanent magnetization of the dilute antiferromagnets Mn1-xZnxF2 at very low magnetic fields

The magnetization of Mn1-xZnxF2 single crystals with x = 0.25 and 0.51 was studied in low magnetic fields directed along the easy axis (c axis). Data were taken for axial fields Haxial between approximately 10-3 Oe and approximately 10 Oe. Below the Neel temperature TN, the magnetization M for given H,axial and temperature T depended on the history of the sample. Data obtained while cooling in a constant Haxial (FC procedure) show a dramatic rise of M below TN. This rise corresponds to the development of a thermoremanent magnetization M,. The sign and magnitude of M, depend on the axial field present while cooling; Mr is proportional to Haxial at low axial fields, but approaches saturation at Haxial approximately 1 Oe. The measured values of Mr(t)/Mr(0), where t = T/TN is the reduced temperature, are independent of Haxial and are the same for both samples. They also agree with values of Mr(t)/Mr(0) measured in K2Fe1-xInxCl5.H20, but not with those measured in K2Fe(Cl1-xBrx)5.H20. Fits of the temperature dependence of M, near TN yield an effective critical exponent B,. Extrapolated values of B, very close to TN are between 0.35 and 0.40. Experiments in which Haxial is changed below TN show that the remanent magnetization is controlled only by the field Haxial(TN) present while cooling through TN. The observed properties of Mr, particularly the saturation in axial fields of approximately 1 Oe, cannot be explained in terms of domains caused by random fields. Another explanation that fails is based on the statistical difference between the number of up and down spins in each of the antiferromagnetic domains, which exist even in the absence of random fields. It is possible that Mr arises from the walls between such domains. but since this explanation is yet to be tested other possible explanations cannot be ruled out.

Random-field-induced rounding of the Ising-type transition in physisorbed (CO)1-x(N2)x mixtures: Monte Carlo studies of a simple model

The authors propose a simple model for (CO)1-x(N2)x mixtures adsorbed on graphite where a lattice site carries a spin Si=+or-1 representing the orientations of the CO electric dipole moment if the site is occupied by a CO molecule, while the spin Si=0 if the site is taken by an N2 molecule, which has a quadrupole moment only. Assuming a bilinear dipole-quadrupole coupling, randomly quenched N2 impurities then act as random fields would act on an Ising antiferromagnet. For simplicity, a square lattice is treated and the range of all interactions is restricted to nearest neighbours. Monte Carlo studies are performed for a range of lattice linear dimensions L from L=24 to L=50, and the specific heat order parameter and susceptibility, as well as the fourth-order cumulant, are studied, applying finite-size scaling concepts where appropriate. The specific heat results display a striking qualitative similarity to the experimental data of Wiechert and Arlt, and provide evidence that the transition is already rounded by arbitrarily small dilution, consistent with theoretical predictions for the two-dimensional random field Ising model. While the experiments needed to rely on the specific heat only, the data for the (strongly rounded) ordering susceptibility and the cumulant (where the common intersection point disappears, consistent with the absence of a transition) provide compelling evidence for this picture. The crossover scaling analysis first proposed by Ferreira et al. for dilute antiferromagnets in a field also works out reasonably well for the present model.

Relaxation of the remanent magnetization of dilute anisotropic antiferromagnets.

The relaxation of the remanent magnetization of metastable domains in field-cooled, dilute antiferromagnets is studied with use of Monte Carlo simulations. The relaxation is extremely slow due to strong pinning by magnetic vacancies, as previously observed. The function ${\mathit{M}}_{\mathrm{\ensuremath{\tau}}}$(t)=${\mathit{M}}_{0}$exp{-A[ln(t/t')${]}^{\mathit{y}}$}, suggested by results of recent experiments on ${\mathrm{Fe}}_{0.47}$${\mathrm{Zn}}_{0.53}$${\mathrm{F}}_{2}$, is used to fit the simulation data and yields excellent fits with a greater than unity value for y, consistent with the experimental results. This form appears to fit the simulation data much better than either of the functions proposed earlier, namely the power law ${\mathit{M}}_{\mathrm{\ensuremath{\tau}}}$(t)=${\mathit{M}}_{0}$${\mathit{t}}^{\mathit{x}}$ and the equation ${\mathit{M}}_{\mathit{r}}$(t)=A[ln(t/${\mathit{t}}_{0}$)${]}^{\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\psi}}}$, where \ensuremath{\psi}\ensuremath{\approxeq}0.4.

Dipolar interactions in the dilute antiferromagnet in a uniform field

The authors examine the role played by dipolar interactions in the equilibrium critical behaviour of the dilute antiferromagnet in a uniform field (DAFF). The DAFF has been known to map onto a random field model, and we perform a similar mapping, only this time including dipolar interactions. They conclude that dipolar forces affect the DAFF in a way no different from the case for the corresponding pure system. Dilution does not generate any additional long-range forces or other effects arising from dipolar forces. In particular, in the final random field model which the DAFF maps onto, they find that the mean-field propagator is unaffected by the inclusion of dipolar interactions save for some constant terms. They restrict the work to the critical region close to the transition temperature and assume a domain-free state.

Dynamical Process of Disorderingin a Percolation Magnet under Random Fields

The kinetics of the disordering process from an initial long-range ordered state to a final microdomain state has been elucidated with a two-dimensional dilute Ising antiferromagnet, Rb 2 Co 0.6 Mg 0.4 F 4 . The present results have revealed that the temporal change in the order of ramified clusters obeys a logarithmic law, at low temperatures, independent of both the temperature and the strength of the external field. This fact indicates that the kinetics of disordering is governed by a random magnetic field.

Low-concentration series in general dimension

We discuss recent work on the development and analysis of low-concentration series. For many models, the recent breakthrough in the extremely efficient no- free-end method of series generation facilitates the derivation of 15th-order series for multiple moments in general dimension. The 15th-order series have been obtained for lattice animals, percolation, and the Edwards-Anderson Ising spin glass. In the latter cases multiple moments have been found. From complete graph tables through to 13th order, general dimension 13th-order series have been derived for the resistive susceptibility, the moments of the logarithms of the distribution of currents in resistor networks, and the average transmission coefficient in the quantum percolation problem, 11th-order series have been found for several other systems, including the crossover from animals to percolation, the full resistance distribution, nonlinear resistive susceptibility and current distribution in dilute resistor networks, diffusion on percolation clusters, the dilute Ising model, dilute antiferromagnet in a field, and random field Ising model and self-avoiding walks on percolation clusters. Series for the dilute spin-1/2 quantum Heisenberg ferromagnet are in the process of development. Analysis of these series gives estimates for critical thresholds, amplitude ratios, and critical exponents for all dimensions. Where comparisons are possible, our series results are in good agreement with bothe-expansion results near the upper critical dimension and with exact results (when available) in low dimensions, and are competitive with other numerical approaches in intermediate realistic dimensions.

The random field Ising model in one and two dimensions: A renormalization group approach

We study the one- and two-dimensional random field Ising models, using a real space renormalization group approach. We consider a bimodal distribution such that the random field assumes the values of + H or − H with probabilities p and1 − p, respectively (instead of the usual case p = 1 2 ). We obtain the phase diagrams and exponents associated with the uniform ( p = 0, 1) and the random field ( p = 1 2 ) problems. Our results are consistent with the absence of a spontaneous magnetization for H ≠ 0 and p ≠ 0, 1 in d = 1, 2 even at zero temperature. We finally discuss the nature of the singularities in the thermodynamics quantities occurring at T = 0 for discrete values of the random field intensity. We compare these results with those obtained previously for the dilute antiferromagnet in a uniform field using the same approach.

Evidence for a spin-glass behavior in the diluted antiferromagnet FexZn1−xF2

We report dc susceptibility ( χ) measurements in the diluted antiferromagnet Fex Zn1−x F2 with concentrations x=0.10, 0.25, 0.31, and 0.46. The field and temperature dependencies of χ in the x=0.10 and 0.25 samples reveal that a spin-glass (SG) phase appears at low temperatures. For x=0.31, which is slightly above the percolation limit (xp=0.24), the SG phase is also present at low temperatures, but there is a clear indication of long-range antiferromagnetic (AF) ordering at intermediate temperatures. Finally, in the sample with x=0.46, AF ordering with random-field effects determines the characteristic behavior. These studies will help in the understanding of the crossover from random field to SG behavior in dilute antiferromagnets.