Crystal Electric Field Research Articles

Crystal electric field effects and thermal expansion of rare-earth hexaborides

Abstract Anomalies in the magnetic contribution to the thermal expansion coefficients ∆β(T) of the CeB 6 , PrB 6 , and NdB 6 hexaborides in the range of 5–300 K were found by comparison with diamagnetic LaB 6 . The characteristic of the anomalies was the same in all the studied borides: a distinct peak at low temperatures, followed by a broad maximum at higher temperatures (50–100 K), then a decrease and transition to the region of negative values as the temperature increases further. The features of ∆β(T) are explained by the effects of the magnetic order (sharp low temperature peaks) and the crystal electric field (CEF). The β CEF (T) dependencies were calculated using Raman and neutron scattering data on the splitting of the rare-earth (RE) ions R 3+ f-level by the CEF. A satisfactory consistency between the values of β CEF (T) and ∆β(T) was obtained for the studied hexaborides. Additionally, we determined the values of the Gruneisen parameter γ i that correspond to the transition between the ground and excited multiplets of R 3+ ions f-level splitting.

Giant rotating magnetocaloric effect in RNi5 single crystals

In this paper we theoretically discuss the rotating magnetocaloric effect in RNi5(R=Nd,Tb,Dy,Er) single crystals, by using a model of interacting magnetic moments including the interaction with the crystal electric field. Our theoretical calculations show that the rotating magnetocaloric effect in RNi5 single crystals is as large as the conventional one. This fact points out that these single crystals are also good candidates to be used in magnetic refrigerators working at low temperatures and based on the rotating magnetocaloric effect.

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).

Crystal structure and anisotropic magnetic properties of new ferromagnetic Kondo lattice compound Ce(Cu,Al,Si)2

Single crystals of the new compound CeCu0.18Al0.24Si1.58 have been grown by high-temperature solution growth method using a eutectic Al-Si mixture as flux. This compound is derived from the binary CeSi2 (tetragonal α-ThSi2-type, Pearson symbol tI12, space group I41/amd) obtained by partial substitution of Si by Cu and Al atoms but showing full occupation of the Si crystal site (8e). While CeSi2 is a well-known valence-fluctuating paramagnetic compound, the CeCu0.18Al0.24Si1.58 phase orders ferromagnetically at TC=9.3K. At low temperatures the easy-axis of magnetization is along the a-axis, which re-orients itself along the c-axis above 30K. The presence of hysteresis in the magnetization curve, negative temperature coefficient of resistivity at high temperatures, reduced jump in the heat capacity and a relatively lower entropy released up to the ordering temperature, and enhanced Sommerfeld coefficient (≈100mJ/mol K2) show that CeCu0.18Al0.24Si1.58 is a Kondo lattice ferromagnetic, moderate heavy fermion compound. Analysis of the high temperature heat capacity data in the paramagnetic region lets us infer that the crystal electric field split doublet levels are located at 178 and 357K, respectively, and Kondo temperature (8.4K) is of the order of TC in CeCu0.18Al0.24Si1.58.

The features of thermal properties and CEF-influence in intermediate valence compound CeB4 at the temperatures of 2–300 K

Heat capacity and lattice parameters of cerium tetraboride were experimentally determined at 2 – 300K. An anomalously large contribution of free electrons to the heat capacity was influenced by Fermi liquid state in the cerium boride. The parameters of Einstein and Debye contributions to CeB4 heat capacity, as well as free electron gas contribution and Schottky heat capacity have been determined. A negative thermal expansion (NTE) of CeB4 was found (5–25K). We were not able to explain the NTE by the influence of intermediate valence of cerium ions. The NTE was attributed to the influence of the crystal electric field (CEF) on Ce3+ ions.

Low-temperature physical properties of single crystal α-US1.82

We have studied a single crystal of α-US1.82 by measuring the magnetization M, electrical resistivity ρ, magnetoresistance MR and specific heat Cp. Our experimental data establish that α-US1.82 is an antiferromagnet with TN = 35 K and the easy magnetization is along the c-axis. Low-temperature properties of α-US1.82 are characterized also by an enhanced Sommerfeld coefficient γ = 47 mJ/molK2 and metamagnetic transition at μ0Hcr = 5.5 T. The latter behaviour accompanies with a huge MR of −52 % and abrupt collapse in the γ(H) dependence, pointing to magnetic field-induced change of both magnetic superzone boundaries and density of states at the Fermi level. The temperature dependence of magnetic specific heat below 20 K is found to follow a function of thermally activated magnons: Cmag∝Tnexp(−Δ/kBT), with Δ/kB = 3.5–6.9 K and n = 1.5–2.0. The observed exponent values seem to suggest the coexistence of ferromagnetic and antiferromagnetic interactions or two-dimensional antiferromagnetic arrangements of magnetic uranium moments. The MR and Cp data show evidence of short-range interactions in the temperature range TN − 2TN, presumably caused by non-stoichiometric character of compound. The specific heat behaviour is discussed invoking the Kondo state with Kondo temperature TK ∼ 15 K and crystal electric field effect with splitting energy of 150–190 K.

Raman active high energy excitations in URu2Si2

We have performed Raman scattering measurements on URu2Si2 single crystals on a large energy range up to ∼1300cm−1 and in all the Raman active symmetries as a function of temperature down to 15K. A large excitation, active only in the Eg symmetry, is reported. It has been assigned to a crystal electric field excitation on the Uranium site. We discuss how this constrains the crystal electric field scheme of the Uranium ions. Furthermore, three excitations in the A1g symmetry are observed. They have been associated to double Raman phonon processes consistently with ab initio calculations of the phonons dispersion.

Physical properties of single crystallineRMg2Cu9(R=Y,Ce−Nd,Gd−Dy,Yb)and the search for in-plane magnetic anisotropy in hexagonal systems

Single crystals of $R$Mg$_{2}$Cu$_{9}$ ($R$=Y, Ce-Nd, Gd-Dy, Yb) were grown using a high-temperature solution growth technique and were characterized by measurements of room-temperature x-ray diffraction, temperature-dependent specific heat and temperature-, field-dependent resistivity and anisotropic magnetization. YMg$_{2}$Cu$_{9}$ is a non-local-moment-bearing metal with an electronic specific heat coefficient, $\gamma \sim$ 15 mJ/mol K$^2$. Yb is divalent and basically non-moment bearing in YbMg$_{2}$Cu$_{9}$. Ce is trivalent in CeMg$_{2}$Cu$_{9}$ with two magnetic transitions being observed at 2.1 K and 1.5 K. PrMg$_{2}$Cu$_{9}$ does not exhibit any magnetic phase transition down to 0.5 K. The other members being studied ($R$=Nd, Gd-Dy) all exhibits antiferromagnetic transitions at low-temperatures ranging from 3.2 K for NdMg$_{2}$Cu$_{9}$ to 11.9 K for TbMg$_{2}$Cu$_{9}$. Whereas GdMg$_{2}$Cu$_{9}$ is isotropic in its paramagnetic state due to zero angular momentum ($L$=0), all the other local-moment-bearing members manifest an anisotropic, planar magnetization in their paramagnetic states. To further study this planar anisotropy, detailed angular-dependent magnetization was carried out on magnetically diluted (Y$_{0.99}$Tb$_{0.01}$)Mg$_{2}$Cu$_{9}$ and (Y$_{0.99}$Dy$_{0.01}$)Mg$_{2}$Cu$_{9}$. Despite the strong, planar magnetization anisotropy, the in-plane magnetic anisotropy is weak and field-dependent. A set of crystal electric field parameters are proposed to explain the observed magnetic anisotropy.

Hyperfine and crystal field interactions in multiferroic HoCrO3

We report a comprehensive specific heat and inelastic neutron scattering study to explore the possible origin of multiferroicity in HoCrO3. We have performed specific heat measurements in the temperature range 100 mK–290 K and inelastic neutron scattering measurements were performed in the temperature range 1.5–200 K. From the specific heat data we determined hyperfine splitting at 22.5(2) μeV and crystal field transitions at 1.379(5) meV, 10.37(4) meV, 15.49(9) meV and 23.44(9) meV, indicating the existence of strong hyperfine and crystal field interactions in HoCrO3. Further, an effective hyperfine field is determined to be 600(3) T. The quasielastic scattering observed in the inelastic scattering data and a large linear term mJ mol−1 K−2 in the specific heat is attributed to the presence of short range exchange interactions, which is understood to be contributing to the observed ferroelectricity. Further the nuclear and magnetic entropies were computed to be, ∼17.2 Jmol−1 K−1 and ∼34 Jmol−1 K−1, respectively. The entropy values are in excellent agreement with the limiting theoretical values. An anomaly is observed in the peak position of the temperature dependent crystal field spectra around 60 K, at the same temperature an anomaly in the pyroelectric current is reported. From this we could elucidate a direct correlation between the crystal electric field excitations of Ho3+ and ferroelectricity in HoCrO3. Our present study, along with recent reports, confirm that HoCrO3, and RCrO3 (R = rare earth) in general, possess more than one driving force for the ferroelectricity and multiferroicity.

La-doping effect on spin–orbit coupled Sr2IrO4 probed by x-ray absorption spectroscopy

Sr2IrO4 was predicted to be an unconventional superconductor upon carrier doping since it highly resembles the high-temperature cuprates. Here, to understand carrier doping effect on spin–orbit coupled Mott insulator Sr2IrO4, the electronic structure and local structure distortion for Sr2 − xLaxIrO4 system have been investigated by x-ray absorption spectroscopy. By comparing the intensity of white-line features at the Ir L2,3 absorption edges, we observe remarkably large branching ratios in La-doped compounds, greater than that of the parent material Sr2IrO4, suggesting a strong spin-orbit interaction for Sr2IrO4-based system. Moreover, extended x-ray absorption fine structure spectra demonstrate more regular IrO6 octahedra, i.e. the weakened crystal electric field versus La-doping. By theoretical calculations, the synergistic effect of regular IrO6 octahedra and electron doping is established, which accounts for the transition from a Mott insulator to a conductive state in Sr2 − xLaxIrO4-based system.

Thermal and electron transport properties of Ce2Ni3Ge5 and Ce3NiGe2: Example of Kondo behavior in the presence of the crystalline field effect

Thermal and electron transport properties of the two Kondo compounds Ce2Ni3Ge5 and Ce3NiGe2 and of their nonmagnetic reference compounds La2Ni3Ge5 and La3NiGe2 were investigated by measurements of the thermoelectric power S, thermal conductivity κ, and electrical resistivity ρ. The effects of an applied magnetic field on the thermal and electron transport properties of both Ce compounds were examined. The temperature dependences of the 4f electron contribution to the electrical resistivity ρ4f, thermoelectric power S4f, and thermal resistivity W4f ·T exhibited −lnT behavior in two different temperature regions, which indicates that Ce2Ni3Ge5 and Ce3NiGe2 can be classified as Kondo systems with strong crystal-electric field (CEF) interactions. The total measured κ of Ce2Ni3Ge5 and Ce3NiGe2 was reduced compared with that of reference La compounds owing to the Kondo effect on Ce3+ ions. Within the framework of the Callaway model, the lattice component of thermal conductivity κph of both Ce compounds was analyzed while considering various relaxation processes governed by the scattering of phonons.

RESPECT: Neutron resonance spin-echo spectrometer for extreme studies

We propose the design of a REsonance SPin-echo spECtrometer for exTreme studies, RESPECT, that is ideally suited for the exploration of non-dispersive processes such as diffusion, crystallization, slow dynamics, tunneling processes, crystal electric field excitations, and spin fluctuations. It is a variant of the conventional neutron spin-echo technique (NSE) by (i) replacing the long precession coils by pairs of longitudinal neutron spin-echo coils combined with RF-spin flippers and (ii) by stabilizing the neutron polarization with small longitudinal guide fields that can in addition be used as field subtraction coils thus allowing to adjust the field integrals over a range of 8 orders of magnitude. Therefore, the dynamic range of RESPECT can in principle be varied over 8 orders of magnitude in time, if neutrons with the required energy are made available. Similarly as for existing NSE-spectrometers, spin echo times of up to approximately 1μs can be reached if the divergence and the correction elements are properly adjusted. Thanks to the optional use of neutron guides and the fact that the currents for the correction coils are much smaller than in standard NSE, intensity gains of at least one order of magnitude are expected, making the concept of RESPECT also competitive for operation at medium flux neutron sources. RESPECT can also be operated in a MIEZE configuration allowing the investigation of relaxation processes in depolarizing environments as they occur when magnetic fields are applied at the sample position, i.e. for the investigation of the dynamics of flux lines in superconductors, magnetic fluctuations in ferromagnetic materials, and samples containing hydrogen.

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.

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.

Two-dimensional photonic crystal slabs as a tunable polarization mode converter

Two dimensional photonic crystal slabs with elliptical holes exposed to the normal incident laser light are proposed and designed as a tunable broadband polarization rotator. The photonic crystal electric field mode due to the eccentricity and orientation of the holes will provide a mean to exchange power between two orthogonal polarization states. Around guided resonance wavelengths of photonic crystals with 45° oriented elliptical holes, 20% polarization mode conversion is achieved. By tuning of the difference of the two radii of the elliptical holes we are able to span a bandwidth of 130nm and 70nm around wavelengths of 1445nm and 1650nm. The unique properties of these devices such as ease of engineering and simplified light coupling scheme will make them a promising polarization mode converter in high speed polarization-multiplexed optical transmission systems.

Electric-field influence on the neutron diffuse scattering near the ferroelectric transition of Sr0.61Ba0.39Nb2O6

ABSTRACTUniaxial relaxor ferroelectric Sr0.61Ba0.39Nb2O6 single crystal has been investigated in the vicinity of its phase transition using neutron scattering and dielectric spectroscopy. A global-type thermal hysteresis is evidenced by both techniques in the ferroelectric phase and up to about 15 K above Tc. In addition, a part of the transverse neutron diffuse scattering in the 001 Brillouin zone, presumably related to static nanodomain structure, can be suppressed by prior poling the crystal in electric field of 3 kV/cm. The remaining part of the transverse neutron diffuse scattering and the real part of permittivity show a similar temperature dependence. The temperature position of the maximal scattering intensity Tmax depends significantly on the scattering wave vector. Tmax shifts monotonically to higher temperature with the increasing wave vector in all investigated cooling and heating regimes. It is concluded that the critical fluctuations have space correlations which depend on frequency and wave vector.

Magnetization and transport properties of single crystalline RPd2P2 (R=Y, La–Nd, Sm–Ho, Yb)

Single crystals of RPd2P2 (R=Y, La–Nd, Sm–Ho, Yb) were grown out of a high temperature solution rich in Pd and P and characterized by room-temperature powder X-ray diffraction, anisotropic temperature- and field-dependent magnetization and temperature-dependent in-plane resistivity measurements. In this series, YPd2P2 and LaPd2P2 YbPd2P2 (with Yb2+) are non-local-moment bearing. Furthermore, YPd2P2 and LaPd2P2 are found to be superconducting with Tc≃0.75 and 0.96K respectively. CePd2P2 and PrPd2P2 magnetically order at low temperature with a ferromagnetic component along the crystallographic c-axis. The rest of the series manifest low temperature antiferromagnetic ordering. EuPd2P2 has Eu2+ ions and both EuPd2P2 and GdPd2P2 have isotropic paramagnetic susceptibilities consistent with L=0 and J=S=72 and exhibit multiple magnetic transitions. For R=Eu–Dy, there are multiple, T>1.8K transitions in zero applied magnetic field and for R=Nd, Eu, Gd, Tb, and Dy there are clear metamagnetic transitions at T=2.0K for H<55kOe. Strong anisotropies arising mostly from crystal electric field (CEF) effects were observed for most magnetic rare earths with L≠0. The experimentally estimated CEF parameters B20 were calculated from the anisotropic paramagnetic θab and θc values and compared to theoretical trends across the rare earth series. The ordering temperatures as well as the polycrystalline averaged paramagnetic Curie–Weiss temperature, θave, were extracted from magnetization and resistivity measurements, and compared to the de-Gennes factor.

The influence of crystal electric field on thermal properties of non-stoichiometric ErB50 boride at low temperatures

The temperature dependences of heat capacity, Cp(T), and lattice parameters, a(T), b(T), c(T), of ErB50 in the temperature range of 2–300 K were experimentally studied. Two features in Cp(T) were observed: a maximum at Tm1 = 3.12 K, that is associated with a magnetic ordering (transition to an antiferromagnetic state), and a broad anomaly at about Tm2 = 27 K that is due to the effects of the crystal electric field (CEF) on the boride heat capacity. Based on these data a scheme of splitting of Er3+ions f-levels by the crystal field was suggested. Comparison of the temperature dependence of unit cell volume V(T) for ErB50 with the literature data for LuB50 revealed an excess contribution into the thermal expansion of erbium boride at low temperatures. It was determined that this contribution is due to the CEF effects on ErB50 thermal expansion.

P-199L:Late-News Poster: Optical Phase Modulation Properties of 1 μm-Pitch LCOS with Dielectric Walls for Wide-Viewing-Angle Holographic Displays

We achieved individual-pixel phase modulation of 1 pm-pitch liquid crystal on silicon (LCOS) using dielectric shield walls for wide-viewing-angle holographic displays. The simulation results clarified the dielectric walls could suppress the alignment disorder by the effect of elastic force of liquid crystal (LC) and fringe electric field to adjacent pixels. The LC alignment on the walls was also discussed experimentally.

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.