Effect Of Random Field Research Articles

Random field effects in the three dimensional Ising magnet: Fe x Zn1?x F2

We have carried out a comprehensive neutron scattering study of random field effects in the diluted three dimensional Ising antiferromagnet Fe x Zn1−xF2 withx=0.35 and 0.5. Emphasis is on the global trands from the small to the large random field regimes. It is found, as in previous experiments, that when the system is cooled in a field it evolves from the high temperature paramagnetic state to a low temperature domain wall state. The low temperature peaks are well-described by Lorentzian squared profiles although for thex=0.5 sample extinction made the measurements difficult. In both samples, the results show that in the field-cooled state the correlation length varies asH−v withv=2.2±0.1. In thex=0.35 sample this power law holds over a length scale varying from 2 to 1500 lattice constants. At low fields pretransitional behavior similar to that observed previously in Fe0.6Zn0.4F2 is found. AtT N (H=0) it is found that the correlation length also scales algebraically withH but withv=0.86±0.04. Pronounced history-dependent effects are observed below the phase boundary determined by the peak in the critical scattering. For example, on cooling in zero-field, raising the field and then warming, long range order survives up to the phase boundary; at this point it appears to convert abruptly into the finite correlation length field cooled state although elucidation of the explicit nature of this transition is complicated by rounding due to a concentration gradient. These results are discussed in the context of recent theories incorporating metastability effects as well as recent experiments.

Landau-Lifshitz analysis for stepped surfaces

We consider phase transitions on stepped surfaces. The Landau-Lifshitz rules are used as criteria for determining those (commensurate) superlattice structures that are “allowed”, i.e., may be reached by continuous phase transitions. The problem is reduced to an essentially two-dimensional case which allows one to make use of the results of Rottman. Tables of all possible allowed (commensurate) structures (with scalar order parameters) are given, along with a step-by-step procedure for determining whether a given superlattice structure on a given stepped surface is allowed. Some examples are treated in detail. It is also determined that all allowed transitions are in either the Ising or Xminus; Y with cubic anisotropy universality classes. The effects of random fields generated by non-uniform terrace width distributions are also mentioned.

Random-field effects in site-disordered Ising antiferromagnets

We describe a simple and unambiguous way of mapping the site-dilute Ising antiferromagnet in a uniform field onto the problem of a random-field ferromagnet, and identify the effective random field, in the weak-field limit.

Random-field effects on the critical behavior of an interacting Bose model

The critical properties of a $d$-dimensional Bose model in the presence of a random quenched field are investigated by renormalization-group techniques via the replica trick. To first order in $\ensuremath{\epsilon}=6\ensuremath{-}d$ it is found that both at nonzero- and zero-temperature regimes the grand-canonical critical exponents are the same as those of the corresponding classical model so that thermal and quantum fluctuations appear to be irrelevant. Furthermore, at zero temperature, the scaling laws already established for the pure model are retrieved with the replacement of $d$ with $d\ensuremath{-}4$, but the random critical exponents are not derivable from the pure ones with the dimensional shift $d\ensuremath{\rightarrow}d\ensuremath{-}4$.

Neutron scattering studies of the anomalous magnetic alloyFe0.7Al0.3

Small-angle total and inelastic neutron scattering measurements were performed on a single crystal of the ordered alloy ${\mathrm{Fe}}_{0.7}$${\mathrm{Al}}_{0.3}$. The behavior of the $Q$ dependence of the small-angle intensity can be classified into four temperature regions which correspond to the bulk behavior: (i) $Tg{T}_{c}=510$ K (paramagnetic region); the line shape is Lorentzian with $\ensuremath{\kappa}\ensuremath{\rightarrow}0$ as $Tg{T}_{c}$. (ii) $300 \mathrm{K}lTl{T}_{c}$ (ferromagnetic region); $I(Q)\ensuremath{\sim}{Q}^{\ensuremath{-}2}$ as expected from spin waves. (iii) $100 \mathrm{K}lTl300 \mathrm{K}$ (near ${T}_{c}^{\mathrm{inv}}$); $I(Q)\ensuremath{\sim}{Q}^{\ensuremath{-}\ensuremath{\alpha}}$, with $\ensuremath{\alpha}$ being $T$ dependent and reaching a maximum value $\ensuremath{\alpha}=2.6$. In this region the $T$ dependence of the intensity exhibits a peak which is $Q$ dependent. Near ${T}_{c}^{\mathrm{inv}}\ensuremath{\approx}160$ K, a thermal hysteresis and novel time dependence of the scattering is observed. (iv) $Tl100$ K (spin-glass regime); the line shape is again Lorentzian with $\ensuremath{\kappa}$ increasing with decreasing $T$. No anomaly is observed at ${T}_{f}\ensuremath{\approx}90$ K. The inelastic measurements reveal that spin waves exist in the ferromagnetic regime but disappear as the temperature is lowered. For temperatures less than ${T}_{c}^{\mathrm{inv}}$, an elastic central peak appears which increases as $T$ is decreased. The results are interpreted in terms of random-field effects.

Field dependence of the d.c. magnetic susceptibility in FexMg1-xCl2

The authors have studied the temperature dependence of the susceptibility of insulating FexMg1-xCl2 in various uniform magnetic fields up to 8000 Oe. For x=0.286 spin glass behaviour is observed and the reversibility temperature moves down with field. For x=0.552 results give evidence for two transitions: paramagnetic-antiferromagnetic phase and antiferromagnetic-spin glass phases; the uniform magnetic field enlarges the domain of existence of the spin glass phase (H<5000 Oe), giving an experimental illustration of random field effects.

Random-field critical behavior of ad=3Ising system

Optical birefringence studies of the randomly diluted, $d=3$ Ising antiferromagnet ${\mathrm{Fe}}_{0.6}$${\mathrm{Zn}}_{0.4}$${\mathrm{F}}_{2}$ reveal that the magnetic specific heat exhibits a symmetric logarithmic singularity, consistent with an effective dimensionality $\overline{d}\ensuremath{\simeq}2$, in small magnetic fields $H$ applied parallel to the unique axis. The nature and the sharpness of the phase transition for $H\ensuremath{\le}20$ kOe and reduced temperature $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}\ensuremath{\le}t\ensuremath{\le}{10}^{\ensuremath{-}1}$ suggest that the lower critical dimensionality ${d}_{l}l3$. Both of these results are inconsistent with the predicted mapping $\overline{d}=d\ensuremath{-}2$, for the random-field problem, obtained from perturbation theory. The observed crossover exponent $\ensuremath{\varphi}=1.40\ifmmode\pm\else\textpm\fi{}0.05$ agrees with both the measured and predicted random-exchange susceptibility exponent $\ensuremath{\gamma}$ as is to be expected. The observed amplitude of the shift in ${T}_{c}$ with $H$ agrees with a new theory of random-field effects in diluted antiferromagnets.

Random field effects in magnets

Random field effects in magnets

Random-field effect in diluted Ising antiferromagnets

It is argued that near the percolation threshold of diluted systems there should be an instability of the long-range order in spatially random fields much smaller than the local molecular fields as a result of the strong ramification of the infinite percolation cluster, in all dimensions. This may give a possible explanation for the experiments of Yoshizawa et al., who find a destruction of the long-range order due to relatively small external magnetic fields in diluted two- and three-dimensional Ising antiferromagnets.

Effects of random fields on the phase diagram ofMn0.875Zn0.125F2

Phase transitions in ${\mathrm{Mn}}_{1\ensuremath{-}x}{\mathrm{Zn}}_{x}{\mathrm{F}}_{2}$, $x=0.125$, were investigated using thermal-expansion, magnetostriction, and ultrasonic-attenuation measurements. The phase diagram was determined for 4.2 $\mathrm{K}\ensuremath{\le}T\ensuremath{\le}{T}_{N}$ and $0\ensuremath{\le}H\ensuremath{\le}140$ kOe, where ${T}_{N}=58.4$ K is the N\'eel temperature. The magnetic field $\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}$ was parallel to [001]. The random field ${H}_{R}$ induced by $H$ influences the shape of the $\ensuremath{\lambda}$ anomaly at the paramagnetic-antiferromagnetic transition, and depresses the transition temperature ${T}_{c}^{\ensuremath{\parallel}}$. Some evidence for an irreversible behavior near ${T}_{c}^{\ensuremath{\parallel}}$ is found for $H\ensuremath{\ne}0$. The paramagnetic---spin-flop boundary ${T}_{c}^{\ensuremath{\perp}}(H)$ exhibits a large "bulge" towards high $T$. At 4.2 K, the spin-flop field ${H}_{\mathrm{sf}}$ is 78 kOe, which is lower than that predicted by mean-field theory. The discrepancy is explained by considering the effect of the random fields. As $T$ increases from 4.2 K, ${H}_{\mathrm{sf}}$ first increases but then decreases as $T$ approaches the bicritical temperature ${T}_{b}=55$ K. It is possible that the latter portion of the spin-flop line is actually one of two second-order lines which surround an intermediate phase. The N\'eel temperature is in reasonable agreement with mean-field theory.

Spin correlations near the ferromagnetic-spin glass crossover in EuxSr1−xS

Bulk susceptibility and high-resolution neutron-diffraction measurements have been performed on single crystals of EuxSr1−xS for x = 0.52 and 0.54 near the ferromagnet (FM)-spin glass (SG) crossover. A re-entrant phase boundary is established, discussed by random-field effects. As the temperature is reduced the FM correlation length ξ passes through a resolution-limited maximum where a “frustrated FM” phase is observed. In the SG at lower temperature, ξ decreases again and a coexisting FM component can be excluded.

Critical phenomena in systems with random anisotropies

Current theoretical understanding of the effects of random fields and random anisotropies is reviewed, with emphasis on open questions.

Random-field effects and magnetic susceptibility in diluted Ising antiferromagnets

Random-field effects have been studied in the two-dimensional dilute antiferromagnets Rb2CocMg1-cF4 (c=0.8, 0.7 and 0.6), using static susceptibility under a uniform magnetic field H0. The author found that in dilute systems the static susceptibility diverges at the Neel temperature, which originates from the coupling between uniform and staggered fluctuations. It is remarkable that the H0-induced rounding of the transition peaks was observed, consistent with the destruction of the phase transition under random magnetic fields.

Random-field effects in Fe1−xMgxCl2

We analyze in detail how random fields are generated in a site-random uniaxial antiferromagnet when a uniform magnet field is applied. Explicit expressions are given for the mean-square random field. We also report on a systematic specific heat study of two three-dimensional Ising systems, pure FeCl2 and site-random Fe0.682Mg0.318Cl2 (MG318), in constant applied fields. The contrasting behavior of the two provide a vivid demonstration of random-field effects. The unusual changes in the shape of the specific heat anomaly observed in MG318 are explained as crossover behavior and not a manifestation of new critical behavior. The crossover exponent φ associated with the random fields is determined from the shape of the magnetic phase boundary. We find φ=1.25±0.10, in excellent agreement with theoretical prediction.

Random-field effects in metamagnet tricritical-point measurements

It is argued that in metamagnets in finite applied fields, the random fields, both staggered and uniform, generated by the impurity-induced random interactions fundamentally alter the behavior near the tricritical point. As this point is approached along the first-order boundary, two consecutive crossovers are expected, from classical tricriticality to three-dimensional Ising criticality, and then to a rounded transition. This stepwise cross-over occurs asymmetrically in the coexisting phases. These effects are of significant practical importance in many multicritical experiments.

Hyperscaling and crossover exponents near the percolation threshold

The critical exponents which describe quantities which are measured per unit 'mass' of the infinite cluster near percolation are shown to be shifted by beta p (the exponent describing the probability of belonging to this cluster). The fractal dimensionality of the infinite cluster then replaces the Euclidean one in hyperscaling relations. The crossover exponent for the effects of random fields on dilute Ising models are zero temperature is then shown to be phi h= gamma p+ beta p. Similarly, that for random local concentrations is phi p= alpha p+ beta p.

Random-Field Effects on Critical Behavior of Diluted Ising Antiferromagnets

Random-field effects have been studied, using linear birefringence, in the random Ising antiferromagnets ${\mathrm{Fe}}_{x}{\mathrm{Zn}}_{1\ensuremath{-}x}{\mathrm{F}}_{2}$ and ${\mathrm{Mn}}_{x}{\mathrm{Zn}}_{1\ensuremath{-}x}{\mathrm{F}}_{2}$. with $0&lt;{H}_{0}&lt;~20$ kOe parallel to $c$, large shifts in ${T}_{c}$ and dramatic changes in the shapes of the transition peaks were observed. These results confirm some, but not all, theoretical predictions and suggest an effective dimensionality $d\ensuremath{\simeq}2$. No ${H}_{0}$-induced rounding was observed. This is shown to be consistent with the rounding seen in other experiments at larger values of $\frac{g{\ensuremath{\mu}}_{\mathrm{B}}{H}_{0}}{k{T}_{c}}$.

Spin correlations near the ferromagnetic—spin-glass crossover point in amorphous Fe-Mn alloys

We have performed a neutron scattering study of the spin correlations in the amorphous alloys ${({\mathrm{Fe}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x})}_{75}{\mathrm{P}}_{16}{\mathrm{B}}_{6}{\mathrm{Al}}_{3}$ with $x$=0.35 and 0.25; the former exhibits short-range spin correlations at all temperatures. The latter displays a paramagnetic-ferromagnetic transition followed by a gradual evolution into a state characterized by ${Q}^{\ensuremath{-}2.6}$ power-law decay at low temperatures. We present a simple model for this behavior based on random field effects.

NMR Study of Random-Field Effects in a Diluted Antiferromagnet

NMR of 19 F with no magnetic near neighbors (F o ) in the diluted antiferromagnet Mn 0.65 Zn 0.35 F 2 was used to study “random-field” effects on the critical behavior. From the temperature dependence of (1/ T 1 ), for fields applied parallel and perpendicular to the easy (c) axis, it was found that the transition temperature T c depressed substantially with field only for H o ∥ c . The field dependence of Δ T c = T c ⊥ - T c || is in general accord with the theory for random-field effects in disordered, anisotropic antiferromagnets, Δ T c ∝ h 2/φ , where h =µ H o / k T c . The value determined for the shift exponent φ=1.38±0.2 is in reasonable agreement with the prediction φ≃1.25.

Effects of random fields on the phase diagram of Mn0.957 Zn0.043F2

The phase diagram of Mn0.957Zn0.043F2 was measured in magnetic fields H↘ up to 175 kOe, directed along the easy axis. The para-antiferro transition, at T∥C(H), shows an increased roundling at finite H. At low H, the slope −dT∥Cd(H2) is considerably larger than predicted by mean field theory. The paraspinflop boundary exhibits a much larger ’’bulge’’ than in pure MnF2. All these features are attributed to random fields. Several discrepancies from early predictions for the effects of random fields are noted, and are attributed to the absence of a genuine order-disorder transition on the line T∥C (except at H = 0).