Crystal Electric Field Splitting Research Articles

Crystal electric field and properties of 4f magnetic moments at the surface of the rare-earth compound TbRh2Si2

By means of 4$f$ photoemission measurements and first-principles calculations, the authors demonstrate here how the crystal electric field (CEF) and related magnetic properties can be modified at the surface of rare-earth materials. For TbRh${}_{2}$Si${}_{2}$, CEF at the Tb surface makes the 4$f$ moments orthogonal to those in the bulk. For the Tb layer below the Si termination, the temperature-dependent photoemission data reveal larger CEF splitting relative to the bulk. The methodology used here can facilitate unveiling of the surface magnetic properties of layered 4$f$ systems.

Anisotropic magnetic and transport properties of orthorhombic o-Pr2Co3Ge5

The crystal structure, electron energy-loss spectroscopy (EELS), heat capacity, and anisotropic magnetic and resistivity measurements are reported for Sn flux grown single crystals of orthorhombic Pr2Co3Ge5 (U2Co3Si5-type, Ibam). Our findings show that o-Pr2Co3Ge5 hosts nearly trivalent Pr ions, as evidenced by EELS and fits to temperature dependent magnetic susceptibility measurements. Complex magnetic ordering with a partially spin-polarized state emerges near T sp = 32 K, with a spin reconfiguration transition near T M = 15 K. Heat capacity measurements show that the phase transitions appear as broad peaks in the vicinity of T sp and T M. The magnetic entropy further reveals that crystal electric field splitting lifts the Hund’s rule degeneracy at low temperatures. Taken together, these measurements show that Pr2Co3Ge5 is an environment for complex f state magnetism with potential strongly correlated electron states.

Magnetic glassiness and crystal field effects on thermal and electrical properties of Er5Pd2-type compounds

Magnetic properties, thermal expansion, heat capacity, and electrical resistivity of the cluster-glass compound Er4.8Pd2 and its paramagnetic isostructural counterpart Lu4.8Pd2 have been studied in the temperature range 2–300 K and in applied magnetic fields up to 140 kOe. Short-range antiferromagnetic (AFM) correlations of localized magnetic moments of Er3+ ions were found to develop in Er4.8Pd2 on cooling below T* ≈ 40 K. A cluster-glass magnetic state was observed below freezing temperature Tf ≈ 13.3 K, while Lu4.8Pd2 showed paramagnetic behavior. The crystal electric field (CEF) was found to substantially affect both the heat capacity and the thermal expansion of Er4.8Pd2. The CEF splitting of the Er3+ ion multiplet 4I15/2 was estimated to be as high as 280 K with a doublet ground state. Both the Schottky-type anomaly and short-range antiferromagnetic order contributions were found to give rise to a large volumetric heat capacity of Er4.8Pd2 at low temperatures. High direct magnetocaloric effect with −ΔSM(T)60kOe = 18.8 J mole−1 K−1 was confirmed to exist in Er4.8Pd2 while no inverse magnetocaloric effect was observed at low temperatures. Electrical resistivity of Er4.8Pd2 revealed a non-metallic behavior at low temperatures which was ascribed to an inhomogeneous electronic state due to the formation of clusters with the AFM short-range correlations.

Signature of CEF-phonon coupling in Kondo lattice system CeCuGa3

We present the results of inelastic neutron scattering (INS) measurements on Kondo lattice heavy fermion CeCuGa3. The low-temperature magnetic susceptibility exhibits an anomaly near 2.6 K associated with an antiferromagnetic transition which is further confirmed by the heat capacity measurement. The analysis of magnetic heat capacity C mag (T) based on the crystal electric field (CEF) model reveals an overall CEF splitting of ∼ 21 meV. The INS data reveal two strong magnetic excitations near 4.5 and 6.9 meV, which, however failed to reproduce the observed C mag (T). We therefore analyze the INS data by a model based on magneto-elastic (i.e. CEF-phonon) coupling which suggests that the excitations observed near 4.5 and 6.9 meV originate from the CEF-phonon coupling as observed in CeCuAl3 and CeAuAl3.

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.

Nonsaturating magnetoresistance, anomalous Hall effect, and magnetic quantum oscillations in the ferromagnetic semimetal PrAlSi

We report a comprehensive investigation of the structural, magnetic, transport and thermodynamic properties of a single crystal PrAlSi, in comparison to its nonmagnetic analogue LaAlSi. PrAlSi exhibits a ferromagnetic transition at $T_C$ = 17.8 K which, however, is followed by two weak phase transitions at lower temperatures. Based on the combined dc and ac magnetic susceptibility measurements, we propose the two reentrant magnetic phases below $T_C$ to be spin glasses or ferromagnetic cluster glasses. When the magnetic glassy states are suppressed by small field, several remarkable features appear. These include a linear, nonsaturating magnetoresistance as a function of field that is reminiscent of a topological or charge-compensated semimetal, and a large anomalous Hall conductivity amounting to $\sim$2000 $\Omega ^{-1}$cm$^{-1}$. Specific-heat measurements indicate a non-Kramers doublet ground state and a relatively low crystal electric field splitting of the Pr$^{3+}$ multiplets of less than 100 K. Shubnikov-de Hass oscillations are absent in LaAlSi, whereas they are clearly observed below about 25 K in PrAlSi, with an unusual temperature dependence of the dominating oscillation frequency $F$. It increases from $F$ = 18 T at 25 K to $F$ = 33 T at 2 K, hinting at an emerging Fermi pocket upon cooling into the ordered phase. These results suggest that PrAlSi is a new system where a small Fermi pocket of likely relativistic fermions is strongly coupled to magnetism. Whether hybridization between $f$ and conduction band is also involved remains an intriguing open problem.

Crystal electric field effects and heavy-fermion behavior in cubic PrCu2Au3 compound

We report the crystal structure as well as the magnetic, electronic and transport properties of PrCu2Au3 which crystallizes in the MgCu4Sn-type structure with the cubic space group F4¯3m (No. 216). In this structure, the Pr3+ ion sits on a lattice site with the cubic Td symmetry which dictates the crystal electric field (CEF) splitting of the Hund’s 3H4 ground multiplet into four levels. The sample has been investigated by measurements of temperature dependences of specific heat, Cp(T), electrical resistivity, ρ(T), magnetic susceptibility, χ(T), isothermal magnetization, M(B,T), thermal conductivity, κT(T) and thermoelectric power, S(T). χ(T) follows a Curie-Weiss behavior above 100 K with an effective magnetic moment, μeff = 3.3 μB/Pr which is comparable to a calculated value of 3.58 μB/Pr for a free Pr3+ ion and a Weiss temperature, θCW = 15.70 K indicating a dominant ferromagnetic interaction. From the analysis of M(B,T) and the 4f-electron derived specific heat (C4f(T)) results, the CEF ground state is a Γ5 magnetic triplet and the CEF energy scheme is presented. The Sommerfeld coefficient, γ estimated from the low-temperature C4f(T) is 304 mJ/(mol K2) indicating a mass enhancement of the conduction electrons at low temperatures. Further analysis of the heavy fermion properties based on the Sommerfeld-Wilson ratio supports the formation of a heavy fermion state in PrCu2Au3. However, the absence of an enhancement in S/T at low temperatures possibly suggests a weak correlation between the conduction electrons and the 4f-electrons at the Fermi energy. The thermal transport properties suggest that PrCu2Au3 is likely a compensated metal.

Dramatic impact of intermediate-valence impurity on induced magnetism in singlet ground state system PrNi

We studied the influence of La (nonmagnetic) and Ce (intermediate valence) impurities on the ferromagnetic ordering temperature Tc of compounds RE1-x(La,Ce)xNi (RE = Pr, Gd). The ordering temperature Tc was measured in a wide range of impurity concentration. Crystal electric field (CEF) splitting for the PrNi and Pr0.25Ce0.75Ni was defined by neutron spectroscopy measurements. The strong difference in the influence of La and Ce on Tc of PrNi and GdNi based systems has been obtained. The introduction of a spin-fluctuating intermediate valence impurity in PrNi leads to a dramatic increase in the area of the ordered state on the phase diagram, due to an increase in Tc, compared to the impact of La-impurity over the entire concentration range. The dependence of Tc on the Ce concentration for the Pr1-xCexNi was calculated within the framework of the model of microscopic states. The essential modification of the CEF splitting by the Ce impurity appears to be the decisive factor affecting Tc wherein the Ce ion carries zero static magnetic moments similar to the La case. The latter explains the identical dependencies of the ordering temperature on the impurity concentration observed in systems with a long-range order of local magnetic moments Gd1-xLaxNi and Gd1-xCexNi.

Three-dimensional and temperature-dependent electronic structure of the heavy-fermion compound CePt2In7 studied by angle-resolved photoemission spectroscopy

The three-dimensional electronic structure and Ce 4f electrons of the heavy fermion superconductor CePt2In7 is investigated. Angle-resolved photoemission spectroscopy using variable photon energy establishes the existence of quasi-two and three dimensional Fermi surface topologies. Temperature-dependent 4d-4f on-resonance photoemission spectroscopies reveal that heavy quasiparticle bands begin to form at a temperature well above the characteristic (coherence) temperature T*. T* emergence may be closely related to crystal electric field splitting, particularly the low-lying heavy band formed by crystal electric field splitting.

Crystal electric field splitting and f -electron hybridization in heavy-fermion CePt2In7

We use high-resolution angle-resolved photoemission spectroscopy to investigate the electronic structure of the antiferromagnetic heavy fermion compound CePt2In7, which is a member of the CeIn3-derived heavy fermion material family. Weak hybridization among 4f electron states and conduction bands was identified in CePt2In7 at low temperature much weaker than that in the other heavy fermion compounds like CeIrIn5 and CeRhIn5. The Ce 4f spectrum shows fine structures near the Fermi energy, reflecting the crystal electric field splitting of the 4f^1_5/2 and 4f^1_7/2 states. Also, we find that the Fermi surface has a strongly three-dimensional topology, in agreement with density-functional theory calculations.

Pressure-driven collapse of the relativistic electronic ground state in a honeycomb iridate

Honeycomb-lattice quantum magnets with strong spin-orbit coupling are promising candidates for realizing a Kitaev quantum spin liquid. Although iridate materials such as Li2IrO3 and Na2IrO3 have been extensively investigated in this context, there is still considerable debate as to whether a localized relativistic wavefunction (Jeff = 1/2) provides a suitable description for the electronic ground state of these materials. To address this question, we have studied the evolution of the structural and electronic properties of α-Li2IrO3 as a function of applied hydrostatic pressure using a combination of x-ray diffraction and x-ray spectroscopy techniques. We observe striking changes even under the application of only small hydrostatic pressure (P ≤ 0.1 GPa): a distortion of the Ir honeycomb lattice (via X-ray diffraction), a dramatic decrease in the strength of spin-orbit coupling effects (via X-ray absorption spectroscopy), and a significant increase in non-cubic crystal electric field splitting (via resonant inelastic X-ray scattering). Our data indicate that α-Li2IrO3 is best described by a Jeff = 1/2 state at ambient pressure, but demonstrate that this state is extremely fragile and collapses under the influence of applied pressure.

Electronic properties of [formula omitted]Al20 (R = La, Ce, Yb, Th, U; X = Ti, V, Cr and Mn) cage compounds

Non-spin-polarized electronic structures and Fermi surface properties of RX2Al20 (R = La, Ce, Yb, Th, U; X = Ti, V, Cr, Mn) intermetallic compounds were calculated using the full potential all-electron local orbital (FPLO) approach in the framework of the local density approximation (LDA). Trends of the magnetism are discussed in terms of the characteristics of X-3d bands with a quantitative analysis of the relationship between band electron filling and crystal electric field splitting. Since coordination icosahedra of X-atoms have small trigonal distortion, crystal electric field splits the fivefold degenerate X-3d state into low-energy singlet a1g and two higher-energy doublets eg. In RTi2Al20 and RV2Al20 the population of the related 3d sub-band is not sufficient to cause energetically favorable spin polarization, whereas magnetic instabilities develop in the RCr2Al20 series. Finally, a manifestation of strong repulsive interactions between itinerant Mn-d electrons become most pronounced in ferromagnetic UMn2Al20. The influence of non-magnetic R-f states on magnetic and thermodynamic properties is discussed with special emphasis on the role of the f–p and f–d hybridization. For LaTi2Al20 and LaV2Al20 the calculated quantum oscillation frequencies are in accord with experimental reports.

Tracing crystal-field splittings in the rare-earth-based intermetallic CeIrIn5

Crystal electric field states in rare earth intermetallics show an intricate entanglement with the many-body physics that occurs in these systems and that is known to lead to a plethora of electronic phases. Here, we attempt to trace different contributions to the crystal electric field (CEF) splittings in CeIrIn$_5$, a heavy-fermion compound and member of the Ce$M$In$_5$ ($M$= Co, Rh, Ir) family. To this end, we utilize high-resolution resonant angle-resolved photoemission spectroscopy (ARPES) and present a spectroscopic study of the electronic structure of this unconventional superconductor over a wide temperature range. As a result, we show how ARPES can be used in combination with thermodynamic measurements or neutron scattering to disentangle different contributions to the CEF splitting in rare earth intermetallics. We also find that the hybridization is stronger in CeIrIn$_5$ than CeCoIn$_5$ and the effects of the hybridization on the Fermi volume increase is much smaller than predicted. By providing the first experimental evidence for $4f_{7/2}^{1}$ splittings which, in CeIrIn$_5$, split the octet into four doublets, we clearly demonstrate the many-body origin of the so-called $4f_{7/2}^{1}$ state.

Single crystal growth and anisotropic magnetic properties of HoAl2Ge2

We have grown a single crystal of HoAl2Ge2, which crystallizes in the hexagonal CaAl2Si2 type structure with Ho ions in the trigonal coordination in the ab plane. The data obtained from the bulk measurement techniques of magnetization, heat capacity and transport reveal that HoAl2Ge2 orders antiferromagnetically at TN ∼6.5 K. The susceptibility below TN and isothermal magnetization at 2 K indicate the ab plane as the easy plane of magnetization. Heat capacity data reveal a prominent Schottky anomaly with a broad peak centered around 25 K, suggesting a relatively low crystal electric field (CEF) splitting. The electrical resistivity reveals the occurrence of a superzone gap below TN. The point charge model of the CEF is applied to the magnetization and the heat capacity data. While a good fit to the paramagnetic susceptibility is obtained, the CEF parameters do not provide a satisfactory fit to the isothermal magnetization at 2 K and the Schottky anomaly.

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.

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.

Detailed investigation of thermal and electron transport properties in strongly correlated compound Ce6Pd12In5 and its nonmagnetic analog La6Pd12In5

An in-depth study of thermal and electron transport properties including thermal conductivity κ(T), thermoelectric power S(T), and electrical resistivity ρ(T) of the heavy fermion Kondo lattice Ce6Pd12In5 and its nonmagnetic reference compound La6Pd12In5 is presented. The absolute κ(T) value of Ce6Pd12In5 is smaller that than of La6Pd12In5, which indicates that conduction electron–4f electron scattering has a large impact on the reduction of thermal conductivity. The isolated 4f electron contributions to the electrical resistivity ρ4f(T), electronic thermal resistivity displayed in the form Wel,4f(T)·T, and thermoelectric power S4f(T) reveal a low- and high-temperature –lnT behaviour characteristic of Kondo systems with strong crystal-electric field (CEF) interactions. The analysis of phonon scattering processes of lattice thermal conductivity κph(T) in (Ce, La)6Pd12In5 was performed over the whole accessible temperature range according to the Callaway model. In the scope of a theoretical approach based on the perturbation type calculation, we were able to describe our experimental data of ρ4f(T) and Wel,4f(T)·T by using the model incorporating simultaneously the Kondo effect in the presence of the CEF splitting, as it is foreseen in the framework of the Cornut-Coqblin and Bhattacharjee-Coqblin theory. Considering the fact that there are not many cases of similar studies at all, we also show the numerical calculations of temperature-dependent behaviour of spin-disorder resistivity ρs(T), magnetic resistivity ρ4f(T), and occupation number ⟨Ni⟩ due to the various types of degeneracy of the ground state multiplet of Ce3+ (J = 5/2).

Elastic Softening in HoFe2Al10 due to the Quadrupole Interaction under an Orthorhombic Crystal Electric Field

To investigate 4f electronic states in HoFe2Al10 under an orthorhombic crystal electric field (CEF), we measured the specific heat, magnetic susceptibility, magnetization, and elastic modulus of single-crystalline samples. We found elastic softening of the transverse elastic moduli C55 and C66 below 20 and 130 K, respectively. With further decreasing temperature, C66 shows further elastic softening below 5 K. We observed two Schottky peaks in the specific heat at 2.2 and 20 K and small anisotropy of the magnetic susceptibility and magnetization in the paramagnetic region. By analyzing these experimental data, we obtained the CEF parameters of HoFe2Al10. From the analysis, we clarified that the softening of C55 and C66 originates from indirect quadrupole interactions of Ozx and Oxy, and propose that the overall CEF splitting is about 85 K.

Magnetic, thermodynamic and transport properties of novel non-centrosymmetric RCoSi3 (R=Pr, Nd and Sm) compounds

Novel non-centrosymmetric RCoSi3 (R = Pr, Nd and Sm) compounds crystallize in tetragonal BaNiSn3 type structure with space group I4mm. The bulk magnetic ordering of all the compounds were confirmed from heat capacity data. Magnetization measurements indicate that PrCoSi3 orders ferromagnetically at 5.9K, while NdCoSi3 and SmCoSi3 order antiferromagnetically at 4K and 8K respectively. The magnetic transitions were also manifested by the slope change of temperature dependent resistivity at low temperatures. The energy level schemes created by crystal electric field splitting are determined from Schottky contribution to specific heat. The existence of magnon gap like features at low temperatures are consistent in both heat capacity and resistivity for NdCoSi3 and SmCoSi3. Large magnetoresistance is observed in NdCoSi3 and SmCoSi3. First principles electronic structure calculation based on density functional theory framework have been performed and compared with experimental data.

ARPES view on surface and bulk hybridization phenomena in the antiferromagnetic Kondo lattice CeRh2Si2.

The hybridization between localized 4f electrons and itinerant electrons in rare-earth-based materials gives rise to their exotic properties like valence fluctuations, Kondo behaviour, heavy-fermions, or unconventional superconductivity. Here we present an angle-resolved photoemission spectroscopy (ARPES) study of the Kondo lattice antiferromagnet CeRh2Si2, where the surface and bulk Ce-4f spectral responses were clearly resolved. The pronounced 4f 0 peak seen for the Ce terminated surface gets strongly suppressed in the bulk Ce-4f spectra taken from a Si-terminated crystal due to much larger f-d hybridization. Most interestingly, the bulk Ce-4f spectra reveal a fine structure near the Fermi edge reflecting the crystal electric field splitting of the bulk magnetic 4f 15/2 state. This structure presents a clear dispersion upon crossing valence states, providing direct evidence of f-d hybridization. Our findings give precise insight into f-d hybridization penomena and highlight their importance in the antiferromagnetic phases of Kondo lattices.