Crystal Electric Field Research Articles

Elastic moduli of the distorted Kagome-lattice ferromagnet Nd3Ru4Al12

The distorted kagome-lattice compound Nd3Ru4Al12 has the hexagonal structure. This compound is reported as a ferromagnet in which spins are aligned along the c-axis with the Curie temperature TC=39K. The nature of localized f-electrons is expected in Nd3Ru4Al12, and magnetic anisotropy can be attributed to a crystal electric field (CEF) effect. We performed ultrasonic measurements on a Nd3Ru4Al12 single-crystalline sample in order to investigate the phase transition at TC and the CEF effect. All longitudinal and transverse elastic moduli increase monotonically with decreasing temperature, and no clear elastic softening due to a quadrupole interaction is detected under the hexagonal CEF. This result is in contrast to an isomorphic compound Dy3Ru4Al12 with a remarkable elastic softening of the transverse modulus C44. At the ferromagnetic phase transition, the moduli show obvious elastic anomalies, suggesting characteristic couplings between a strain and a magnetic order parameter.

Crystal-field effects in Er3+ - and Yb3+ -doped hexagonal NaYF4 nanoparticles

Since the up-conversion phenomenon in rare-earths (REs) doped ${\mathrm{NaYF}}_{4}$ is strongly affected by the crystal electric field (CF), determining the CF parameters, wave functions, and scheme of the energy levels of the RE $J$ multiplets could be crucial to improve and tune the up-conversion efficiency. In this work, the temperature and magnetic field dependent magnetization of ${\mathrm{NaY}}_{1\ensuremath{-}x}{[\mathrm{Er}(\mathrm{Yb})]}_{x}{\mathrm{F}}_{4}$ hexagonal nanoparticles (NPs) is reported. The data were best fit using the appropriated CF Hamiltonian for the $J=15/2\phantom{\rule{0.16em}{0ex}}(J=7/2)$ ground state multiplet of ${\mathrm{Er}}^{3+}\phantom{\rule{0.16em}{0ex}}({\mathrm{Yb}}^{3+}$) ions. The ${B}_{2}^{0}, {B}_{4}^{0}, {B}_{6}^{0}$, and ${B}_{6}^{6}$ CF parameters were considered in the Hamiltonian for RE ions located at the hexagonal ${\mathrm{C}}_{3h}$ point symmetry site of the ${\mathrm{NaYF}}_{4}$ host lattice. These results allowed us to predict an overall CF splitting of $\ensuremath{\sim}214$ ($\ensuremath{\sim}356$ K) for ${\mathrm{Er}}^{3+}$ (${\mathrm{Yb}}^{3+}$) and the wave functions and their energy levels for the $J=15/2$ ($J=7/2$) ground state multiplet which are in good agreement with the low temperature electron spin resonance experiments. Besides, our measurements allowed us to calculate all the excited CF $J$ multiplets that yield to a good estimation of the up-conversion light emission linewidth. The nonlinear optical light emission of the studied ${\mathrm{NaY}}_{1\ensuremath{-}x}{[\mathrm{Er}(\mathrm{Yb})]}_{x}{\mathrm{F}}_{4}$ hexagonal NPs was also compared with the most efficient up-conversion codoped ${\mathrm{NaY}}_{1\ensuremath{-}x\ensuremath{-}y}{\mathrm{Er}}_{x}{\mathrm{Yb}}_{y}{\mathrm{F}}_{4}$ hexagonal NPs.

Features of thermal and magnetic properties of nonstoichiometric DyB50 boride: The influence of the magnetic phase transition and crystal electric field

The specific heat, thermal expansion and magnetic properties of polycrystalline sample of nonstoichiometric dysprosium boride DyB50, that was synthesized by boron-thermal reduction of the metal from its oxide in vacuum, were studied at 2–300 K. The measurements revealed a heat capacity and magnetic susceptibility anomalies at about TN ≈ 6.3 K, caused by the transition to an antiferromagnetic state. The anomalies of studied properties of DyB50 at higher temperatures have been ascribed to the influence of crystal electric field (CEF). The scheme of CEF-splitting of Dy3+ ion ground level in boride has been proposed.

Magnetic Structure and Excitations in CeCuxAl4-x System.

CeCuAl3 crystallizing in the tetragonal BaNiSn3-type structure and CeCuxAl4-x solid solutions were investigated by means of elastic and inelastic neutron scattering. Powder neutron diffraction brought information on both temperature evolution of crystallographic parameters and magnetic order at low temperatures. No structural change was observed in the investigated temperature range from 1.5 to 300 K. Weak magnetic peaks outside nuclear Bragg positions observed in solid solutions with 0.90 ≤ x ≤ 1.10 were described by the propagation vector k = (0.40 + δx, 0.60 + δy, 0), where δx ≈ 0.02 and δy ≈ 0.01. The magnetic structure of CeCu0.75Al3.25 consists of two components: an anti-ferromagnetic one described by the same k and a ferromagnetic one with k0 = (0, 0, 0) and magnetic moments lying within the tetragonal basal plane. The evolution of magnetic excitations as a function of Cu-Al concentration in CeCuxAl4-x was studied by inelastic neutron scattering. The measured spectra of CeCuAl3 and the solution with x = 0.95 point to a three-magnetic-peak energy scheme, while only two excitations are expected from the local symmetry conditions on Ce atoms. The standard two-peak spectrum of crystal electric field excitations was observed for Cu-Al substitutions further from the 1:1:3 stoichiometry (x = 0.75 and 1.10). The intermediate concentrations (x = 0.90 and 1.05) exhibit spectra on the border between the former cases with a less clear pronounced first inelastic magnetic peak. The observed behavior is discussed considering the evolution of structural parameters in the CeCuxAl4-x system and the coupling between the lattice vibrations and the crystal electric field excitations.

Impact of the crystal electric field on magnetocaloric properties of CsGd(MoO4)2

Magnetocaloric effect (MCE) was investigated in the single crystal of CsGd(MoO4)2 in the temperature range from 2 to 30 K and fields up to 5 T applied along the easy and hard magnetic axis. The analysis of specific heat and magnetization provided the refinement of crystal electric field (CEF) parameters supporting the dominance of uniaxial symmetry. The knowledge of CEF energy levels enabled the extrapolation of MCE parameters outside the experimental region. Consequently, maximum values of the isothermal entropy change, −ΔSM, in magnetic fields up to 5 T are expected to occur at temperatures between 1 and 2 K. While −ΔSM achieves 19.2 J/kgK already for the field 1 T, for the field change 7 T, maximal −ΔSM≈ 26.8 J/kgK with a refrigerant capacity of 215 J/kg is expected. The absence of thermal hysteresis and the losses due to eddy currents as well as good chemical stability makes the compound CsGd(MoO4)2 attractive for magnetic refrigeration at low temperatures. The possibilities of further enhancement of MCE parameters are discussed.

Muon spin relaxation and inelastic neutron scattering investigations of the all-in/all-out antiferromagnetNd2Hf2O7

${\mathrm{Nd}}_{2}{\mathrm{Hf}}_{2}{\mathrm{O}}_{7}$, belonging to the family of geometrically frustrated cubic rare-earth pyrochlore oxides, was recently identified to order antiferromagnetically below ${T}_{\mathrm{N}}\ensuremath{\approx}0.55$ K with an all-in/all-out arrangement of ${\mathrm{Nd}}^{3+}$ moments, however, with a much reduced ordered state moment. Herein, we investigate the spin dynamics and crystal-field states of ${\mathrm{Nd}}_{2}{\mathrm{Hf}}_{2}{\mathrm{O}}_{7}$ using muon spin relaxation $(\ensuremath{\mu}\mathrm{SR})$ and inelastic neutron scattering (INS) measurements. Our $\ensuremath{\mu}\mathrm{SR}$ study confirms the long-range magnetic ordering and shows evidence for coexisting persistent dynamic spin fluctuations deep inside the ordered state down to 42 mK. The INS data show the crystal electric field (CEF) excitations due to the transitions both within the ground-state multiplet and to the first excited state multiplet. The INS data are analyzed by a model based on CEF and crystal-field states are determined. Strong Ising-type anisotropy is inferred from the ground-state wave function. The CEF parameters indicate the CEF-split Kramers doublet ground state of ${\mathrm{Nd}}^{3+}$ to be consistent with the dipolar-octupolar character.

Anisotropic exchange in LiCu2O2

We investigate the magnetic properties of the multiferroic quantum-spin system LiCu$_2$O$_2$ by electron spin resonance (ESR) measurements at $X$- and $Q$-band frequencies in a wide temperature range $(T_{\rm N1} \leq T \leq 300$\,K). The observed anisotropies of the $g$ tensor and the ESR linewidth in untwinned single crystals result from the crystal-electric field and from local exchange geometries acting on the magnetic Cu$^{2+}$ ions in the zigzag-ladder like structure of LiCu$_2$O$_2$. Supported by a microscopic analysis of the exchange paths involved, we show that both the symmetric anisotropic exchange interaction and the antisymmetric Dzyaloshinskii-Moriya interaction provide the dominant spin-spin relaxation channels in this material.

Insight into the temperature dependent properties of the ferromagnetic Kondo lattice YbNiSn

Analyzing temperature dependent photoemission (PE) data of the ferromagnetic Kondo-lattice (KL) system YbNiSn in the light of the Periodic Anderson model (PAM) we show that the KL behavior is not limited to temperatures below a temperature T_K, defined empirically from resistivity and specificic heat measurements. As characteristic for weakly hybridized Ce and Yb systems, the PE spectra reveal a 4f-derived Fermi level peak, which reflects contributions from the Kondo resonance and its crystal electric field (CEF) satellites. In YbNiSn this peak has an unusual temperature dependence: With decreasing temperature a steady linear increase of intensity is observed which extends over a large interval ranging from 100 K down to 1 K without showing any peculiarities in the region of T_K ~ TC= 5.6 K. In the light of the single-impurity Anderson model (SIAM) this intensity variation reflects a linear increase of 4f occupancy with decreasing temperature, indicating an onset of Kondo screening at temperatures above 100 K. Within the PAM this phenomenon could be described by a non-Fermi liquid like T- linear damping of the self-energy which accounts phenomenologically for the feedback from the closely spaced CEF-states.

Frustrated magnetism in the Heisenberg pyrochlore antiferromagnets AYb2X4 ( A=Cd , Mg; X=S , Se)

Our polycrystalline sample study on the Yb-based chalcogenide spinels $A$Yb$_2$$X_4$ ($A =$ Cd, Mg, $X =$ S, Se) has revealed frustrated magnetism due to the antiferromagnetically coupled Heisenberg spin on the pyrochlore lattice. Our crystal electric field analysis indicates the Yb ground state has nearly Heisenberg spins with a strong quantum character of the ground doublet. All the materials exhibit an antiferromagnetic order at 1.4-1.8 K, much lower temperature than the antiferromagnetic exchange coupling scale of $\sim 10$ K. The magnetic specific heat $C_{\rm M}$ shows a $T^{3}$ dependence, indicating the gapless feature in the Yb-based chalcogenide spinels. The magnetic entropy change much smaller than $R$ ln 2 below the N\'{e}el temperature and the small local magnetic field estimated from the $\mu$SR measurements strongly suggest the significantly reduced size of the ordered moment in comparison with the bare moment size 1.33 $\mu_{\rm B}$/Yb supporting strong fluctuations in the commensurate and incommensurate ordered states in CdYb$_2$S$_4$ and MgYb$_2$S$_4$, respectively.

Magnetocaloric effect in Laves-phase rare-earth compounds with the second-order magnetic phase transition: Estimation of the high-field properties

High-field magnetocaloric effect of the rare-earth Laves-phase compounds, which show the second-order magnetic phase transition at low temperatures, has been studied theoretically and experimentally. Both direct and indirect methods are used to characterize the high-field properties of the adiabatic temperature change, ΔTad, and the magnetic entropy change, ΔSmag, for TbNi2 and DyNi2 compounds, which order ferromagnetically below 37 and 22 K, respectively. Experimental data are compared with theoretical results obtained in the frame of the microscopic model which takes into account the Zeeman exchange interaction and the crystal electric field anisotropy. The high-field magnetocaloric properties near the phase transition are also discussed in the framework of the Landau theory for the second-order phase transitions.

Influence of chemical composition on the X-ray photoemission, thermopower, specific heat, and magnetic properties of CeNi2(Si1-yGey)2

We report our studies of the intermediate compositions between CeNi2Si2 and CeNi2Ge2, i.e., the alloys CeNi2(Si1-yGey)2 by means of the thermopower, electrical resistivity, specific heat, magnetic susceptibility, and X-ray photoemission measurements. CeNi2Si2 is a fluctuating valence system and CeNi2Ge2 is known to show the heavy fermion behaviour. The change of the temperature dependence of the resistivity towards the typical metallic behaviour occurs below y ~ 0.25. The transition between CeNi2Si2 and CeNi2Ge2 is discussed in the frames of competition between the crystal electric field and Kondo interactions. It is found that valence stabilisation occurs for Ge content y > 0.25. The hybridization energy Δ determined from the XPS Ce 3d spectrum reflects well the behaviour of the parameter Eex obtained from the analysis of the magnetic susceptibility by the interconfiguration fluctuation model. It has been also shown that thermopower data can be successfully described employing the single ion model for 0.6 < y < 1.0 and two-band model including the crystal electric field splitting for y ≤ 0.25.

Low-temperature transport and thermodynamic properties of dense Kondo alloys [formula omitted

The alloys Ce8Pd24(Al1−xSnx) with 0≤x≤1 were studied by means of electrical resistivity, thermal conductivity, thermoelectric power, magnetic susceptibility and magnetization measurements. In the entire composition range, an antiferromagnetic (AFM) long-range ordering has been established at low temperatures, with the Néel temperature increasing linearly from TN = 4.3 K for Ce8Pd24Al to TN = 7 K for Ce8Pd24Sn. Below TN, the electrical resistivity is dominated by scattering conduction electrons on spin-wave excitations. In the paramagnetic state, the electrical transport in the alloys with 0≤x≤0.7 reveals both coherent Kondo lattice scattering and crystal-electric field (CEF) effect, while that in the alloys with x≥0.8 appears governed by CEF only. Above TN, all the alloys exhibit well localized magnetic behavior due to trivalent Ce ions. At high temperatures, the thermoelectric power can be interpreted in terms of a phenomenological resonance model giving an estimate of the CEF effect. The thermoelectric figure of merit of Al-rich alloys is small compared to those of commercial thermoelectric materials.

Study of crystal-field splitting in ultrathinCePt5films by Raman spectroscopy

Low-temperature electronic properties of rare-earth intermetallics are substantially influenced by the symmetry and magnitude of the crystal electric field. The direct spectroscopic analysis of crystal field splitting can be challenging, especially in low-dimensional systems, because it requires both high spectral resolution and pronounced sensitivity. We demonstrate the eligibility of electronic Raman spectroscopy for this purpose by the direct determination of the $4f$ level splitting in ultra-thin ordered CePt$_5$ films down to 1.7 nm thickness on Pt(111). Crystal field excitations of Ce $4f$ electrons give rise to Raman peaks with energy shifts up to $\approx$ 25 meV. Three distinct peaks occur which we attribute to inequivalent Ce sites, located (i) at the interface to the substrate, (ii) next to the Pt-terminated surface, and (iii) in the CePt$_5$ layers in between. The well-resolved Raman signatures allow us to identify a reduced crystal field splitting at the interface and an enhancement at the surface, highlighting its strong dependence on the local atomic environment.

Spectral Characteristics of Ultrafine Particles Zn2 SiO4-Mn, Precipitated From an Aqueous Solution on the Substrate in Electric or Magnetic Fields

The spectral parameters ultrafine particles Zn2SiO4-Mn, precipitated on the substrate in a magnetic or electric field have been investigated. For getting fine particles industrial phosphor K-60 (Zn2SiO4-Mn) was used. Luminescence spectra were obtained on a sample when exposed to ultraviolet light or a beam of charged oxygen ions. When excited by ultraviolet spectral characteristics have difference for samples with different dimensions of the crystals. As for the industrial design luminescence spectrum had a band with λmaх = 521 nm, and for the ultrafine crystals willemite spectral band had λmax = 550 nm. Analysis ionoluminescence spectra showed that the reduction of crystal size Zn2SiO4-Mn not affect the spectral characteristics of the excitation beam with low energy oxygen ions. The luminescence spectrum when exposed to low-energy ions (1-3 KeV) has a band with λmax = 521 nm and a half-width Δλ = 41 nm. When measuring the width of the forbidden zone has been established bandgap dependence on the size of the phosphor crystals. The width of the band gap increases with decreasing crystal size to nanoscale sizes. A significant effect was obtained when deposited on a substrate in the nanoscale crystal magnetic or electric field. As for the industrial design the bandgap was 4.16 eV, and for the besieged in the magnetic and electric field of 4.27, 4.29 eV, respectively.

Probing the magnetic ground state of single crystalline Ce3TiSb5

Motivated by the report of superconductivity in R3TiSb5 (R = La and Ce) and possibly Nd3TiSb5 at ∼4 K, we grew single crystals of La3TiSb5 and Ce3TiSb5 by the high-temperature solution method using Sn as a flux. While in both compounds we observed a superconducting transition at 3.7 K for resistivity and low-field magnetization, our data conclusively show that it arose from residual Sn flux present in the single crystals. In particular, the heat capacity data do not present any of the anomalies expected from a bulk superconducting transition. The anisotropic magnetic properties of Ce3TiSb5, crystallizing in a hexagonal P63/mcm structure, were studied in detail. We find that the Ce ions in Ce3TiSb5 form a Kondo lattice and exhibited antiferromagnetic ordering at 5.5 K with a reduced moment and a moderately normalized Sommerfeld coefficient of 598 mJ/mol K2. The characteristic single-ion Kondo energy scale was found to be ∼8 K. The magnetization data were subjected to a crystal electric field (CEF) analysis. The experimentally observed Schottky peak in the 4f-electron heat capacity of Ce3TiSb5 was reproduced fairly well by the energy levels derived from the CEF analysis.

Defect mode and crystal-electric-field effects on the thermal expansion and heat capacity of RB50 boride

Specific heat and thermal expansion in LuB50 and TbB50 borides at 2–300 K were experimentally studied. In both compounds, for a large range of low temperatures a negative thermal expansion caused by defects in the crystal lattice was observed. The effect of the crystal electric field on the thermal characteristics of TbB50 was observed as a Schottky anomaly in the temperature dependence of the heat capacity and as an additional negative contribution to the thermal expansion. The analysis of the heat capacity data suggests that the ground state of the ion Tb3+ is a quasi-quintet, consisting of close-located singlet and two doublets. The phase transition of TbB50 to the antiferromagnetic state appears as a very weak broad anomaly in the temperature dependence of the heat capacity; within the scattering of the experimental data, it is not visible in the temperature dependence of the unit cell volume.

A critical point in Sr2-xIrO4 and less distorted IrO6 octahedra induced by deep Sr-vacancies

For the Sr2-xIrO4 system, recent work pointed out the abnormal electronic and magnetic properties around a critical point. Here, to understand Sr-vacancy effect on spin-orbit coupled Mott insulator Sr2IrO4, the electronic structure and local structure distortion for Sr2-xIrO4 system have been investigated by x-ray absorption spectroscopy (XAS). By comparing the intensity of white-line features at the Ir L2,3-edge x-ray absorption near-edge spectroscopy (XANES), we observe a sudden rise of the branching ratio in the vicinity of the critical point. Further analysis on the Ir L3-edge extended x-ray absorption fine structure (EXAFS) and calculated data demonstrated that the abrupt enhancement of the branching ratio is intimately related to the less distorted IrO6 octahedra induced by deep Sr-vacancies, which in turn alters the relatively strength of the spin-orbit coupling (SOC) and crystal electric field (CEF) that would dictate the abnormal behavior of electronic and magnetic structure near the critical point.

Crystal electric field excitations in the quasicrystal approximantTbCd6studied by inelastic neutron scattering

We have performed inelastic neutron scattering measurements on powder samples of the quasicrystal approximant, ${\mathrm{TbCd}}_{6}$, grown using isotopically enriched $^{112}\mathrm{Cd}$. Both quasielastic scattering and distinct inelastic excitations were observed below 3 meV. The intensity of the quasielastic scattering measured in the paramagnetic phase diverges as ${T}_{\mathrm{N}}\ensuremath{\sim}22$ K is approached from above. The inelastic excitations, and their evolution with temperature, are well characterized by the leading term, ${B}_{2}^{0}{O}_{2}^{0}$, of the crystal electric field (CEF) level scheme for local pentagonal symmetry for the rare-earth ions [S. Jazbec et al., Phys. Rev. B 93, 054208 (2016)] indicating that the Tb moment is directed primarily along the unique local pseudofivefold axis of the Tsai-type clusters. We also find good agreement between the inverse susceptibility determined from magnetization measurements using a magnetically diluted ${\mathrm{Tb}}_{0.05}{\mathrm{Y}}_{0.95}{\mathrm{Cd}}_{6}$ sample and that calculated using the CEF level scheme determined from the neutron measurements.

Ultrasonic Study on the Hexagonal Antiferromagnet Dy3Ru4Al12

In the distorted kagome lattice antiferromagnet Dy3Ru4Al12 with TN = 7 K, a crystal electric field (CEF) effect is expected at high temperatures. To investigate the CEF effect and the phase transition at TN, we performed ultrasonic measurements on a single-crystalline sample. At high temperatures, both the longitudinal elastic modulus C11 and the transverse modulus C44 increase monotonically with decreasing temperature. Below 60 K a characteristic elastic softening is observed in C44 in contrast to C11 with monotonic hardening down to TN. We analyzed C44 using the Curie-Weiss-type equation and obtained a negative parameter: Θ which is proportional to a quadrupole-quadrupole coupling constant under the hexagonal CEF. With further decreasing temperature, both moduli exhibit abrupt elastic hardening at TN due to a magnetostriction.

Anisotropic Thermal Expansion of α-YbAlB4

Thermal expansion measurements were performed for α-YbAlB4 using powder X-ray diffraction and our high resolution capacitance dilatometry. Highly anisotropic thermal expansion, which is much larger along the c-axis compared to the a- and b-axes, was observed. In addition, high resolution capacitance dilatometry revealed negative thermal expansion appears below 90 K only along the a-axis, not along the c-axis. The observation is consistent with anisotropic hybridization stronger in the ab-plane, suggesting the formation of anisotripic heavy fermion well below the valence fluctuation temperature scale of 200 ∼ 300 K. Furthermore, linear thermal expansion coefficient along the a-axis starts to decrease below 115 K. The characteristic temperature scale of 90 - 115 K may correspond to the crystal electric field excited level. The in-plane negative thermal expansion can be regarded as a development of anisotropic hybridization due to |Jz = ±5/2 > crystal electric field ground states which becomes dominant on cooling below the excited states.