Axial Crystal Field Research Articles

Effect of a distribution of exchange parameters within a simple localized-itinerant model

The magnetic behavior at T = 0 K of a system consisting of conduction electrons coupled to localized electrons submitted to an axial crystal field is studied in the molecular field approximation. We assume that the exchange parameter J varies spatially, with a Gaussian probability distribution. We define an average ionic magnetic moment and obtain the condition for spontaneous magnetic order, involving the crystal field parameter, the width and the mean value of the exchange parameter distribution. We also obtain graphs of the magnetic moment versus mean value of the exchange parameter distribution, for different distributions showing that the distribution of the J's reduces the rate of increase of magnetization versus the mean J.

Fe[S2CNC4H8]2I: A quasi-two-dimensional XY antiferromagnet

The magnetic properties of Fe[S2CNC4H8]2I have been studied, the first pentacoordinate Fe(III) system of this type with a cyclic terminal group, rather than an alkyl group, to be examined in detail. The susceptibility of a polycrystalline sample is of Curie–Weiss form above 30 K, with ḡ=2.16 ±0.02 and S=3/2 and with θ=−0.75±1.0 K. Thus the unusual intermediate spin state occurs here as in earlier examples. The susceptibility can be fit quite well down to about 6 K assuming that axial and rhombic crystal field distortions occur, represented by D[Ŝ2z − S(S + 1)/3] and E[Ŝ2x − Ŝ2y] terms in the spin Hamiltonian, and incorporating exchange interactions in a mean-field approximation. Fitted parameters are D/k=9.3± 0.5 K, E/k=−0.6±0.2 K, gx=2.23± 0.05, gy= 2.19 ± 0.05, gz=2.04 ± 0.05, and zJ/k=−0.235 ±0.02 K. At low temperatures the susceptibility exhibits a broad maximum with T(χmax)=3.23± 0.04 K and χmax =0.376±0.004 emu/mol. An antiferromagnetic transition at Tc=2.21±0.01 K is inferred from the position of a maximum in (∂χ/∂T), an ordering temperature in reasonable agreement with earlier Mössbauer results. The ratio Tc/T(χmax) =0.68±0.01 is suggestive of quasi-two-dimensionality. In the region of the maximum an acceptable fit according to a 2D- XY model with plausible parameter values can be achieved, but only with a ferromagnetic interlayer exchange interaction about 28% as strong as the leading antiferromagnetic intralayer interaction. Isotherms of M vs H show somewhat unusual curvature, the explanation of which is unclear.

Ferromagnetism of Ni(SCN)2(C2H5OH)2

The magnetic properties of Ni(SCN)2(C2H5OH)2 have been studied, the first Ni(II) system in the general family of compounds M(SCN)2(ROH)2 (where M=divalent Mn, Fe, Co, or Ni and R=CH3, C2H5, i- or n-C3H7) to be examined at low temperatures. In contrast to previously studied Mn(II) and Co(II) members of this family, which exhibit predominant antiferromagnetism, the present compound is ferromagnetic. The susceptibility of a polycrystalline sample is of Curie–Weiss form only above 75 K, with ḡ = 2.175 ± 0.01 and S=1 and with θ=24.1±1.0 K. The initial susceptibility is well accounted for by an asymptotic critical law, χ0 = Γ[T/Tc − 1]−γ, in the reduced temperature range 0.147–0.013, with Tc = 13.081 ± 0.01 K, γ=1.354±0.02, and Γ=0.0925±0.003 emu/mol. The γ value is between 3D-XY and 3D-Heisenberg model predictions. The susceptibility in the paramagnetic regime well above Tc is analyzed including the effects of axial and rhombic crystal field distortions, represented by D[Ŝ2z − S(S + 1)/3] and E[Ŝ2x − Ŝ2y] terms in the spin Hamiltonian, and incorporating exchange interactions in a mean-field approximation. An excellent fit is obtained with g=2.175, D/k=−64.3±5 K, E/k=23.1±4 K, and zJ/k=19.4±1 K. The magnitude of D is the largest we know of in a Ni(II) compound. The three spin states of the 3A crystal field ground term are strongly split, probably contributing to the relatively low value of Tc compared to zJ/k. Some two-dimensional character in the exchange, as has been found for other members of this family of compounds, may also contribute.

Effect of a distribution of exchange parameters within a simple localized-itinerant model (abstract)

The magnetic behavior at T=0 K of a system consisting of conduction electrons coupled to localized electrons is studied in the molecular-field approximation with a simple exchange parameter distribution. The localized electrons are also submitted to an axial crystal field. We define an average ionic magnetic moment and obtain a condition for the spontaneous magnetic order involving the crystal field, the width, and the center of the exchange distribution. We also study the magnetic behavior in the para- and ferromagnetic regions of the phase diagram. In a previous study1 the same model was applied to a system containing a crystal-field distribution.

Magnetic and magneto-optical properties of rare-earth transition-metal alloys containing Dy, Ho, Fe, Co

Amorphous rare-earth transition-metal alloys of composition REl−xTMx with RE=Dy, Ho; TM=Fe,Co and 0<x<1 and Dyl−x(Fe,Co)x were prepared by evaporation. The saturation magnetization, uniaxial anisotropy, coercivity, and Faraday rotation were investigated as a function of composition and temperature. Also, the spectral variation of the Kerr rotation was measured. The magnetization data indicate a strong dispersion of the RE moments due to randomly oriented local crystal field axes. The strong turndown of the Curie temperature for the Fe-rich alloys suggests that an additional dispersion is present in the Fe subnetwork. The mean field theory was used to analyze the temperature variation of the magnetization yielding smaller TM spin values and exchange coupling constants as compared with those of the Gd and Tb analogs. The uniaxial anisotropy constant Ku for Dy-Co based alloys was found to vary with the square of the Dy subnetwork magnetization as predicted by the random single-ion theory. The anisotropy of Dy-Fe and Ho based alloys require additionally dipolar terms to account for the measured temperature dependence of Ku. The coercive field Hc follows a relation Hc ∼ K1.5u/Ms. The magneto-optical effects are primarily caused by the transition metals and therefore their compositional, temperature, and spectral dependence correspond to that of their Gd and Tb analogs. Optical recording experiments on Dy-FeCo disks yield good write and erase sensitivities and carrier-to-noise ratios up to 60 dB which are comparable to those of GdTb-Fe and Tb-FeCo disks.

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.

Generalization of the Callen and Shtrikman generating function for a Heisenberg S=1 ferromagnet to include a strong axial crystal field interaction

The Callen and Shtrikman result, which demonstrates an exact correspondence between the higher order moments (szn) of the Heisenberg ferromagnet calculated using either the RPA or an effective single-particle density matrix is generalized to include a strong axial crystal field interaction. In particular, it is shown that a two parameter analogue for the Callen and Shtrikman result can be obtained for the S=1 easy-axis ferromagnet using the transformed Hamiltonian/random phase approximation (TH/RPA).

Magnetic circular dichroism spectroscopy and magnetization studies of iron atoms isolated in xenon matrices

Absorption and magnetic circular dichroism (MCD) spectra of iron atoms isolated in xenon matrices have been measured and their magnetization properties studied. The high signal intensity and optical quality of the matrices has allowed the assignment of many more transitions than hitherto. The magnetization measurements reveal considerable guest host interaction, though there is little evidence of this in the spectra. Detailed analysis of the magnetization data shows that they can be interpreted quite well in terms of an essentially axial crystal field splitting of the 5 D4 ground state which places the two ‖MJ‖=4 levels about 100 cm−1 below the ‖MJ‖=3. By extending the theoretical treatment to include a small mixing of the two ‖MJ‖=4 levels it is possible to improve the fit of the higher temperature data. These results demonstrate the value of MCD measurements, particularly where a system is electron paramagnetic resonance (EPR) silent.

A simple model for localized-itinerant magnetic systems: Crystal field effects

The magnetic behavior of a system consisting of localized electrons coupled to conduction electrons and submitted to an axial crystal field at T = 0 K is investigated within the framework of the molecular field approximation. An analytical ionic magnetic state equation is deduced; it shows how the magnetization depends on the model parameters (exchange, crystal field, band occupation) and external magnetic field. A condition for the onset of spontaneous magnetic order is obtained and the ferro- and paramagnetic phases are studied. This study displays several features of real magnetic systems, including quenching or total suppression of the magnetic moments (depending on the relative value of the crystal field parameter) and exchange enhancement. The relevance of such model for the description of rare-earth intermetallic compounds is discussed.

Observability of forbidden hyperfine transitions along the principal axes in the EPR of low-symmetry complexes

It is shown that forbidden hyperfine transitions of non-zero intensity are not observable for the Zeeman field orientation along the two-fold symmetry axis, when it is parallel to a crystal-field axis, of paramagnetic complexes, characterized by monoclinic site symmetry; on the other hand, they are observable for all orientations of the Zeeman field for complexes characterized by triclinic symmetry. Under the assumptions of isotropic hyperfine tensor and vanishing nuclear quadrupole interaction expressions are given for the intensities of the forbidden hyperfine transitions (ΔM=±1, Δm=±1; M and m are the electronic and nuclear magnetic quantum numbers, respectively), relative to those of the allowed hyperfine transitions (ΔM=±1, Δm=0) for an arbitrary Zeeman-field orientation. The three cases, where the monoclinic symmetry axis is parallel to a crystal-field (magnetic) axis have been specifically considered.

An improved method for efficient computation of paramagnetic57Fe(III) Mossbauer relaxation spectra

The supermatrix Liouville formalism for the computation of Mossbauer relaxation spectra, if applied to the 6S5/2 state of 57Fe(III), leads to a 288-dimensional non-Hermitian matrix. Diagonalisation and inversion of this matrix requires far too much computer time to be used within least-squares fitting routines. Provided that an axial crystal field of sufficient strength acts on the electronic states of Fe(III), only a few of the states described by the supermatrix are necessary to simulate Mossbauer spectra. Thus the dimension of this matrix can be reduced to at least a third. Such confinement to a fraction of the original supermatrix involves no approximation for either the description of the six electronic states of Fe(III) or their time-independent interactions with surroundings and nucleus. In addition, no restrictions beyond those common to previous computations are imposed on the description of those interactions which define the relaxation matrix. The authors present a detailed description of two methods to calculate Fe(III) Mossbauer relaxation spectra; both allow not only the comprehensive simulation of theoretical Fe(III) relaxation spectra but also, for the first time, the application of least-squares procedures to interpret experimental spectra reliably.

Mössbauer spectra of a paramagnetic ion in an axial crystal field in the presence of spin-lattice relaxation

The influence of spin-lattice relaxation on the Mossbauer hyperfine spectra of the Fe3+ ion is investigated in the case of an axial crystal field. All the various influences of the relaxation process on the spectra can be explicitly described using two relaxation parameters. A detailed analysis of the Mossbauer relaxation spectra for the various temperatures, relations between the relaxation parameters and external magnetic field directions is carried out. When the magnetic field direction is nearly collinear with the symmetry axis and one of the relaxation parameters is small, the dynamics of Mossbauer spectra is shown to have anomalous features. The influence of random magnetic fields is shown to give an unconventional development of patterns as a function of the relaxation parameters.

Identification of a paramagnetic Bi 0 center in X-irradiated KCl.Bi crystals

Crystals of KCl doped with bismuth exhibit after X-irradiation at room temperature the presence of a paramagnetic defect with tetragonal 〈100〉 symmetry. Based on the analysis of the ESR spectra a structural model based on a Bi 06 p 3 atom center is proposed. The strong axial crystal field is due to the presence of a vacancy in the first neighbourhood and/or a static Jahn-Teller distortion of E g character.

A new method of computing57Fe(III)-Mössbauer relaxation spectra

The supermatrix-Liouville formalism to compute Mossbauer relaxation spectra leads, applied to the6S5/2-state of57Fe(III) to a 288-dimensional nonhermitian matrix. Provided that an axial crystal field acts on the electronic states, only few of the states described by the supermatrix are necessary to simulate theoretical spectra and the dimension of this matrix can be reduced to at least 1/3. This confinement implies no approximation for the description of the six electronic states of Fe(III) and for the interactions of them with environment and nucleus.

ESR study of a sol-gel-derived amorphous Fe 2O 3-SiO 2 system

Iron-containing silica gels and glasses were prepared using the sol-gel method and the state of iron ions in them was examined by means of ESR spectroscopy. The iron ions were homogeneously distributed in both axial and orthorhombic crystal fields in the low concentration region in the gels. The fraction of iron ions at the former sites decreased while that at the latter sites increased with increasing the concentration of iron ions. At a higher concentration than 3 mol% of Fe2O3, Fe-O-Fe spin pairs appeared. In the glasses obtained by heating the gels, almost all the iron ions existed as spin pairs. Such a state of iron ions in the glasses was considered to depend on their chemical environment in the precursor gels.

Crystal and molecular structure of di-(2,2?-pyridylpyridinium)tetrachlorodioxouranate (VI)

The authors interest is concerned with the study of the optical behavior (polarized absorption and luminescence electronic spectra) of single crystals of the type (R/sub 4/N)/sub 2/UO/sub 2/X/sub 4/ (R = alkyl or aryl group and X = Cl, Br), in relation to their structural properties, and in particular with the elucidation of the effects of the arrangement of the equatorial ligands and of an axial crystal field on the electronic structure of the UO/sub 2//sup 2 +/ ion. The aim of this work is the determination of the crystal structure of the title compound in order to interpretate its low-temperature absorption and luminescence spectra.

EPR studies of Gd 3+ centres in the cubic phase of CsCaCl 3 and CsPbCl 3

The spectra of three type Gd 3+ centres with cubic, 〈100〉 tetragonal and 〈111〉 trigonal symmetry have been investigated in the cubic phase of CsCaCl 3( T = 300 K) and CsPbCl 3( T = 330 K). The Gd 3+ ion is substituted for Ca 2+ or Pb 2+ions. The hexadecapolar crystal field parameter b 4 is discussed within the framework of Newman's superposition model for cubic centres. The trigonal centre of CsCaCl 3 results from a slight 〈111〉 distortion of the cubic local symmetry at Gd 3+ sites connected with a Cs vacancy. The tetragonal centre corresponds to charge compensation by S 2− impurities substituted to Cl − ions which results in a strong 〈001〉 axial crystal field. The spin Hamiltonian parameter b 2 0 which reflects this essential feature of the centre is tentatively discussed in the light of some existing theoretical models.

Ground-state properties of a Ce ion: Anisotropic susceptibility due to axial crystal fields

Abstract The Bethe-ansatz equations for the ground state of the Coqblin-Schrieffer model for j= 5 2 are solved in the presence of an axial crystal field and a small magnetic field. The occupations of the crystal field levels and the susceptibility parallel and perpendicular to the axis are obtained as a function of the crystal field strength.

Optical properties of complex defects created by Ag diffusion in ZnTe.

Several complex defects in ZnTe created by Ag diffusion at a rather high doping level are studied by optical spectroscopy. In addition to the usual substitutional ${\mathrm{Ag}}_{\mathrm{Zn}}$ acceptor bound exciton (BE) at 2.3737 eV, a new prominent BE, ${S}_{1}$, with a lowest energy of 2.3149 eV appears. This transition has a strong phonon coupling and corresponds to a neutral isoelectronic defect. Two electronic states at zero field are revealed by transmission data; a doublet at the lowest state (2.3149 eV) and a singlet at slightly higher energy (2.3155 eV). The electronic properties of the ${S}_{1}$ BE are revealed by optical data, including the magneto-optical Zeeman spectra. The electronic structure can be understood as a consequence of a strong compressional axial local crystal field in combination with an electron-hole exchange interaction. It is further concluded that both carriers are bound to the complex defect by an attractive central-cell potential. The identity of the ${S}_{1}$ defect as a pair of substitutional ${\mathrm{Ag}}_{\mathrm{Zn}}$ and interstitial ${\mathrm{Ag}}_{\mathrm{i}}$ in the 〈111〉 direction is consistent with the trigonal symmetry observed in magneto-optical data. In addition to the ${S}_{1}$ defect, several acceptorlike complex defects are created, of which ${S}_{2}$ is a BE with its lowest electronic line at 2.3486 eV, and ${S}_{3}$ similarly at 2.365 eV. These BE excitations give rise to several electronic levels both in the ground state (the acceptor hole) and in the excited state (the BE state). The complicated electronic structure can be explained by a combination of a low-symmetry crystal field and an exchange interaction. An identification of the defects ${S}_{2}$ and ${S}_{3}$ as composed of three atoms is suggested.

Neutral (Cu-Li) complexes in GaP: The (Cu-Li)III bound exciton at 2.242 eV.

A photoluminescence study is reported in order to identify a new radiative center in GaP co-doped with Cu and Li. This center, denoted (Cu-Li${)}_{\mathrm{III}}$, binds an exciton with binding energy 110 meV. The bound-exciton spectrum shows sharp electronic lines and a structured phonon sideband with well-resolved replicas. The group of electronic transitions consists of spin-only-like singlet-triplet pairs, which are characteristic of tightly bound holes in a strong compressive axial crystal field. Two such singlet-triplet pairs are observed for the (Cu-Li${)}_{\mathrm{III}}$ center, instead of the usual one pair. A model taking into account the splitting of electron states as well as hole states is proposed to explain this additional splitting. The experimental work includes photoluminescence spectroscopy and time-resolved and Zeeman measurements as well as optically detected magnetic resonance measurements. The careful doping procedure includes isotope doping with both $^{63}\mathrm{Cu}$${,}^{65}$Cu and $^{6}\mathrm{Li}$${,}^{7}$Li. The Li-isotope doping was clearly reflected in the phonon sideband. A neutral molecular associate of isoelectronic nature is suggested, with the (Cu-Li${)}_{\mathrm{III}}$ center involving ${\mathrm{Cu}}_{\mathrm{Ga}}$ and a pair of interstitial atoms, ${\mathrm{Cu}}_{\mathrm{i}}$ and ${\mathrm{Li}}_{\mathrm{i}}$.