Crystal Field Model Research Articles

Pressure-induced ferromagnetism with strong Ising-type anisotropy in YbCu2Si2

We report dc magnetic measurements on YbCu$_2$Si$_2$ at pressures above 10 GPa using a miniature ceramic anvil cell. YbCu$_2$Si$_2$ shows a pressure-induced transition from the non-magnetic to a magnetic phase at 8 GPa. We find a spontaneous dc magnetization in the pressure-induced phase above 9.4 GPa. The pressure dependence of the ferromagnetic transition temperature T_C and the spontaneous magnetic moment m_0 at 2.0 K have been determined. The value of m_0 in the present macroscopic measurement is less than half of that determined via Mossbauer experiment. The difference may be attributed to spatial phase separation between the ferromagnetic and paramagnetic phases. This separation suggests that the pressure-induced phase boundary between the paramagnetic and ferromagnetic states is of first order. Further, we have studied the magnetic anisotropy in the pressure-induced ferromagnetic state. The effect of pressure on the magnetization with magnetic field along the magnetic easy $c$-axis is much larger than for field along the hard $a$-axis in the tetragonal structure. The pressure-induced phase has strong Ising-type uniaxial anisotropy, consistent with the two crystal electric field (CEF) models proposed for YbCu$_2$Si$_2$.

Absorption spectra and crystal-field modeling of Er3+ doped in Y3Sc2Ga3O12 crystal

Er3+-doped Y3Sc2Ga3O12 (Er:YSGG) single crystal is grown by Czochralski method successfully, and the absorption spectra are measured in a wider spectral wavelength range (340-1700 nm). The experimental energy levels are analyzed and identified. The free-ion and crystal-field parameters are fitted by the experimental energy levels with a root mean square deviation of 10.34 cm-1, and 102 Stark energy levels of Er3+ in YSGG host crystals are assigned. It indicates that the fitting results of Stark energy levels are more satisfactory with the experimental spectra. Finally, the fitting results of free-ion and crystal-field parameters are compared with those already reported of Er:YAG crystal. A conclusion is drawn that the Er:YSGG has higher laser efficiency than Er:YAG, which may result from Er:YSGG that has a strong crystal field interaction.

Phase diagrams of the spin-3/2 random transverse crystal field model

The mean-field approximation is used to calculate the phase diagrams of the spin-3/2 random transverse crystal field (RTCF) model. A bimodal distribution of the RTCF is employed in which one of the modes is in competition with the other mode whose strength is adjusted with a controllable parameter α. Thus, some sites in the lattice are under the effect of RTCF Dx with probability p and the rest of the sites are under the effect of αDx with 1 − p. The phase diagrams of the model are obtained on the RTCF-temperature planes by varying p on square lattices. Both second- and first-order phase transitions are displayed and thus tricritical points are also observed. The critical end points and end points for the first-order phase transition lines were also found.

Theoretical analysis of optical spectra of Ce3+ in multi-sites host compounds

Theoretical analysis of optical properties of two recently synthesized phosphors with the Ce3+ ions (Na3LuSi2O7 and NaSr4(BO3)3) was performed. The exchange charge model of crystal field was used to calculate the crystal field parameters and cerium 5d states splittings for each site in Na3LuSi2O7. Analysis of vibronic coupling of Ce3+ in NaSr4(BO3)3 resulted in a quantitative modeling and theoretical simulation of the experimental spectra. Electronic energy levels, vibrational frequencies and ion-lattice vibronic coupling strength are determined specifically for Ce3+ at different sites. The performed analysis allows for getting detailed description of the optical properties of trivalent cerium in the considered crystals and provides a general guide to understanding and characterizing other Ce3+ activated phosphors.

Magnetooptics of non-Kramers Eu3+ ions in garnets: analysis complemented by crystal-field splitting modeling calculations

Spectra of absorption, luminescence, magnetic circular dichroism (MCD), and magnetic circular polarization of luminescence (MCPL) in Gd3Ga5O12:Eu3+ and Eu3Ga5O12 garnets were studied within the visible spectral range at 300 K. Analysis of the spectral and temperature dependences of the magnetooptical and optical spectra made it possible to identify the magneto-dipole (MD) and electro-dipole (ED) 4f→4f transitions occurring between Stark sublevels of the 7FJ (J=1, 2) and 5D0 multiplets in Eu3+-containing garnet structures. Quantum mechanical “mixing” had significant influence on quasi-degenerate states of the non-Kramers rare-earth Eu3+ ion for Eu3Ga5O12 in MCD due to forbidden MD transition 7F1→5D0 and for Gd3Ga5O12:Eu3+ in MCPL due to MD 4f→4f transition 5D0→7F1 and forced ED-transition 5D0→7F2. A parameterized Hamiltonian defined to operate within the entire 4f(6) ground electronic configuration of Eu3+ ion was used to model the experimental Stark levels, including their irreducible representations and wavefunctions. The crystal-field parameters were determined through a Monte-Carlo method in which nine independent crystal-field parameters, Bkq, were given random starting values and optimized using standard least-squares fitting between calculated and experimental levels. The final fitting standard deviation between 57 calculated-to-experimental levels was 0.73 meV.

Phenomenological crystal-field model of the magnetic and thermal properties of the Kondo-like system UCu2Si2

The transport properties described previously [Tro\ifmmode \acute{c}\else \'{c}\fi{} et al., Phys. Rev. B 85, 224434 (2012)] as well as the magnetic and thermal properties presented in this paper, observed for single-crystalline UCu${}_{2}$Si${}_{2}$, are discussed by assuming a dual (localized-itinerant) scenario. The electronic states of the localized 5$f$ electrons in UCu${}_{2}$Si${}_{2}$ are constructed using the effective Hamiltonian known for ionic systems, allowing us to treat the Coulomb, spin-orbital, and crystal-field interactions on equal footing. The space of parameters has been restricted in the initial steps with the aid of the angular overlap model approximation. The final crystal-field parameters, obtained from the refined steps of calculations, are relatively large (in absolute values), which we attribute to the hybridization characteristic of the metallic systems on the verge of localization. The proposed crystal-field model reproduces correctly with satisfactory accuracy the magnetic and thermal properties of UCu${}_{2}$Si${}_{2}$ in agreement also with the transport properties reported previously. Considerable crystal-field splitting of the ground multiplet of 2760 K is responsible for a large anisotropy in the magnetic behavior, observed in the whole temperature range explored.

Quantifying the σ and π Interactions between U(V) f Orbitals and Halide, Alkyl, Alkoxide, Amide and Ketimide Ligands

f Orbital bonding in actinide and lanthanide complexes is critical to their behavior in a variety of areas from separations to magnetic properties. Octahedral f(1) hexahalide complexes have been extensively used to study f orbital bonding due to their simple electronic structure and extensive spectroscopic characterization. The recent expansion of this family to include alkyl, alkoxide, amide, and ketimide ligands presents the opportunity to extend this study to a wider variety of ligands. To better understand f orbital bonding in these complexes, the existing molecular orbital (MO) model was refined to include the effect of covalency on spin orbit coupling in addition to its effect on orbital angular momentum (orbital reduction). The new MO model as well as the existing MO model and the crystal field (CF) model were applied to the octahedral f(1) complexes to determine the covalency and strengths of the σ and π bonds formed by the f orbitals. When covalency is significant, MO models more precisely determined the strengths of the bonds derived from the f orbitals; however, when covalency was small, the CF model was better than either MO model. The covalency determined using the new MO model is in better agreement with both experiment and theory than that predicted by the existing MO model. The results emphasize the role played by the orbital energy in determining the strength and covalency of bonds formed by the f orbitals.

Features of the magnetic and magnetoelectric properties of HoAl3(BO3)4

The main features of the magnetic and record magnetoelectric properties of a HoAl3(BO3)4 aluminoborate single crystal have been studied experimentally and theoretically. It has been found that the electric polarization that was previously detected in HoAl3(BO3)4 and is record for multiferroics is significantly larger, ΔPba(Ba) ≈ −5240 μC/m2, with an increase in the magnetic field to 9 T at T = 5 K. The measured magnetic properties and revealed features have been interpreted within a united theoretical approach based on the molecular field approximation and on calculations in the crystal field model for a rare-earth ion. The experimental temperature (from 3 to 300 K) and field (up to 9 T) dependences of the magnetization have been described. The parameters of the crystal field of trigonal symmetry for a Ho3+ ion in HoAl3(BO3)4 have been determined from the interpretation of the experimental data.

Magnetic properties of the rare-earth ferroborate SmFe3(BO3)4

The magnetic properties of trigonal antiferromagnet SmFe3(BO3)4 are studied experimentally and theoretically. The measured characteristics are considered in terms of a theoretical approach based on the molecular field approximation and a crystal field model for a rare-earth ion. The temperature dependences of the initial magnetic susceptibility and the field and temperature dependences of magnetization in fields up to 5 T are described, and the anomaly in the magnetization curve for B ⊥ c near 1 T, which points to a first-order phase transition, is analyzed.

Calculation of the spectral, structural, and electronic properties of NaCrSi2O6 and LiCrSi2O6 crystals

Spectral, structural and electronic properties of two Cr3+-bearing systems (NaCrSi2O6, LiCrSi2O6) have been theoretically modeled using two different approaches: semi-empirical model of crystal field, in the framework of the Exchange Charge Model and two ab initio DFT-based calculations, as implemented in the CASTEP module [1] of Materials Studio package [2] and, for reliability, CRYSTAL09 code [3]. The first one allows for calculations of the electronic levels of sixfold coordinated Cr3+ ions in a crystal field of host’s ligands and direct comparison with experimental absorption spectra [4]. The latter two allow for the analysis of the band structure and density of states (DOS), after optimization of the crystal lattice structures of these materials. In particular, a special attention was paid to the energetic position of the Cr3+ 3d states. All obtained results are compared with corresponding experimental values and discussed.

Ligand Field Theory: An ever-modern theory

The Ligand Field (LF) model in molecular science or the Crystal Field model in condensed matter science has been introduced more than eighty years ago. Since then, this theory plays a central role each time that molecules containing d- and/or f-elements with open shells are adressed. No doubt, this fact is related to the dominant localisation of the frontier orbitals within the metal-sphere. This common feature enables us to describe approximately the electronic structure of these molecules using orbitals that are centred on a single atom and to treat their interaction with the chemical environment essentially as a perturbation. Another reason for the success of this simple theory is the fact that the more accurate molecular orbital theory does generally over-estimate covalence of transition metal atoms and thus yields wave functions that are too delocalized.We give here a survey of the development of LF theory since its introduction simultaneously by Hans Bethe and John Hasbrouck van Vleck more than eighty years ago. Over the years, LF theory was a semi-empirical model with adjustable parameter until the end of last century when we introduced non-empirical LF theory that is based on DFT calculations. The results of this first-principle prediction are in very good agreement with the experimental observations. Sample calculations of tetrahedral and octahedral Cr-complexes and hexa-acquo Ni(II)-complexes are used to validate the new model and to analyse the calculated parameters

Electronic structure of the kagome staircase compounds Ni3V2O8and Co3V2O8

The electronic structure of the kagome staircase compounds, Ni${}_{3}$V${}_{2}$O${}_{8}$ and Co${}_{3}$V${}_{2}$O${}_{8}$, has been investigated using soft x-ray absorption, soft x-ray emission, and resonant inelastic x-ray scattering. Comparison between the two compounds, and with first-principles band structure calculations and crystal-field multiplet models, provides unique insight into the electronic structure of the two materials. Whereas the location of the narrow (Ni,Co) $d$ bands is predicted to be close to ${E}_{\mathrm{F}}$, we experimentally find they lie deeper in the occupied O $2p$ and unoccupied V $3d$ manifolds, and determine their energy via measured charge-transfer excitations. Additionally, we find evidence for a $dd$ excitation at 1.5 eV in Ni${}_{3}$V${}_{2}$O${}_{8}$, suggesting the V $d$ states may be weakly occupied in this compound, contrary to Co${}_{3}$V${}_{2}$O${}_{8}$. Good agreement is found between the crystal-field $dd$ excitations observed in the experiment and those predicted by atomic multiplet theory.

Modeling the properties of uranium-based single ion magnets

We analyze the magnetic behavior of the five uranium-based SIMs reported in the literature. By combining a corrected crystal field model with the magnetic experimental data, we obtain the lowest-lying magnetic levels and the associated wave functions of the nanomagnets, which are found to be compatible with the observed SMM behavior. Additionally, this approach has allowed us to propose some geometrical considerations and practical advice for experimentalists aiming for the rational design of SIMs and spin qubits based on uranium.

Effect of magnetic field in heavy-fermion compound YbCo2Zn20

Inelastic neutron scattering experiments on poly crystalline sample of heavy-fermion compound YbCo2Zn20 were carried out in order to obtain microscopic insights on the ground state and its magnetic field response. At zero field at 300 mK, inelastic response consists of two features: quasielastic scattering and a sharp peak at 0.6 meV. With increasing temperature, a broad peak comes up around 2.1 meV, whereas quasielastic response gets broader and the peak at 0.6 meV becomes unclear. By applying magnetic field, the quasielastic response exhibits significant broadening above 1T, and the peak at 0.6 meV is obscure under fields. The peaks in inelastic spectra and its temperature variation can be ascribed to the suggested crystal-field model of Γ6 − Γ8 − Γ7 with the overall splitting of less than 3meV. The observed quasielastic response and its rapid broadening with magnetic field indicates that the heavy-electron state arises from the ground state doublets, and are strongly suppressed by external field in YbCo2Zn20,

The nature of Cr center in GaN: Magnetic anisotropy of GaN:Cr single crystals

Magnetization measurements of the strain-free bulk GaN:Cr single crystals of wurtzite structure are reported. Strong magnetic anisotropy at low temperatures (2–10 K) was observed. The data were analyzed assuming Cr2+(d4) configuration. The crystal field model taking into account cubic field of tetrahedral symmetry, trigonal field along the c-axis simulating hexagonal structure, tetragonal static Jahn-Teller distortion, and the spin-orbit interaction provide a good description of the experimental magnetization data.

Induced quadrupole effects near a crossover in a tetragonal TbLiF4 sheelite in a strong magnetic field up to 50 T

The anomalies of magnetic properties of TbLiF4 caused by the interaction of the energy levels of a rare-earth ion in a strong magnetic field up to 50 T directed along the [100] and [110] axes are studied experimentally and theoretically. The jumps in magnetization M(H) and the maxima of the differential magnetic susceptibility dM(H)/dH are found in critical fields H c = 28 and 31 T, where the lower component of the excited doublet approaches the ground-state singlet of a Tb3+ ion. Based on the crystal-field model with known interaction parameters, we calculated the Zeeman effect and the magnetization and magnetic susceptibility curves for the TbLiF4 crystal, which adequately describe magnetic anomalies and critical parameters of a crossover. It is shown that the jumpwise change in the α- and γ-symmetry quadrupole interactions in TbLiF4 caused by changes in the corresponding quadrupole moments during the crossing of energy levels leads, in accordance with experiments, to a decrease in the critical field H c by approximately 4 T and an increase in the maximum of the differential susceptibility dM(H)/dH near the crossover more than twofold. This behavior can be considered as an analog of the induced quadrupole transition caused by a change of the ground state of the rare-earth ion during crossover.

Spectroscopy and Calculations for 4fN → 4fN–15d Transitions of Lanthanide Ions in K3YF6

In the present work, we report on the combined experimental and theoretical studies of the 4f-5d spectra of Ce(3+), Pr(3+), Nd(3+), Eu(3+), Gd(3+), Tb(3+), Dy(3+), and Er(3+) ions in a newly synthesized K3YF6 matrix. The low temperature experimental 4f-5d excitation spectra have been analyzed and compared with the results of the energy-level and intensity calculations. For this theoretical analysis, the extended phenomenological crystal-field model for the 4f(N-1)5d configuration (i.e., the extended f-shell programs, developed by Prof. M. F. Reid) and exchange charge model (developed by Prof. B. Z. Malkin) have been used together to estimate the crystal field parameters and implement the spectral simulations. On the basis of the results of the performed theoretical analysis, we suggest the most probable positions occupied by optically active ions. Although the spectra of only eight lanthanide ions have been studied, the Hamiltonian parameters of the 4f(N-1)5d configuration have been evaluated for the whole lanthanide series and reported here for the first time, to give a complete and unified description of the spectroscopic properties of the trivalent rare earth ions in the chosen host. In addition to the studies of the 4f-5d transitions, various possible competitive excitation channels overlapping with 4f-5d ones have also been discussed, where a theoretical scheme giving rudiments to understand 4f-6s spectra are proposed for the first time. An excellent agreement between the calculated and measured excitation spectra shapes confirms validity of the performed analysis. The obtained parameters of the crystal field Hamiltonians for different ions and various electron configurations can be used in a straightforward way to generate the energy level positions and calculate the particular transition intensities for any rare earth ion in any particular spectral region. With the aid of the obtained parameters, the positions of the lowest energy levels of the 4f(N), 4f(N-1)5d ,and 4f(N-1)6s configurations of rare earth ions and 4f(N+1)(np)(5) configuration of rare earth ions and ligands (corresponding to the ligand-impurity ion charge transfer transitions) in the band gap of K3YF6 have all been estimated. The obtained Hamiltonian parameters and energy levels diagrams, which include the electronic structure of a host material, can be used as a starting point for analysis of spectroscopic properties of trivalent lanthanides in similar fluorides.

Librational motion of CO in solid Ar: Raman and IR spectra and quantum simulations

Rovibrational Raman spectra of CO molecules isolated in solid Ar are measured at temperatures of 9–30 K and compared to past and present IR spectra. The fundamental band appears as a triplet-split structure, while the center peak has completely different IR and Raman responses to temperature. The Raman peak is sharp and stable but broadens reversibly beyond recognition in the IR upon annealing. The red-shifted, intense line of the triplet is thermally inert in both spectroscopies. The third line is the weakest, and since it is concentration dependent, it is ascribed to a dimer, as before. The CO-H2O impurity complex is identified as a side band. We employ crystal field and quantum chemical modeling to interpret the disparity between the spectroscopies. The stable and broadened lines are assigned to double- and single-substitution sites, respectively. Thermal excitation is not effective in the former case of an angularly tight-confined, deep potential well. In the single-substitution case, the librational level structure shows up as a difference in the Raman and IR selection rules. An effectively ΔJ = 0 totally symmetric transition is found for the Raman spectrum that is uncoupled from lattice phonons and related broadening mechanisms. The low-temperature limit necessitates the use of a fixed lattice approach, while the warmer end of the range is best described by an adiabatic, pseudorotating lattice approach.

High-field magnetospectroscopy to probe the1.4-eV Ni color center in diamond

A magneto-optical study of the $1.4$-eV Ni color center in boron-free synthetic diamond, grown at high pressure and high temperature, has been performed in magnetic fields up to 56 T. The data are interpreted using the effective spin Hamiltonian of Nazar\'e, Nevers, and Davies [Phys. Rev. B 43, 14196 (1991)] for interstitial Ni${}^{+}$ with the electronic configuration $3{d}^{9}$ and effective spin $S=1/2$. Our results unequivocally demonstrate the trigonal symmetry of the defect, which preferentially aligns along the [111] growth direction on the (111) face, but reveal the shortcomings of the crystal field model for this particular defect.

Influence of high pressure on Sr2SiO4:Eu2+ luminescence

Eu2+ doped Sr2SiO4 phosphors were synthesized by solid state synthesis technique. The purity and crystal structure of the materials was studied with the X-ray powder diffraction. Depending on the synthesis method the materials contain one (α′) or two (α′+β) crystal phases. Luminescence properties were studied in UV–Vis range at ambient and high hydrostatic pressure. Two broad emission bands in the yellow–orange and blue–green region were attributed to the 9-fold coordinated and 10-fold coordinated Eu2+, respectively. We found that increasing pressure causes a red shift of the yellow–orange emission. This is typical pressure dependence related to 4f65d1 → 4f7 transition in Eu2+ observed also in other materials. In the case of blue–green band, when pressure increases from ambient to 50kbar, the emission band shifts strongly to higher energy, and for pressure higher than 50kbar does not depend on pressure. This effect was considered in framework of crystal field model. We presumed that electrostatic field in a 10-fold coordinated site is a superposition of crystal field of four ligands that belong to tetrahedral coordination and six ligands belonging to octahedral coordination. We discussed untypical pressure dependence of the blue–green emission band as a result of pressure influence on the lower excited state in Eu2+, i.e. 4f65d1(e) at octahedral and 4f65d1(t) at tetrahedral coordination.