Random Crystal Field Research Articles

Phase Diagrams of a Spin‐One Ising Model with a Random Crystal Field in the Correlated Effective‐Field Treatment

AbstractThe phase diagram of the spin‐one Ising model with a random crystal field Di on a square lattice is investigated by the use of the correlated effective‐field theory, when the random crystal field is distributed according to the law P(Di) = pδ (Di − D) + (1 − p) δ (Di). A number of characteristic phenomena are obtained, such as the p‐dependence of the tricritical point and the reentrant phenomenon due to the disorder of the crystal field.

Electron paramagnetic resonance and luminescence of Gd3+in the mixed fluorides Ca1-xLaxF2+xand Ca1

Abstract In this paper we present an study on the EPR and photoluminiscence spectra of Gd3+ in the mixed crystals Ca0.998-xRxGd0.002F0.002+x(x≤0.35, R=La or Y). For x <0.1 the EPR spectrum shows a main signal due to cubic Gd3+ that is broadened as x increases. Different broadenings are found for La and Y samples For high x values the EPR spectrum is similar to that in glass matrices. The results are explained taking to account a random second rank crystal field due to the extra charges associated with R3+ and fluorine intersitials. The 6P→6S emission of Gd3+ also has been measured. The influence of R concentration on this luminiscence has been studied.

The random phase approximation and crystal field effects in magnetism

A novel solution to the problem of incorporating a strong axial crystal field interaction into the RPA model of a Heisenberg ferromagnet is presented and discussed. The method is based on technique widely used in the interpretation of nuclear quadrupole resonance (NQR) experiments, where the Hamiltonian is first transformed into the interaction picture and terms which oscillate rapidly in time are subsequently dropped. It is shown that when this method is applied to an S=1 Heisenberg ferromagnet with an axially symmetric quadrupole interaction, unique solutions can be obtained for the ensemble averages (Szn). The results are compared with those of earlier workers and it is shown that (i) in the limit T to 0 K and D to 0 the usual spin wave result is obtained, (ii) both excitation branches exhibit dispersion at finite temperatures, and (iii) a unique solution can be obtained for the Curie temperature Tc in the presence of crystal fields, in contrast to previous work.

The random phase approximation and crystal field effects in magnetism: S=3/2

A novel solution to the problem of incorporating crystal field interactions into the RPA model of an Heisenberg ferromagnet, known as the transformed Hamiltonian/random phase approximation (TH/RPA), is applied to an easy axis S=3/2 Heisenberg ferromagnet, subject to an axially symmetric quadrupole interaction. It is demonstrated that unique solutions can be obtained for the ensemble averages. In addition, it is shown that (i) in the limit T to 0 K and D to O the usual spin-wave result is obtained, (ii) three excitation branches are present, which exhibit dispersion at finite temperatures, (iii) a unique solution can be obtained for the Curie temperature Tc in the presence of crystal fields, in contrast to earlier work, and (iv) a two-parameter analogue of the Callen and Shtrikman single-particle generating function can be constructed which exactly mimics the TH/RPA ensemble averages.

Comparison of effective-field and mean-field theories for the spin-one Ising model with a random crystal field

The phase diagram of the spin-one Ising model with a random crystal field is investigated by the use of the effective-field theory with correlations. The important differences from the results obtained by the standard mean-field theory are indicated. The differences are very similar to those found in the dilution problem of magnetic systems.

Mean-field phase diagram of the spin-1 Ising ferromagnet in a Gaussian random crystal field

The authors consider the mean-field version of a spin-1 Ising ferromagnet in a random crystal field described by a Gaussian probability distribution. Depending on the width of the Gaussian, they obtain a rich phase diagram, with critical and coexistence lines and some multicritical points. At low temperatures, their numerical results are supported by some analytic asymptotic expansions. They also calculate the ground state for a suitable two-valued delta-function distribution to compare with the results for the Gaussian case.

On a magnetic analogy of the de Gennes' ant in a labyrinth

The authors present a rigorous proof that the discrete Laplace transforms of the displacement probabilities of the myopic and the blind ant are proportional to the spin-spin correlation functions of a system of continuous spins in a random crystal field. From this it follows that one can use the Hamiltonian of the spin system to calculate, for instance, the fractal properties of the paths of the ants in a random medium, and in particular one can demonstrate in a simple way that the asymptotic properties of the two ants are equivalent.

Exact results for a spin-one Ising model with random crystal field

An Ising spin-one model with an arbitrary distribution P( Delta ) of crystal field interaction Delta , described with Blume-Emery-Griffiths Hamiltonian is considered for the annealed case in which the system is in complete thermal equilibrium. The critical temperature, under some restrictive condition on the interaction parameters, is obtained exactly for the honeycomb lattice.

Mean-field theory of the spin-1 Ising model with a random crystal field

A spin-1 Ising model with a random crystal field Delta i has been studied within the mean-field approximation. For the particular two-valued distribution P( Delta i)=1/2( Delta ( Delta i- Delta (1+ alpha ))+ delta ( Delta i- Delta (1- alpha '))), depending upon the value of alpha , three types of diagram have been found in the ( Delta ,T) plane.

Comment on the mean-field phase diagram of the spin-1 Ising model in a random crystal field

The authors show the existence of additional ferromagnetic phases and transition lines in the mean-field calculations of Benyoussef and collaborators (see J. Phys. C: Solid State Phys., vol.20, p.5349, 1987) for the phase diagram of a spin-1 Ising model in a random crystal field Delta i with probability distribution P( Delta i)=p delta ( Delta i- Delta )+(1-p) delta ( Delta i).

Magnetic properties of the mixed spin system with a random crystal field

The effects of a random crystal field on the magnetic properties (phase diagram, magnetization and initial susceptibility) of a spin- 1 2 and spin-1 mixed Ising spin system are investigated by using effective-field theory with correlations. We find a variety of interesting phenomena resulting from a fluctuation of the crystal field interaction. In particular, the reentrant phenomenon induced by the fluctuation of the crystal field is found.

A new disordered phase and its physical contents of a mixed Ising system with a random crystal field

A new disordered phase of a mixed spin-1 and spin -1 2 Ising system with a random crystal field is found and investigated by the use of the effective-field theory with correlations. The phase including the reentrant phenomenon results from the fluctuation of crystal field at its critical value where the transition temperature reduces to zero. In order to examine the physical contents of the phase, its magnetic behavior is studied under applied magnetic fields.

Phase transition of the mixed spin system with a random crystal field

Abstract The effect of a random crystal field on the transition temperature of the spin- 1 2 and spin-1 mixed Ising spin system is investigated with the use of an effective-field theory with correlations. We find a variety of interesting phenomena resulting from the fluctuation of the crystal field interaction.

The phase transition of the spin-one Ising model with a random crystal field

The effect of a random crystal field on the tri-critical behaviour of the spin-one Ising model is investigated by the use of the effective-field theory with correlations. The author finds that the order of the phase transition changes from first to second and that the temperature dependence of the magnetisation then exhibits some characteristic behaviour, when the crystal field fluctuates near the tri-critical point.

The spin-1 Ising model with a random crystal field: the mean-field solution

A spin-1 Ising model with a random crystal field Delta i has been studied within the mean-field approximation. For the particular two-valued distribution P( Delta i)=p delta ( Delta i- Delta )+(1-p) delta ( Delta i), three types of diagrams have been found in the ( Delta ,T) plane, the type depending on the concentration p.

Resonant nearly degenerate backward four-wave mixing in open and closed systems.

This paper presents perturbation calculations using the density matrix to describe the nearly degenerate four-wave-mixing spectral response in resonant systems subject to state-specific reservoir coupling. The calculations provide physical insight into the origin of narrow resonances observed in recent experimental work in atomic sodium and ultranarrow resonances in crystals. The calculations are for systems which are homogeneously broadened as well as systems which are inhomogeneously broadened due to velocity effects or random crystal fields. The calculations show that it is possible to eliminate the effects of either kind of broadening and measure the decay rate of the dipole coherence as well as the decay rates of both states of the transition. Furthermore, the calculations indicate that the method of cross-correlated optical fields which was used to eliminate the effects of laser jitter in longitudinal relaxation rate measurements could be extended to the measurements of slow dephasing rates in crystals.

Field-induced neutron depolarization in amorphous RE-TM spin glasses

Neutron depolarization induced by an applied magnetic field is reported for the amorphous spin glass compositions DyCu, GdAl 2 and NdFe 2. The different field-cooled behavior observed in the first two compositions is attributed to the different mechanisms (exchange fluctuations and random crystal field anisotropy) believed to stabilize the spin glass state in the two cases.

Magneto-optic properties of amorphous Tb-Fe films

The magnetization of Tb-Fe amorphous alloy films show large deviations from saturation for both the Tb and Fe magnetic subsystems caused by random crystal field anisotropy. The Faraday rotation is adequately accounted for by the influence of the Hall angle, and the Kerr effect is shown to be proportional to the Faraday rotation.

Quadrupolar crystal fields in random CeAl3

Abstract An excess of low temperature entropy above the k B ln 2 of a single Kramers doublet per Ce-ion is interpreted as the “softening” of the excitation to the next doublet without affecting the total crystal field splitting. A model is proposed which relates this feature to random quadrupolar crystal fields.

Breakdown of ferromagnetic order in dilute alloys

Using magnetoresistance measurements, it is shown that in PdCo and PtFe dilute alloys strict ferromagnetic order is broken down by weak random crystal fields. The disorder can be suppressed by applying moderate magnetic fields.