Presence Of Crystal Field Research Articles

Geometrical aspects of the multicritical phase diagrams for the Blume–Emery–Griffiths model

As a continuation of our preceding work [R. Erdem and N. Alata, Eur. Phys. J. Plus 135, 911 (2020), https://doi.org/10.1140/epjp/s13360-020-00934-3], we used the thermodynamic geometry in the Ruppeiner formalism to study the geometrical aspects of the multicritical phase diagrams for the spin-1 Blume-Emery- Griffiths model in the presence of crystal field. We derived an expression for the thermodynamic curvature or Ricci scalar (R) and analyzed its temperature and crystal field behaviours near interesting critical and multicritical points. Our findings are presented as geometrical phase diagrams including critical and multicritical topology. From these diagrams, new vanishing curvature lines (R = 0) extending into the ferromagnetic or paramagnetic phases beyond the critical points and zero point temperature are observed.

Anomalous thermodynamics in a mixed spin-1/2 and spin-1 hexagonal nanowire system

The mixed spin-1/2 Ising model and spin-1 Blume–Capel model in an hexagonal nanowire structure under the presence of crystal field is considered. The free energy is obtained through the transfer matrix technique, which is solved numerically. Our main result lies in the presence of pseudo-transition in low temperature region near the ferrimagnetic/ferromagnetic boundary, due to the influence of a crystal field. The evidence of a pseudo-transition is observed in several quantities. Free energy first derivative quantities like entropy and internal energy show an abrupt but continuous jump, whereas quantities associated with second derivatives of the free energy like the specific heat exhibit a strong sharp peak, quite similar to a second order phase transition. We also investigate magnetization patterns and do not find evidence of spontaneous magnetization. Nevertheless, assuming a small magnetic field, we can induce a magnetization which resembles a spontaneous magnetization at a pseudo-critical temperature.

Inherent orbital spin textures in Rashba effect and their implications in spin–orbitronics

The Rashba effect gives rise to the key feature of chiral spin texture. Recently it was demonstrated that the orbital angular momentum (OAM) texture forms the underlying basis for Rashba spin texture. Here we solve a model Hamiltonian of a generic p-orbital system in the presence of crystal field, internal spin–orbit coupling (SOC) and inversion symmetry breaking (ISB), and demonstrate, in addition to OAM and spin texture, the existence of orbital projection (OP) of the spin texture in a general Rashba system. The unique form of the OP pattern follows from the same condition for the existence of chirality of the spin texture. From the analytical results, we obtained the spin polarization as a function of parameters such as the SOC strength, crystal field splitting and degree of ISB, and compare them with those from numerical solutions and ab initio calculations. All three methods yield highly consistent results. Our results suggest means of external modulation, and elucidate the multi-orbital nature of the Rashba effect and the underlying OP of the spin texture. The understanding has potential applications in fields such as spin–orbitronics that requires delicate control between orbital occupancy and spin momentum.

The Phase Diagrams and Reentrant Phenomena in a Cylindrical Transverse Ising Nanowire with the Presence of Crystal Field

Within the framework of the effective field theory (EFT) with correlations, the phase diagrams of a cylindrical spin-1 transverse Ising nanowire are investigated depending on the ratio of the Hamiltonian parameters. We discuss in detail the influence of interfacial coupling, shell surface coupling, and single-ion anisotropy, i.e., crystal field and transverse field ratio on the phase diagrams. We found some characteristic phenomena such as reentrant behavior, tricritical point, and first-order transitions.

Dependence of magnetization on crystal fields and exchange interactions in magnetite

In this work, we study the magnetization of magnetite (Fe3O4) with different exchange interactions and crystal fields using variational method based on the Bogoliubov inequality for the Gibbs free energy within the mean field theory. The magnetic behavior was investigated in the absence and presence of crystal fields. The investigations also revealed that the transition temperature depends on the crystal fields of the octahedral and tetrahedral sites. Magnetite exhibits ferrimagnetic phase with second order transition to paramagnetic phase at 850K. This result is confirmed using the mean field theory within the Heisenberg model. Important factors that can affect the magnetic behavior of the system are exchange interactions and crystal field. Indeed, a new magnetic behavior was observed depending on these parameters. A first order phase transition from ferrimagnetic to ferromagnetic was found at low temperature, and a second order transition from ferromagnetic to paramagnetic was observed at high temperature.

Magnetization Study of Cobalt Ferrite by Mean Field Approximation

The magnetic properties of cobalt ferrite (CoFe2O4) have been studied with the mean field approximation using the Bogoliubov inequality. An influence of temperature on the magnetization of cobalt ferrite was investigated in the absence and presence of crystal fields. The effect of exchange interactions revealed different behaviors of the magnetization versus the temperature; a pure ferrimagnetic state and a frustrated magnetic behavior were observed for the cobalt ferrite. In addition, the study of the exchange interactions effect on the total magnetization shows that for strong coupling interactions, the total magnetization of the system exhibits a jump at a given temperature. A first order phase transition from ferrimagnetic to ferromagnetic phase, a second order transition from ferromagnetic to paramagnetic phase and from ferrimagnetic to paramagnetic phase were observed.

The magnetic properties of a decorated Ising nanotube examined by the use of the Monte Carlo simulations

The magnetic properties of nanotube are investigated by Monte Carlo simulations. The nanotube is considered as a lattice of spins σ=±1/2 and S=±1,0. For each block lattice σi and Si, the blocking temperature versus values of crystal field is estimated. The magnetization of each spin configuration is computed versus the exchange interaction between the spins of each bloc lattice in the absence and the presence of crystal field at fixed temperature. In addition, the hysteresis cycle for different temperature values in the absence and presence of the crystal field is deduced.

Energy levels of nitride quantum dots: Wurtzite versus zinc-blende structure

Nitride based III-V quantum dots (QD's) GaN, InN, and AlN have been investigated theoretically using the hole effective mass Hamiltonian derived by the $\stackrel{\ensuremath{\rightarrow}}{k}\ensuremath{\cdot}\stackrel{\ensuremath{\rightarrow}}{p}$ method. The nitride based QD's have significantly different properties compared to II-VI based QD's and also other III-V based QD's such as GaAs and InP. III-V based nitrides can have both zinc blende and wurtzite crystal structures whereas GaAs and other III-V and II-VI QD's exist only in the zinc blende structure. The study of nitride QD's therefore offers an unique opportunity of studying the role of the crystal field which is present in the wurtzite structure and is absent in zinc blende structure. The energies and the eigenfunctions for spherical quantum dots have been calculated as functions of the dot radius R for both zinc blende and wurtzite structures for both the zero spin orbit coupling (SOC) and finite SOC. For low lying states, in the zero SOC limit, the energies have a ${1/R}^{2}$ dependence at all R for zinc blende structures but the presence of crystal field in wurtzite modifies the ${1/R}^{2}$ dependence at intermediate R but not in small and large R. The addition of SOC further modifies the behavior at large R and the energies vary more slowly than ${1/R}^{2}$ for both the zinc blende and wurtzite structures. For very high excited states of large QD's, the wurtzite pattern approaches that of the zinc blende.

Longitudinal and transverse magnetizations of spin- [formula omitted] transverse Ising model with the crystal field on square lattice

Within the framework of the effective-field theory with correlations, the temperature dependence of the longitudinal and transverse magnetizations in the spin- 3 2 transverse Ising model with the presence of crystal field on the square lattice are studied. A number of characteristic behaviors for their thermal variations are obtained in detail especially for the system with the crystal field constant in the critical region where the ground-state configuration may change from the spin- 1 2 state to the spin- 3 2 state.

Antiferromagnetism in CeAu2Si2- and CeAg2Si2-based Kondo-lattice systems

We report the electrical resistivity rho , thermopower S and thermal conductivity lambda of Ce1-xLaxAu2Si2, Ce1-yYyAu2Si2, Ce1-xLaxAg2Si2 and Ce1-yYyAg2Si2 (0<or=x, y<or=1) systems. The rho curves show a sudden change in slope at the antiferromagnetic ordering temperature TNrho . In the CeAu2Si2-based alloys, the TN depression, due to the dilution of Ce atoms by La or Y, is accounted for solely by the weakening of the inter-site interaction temperature scale TRKKY. On the other hand, in the CeAg2Si2-based alloys, apart from TRKKY, the single-ion Kondo temperature TK also plays an important role in determining the nature of the TN variation. The rho and lambda behaviours, at both low and high temperatures, show clear evidence for the Kondo effect in the presence of crystal fields.

Magnetic and transport studies of the antiferromagnetic Kondo lattice CePtSn

CePtSn has been studied by means of neutron scattering, electrical resistivity and magnetic susceptibility measurements. Refinement of neutron powder diffraction data showed the crystal structure to be of the orthorhombic TiNiSi-type. Magnetic susceptibility measurements revealed the presence of two antiferromagnetic phase transitions at 8 and 5.5K respectively. Inelastic neutron scattering showed two well defined crystal field excitations at 24.0 and 34.9 meV. The temperature dependence of the resistivity can be understood as arising from the Kondo effect in the presence of crystal fields.

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.

Specific heat of the ytterbium monopnictides above 5 K from a band-structure calculation.

Applying the self-consistent large-degeneracy expansion to the degenerate Anderson impurity model in the presence of crystal fields, we compute the specific heat of YbN, YbP, and YbAs above 5 K. Each crystal-field level couples to the band states with its own hybridization function, determined from a tight-binding fit to an ab initio band-structure calculation. The different amplitudes of the couplings naturally explain the anomalous crystal-field splittings observed by inelastic neutron scattering. Our calculations reproduce the hitherto unexplained excess specific-heat peak seen in all three compounds around 5 K, which we interpret as being due to the Kondo effect for the ground-state doublet.

Conductivity of Kondo-type systems in the presence of crystal fields.

By starting with the expression for the conductivity of Kondo-type systems in the presence of crystal fields as calculated by the Kubo formalism, we derive the expression found from the Boltzmann equation. To rewrite the compact Kubo expression in the more cumbersome expression found in the semiclassical Boltzmann approach, we use a generalization of the optical theorem to finite-temperature propagators. Also, we calculate the conductivity through third order in the coupling constant J=${V}^{2}$/${E}_{f}$ and obtain agreement with previous results.

Specific heat of the degenerate Kondo model: Exact results in the presence of crystal fields.

Specific heat of the degenerate Kondo model: Exact results in the presence of crystal fields.

Effect of exchange and crystal fields on temperature dependence of SM3+magnetization

In Sm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3+</sup> ion the energy separation between the ground multiplet level and the first excited multiplet level is small and therefore the exchange and crystal fields can considerably admix these levels. As a result of this admixture by exchange fields alone, the Sm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3+</sup> magnetization in magnetically ordered compounds changes sign or shows a crossover at a temperature of about 300 K. Thus in samarium compounds with transition elements, where the transition element has a moment, the samarium moment couples parallel to transition element moment below 300 K and antiparallel above 300 K. We have investigated the effects of crystal fields (of hexagonal symmetry) on Sm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3+</sup> magnetization and find that the crossover temperature in magnetization is considerably altered by crystal fields (and also by exchange fields in the presence of crystal fields) from the value of 300 K for free Sm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3+</sup> ion. The magnetization results on SmCo <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</inf> are discussed in the light of these calculations.

Sign reversal of the4fcontribution to the hyperfine field at Sm in paramagnetic samarium compounds

In paramagnetic rare-earth compounds, in the presence of an applied magnetic field, the $4f$ electrons produce a field at the rare-earth nuclear site, which, for the free ${\mathrm{Sm}}^{3+}$ ion, is positive at all temperatures. It is shown that because of crystal-field effects, the $4f$ contribution to the hyperfine field at Sm reverses its sign at one or two temperatures, unlike in the free ion. Exchange interaction between ${\mathrm{Sm}}^{3+}$ ions, in the presence of crystal fields, may induce or suppress the sign reversals in the hyperfine field.

Orbital Effects on Exchange Interactions

Many magnetic materials contain ions in which the orbital contribution to the magnetic moment is important. This is normally the case in the rare earths and the actinides, where there is strong spin-orbit coupling and weak crystal fields, and it also occurs in transition metal ions like Fe2+ and Co2+. This orbital contribution leads to asymmetric charge clouds and the corresponding asymmetry of the transfer and overlap integrals means that the exchange interaction between pairs of such ions is not of the Heisenberg form but contains more complicated functions of the angular momentum operators. The microscopic form of the exchange and coulomb interaction between pairs of electrons is considered in the single-electron representation and transformed to the (L, S) and J representations of many-electron atomic states, and finally to a pseudospin representation which spans the lowest-lying atomic states in the presence of crystal fields. The symmetry restrictions on this pseudospin Hamiltonian are considered. Detailed calculations are made of a model of UO2 using Anderson's kinetic exchange mechanism.

(?, ?)-Richtungskorre!ationen im Zerfall des Tm170

The beta-gamma directional correlation between the inner beta-group and the following 84.2 keV gamma ray was measured as a function of the energy of the beta-particles. Details of the apparatus and the experimental procedure are given. The results are corrected for the contribution of internal bremsstrahlung and the attenuation of the directional correlation due to the relatively long lifetime of the excited state in Yb170 and the presence of crystal fields. The measurements of these corrections are described in the following paper.