Crystal Electric Field Research Articles

Unconventional magnetic order emerging from competing energy scales in the new RRh3Si7 intermetallics ( R = Gd-Yb)

The competition between Ruderman-Kittel-Kasuya-Yosida (RKKY), crystal electric field (CEF), and Kondo energy scales has recently emerged at the heart of complex magnetism in several Ce- or Yb-based intermetallics. Hard axis magnetic order has been observed in a handful of these compounds, independent of the crystal symmetry, size of the ordered moment, or the relative scale of the Kondo and magnetic ordering temperatures. This raises the question of the role of each energy scale in driving the ground state properties. In focusing on a single class of compounds, the rhombohedral R${\mathrm{Rh}}_{3}{\mathrm{Si}}_{7}$, we compare the anisotropy and magnetic ground states in members of this series with only RKKY interactions (R = Gd), or RKKY and CEF effects (R = Tb-Tm), with the behavior of the R = Yb compound, where all three energy scales (RKKY, CEF, Kondo) are at play. Moreover, we extend the comparison to two other isostructural Kondo systems ${\mathrm{YbIr}}_{3}{\mathrm{Si}}_{7}$ and ${\mathrm{YbIr}}_{3}{\mathrm{Ge}}_{7}$, where hard axis magnetic order is also observed. The non-Kondo compounds R${\mathrm{Rh}}_{3}{\mathrm{Si}}_{7}$ (R = Tb-Tm) lack the complexity of magnetic order along the hard CEF axis, pointing to the dominant role of the Kondo effect in driving this magnetic order. However, the CEF-RKKY competition is still responsible for complex magnetic ground states, and it appears that the electronic and magnetic degrees of freedom are entangled in all magnetic members of this series of compounds.

Importance of dynamic lattice effects for crystal field excitations in the quantum spin ice candidate Pr2Zr2O7

Pr$_2$Zr$_2$O$_7$ is a pyrochlore quantum spin-ice candidate. Using Raman scattering spectroscopy we probe crystal electric field excitations of Pr$^{3+}$, and demonstrate the importance of their interactions with the lattice. We identify a vibronic interaction with a phonon that leads to a splitting of a doublet crystal field excitation at around 55~meV. We also probe a splitting of the non-Kramers ground state doublet of Pr$^{3+}$ by observing a double line of the excitations to the first excited singlet state $E^0_g \rightarrow A_{1g}$. We show that the splitting has a strong temperature dependence, with the doublet structure most prominent between 50~K and 100~K, and the weight of one of the components strongly decreases on cooling. We suggest a static or dynamic deviation of Pr$^{3+}$ from the position in the ideal crystal structure can be the origin of the effect, with the deviation strongly decreasing at low temperatures.

A new look at the ground state properties of Ce2Ir3Al9: Coexistence of two competing energy scales

We present an extended research on characterization of the ground state in a polycrystalline compound Ce2Ir3Al9 using powder x-ray diffraction, magnetic susceptibility χ(T), isothermal magnetization M(B), specific heat Cp(T), electrical resistivity ρ(T), magnetoresistivity ρ(B), thermoelectric power S(T) and thermal conductivity κ(T) measurements, together with a theoretical description of the obtained data to develop a more profound understanding of the physics in this compound. Ce2Ir3Al9 crystallizes in the orthorhombic Y2Co3Ga9-type of structure (space group Cmcm, No. 63, oC56, Z = 4). The χ(T) and Cp(T)/T data reveal the signatures of intermediate valence behaviour on Ce ions with the approximate value of the Kondo temperature TK = 96 K and the Sommerfeld coefficient γ = 31 mJ/mol ⋅ K2. In contrast to the magnetometric and thermodynamic measurements, the transport data (ρ(T) and S(T)) indicate the development of the Kondo lattice state. Accordingly, we expect that for Ce2Ir3Al9 the most likely scenario, which develops in a wide T range is the coexistence and competition of two energy scales of interactions between conduction electrons and 4f spins on Ce ions, located in one unique crystallographic site in the unit cell, in consequence carrying out our system from Ce4+Temp.→ Ce3+. At higher temperatures, where the Kondo interaction becomes dominant the influence of the crystal electric field effect seems to play an influential role in the ground state of this compound too.

Experimental and theoretical analysis of magnetocaloric behavior ofDy1−xErxNi2intermetallics(x=0.25,0.5,0.75)and their composites for low-temperature refrigerators performing an Ericsson cycle

In the present work, the structural, magnetic, and thermodynamic properties of ${\mathrm{Dy}}_{1\ensuremath{-}x}{\mathrm{Er}}_{x}{\mathrm{Ni}}_{2}$ $(x=0.25,\phantom{\rule{0.16em}{0ex}}0.5,\phantom{\rule{0.16em}{0ex}}0.75)$ Laves-phase intermetallics, being continuous solid solutions in the ${\mathrm{DyNi}}_{2}\text{\ensuremath{-}}{\mathrm{ErNi}}_{2}$ system, synthesized by arc melting, are experimentally studied and analyzed in accordance with mutual substitution within the rare-earth sublattice. The existence of Laves-phase superstructure (space group $F\overline{4}3m$) in the substituted ${\mathrm{Dy}}_{1\ensuremath{-}x}{\mathrm{Er}}_{x}{\mathrm{Ni}}_{2}$ compounds was found by x-ray diffraction analysis. Low-temperature magnetic studies showed the ferromagnetic behavior of the compounds; their Curie temperatures correlate with the erbium content; namely, they decrease from 16.8 K for ${\mathrm{Dy}}_{0.75}{\mathrm{Er}}_{0.25}{\mathrm{Ni}}_{2}$ to 10.0 K for ${\mathrm{Dy}}_{0.25}{\mathrm{Er}}_{0.75}{\mathrm{Ni}}_{2}$. Heat capacity measurements performed in magnetic fields of 1 and 2 T allowed us to estimate the isothermal magnetic entropy and adiabatic temperature changes for ${\mathrm{Dy}}_{1\ensuremath{-}x}{\mathrm{Er}}_{x}{\mathrm{Ni}}_{2}$. Independently, a theoretical analysis was performed for a polycrystalline sample in the frame of a model Hamiltonian taking into account the Zeeman exchange interaction and crystal electric field anisotropy and was expanded to experimental results. Composites with optimum proportions of the individual ${\mathrm{Dy}}_{0.75}{\mathrm{Er}}_{0.25}{\mathrm{Ni}}_{2}$, ${\mathrm{Dy}}_{0.5}{\mathrm{Er}}_{0.5}{\mathrm{Ni}}_{2}$, and ${\mathrm{Dy}}_{0.25}{\mathrm{Er}}_{0.75}{\mathrm{Ni}}_{2}$ components were theoretically determined. The results indicate that the proposed composites are good candidates to be used as the refrigerant material in a magnetic refrigerator performing an Ericsson cycle at low temperatures. The relative cooling power RCP, refrigerant capacity RC, temperature averaged entropy change TEC, and the changes of emitted or absorbed quantity of heat \ensuremath{\Delta}Q were calculated for investigated samples. Direct measurements of the adiabatic temperature change in the vicinity of the magnetic transition temperature were carried out in magnetic fields up to 14 T. The regularities found are discussed in terms of Landau's theory of second-order magnetic phase transitions.

A new theoretical approach to the strain dependence of magnetic crystal-field anisotropy

We report on the derivation of analytical equations for ab-initio calculations of the strain dependence of crystal-electric-field (CEF) parameters for arbitrary deformations. The calculation is based on the fundamental assumption that the charge distribution deforms in the same way as the crystal. Based on this deformed-charge model, simple formulas for the practical usage are given for various site symmetries of cubic lattices under uniform strain. These formulas can be used to predict the change of the magnetic crystal-field anisotropy under strain, which is important for the design of magnetic materials and devices. As an example for the power of the method, we present a calculation of the magnetic contribution to the thermal expansion in some rare-earth-based materials.

Effects of Y- and La-doping on the magnetic ordering, Kondo effect, and spin dynamics in Ce1−x M x Ru2Al10

The influence of Y- and La-substitution for Ce on the competing Kondo effect and magnetic ordering, as well as on spin dynamics in the Kondo semiconductor CeRu2Al10 have been investigated by means of thermal, electronic, and magnetic properties. The parent compound CeRu2Al10 is known to be a controversial antiferromagnet with high magnetic ordering temperature T 0 = 27 K. A small negative chemical pressure caused by La-doping results rapid suppression of T 0 and spin gap energy Δ m , compared to a small positive pressure caused by Y-doping. Upon Y- and La-doping, the electrical resistivity ρ(T) illustrates the evolution from dense Kondo semiconductor to incoherent single-ion Kondo behaviour, and hence weakens the c–f hybridization and thus lowers the Kondo temperature. The 5% Y- and La-doped compounds show enormous enhancement in the thermoelectric power and complex behaviour in the Hall resistivity below T 0 due to an abrupt change in charge carrier mobility with temperature. The magnetic contribution to electrical resistivity ρ mag(T) (≳50% La) and specific heat C P(T)/T (≳70% La) evidence non-Fermi-liquid behaviour at low temperature in the La-doped system, due to interplay of atomic disorder with spin-fluctuation. Application of magnetic field suppresses the spin-fluctuation in C P(T)/T and eventually emerges to Fermi-liquid state in the 95% La-doped compound in 9 T. The magnetic phase diagram illustrates that the strength of the Kondo interaction in the doped systems are primarily controlled by the effect of volume change as described by the compressible Kondo lattice model. We ascribe the fascinating observation of T K ≃ 4T 0 to anisotropy in the single-ion crystal electric field in the presence of strong anisotropic c–f hybridization.

Spinon Fermi Surface Spin Liquid in a Triangular Lattice Antiferromagnet NaYbSe2

Triangular lattice of rare-earth ions with interacting effective spin-$1/2$ local moments is an ideal platform to explore the physics of quantum spin liquids (QSLs) in the presence of strong spin-orbit coupling, crystal electric fields, and geometrical frustration. The Yb delafossites, NaYbCh$_2$ (Ch=O, S, Se) with Yb ions forming a perfect triangular lattice, have been suggested to be candidates for QSLs. Previous thermodynamics, nuclear magnetic resonance, and muon spin rotation measurements on NaYbCh$_2$ have supported the suggestion of the QSL ground states. The key signature of a QSL, the spin excitation continuum, arising from the spin quantum number fractionalization, has not been observed. Here we perform both elastic and inelastic neutron scattering measurements as well as detailed thermodynamic measurements on high-quality single-crystalline NaYbSe$_2$ samples to confirm the absence of long-range magnetic order down to 40 mK, and further reveal a clear signature of magnetic excitation continuum extending from 0.1 to 2.5 meV. The comparison between the structure of the magnetic excitation spectra and the theoretical expectation from the spinon continuum suggests that the ground state of NaYbSe$_2$ is a QSL with a spinon Fermi surface.

Crystal Field Effect and Electric Field Screening in Multilayer Graphene with and without Twist.

We address the intrinsic polarization and screening of an external electric field in a broad range of ordered and twisted configurations of multilayer graphene, using an ab initio approach combining density functional theory and the Wannier function formalism. We show that multilayer graphene is intrinsically polarized due to the crystal field effect, an effect that is often neglected in tight-binding models of twisted bilayer graphene and similar systems. This intrinsic polarization of the order of up to a few tens of millielectronvolts has different out-of-plane alignments in ordered and twisted graphene multilayers, while the in-plane potential modulation is found to be much stronger in twisted systems. We further investigate the dielectric permittivity ε in same multilayer graphene configurations at different electric field strengths. Our findings establish a deep insight into intrinsic and extrinsic polarization in graphene multilayers and provide parameters necessary for building accurate models of these systems.

Rare-earth pyrocoboltates [formula omitted]Co2O7 (R = Ce, Yb): Effective spin-[formula omitted] antiferromagnetic insulators with strong geometrical frustration

The two new rare-earth pyrocoboltates R2Co2O7 (R = Ce, Yb) adopt the layered monoclinic Ca2Nb2O7-type structure with the space group P21(No. 4). Both compounds have been investigated by DC magnetic susceptibility χdc(T), AC magnetic susceptibility χac(T) and isothermal magnetization M(B) measurements. The observed effective magnetic moment of Ce2Co2O7 indicates a contribution from the Co sublattice while that of Yb2Co2O7 is mainly from the localized 4f13 electronic configuration of Yb3+ ion. A magnetic ordering of the antiferromagnetic-type is observed in Ce2Co2O7 at TN≃ 34 K. This ordering is accompanied by the opening of a magnetic spectral gap, Δ=57.7 K (~ 5.0 meV) in the spin-wave spectrum and it survives in an external magnetic field of 7 T. In addition to the transition at TN,χac(T) measurements reveal a dome-like feature centered at ≃ 20 K in high frequency which indicates the presence of possible short-range correlation. In Yb2Co2O7, a magnetic phase transition is observed below TN=2.94 K, which is suppressed below 1.9 K in an external magnetic field of 3 T. In the low-T region where the crystal electric field effects can be neglected, an effective spin-1/2 state is realized in Yb2Co2O7, with a Landé-g factor of 3.76 which is comparable to values observed from electron spin resonance (ESR) measurements on related systems. In addition, M(B) of Yb2Co2O7 shows a metamagnetic-like feature at a critical field of HC≈2.5 T. Signatures from both compounds reveal the presence of strong magnetic frustrations with frustration index f of 9.17 and 15.12 for Ce2Co2O7 and Yb2Co2O7, respectively.

First-principles study of the role of surface in the heavy-fermion compound CeRh2Si2

In the heavy fermion materials, the characteristic energy scales of many exotic strongly correlated phenomena (Kondo effect, magnetic order, superconductivity, etc.) are at milli-electron-volt order, implying that the heavy fermion materials are surface sensitive. Here, we investigate the electronic structures for Si- and Ce-terminated surfaces of CeRh$_2$Si$_2$ by first-principles methods. Our research reveals three notable impacts of surface effects on electronic structures, which are consistent with recent angle-resolved photoemission spectroscopy (ARPES) experiments. Firstly, the relaxation of surface crystal structures changes the relative position of Fermi level, adjusts the dispersion of bands and enhances the Kondo resonance. Secondly, the decrease of the hybridization between the Ce-4$f$ and conduction electrons in the surface layer leads to a weaker Kondo resonance peak and the shift of spin-orbit bands. Thirdly, the variation of crystal electric field around surface Ce atoms affects the splitting of Kondo resonance peaks, and also pushes down the lower-Hubbard bands of surface 4$f$ electrons. Moreover, we find the characteristic of bulk's lower-Hubbard bands, which was overlooked in previous works. Our investigation suggests that these surface effects are potentially important and highlighted in the future researches on properties of strongly correlated materials.

Lens shape liquid crystals in electric fields

Experimental studies of the structure of plano-convex lens shaped liquid crystal droplets subjected to electric fields are presented. Similar to previous observations by Salamon et al. (2020) in DC magnetic fields, we found the formation of an inversion wall normal to AC electric fields. While at low frequencies the direction of the wall is stationary, at higher frequencies it turns toward the external electric field. In both cases, the defect wall is also swept toward the periphery of the drop, where it eventually disappears. The linear displacement of the electric field-induced defect wall could be described by an exponential time dependence without any fitting parameter. This combined with threshold for director deformation enables to determine both the bend elastic constant and the rotational viscosity using much less substance than existing techniques. The rotation of the defect wall at high frequencies is a result of the antiparallel orientation of the effective moment vector and the electric field due to the lower dielectric constant and higher electric conductivity of the defect wall than of those of the rest of the liquid crystal droplet. Uniform electric field-induced generation, rotation and linear movement of defect walls is a unique phenomenon in soft matters.

Semiconducting behaviour in the Remeika phase: Pr3Ir4Ge13

We report the magnetic, electronic and transport properties of the quasi-skutterudite compound Pr3Ir4Ge13 by means of magnetic susceptibility χ(T), electrical resistivity ρ(T), specific heat Cp(T), thermal conductivity κ(T), thermoelectric power S(T) and Hall coefficient RH(T) measurements. Pr3Ir4Ge13 does not show any phase transition down to 1.9 K. Magnetic, and specific measurements show that the system possesses a crystal electric field singlet ground state that is separated from the first excited state by about 37 K. ρ(T) shows a negative temperature coefficient of resistance for the whole temperature range studied and which can be explained in terms of Mott’s impurity band conduction mechanism. RH(T) measurements show that Pr3Ir4Ge13 is a low-carrier density semiconductor and its transport properties indicate a metallic-non metallic cross over behaviour. Large Seebeck coefficient was observed for the entire temperature range of investigation, and the analysis of temperature variation of S and S∕T showed no sign of strong correlation between the Pr 4f2 and conduction electron states near Fermi level.

The Zeeman effect and CEF parameters of Tb3Ga5O12

The Zeeman effect was observed in Tb3Ga5O12 single crystal for H∥[110]. Obtained results were used to determine the crystal electric field (CEF) parameters of the excited 5D4 multiplet of Tb3+ ion and exclude Γ1 symmetry for the lowest level of 7F6 ground state. The second order CEF parameters of the ground 7F6 multiplet were determined by fitting the magnetization measured for H∥[001] and H∥[110].

Ferrielectric properties of a bilayer structure with RKKY-like interaction: A Monte Carlo study

The ferrielectric properties of a bilayer structure separate by electrical insulating layers, with RKKY interactions in the Blume–Capel model. The system is composed of two interacting A (spin S=5∕2) and B (spin σ=2) planes in which the intralayer couplings are ferroelectric while the interlayer interactions are antiferroelectric. The temperature dependence of the ferroelectricity of a bilayer structure separate by electrical insulating layers, with RKKY interactions in the Blume–Capel model has been investigated. The effects of external longitudinal electric (EZ) and crystal anisotropy DA and DB fields have been investigated. On the other hand, the variation of total and partial polarizations with exchange coupling interactions JA, JB, JRKKY, crystal and external longitudinal electric fields was discussed. Finally, the influence of the exchange interactions and crystal field on the critical temperatures of the system and hysteresis cycles has been examined.

PyCrystalField: software for calculation, analysis and fitting of crystal electric field Hamiltonians

PyCrystalField is a Python software package for calculating single-ion crystal electric field (CEF) Hamiltonians. This software can calculate a CEF Hamiltonian ab initio from a point charge model for any transition or rare earth ion in either the J basis or the LS basis, perform symmetry analysis to identify nonzero CEF parameters, calculate the energy spectrum and observables such as neutron spectrum and magnetization, and fit CEF Hamiltonians to any experimental data. The theory, implementation and examples of its use are discussed.

Crystal structure and magnetic properties of R11Co4In9 (R=Tb, Dy, Ho and Er) compounds

Crystal structure and magnetic properties of the R11Co4In9 compounds (R = Tb–Er) have been investigated by means of X-ray diffraction as well as dc magnetic measurements. The compounds crystallize in the orthorhombic Nd11Pd4In9-type crystal structure (Cmmm space group) in which the rare earth atoms occupy five nonequivalent sublattices. Magnetic properties of the investigated compounds are related mainly to the R3+ ions. The values of effective magnetic moments in the paramagnetic state are close to the free R3+ ion values while the moments in the ordered state at T = 2.0 K (R = Tb, Dy) or T = 1.9 K (R = Ho, Er) and H = 90 kOe are lower than the respective R3+ moments. The compounds show complex magnetic properties below 95 K (Tb), 88 K (Dy), 35 K (Ho) and 5.4 K (Er). With increase of temperature the antiferromagnetic ground state changes to the ferro- or ferrimagnetic one. The critical temperatures of magnetic ordering do not fulfill the de Gennes scaling indicating a strong influence of the crystal electric field (CEF) in stabilizing the magnetic order.

Soft mode behavior and evidence for pressure-induced magnetostructural effects in Pr2O3

The authors use Raman spectroscopy to study anomalous phonon-softening with decreasing temperature and the pressure- and magnetic field-dependent crystal electric field splittings in hexagonal Pr${}_{2}$O${}_{3}$.

Heavy Fermion Metal CeB6 in SubTHz and THz Range: The Electron Spin Resonance and Neutron Scattering Studies

Cerium hexaboride attracts attention of solid-state community for almost 50 years. Nowadays, this material is considered as a unique example of a system with orbital ordering resulting in formation of low-temperature magnetic phase with quadrupolar order, the so-called antiferroquadrupole phase. In crystal electric field 4f 1 state of Ce3+ splits into Γ7 doublet and Γ8 quartet, the latter is believed to be the ground state, as long as just Γ8 allows quadrupolar effects. An additional tool for studying rich physics of CeB6 appeared since the discovery in this material the ESR, which is specific to antiferroquadrupole (AFQ) phase and is missing in the paramagnetic phase. In the present review, we have brought together electron spin resonance and inelastic neutron scattering data, which allowed obtaining most detailed structure of the magnetic resonance modes in the AFQ phase in a wide-frequency range up to 0.6 THz. It is shown that apart paramagnetic resonance main mode with homogeneous precession of the magnetization, there are antiferromagnetic resonance modes as well, some of them existing in the AFQ phase. Analysis of the g factors demonstrates that available theories based on Γ8 ground state are facing difficulties with accounting experimental data, thus providing a challenge for developing of a theory correctly describing dynamic magnetic properties of this interesting material.

Intrinsic Bulk Quantum Oscillations in a Bulk Unconventional Insulator SmB6.

SummaryThe finding of bulk quantum oscillations in the Kondo insulator SmB6 proved a considerable surprise. Subsequent measurements of bulk quantum oscillations in other correlated insulators including YbB12 lent support to our discovery of a class of bulk unconventional insulators that host bulk quantum oscillations. Here we perform a series of experiments to examine evidence for the intrinsic character of bulk quantum oscillations in floating zone-grown single crystals of SmB6 that have been the subject of our quantum oscillation studies. We present results of thermodynamic, transport, and composition analysis experiments on pristine floating zone-grown single crystals of SmB6 and compare quantum oscillations with metallic LaB6 and elemental aluminum. These results establish the intrinsic origin of quantum oscillations from the insulating bulk of floating zone-grown SmB6. The similarity of the Fermi surface in insulating SmB6 with the conduction-electron Fermi surface in metallic hexaborides is at the heart of a theoretical mystery.

Long-range magnetic order in the ${\tilde S}=1/2$ triangular lattice antiferromagnet KCeS$_2$

Recently, several putative quantum spin liquid (QSL) states were discovered in {\tilde S} = 1/2S̃=1/2 rare-earth based triangular-lattice antiferromagnets (TLAF) with the delafossite structure. In order to elucidate the conditions for a QSL to arise, we report here the discovery of a long-range magnetic order in the Ce-based TLAF KCeS_22 below T_{\mathrm N} = 0.38TN=0.38 K, despite the same delafossite structure. Finally, combining various experimental and computational methods, we characterize the crystal electric field scheme, the magnetic anisotropy and the magnetic ground state of KCeS_22.