Crystal Electric Field Levels Research Articles

Extracting the crystal electric field levels of Ce-4f1 states in CeB6 by atomic multiplet simulations

The crystal electric field (CEF) is vital in defining the low-energy electronic structure of lanthanide compound, and thus very essential in understanding the many-body physics of the strongly correlated 4 f electrons. Many efforts have been made to determine the low-energy electronic structure of the intrinsically correlated material CeB6 and its derived compounds. In this paper, we performed atomic multiplet (AM) simulations on the Ce-4f1 states in CeB6 and directly fitted them with previously reported resonant inelastic x-ray scattering spectroscopy (RIXS). The simulation results suggest that the discrepancy of excitations energies extracted from Raman spectroscopy and RIXS is a result of intrinsic varied crystal electric field strength, which can be reconciled by considering the enhanced CEF by eliminating the insulating scenario.

Anisotropic magnetic and quadrupolar H−T phase diagram of CeRh2As2

The tetragonal heavy-fermion compound CeRh2As2 has intriguing low-temperature symmetry-breaking phases whose nature is unclear. The unconventional superconducting phase is complemented by other normal-state phases which presumably involve ordering of 4f electron multipoles supported by the Kramers doublets split by the tetragonal crystal electric field (CEF). The most striking aspect is the pronounced anisotropic H−T phase boundary for in-plane and out-of plane field directions. Using a localized 4f CEF model we demonstrate that its essential features can be understood as the result of competing low-field easy-plane magnetic order and field-induced quadrupolar order of xy type. We present calculations based on coupled multipole random phase approximation response function approach as well as molecular field treatment in the ordered regime. We use an analytical approach for a reduced quasiquartet model and numerical calculations for the complete CEF level scheme. We discuss the quantum critical properties as function of multipolar control parameters and explain the origin of a pronounced ac anisotropy of the H−T phase diagram. Finally, the field and temperature evolution of multipolar order parameters is derived and the high-field phase diagram is predicted. Published by the American Physical Society 2024

Controlling crystal-electric field levels through symmetry-breaking uniaxial pressure in a cubic super heavy fermion

YbPtBi is one of the heavy-fermion systems with largest Sommerfeld coefficient γ and is thus classified as a ‘super’-heavy fermion material. In this work, we resolve the long-debated question about the hierarchy of relevant energy scales, such as crystal-electric field (CEF) levels, Kondo and magnetic ordering temperature, in YbPtBi. Through measurements of the a.c. elastocaloric effect and generic symmetry arguments, we identify an elastic level splitting that is unambiguously associated with the symmetry-allowed splitting of a quartet CEF level. This quartet, which we identify to be the first excited state at Δ/kB ≈ 1.6 K above the doublet ground state at ambient pressure, is well below the proposed Kondo temperature TK ≈ 10 K. Consequently, this analysis of the energy scheme can provide support models that predict that the heavy electron mass is a result of an enhanced degeneracy of the CEF ground state, i.e., a quasi-sextet in YbPtBi. At the same time, our study shows the potential of the a.c. elastocaloric effect to control and quantify strain-induced changes of the CEF schemes, opening a different route to disentangle the CEF energy scales from other relevant energy scales in correlated quantum materials.

Diffusive excitonic bands from frustrated triangular sublattice in a singlet-ground-state system

Magnetic order in most materials occurs when magnetic ions with finite moments arrange in a particular pattern below the ordering temperature. Intriguingly, if the crystal electric field (CEF) effect results in a spin-singlet ground state, a magnetic order can still occur due to the exchange interactions between neighboring ions admixing the excited CEF levels. The magnetic excitations in such a state are spin excitons generally dispersionless in reciprocal space. Here we use neutron scattering to study stoichiometric Ni2Mo3O8, where Ni2+ ions form a bipartite honeycomb lattice comprised of two triangular lattices, with ions subject to the tetrahedral and octahedral crystalline environment, respectively. We find that in both types of ions, the CEF excitations have nonmagnetic singlet ground states, yet the material has magnetic order. Furthermore, CEF spin excitons from the tetrahedral sites form a dispersive diffusive pattern around the Brillouin zone boundary, likely due to spin entanglement and geometric frustrations.

Magnetic structure and crystal field states ofPr2Pd3Ge5:μSRand neutron scattering investigations

We present the results of muon spin relaxation ($\ensuremath{\mu}\mathrm{SR}$), neutron powder diffration (NPD), and inelastic neutron scattering (INS) investigations on polycrystalline ${\mathrm{Pr}}_{2}{\mathrm{Pd}}_{3}{\mathrm{Ge}}_{5}$. The polycrystalline ${\mathrm{Pr}}_{2}{\mathrm{Pd}}_{3}{\mathrm{Ge}}_{5}$ is known to exhibit two antiferromagnetic transitions near ${T}_{\mathrm{N}1}=8.3$ K and ${T}_{\mathrm{N}2}=7.5$ K which is confirmed by the heat capacity measurements on the present sample. In the magnetically ordered state the NPD data show clear evidence for magnetic Bragg peaks, which for $T<{T}_{\mathrm{N}2}$ could be indexed with a propagation vector k = (1, 0, 0), and with k = (1, 0, 0.07) for ${T}_{\mathrm{N}2}<T<{T}_{\mathrm{N}1}$. We have determined the magnetic structure and found a canted antiferromagnetic structure of ordered ${\mathrm{Pr}}^{3+}$ moments. At 7.6 K we find an amplitude modulated incommensurate antiferromagnetic arrangement of ordered moments with a maximum ordered moment of 1.64(3) ${\ensuremath{\mu}}_{\mathrm{B}}$/Pr lying in the $ab$ plane tilted at about ${26}^{\ensuremath{\circ}}$ from the $b$ axis. At 1.8 K the antiferromagnetic structure is found to be commensurate with an ordered moment of 2.80(6) ${\ensuremath{\mu}}_{\mathrm{B}}$/Pr lying in the $ab$ plane tilted at about ${28}^{\ensuremath{\circ}}$ from the $b$ axis. Our zero-field $\ensuremath{\mu}\mathrm{SR}$ spectra at 1.5 K and at shorter time scale (below 0.5 $\ensuremath{\mu}\mathrm{s}$) reveal two oscillatory frequencies further supporting a long-range-ordered magnetic ground state. We have calculated the muon sites using the density functional theory calculation and present the results of internal field calculations at the muon stopping sites, which are in good agreement with the experimental observations. In the paramagnetic state, the INS data show three well defined CEF excitations near 8.0, 12.3, and 18.1 meV arising from the crystal electric field (CEF) split $J=4$ ground state of ${\mathrm{Pr}}^{3+}$. The CEF level scheme is deduced by analyzing the INS data by a model based on the CEF model.

Low-temperature specific heat and heat transport of Tb2Ti2−xZrxO7 single crystals

We report a study on the specific heat and heat transport of Tb$_2$Ti$_{2-x}$Zr$_x$O$_7$ ($x =$ 0, 0.02, 0.1, 0.2, and 0.4) single crystals at low temperatures and in high magnetic fields. The magnetic specific heat can be described by the Schottky contribution from the crystal-electric-field (CEF) levels of Tb$^{3+}$, with introducing Gaussian distributions of the energy split of the ground-state doublet and the gap between the ground state and first excited level. These crystals has an extremely low phonon thermal conductivity in a broad temperature range that can be attributed to the scattering by the magnetic excitations, which are mainly associated with the CEF levels. There is strong magnetic field dependence of thermal conductivity, which is more likely related to the field-induced changes of phonon scattering by the CEF levels than magnetic transitions or spin excitations. For magnetic field along the [111] direction, there is large thermal Hall conductivity at low temperatures which displays a broad peak around 8 T. At high fields up to 14 T, the thermal Hall conductivity decreases to zero, which supports its origin from either the spinon transport or the phonon skew scattering by CEF levels. The thermal Hall effect is rather robust with Zr doping up to 0.2 but is strongly weakened in higher Zr-doped sample.

Crystal electric field level scheme leading to giant magnetocaloric effect for hydrogen liquefaction

In recent years, magnetic refrigeration has attracted considerable attention for hydrogen liquefaction. Most materials used for magnetic refrigeration contain heavy rare earth ions with complex crystalline electric field energy splittings, whose effect on the magnetic entropy change ΔSM has not been systematically studied. In particular, the theoretical upper limits of ∣ΔSM∣ for general heavy earth cases are unknown. Here, we show that the crystalline electric field level schemes result in a large ΔSM for general heavy rare earth cases. We provide a specific example of the magnetic refrigeration material HoB2 using inelastic neutron scattering experiments combined with mean-field calculations with crystal field splitting and exchange interactions. The relationship between ΔSM and crystal field parameters presented in this study can be useful for developing compounds with a large ∣ΔSM∣ and advancing the design of magnetic refrigeration materials.

Crystal electric field and possible coupling with phonons in Kondo lattice CeCuGa3

We investigate the magnetic and crystal electric field (CEF) states of the Kondo lattice system CeCuGa3 by muon spin relaxation (muSR), neutron diffraction, and inelastic neutron scattering (INS) measurements. A noncentrosymmetric BaNiSn3-type tetragonal crystal structure (space group I4mm) is inferred from x-ray as well as from neutron powder diffraction. The low-temperature magnetic susceptibility and heat capacity data show an anomaly near 2.3 - 2.5~K associated with long range magnetic ordering, which is further confirmed by muSR and neutron diffraction data. The neutron powder diffraction collected at 1.7 K shows the presence of magnetic Bragg peaks indexed by an incommensurate magnetic propagation vector k = (0.148, 0.148, 0) and the magnetic structure is best described by a longitudinal spin density wave with ordered moments lying in ab-plane. An analysis of the INS data based on a CEF model reveals the presence of two magnetic excitations near 4.5 meV and 6.9 meV. The magnetic heat capacity data suggest an overall CEF splitting of 20.7 meV, however the excitation between 20 and 30 meV is very broad and weak in our INS data, but could provide an evidence of CEF level in this energy range in agreement with the magnetic entropy. Our analysis of INS data based on the CEF-phonon model indicates that the two excitations at 4.5 meV and 6.9 meV have their origin in CEF-phonon coupling (i.e. splitting of one CEF peak into two peaks, called vibron), with an overall splitting of 28.16 meV, similar to the case of CeCuAl3 and CeAuAl3.

Neutron scattering measurement of crystalline-electric fields in magnesium rare-earth selenide spinels

The symmetry of local moments plays a defining role in the nature of exotic grounds states stabilized in frustrated magnetic materials. We present inelastic neutron scattering (INS) measurements of the crystal electric field (CEF) excitations in the family of compounds MgRE$_2$Se$_4$ (RE $\in$ $\{$Ho, Tm, Er and Yb$\}$). These compounds form in the spinel structure, with the rare earth ions comprising a highly frustrated pyrochlore sublattice. Within the symmetry constraints of this lattice, we fit both the energies and intensities of observed modes in the INS spectra to determine the most likely CEF Hamiltonian for each material and comment on the ground state wavefunctions in the local electron picture. In this way, we experimentally confirm MgTm$_2$Se$_4$ has a non-magnetic ground state, and MgYb$_2$Se$_4$ has effective $S=\frac{1}{2}$ spins with $g_\parallel = 5.188(79)$ and $g_\perp = 0.923(85)~\mu_B$. The spectrum of MgHo$_2$Se$_4$ indicates a ground state doublet containing Ising spins with $g_\parallel = 2.72(46)$, though low-lying CEF levels are also seen at thermally accessible energies $\delta_E = 0.591(36)$, 0.945(30) and 2.88(7)~meV, which can complicate interpretation. These results are used to comment on measured magnetization data of all compounds, and are compared to published results on the material MgEr$_2$Se$_4$.

Electronic structure of the quadrupolar ordered heavy-fermion compound YbRu2Ge2 measured by angle-resolved photoemission

We studied the electronic structure of the heavy fermion compound Yb(Ru$_{1-x}$Rh$_{x}$)$_2$Ge$_2$ with $x=0$ and nominally $x=0.125$ using ARPES and LDA calculations. We find a valence band structure of Yb corresponding to a non-integer valence close to $3+$. The three observed crystal electric field levels with a splitting of 32 and 75 meV confirm the suggested configuration with a quasi-quartet ground state. The experimentally determined band structure of the conduction electrons with predominantly Ru $4d$ character is well reproduced by our calculations. YbRu$_2$Ge$_2$ undergoes a non-magnetic phase transition into a ferroquadrupolar ordered state below 10.2\,K and then to an antiferromagnetically ordered state below 6.5\,K. A small hole Fermi surface shows nesting features in our calculated band structure and its size determined by ARPES is close to the magnetic ordering wave vector found in neutron scattering. The transitions are suppressed when YbRu$_2$Ge$_2$ is doped with 12.5% Rh. The electron doping leads to a shift of the band structure and successive Lifshitz transitions.

Crystal electric field contribution to the thermoelectric power of the CeCoAl4 antiferromagnetic

We report on the thermoelectric power S(T), electrical resistivity and thermal conductivity measurements on the antiferromagnetic CeCoAl4 compound and on the nonmagnetic reference compound, LaCoAl4. The Néel temperature of CeCoAl4 is T[Formula: see text] = 13.5 K and a metamagnetic-like transition occurs in the magnetic field of about 7.5 T. We show that the magnetic contribution to the thermoelectric power, S[Formula: see text](T), exhibits a large peak due to the crystal electric field (CEF) at about 240 K and a small anomaly around the ordering temperature. Surprisingly, the CEF related S[Formula: see text](T) peak is close to the upper CEF excitation energy [Formula: see text] = 202 K, in contrast to the usual case of the peak position being located at a fraction of the observed CEF energy level. The applicability of different theoretical and phenomenological models describing the temperature dependence of the Seebeck effect S[Formula: see text](T) has been tested and finally a calculation is proposed, which incorporates a full CEF levels scheme.

Electronic and magnetic properties of quasi-skutterudite PrCo2Ga8 compound

PrCo2Ga8 is an orthorhombic quasi-skutterudite type compound which crystallizes in the CaCo2Al8 structure type, with space group Pbam (No. 55). The Pr3+ ion has a site symmetry of Cs which predicts a crystal electric field (CEF) level splitting into 9 singlets for J = 4. However, a phase transition at Tm = 1.28 K is observed in electrical resistivity and specific heat results and is reported in this paper. The electrical resistivity shows an upturn below Tm due to the superzone-gap formation. This transition is tuneable in fields and is suppressed to lower temperatures with applied magnetic fields. The electronic specific heat Cp(T)/T increases below Tm and reaches a value of 7.37 J/(mol K2) at 0.4 K. The Sommerfeld coefficient, γ extracted from the low temperature analysis of C4f(T)/T is 637 mJ/(mol K2) indicating a possible mass enhancement of the quasiparticles. The calculated entropy value of 3.05 J/(mol K) is recovered around Tm exhibiting almost 53% of Rln2, where R is the universal gas constant. Magnetic susceptibility results obeys the Curie-Weiss law for data above 100 K with an estimated effective magnetic moment, μeff = 3.37 μB/Pr and Weiss temperature, θp = −124 K.

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.

Crystal-field states of Kondo lattice heavy fermionsCeRuSn3andCeRhSn3

Inelastic neutron scattering experiments have been carried out to determine the crystal field states of the Kondo lattice heavy fermions CeRuSn3 and CeRhSn3. Both the compounds crystallize in LaRuSn3-type cubic structure (space group Pm-3n) in which the Ce atoms occupy two distinct crystallographic sites with cubic (m-3) and tetragonal (-4m.2) point symmetries. The INS data of CeRuSn3 reveal the presence of a broad excitation centered around 6-8 meV which is accounted by a model based on crystal electric field (CEF) excitations. On the other hand, the INS data of isostructural CeRhSn3 reveal three CEF excitations around 7.0, 12.2 and 37.2 meV. The neutron intensity sum rule indicates that the Ce ions at both cubic and tetragonal Ce sites are in Ce3+ state in both CeRuSn3 and CeRhSn3. The CEF level schemes for both the compounds are deduced. We estimate the Kondo temperature T_K = 3.1(2) K for CeRuSn3 from neutron quasielastic linewidth in excellent agreement with that determined from the scaling of magnetoresistance which gives T_K = 3.2(1) K. For CeRhSn3 the neutron quasielastic linewidth gives T_K = 4.6 K. For both CeRuSn3 and CeRhSn3, the ground state of Ce3+ turns out to be a quartet for the cubic site and a doublet for the tetragonal site.

XY antiferromagnetic ground state in the effectiveS=12pyrochloreYb2Ge2O7

We report neutron scattering and muon spin relaxation measurements (muSR) on the pyrochlore antiferromagnet Yb2Ge2O7. Inelastic neutron scattering was used to probe the transitions between crystal electric field levels, allowing us to determine the eigenvalues and eigenvectors appropriate to the J=7/2 Yb3+ ion in this environment. The crystal electric field ground state doublet in Yb2Ge2O7 corresponds primarily to m_J = +/- 1/2 with local XY anisotropy, consistent with an S_eff = 1/2 description for the Yb moments. muSR measurements reveal the presence of an ordering transition at T_N = 0.57 K with persistent weak dynamics in the ordered state. Finally, we present neutron diffraction measurements that reveal a clear phase transition to the k = (000) Gamma_5 ground state with an ordered magnetic moment of 0.3(1) mu_B per Yb ion. We compare and contrast this phenomenology with the low temperature behavior of Yb2Ti2O7 and Er2Ti2O7, the prototypical S_eff = 1/2 XY pyrochlore magnets.

Absence of Magnetic Dipolar Phase Transition and Evolution of Low-Energy Excitations in PrNb2Al20 with Crystal Electric Field Γ3 Ground State: Evidence from 93Nb-NQR Studies

We report measurements of bulk magnetic susceptibility and 93Nb nuclear quadrupole resonance (NQR) in the Pr-based caged compound PrNb2Al20. By analyzing the magnetic susceptibility and magnetization, the crystal electric field (CEF) level scheme of PrNb2Al20 is determined to be Γ3(0 K)–Γ4(21.32 K)–Γ5(43.98 K)–Γ1(51.16 K) within the framework of the localized 4f electron picture. The 93Nb-NQR spectra exhibit neither spectral broadening nor spectral shift upon cooling down to 75 mK. The 93Nb-NQR spin–lattice relaxation rate 1/T1 at 5 K depends on the frequency and remains almost constant below 5 K. The frequency dependence of 1/T1 is attributed to the magnetic fluctuation due to the hyperfine-enhanced 141Pr nuclear moment inherent in the nonmagnetic Γ3 CEF ground state. The present NQR results provide evidence that no symmetry-breaking magnetic dipole order occurs down to 75 mK. Also, considering an invariant form of the quadrupole and octupole couplings between a 93Nb nucleus and Pr 4f electrons, Pr 4f qu...

Faraday effect of bismuth iron garnet thin film prepared by mist CVD method

Metastable bismuth iron garnet (BIG, an abbreviation of Bi3Fe5O12), one kind of garnet-type ferrites, is known to manifest very large Faraday rotation as well as low optical absorption in the visible to infrared region. We report on successful synthesis of thin film composed of single-phase BIG epitaxially grown on single-crystalline gadolinium gallium garnet (Gd3Ga5O12, GGG) substrate by using mist chemical vapor deposition (CVD) method, which is an emerging technique for preparation of thin films. The crystal structure, surface morphology, and magnetic, optical and magneto-optical properties of the resultant thin films have been explored. The BIG thin film has a relatively flat surface free from roughness compared to those prepared by other vapor deposition methods. Saturation magnetization is about 1620 G at room temperature, which is close to that expected from the ideal magnetic structure of BIG. The maximum value of Faraday rotation angle reaches 54.3 deg/µm at a wavelength of 424 nm. This value is rather large when compared with those reported for BIG thin films prepared by other techniques. The wavelength dependence of Faraday rotation angle is analyzed well in terms of the crystal electric field (CEF) level schema. Our result suggests that the mist CVD method is a simple and effective technique to synthesize BIG thin film with excellent magneto-optical properties.

Elastic anomalies of YbIrGe in magnetic fields

The Yb-based heavy-fermion compound YbIrGe, which has the orthorhombic structure, shows the crystal electric field effect at high temperatures and antiferromagnetic orderings at TN = 2.4 K and Tm = 1.4 K. We previously found anomalous elastic softening in zero magnetic field originating from an indirect quadrupole interaction between the ground doublet and the excited doublets, and determined the crystal electric field level scheme: the ground doublet and an excited doublet at 138 K. To investigate the antiferromagnetic orderings at TN and Tm, we performed ultrasonic measurements under magnetic fields along the a-axis on YbIrGe single crystals. Temperature dependence of elastic modulus C11 exhibits elastic hardening below both TN and Tm at 0 T. As increasing the magnetic field along the a-axis, both TN and Tm decrease monotonically, suggesting that both transitions are antiferromagnetic ordering. TN closes around 2 T, and Tm disappears above 1 T. We clarified the magnetic field- temperature phase diagram along the a-axis.

Magnetic properties of the tetragonal RCuGa3 (R=Pr, Nd and Gd) single crystals

Single crystals of tetragonal RCuGa3 (R=La, Pr, Nd and Gd), with BaNiSn3 type structure (space group I4mm), have been grown by high temperature solution growth technique using Ga as flux. Their magnetic properties were determined by heat capacity and the measurement of magnetization and electrical resistivity along [100] and [001] directions. Except LaCuGa3, the compounds order magnetically. PrCuGa3 undergoes a ferromagnetic transition with Curie temperature of 4.6K. NdCuGa3 shows a bulk magnetic transition at 3.3K. The data on GdCuGa3 indicate combined characteristics of spin glass and antiferromagnetic behavior at low temperatures. From the Schottky heat capacity data the crystal electric field level energy spectra have been determined. Further we have performed temperature dependent measurements of electron spin resonance (ESR) on GdCuGa3 between 11K and room temperature. The ESR data indicate an enhancement of magnetic fluctuations associated with spin reorientation and both homogeneous and inhomogeneous thermal broadening of the linewidth.

Crystal field manifestation in inelastic neutron scattering, magnetic susceptibility and specific heat of the antiferromagnetic CeCoAl4

Inelastic and quasielastic excitations in the neutron scattering on the compounds CeCo1−xCuxAl4 (x=0, 0.05, 0.1) have been studied above and below the antiferromagnetic ordering temperature. The quasielastic contribution disappears below the Néel temperature, TN=13.5K, and its linewidth Γ/2 is below TN, therefore these results suggest that Kondo screening is not relevant in these Ce compounds. Based on the example of CeCoAl4 we show that the inelastic excitations provide crystal electric field energy levels scheme, which in consistent way describes both the magnetic susceptibility and the specific heat. The inelastic neutron scattering spectrum below TN is interpreted as the splitting of the crystal electric field levels by the internal molecular field.