Crystalline Electric Field Ground State Research Articles

Finite Temperature Magnetism in the Triangular Lattice Antiferromagnet KErTe2

Abstract After the discovery of the ARECh2 (A = alkali or monovalent ions, RE = rare-earth, Ch = chalcogen) triangular lattice quantum spin liquid (QSL) family, a series of its oxide, sulfide, and selenide counterparts has been consistently reported and extensively investigated. While KErTe2 represents the initial synthesized telluride member, preserving its triangular spin lattice, it was anticipated that the substantial tellurium ions could impart more pronounced magnetic attributes and electronic structures to this material class. This study delves into the magnetism of KErTe2 at finite temperatures through magnetization and electron spin resonance (ESR) measurements. Based on the angular momentum J ^ after spin-orbit coupling (SOC) and symmetry analysis, we obtain the magnetic effective Hamiltonian to describe the magnetism of Er3+ in R 3 ¯ m space group. Applying the mean-field approximation to the Hamiltonian, we can simulate the magnetization and magnetic heat capacity of KErTe2 in paramagnetic state and determine the crystalline electric field (CEF) parameters and partial exchange interactions. The relatively narrow energy gaps between the CEF ground state and excited states exert a significant influence on the magnetism. For example, small CEF excitations can result in a significant broadening of the ESR linewidth at 2 K. For the fitted exchange interactions, although the values are small, given a large angular momentum J = 15/2 after SOC, they still have a noticeable effect at finite temperatures. Notably, the heat capacity data under different magnetic fields along the c axis direction also roughly match our calculated results, further validating the reliability of our analytical approach. These derived parameters serve as crucial tools for future investigations into the ground state magnetism of KErTe2. The findings presented herein lay a foundation for exploration of the intricate magnetism within the triangular-lattice delafossite family.

Effect of Er substitution on the specific heat of GdNiSi

We measured the specific heat (C) of Gd1−xErxNiSi. The values of C for x=0 (GdNiSi) peaked at 11.5 K due to the antiferromagnetic order. The Néel temperature and the values of the entropy of Gd1−xErxNiSi decreased with increasing Er content up to x=1 (ErNiSi). The end member ErNiSi showed two successive transitions at 2.8 K and 2.3 K. The values of C at a temperature at which a peak appeared decreased with an increase in x, except for x=1. These results originate from the reduction of the multiplicity of the crystalline electric field ground state and the atomic randomness due to the Er substitution.

Possible antiferroquadrupolar order in the Kondo semiconductor CeOs4Sb12

We report the results of dc magnetization, thermal expansion, and magnetostriction measurements of the Kondo semiconductor ${\mathrm{CeOs}}_{4}{\mathrm{Sb}}_{12}$. These results provide a magnetic-field--temperature phase diagram for the three principal axes of the cubic crystal [100], [110], and [111] and reveal the magnetic anisotropy of the three ordered phases A, B, and C. The magnetic anisotropy of the transition temperature ${T}_{\mathrm{C}}$ from the paramagnetic phase to the C phase is ${T}_{\mathrm{C}}^{[111]}>{T}_{\mathrm{C}}^{[110]}>{T}_{\mathrm{C}}^{[100]}$. At low temperatures, the magnetization has a distinct magnetic anisotropy in high magnetic fields: ${M}^{[100]}>{M}^{[110]}>{M}^{[111]}$. This ratio of magnetization is in good agreement with that of the magnetically anisotropic ${\mathrm{\ensuremath{\Gamma}}}_{67}$ quartet. The observation indicates that the crystalline electric field ground state is a ${\mathrm{\ensuremath{\Gamma}}}_{67}$ quartet and that the $c\text{\ensuremath{-}}f$ hybridization effect is nearly isotropic. In addition, comparison of the present experimental results with numerical calculations of a two-sublattice model using the mean-field approximation suggests that the C phase is a ${\mathrm{\ensuremath{\Gamma}}}_{5}$-type antiferroquadrupolar ordered state despite the presence of strong $c\text{\ensuremath{-}}f$ hybridization effects. In this case, the increase in ${T}_{\mathrm{C}}$ due to the external field is mainly caused by the ${\mathrm{\ensuremath{\Gamma}}}_{2}$-type antiferro-octupolar interaction.

Evolution of the magnetic properties in the antiferromagnet Ce2RhIn8 simultaneously doped with Cd and Ir.

We report the evolution of the magnetic properties of single crystals. In particular, for () and (), we have solved the magnetic structure of these compounds using single-crystal neutron magnetic diffraction experiments. Taking the magnetic structure of the heavy-fermion antiferromagnet as a reference, we have identified no changes in the magnetic wave vector; however, the direction of the ordered Ce3+ moments rotates toward the plane, under the influence of both dopants. By constraining the analysis of the crystalline electric field (CEF) with the experimental ordered moment's direction and high-temperature magnetic-susceptibility data, we have used a mean-field model with tetragonal CEF and exchange interactions to gain insight into the CEF scheme and anisotropy of the CEF ground-state wave function when Cd and Ir are introduced into . Consistent with previous work, we find that Cd doping in tends to rotate the magnetic moment toward the plane and lower the energy of the CEF excited states' levels. Interestingly, the presence of Ir also rotates the magnetic moment towards the plane although its connection to the CEF overall splitting evolution for the y = 0 samples may not be straightforward. These findings may shed light on the origin of the disordered spin-glass phase on the Ir-rich side of the phase diagram and also indicate that the compounds may not follow exactly the same Rh-Ir CEF effects trend established for the compounds.

Quadrupolar susceptibility and magnetic phase diagram of PrNi2Cd20 with non-Kramers doublet ground state

ABSTRACTIn this study, ultrasonic measurements were performed on a single crystal of cubic PrNi2Cd20, down to a temperature of 0.02 K, to investigate the crystalline electric field ground state and search for possible phase transitions at low temperatures. The elastic constant (C11−C12)/2, which is related to the Γ3-symmetry quadrupolar response, exhibits the Curie-type softening at temperatures below ∼30 K, which indicates that the present system has a Γ3 non-Kramers doublet ground state. A leveling-off of the elastic response appears below ∼0.1 K toward the lowest temperatures, which implies the presence of level splitting owing to a long-range order in a finite-volume fraction associated with Γ3-symmetry multipoles. A magnetic field–temperature phase diagram of the present compound is constructed up to 28 T for H || [110]. A clear acoustic de Haas–van Alphen signal and a possible magnetic-field-induced phase transition at H ∼26 T are also detected by high-magnetic-field measurements.

Dynamical splitting of cubic crystal field levels in rare-earth cage compounds

The Crystalline Electric Field (CEF) influence is usually described by considering an ideally symmetrical rare-earth site. In the case of cage compounds, ample excursions of the rare-earth inside the cage require an adapted CEF description. A corrective, position dependent, CEF term accounts for the deviation from the perfect symmetry. In the paramagnetic range, a CEF level with orbital degeneracy thus acquires a width reflecting the rare-earth spatial distribution. In the case, frequent in cubic systems, of an orbitally degenerate CEF ground state at the center, this width introduces an additional energy scale, influential at low temperature. A spherical simplification allows to identify the major consequences of a cage-split ground multiplet: a Schottky-like anomaly appears in the specific heat with associated reduction of the magnetic entropy and alteration of the magnetic properties. Concomitantly, a centrifugal Jahn-Teller effect develops that expands the distribution of the magnetic ion and softens the rattling phonons. These effects are confronted with anomalous paramagnetic properties of rare-earth cage compounds, notably rare-earth filled skutterudites and hexaborides.

Sinusoidally modulated magnetic structure of Kramers local moments in CePd5Al2

The crystalline electric field (CEF) level scheme and magnetic structure of a tetragonal antiferromagnet CePd5Al2 with K and K were studied by neutron scattering, magnetization and magnetoresistance measurements. Inelastic neutron scattering measurements on the powder sample revealed CEF excitations at 21.3 and 22.4 meV. The derived wave functions of the CEF ground state for the Ce3+ ion consist primarily of under the tetragonal symmetry. By means of single-crystal neutron diffraction, magnetic Bragg peaks characterized by a propagation vector were observed at . Our analysis indicates a sinusoidally modulated magnetic structure with amplitude of 2.0(1) /Ce, where the magnetic moments point to the -axis. The intensity of the third-order harmonic at 0.8 K is 1/30 as small as that expected for an antiphase structure, suggesting that the modulated structure remains at least down to 0.8 K. Both the magnetization and magnetoresistance show several anomalies in the magnetically ordered phase, indicating field-induced successive changes of the magnetic structure.

Multipole interactions of Γ3 non-Kramers doublet systems on cubic lattices

We investigate the multipole interactions between adjacent f2 ions with the Γ3 crystalline electric field (CEF) ground state. In this study, we consider only the Γ8 states as the one-electron states. We construct the Γ3 doublet state of the electrons in the Γ8 states, and indeed, it can become the CEF ground state of a simple model Hamiltonian. To derive the multipole interactions, we apply the second-order perturbation theory with respect to the intersite hopping. We obtain no multipole interaction for a simple cubic lattice and octupole interactions for bcc and fcc lattices. We discuss the similarities and differences in the multipole interactions among the models with the local Γ3 CEF states.

Ising-type Magnetic Anisotropy in CePd2As2

We investigated the anisotropic magnetic properties of CePd2As2 by magnetic, thermal and electrical transport studies. X-ray diffraction confirmed the tetragonal ThCr2Si2-type structure and the high-quality of the single crystals. Magnetisation and magnetic susceptibility data taken along the different crystallographic directions evidence a huge crystalline electric field (CEF) induced Ising-type magneto-crystalline anisotropy with a large c-axis moment and a small in-plane moment at low temperature. A detailed CEF analysis based on the magnetic susceptibility data indicates an almost pure |±5/2〉 CEF ground-state doublet with the dominantly |±3/2〉 and the |±1/2〉 doublets at 290 K and 330 K, respectively. At low temperature, we observe a uniaxial antiferromagnetic (AFM) transition at TN = 14.7 K with the crystallographic c-direction being the magnetic easy-axis. The magnetic entropy gain up to TN reaches almost R ln 2 indicating localised 4 f-electron magnetism without significant Kondo-type interactions. Below TN, the application of a magnetic field along the c-axis induces a metamagnetic transition from the AFM to a field-polarised phase at μ0Hc0 = 0.95 T, exhibiting a text-book example of a spin-flip transition as anticipated for an Ising-type AFM.

Impurity quadrupole Kondo ground state in a dilute Pr system Y1-xPrxIr2Zn20

The electrical resistivity ρ and specific heat C of a dilute Pr system Y1-xPrxIr2Zn20 for 0 ≤ x ≤ 0.44 were measured to study the phenomena arising from active quadrupoles of the Pr3+ ion with 4f2 configuration. On cooling, ρ's of all samples monotonically decrease, while the residual resistivity ratio ρ(300K)/ρ(3K) drastically decreases with x. In the whole range x ≤ 0.44, the magnetic contribution to the specific heat divided by temperature Cm/T shows a broad maximum at around 10K, which can be reproduced by a two-level model with a first-excited triplet separated by 30K from a ground state doublet. This indicates that the crystalline electric field ground state of the Pr ions remains in the Γ3 doublet for the cubic Td point group. On cooling, the Cm/T data for x = 0.085 and 0.44 approach constant values at T<0.3K as expected from the random two-level model. By contrast, Cm/T for x = 0.044 increases continuously down to 0.08K, suggesting a non-Fermi liquid state due to the impurity quadrupole Kondo effect.

Competing Magnetic Interactions in the Kramers Doublet System NdIr2Zn20

Electrical resistivity ρ, magnetization M, and specific heat C measurements are reported for single-crystalline samples of the 4f3 Kramers system NdIr2Zn20. On cooling, ρ(T) monotonically decreases and drops below 0.65 K. The magnetic susceptibility M/B follows the Curie–Weiss law from 300 to 20 K, leading to an effective magnetic moment of μeff = 3.59 μB/Nd and a paramagnetic Curie temperature of θp = −3.6 K. The negative value of θp indicates an antiferro-type interaction, although the enhancement of M(B) in the paramagnetic state implies a ferro-type one. A broad maximum in the magnetic specific heat Cm at around 15 K arises from the excitations from the crystalline electric field ground state of a magnetic Γ6 doublet to the excited Γ8 quartet lying at 39 K above the ground state. A sharp peak in C(T) at 0.65 K coincides with the drop in ρ(T), both of which shift to lower temperatures upon applying a magnetic field. The field dependences indicate that an antiferromagnetic order may occur under the geom...

Structural, Magnetic, and Superconducting Properties of Caged CompoundsROs2Zn20(R= La, Ce, Pr, and Nd)

The electrical resistivity, magnetization, and specific heat of the caged compounds ROs2Zn20 (R = La, Ce, Pr, and Nd) have been measured to study their structural, magnetic, and superconducting properties. These measurements indicate that the compounds undergo structural transitions at Ts = 151, 109, 87, and 62 K, respectively. The decrease in Ts along with the lanthanoid contraction suggests that the high-temperature phase is more stable for a smaller lattice volume. Analysis of the lattice specific heat of LaOs2Zn20 reveals that the Zn atom at the 16c site encapsulated in the R2Zn12 cage vibrates at a low energy of 3 meV. For CeOs2Zn20, the small magnetic susceptibility with a broad maximum indicates the valence-fluctuating state of the Ce ions. In PrOs2Zn20, the crystalline electric field ground state of the 4f2 state of the Pr3+ ion remains in a non-Kramers doublet at T > Ts, which is lifted by symmetry lowering of the Pr site at T < Ts. Thereby, the quadrupolar degrees of freedom are quenched, avoidi...

Crystal structure and thermodynamic properties of NdCu4Au compound

We report the synthesis of the antiferromagnet cubic-type structure NdCu4Au derived by substituting Au for Cu in the parent binary NdCu5 compound. The room temperature X-ray diffraction analysis indicates a cubic MgCu4Sn-type structure with space group F4¯3m (No. 216) for the NdCu4Au compound. The thermodynamic properties of NdCu4Au have been probed by magnetic susceptibility, χ(T), magnetization, M(μ0H), and specific heat, Cp(T), measured down to 1.8K. The low temperature χ(T) data shows probably an antiferromagnetic (AFM)-like anomaly associated with a Néel temperature TN=3.9K. In the paramagnetic region, χ(T) data follows the modified Curie–Weiss law with an effective magnetic moment μeff=3.547(5)μB and Weiss temperature θp=−10.19(8)K. The value for μeff is close to the value of 3.62μB expected for the Nd3+-ion. No evidence of metamagnetic transition was observed from the isothermal M(μ0H) results. Cp(T) data confirm the AFM phase transition at TN=3.5K close to the value of 3.9K observed in χ(T). The 4f-electron specific heat shows a Schottky-type anomaly around 20K associated with crystalline-electric-field (CEF), with energy splitting Δ1=62(5)K and Δ2=109(9)K of the Nd3+ (J=9/2) multiplet, that are associated with the first and second excited state of Nd3+-ion. From the results of the 4f-electron magnetic entropy, it is speculated that the CEF ground state of Nd3+ (J=9/2) ions is the Γ6 doublet for NdCu4Au.

Pronounced −Log T Divergence in Specific Heat of Nonmetallic CeOBiS2: A Mother Phase of BiS2-Based Superconductor

The low-temperature properties of CeOBiS$_2$ single crystals are studied by electrical resistivity, magnetization, and specific heat measurements. Ce 4f -electrons are found to be in a well-localized state split by crystalline-electric-field (CEF) effects. The CEF ground state is a pure $J_z$ = $\pm$ 1/2 doublet, and excited doublets are located far above. At low temperatures in zero field, we observe pronounced $-\log T$ divergence in the specific heat, revealing the presence of quantum critical fluctuations of 4f magnetic moments near a quantum critical point (QCP). Considering that CeOBiS$_2$ is a nonmetal, this phenomenon cannot be attributed to the competition between Kondo and the Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions as in numerous f-electron-based strongly correlated metals, indicating an unconventional mechanism. We suggest that CeOBiS$_2$ is the first material found to be located at a QCP among geometrically frustrated nonmetallic magnets.

Evidence of a High-Field Phase in PrV2Al20 in a [100] Magnetic Field

The DC magnetization of a single crystal of cubic PrV2Al20 was examined at very low temperatures down to \({\sim}0.1\) K and in high fields of up to 14.5 T applied along the [100] direction. A field–temperature (\(H\)–\(T\)) phase diagram is obtained. In addition to the phase transition at 0.6 K, which is known to be rather insensitive to \(H\), we obtained evidence of a new high-field phase (HFP) for \(H\geq 11\) T and \(T\leq 0.75\) K. From the analysis of the temperature dependence of the magnetization in high fields, we point out that the HFP is not due to the crossing of the crystalline electric field levels. The results imply the switching between the order parameters carried by the crystalline electric field ground state of Pr3+.

Elastic Constants of NdCu2Ge2

The components-separated magnetic transition in NdCu2Ge2 was investigated by measuring elastic constant and specific heat. The specific heat shows clear peak at TN = 4.8 K The magnetic entropy change reaches Rln2 at ∼ 6 K and Rln8 at ∼ 72 K with increasing temperature. This result indicates that the crystalline electric field ground state of NdCu2Ge2 is a Kramers doublet. In addition, the results of the elastic constant measurements suggest that no degeneracy of quadrupolar degrees of freedom exists below TN. NdCu2Ge2 has a possibility of another mechanism that suppress the magnetic ordering of the ab-component unlike other compounds showing component-separated magnetic transition.

Nonmagnetic ground states and phase transitions in the caged compounds PrT2Zn20 (T = Ru, Rh and Ir)

We performed electrical resistivity ρ, magnetic susceptibility χ, specific heat C and electron diffraction measurements on single-crystalline samples of PrT2Zn20 (T = Ru, Rh and Ir). The three compounds show the Van Vleck paramagnetic behavior, indicating the nonmagnetic crystalline electric field (CEF) ground states. A Schottky-type peak appears at around 14 K, irrespective of the T element, which can be moderately reproduced by a doublet–triplet model. For T = Ru, a structural transition occurs at Ts = 138 K, below which no phase transition appears down to 0.04 K. On the other hand, for T = Ir, antiferroquadrupole (AFQ) ordering arising from the nonmagnetic Γ3 doublet takes place at TQ = 0.11 K. For T = Rh, despite a structural transition between 170 and 470 K, the CEF ground state is still the non-Kramers Γ3 doublet. However, no phase transition due to the Γ3 doublet was observed even down to 0.1 K.

Spin re-orientation in FeCr2S4

The spinel FeCr2S4has been studied intensely for its peculiar magnetic and local structural changes which are sensitively influenced by the Jahn–Teller properties of Fe2 + in tetrahedral sulfur coordination. Recent muon spin rotation data give strong evidence that the commonly assumed collinear magnetic structure of this compound is only found between the Curie temperature TC = 165 K and 50 K. For lower temperatures a helical structure has been proposed. We present new Mossbauer spectroscopic data taken on the same sample as used for muon spin rotation. Also the hyperfine spectra revealing non-equivalent iron sites support the appearance of a spin re-orientation around 50 K which may be related to the onset of short-range orbital order. Below 20 K severe dynamic broadenings are found which may indicate orbital fluctuations. Orbital order occurs around 11 K accompanied by severe changes in the crystalline electric field ground state as traced from quadrupole interaction.

Low Temperature Magnetic Properties of Pr(Cu,Ga)13with Orbitally Degenerate Ground State

Magnetic susceptibility χ( T ) and the specific heat C ( T ) of a cubic compound Pr(Cu,Ga) 12.85 were measured at low temperatures down to 0.1 K. χ( T ) shows Curie–Weiss behavior down to ∼1 K and turns to saturate at lower temperatures. This behavior is best understood by assuming a Γ 5 magnetic triplet for the crystalline electric field ground state of Pr 3+ (4 f 2 , J =4). The C ( T ) data indicate a continuous releasing of the Γ 5 entropy below ∼12 K, with no evidence of a phase transition down to 0.1 K. At low temperatures below 0.5 K, a 141 Pr nuclear Schottky tail is found to develop in zero field, which can be ascribed to a hyperfine field from the Pr moment. The estimated Pr moment value (1.3 µ B ) is found to be significantly smaller than the full moment value of 2 µ B for the Γ 5 triplet, which is interpreted by fluctuating Pr moments in the ground state whose time scale is comparable to the Pr nuclear spin relaxation time. The analysis yields a large C / T value of 2.2 J/mol·K 2 at low tempera...

Thermal Properties of Filled Skutterudite PrOs4P12

We report the specific heat and thermoelectric power S ( T ) of filled skutterudite PrOs 4 P 12 , which has a Γ 1 crystalline electric field ground state. The electronic specific heat coefficient γ of PrOs 4 P 12 indicates a weak enhanced value (γ Pr /γ La ∼2.3) in comparison with that of LaOs 4 P 12 . The influence in the specific heat by c – f hybridization effect is discussed. S ( T ) of PrOs 4 P 12 exhibits a small maximum around 10 K although there is no such maximum for Ln Os 4 P 12 ( Ln = La, Nd, and Gd). Consequently, S / T for Ln = Pr increases below 20 K, which is consistent with the enhanced γ. We also report the magnetization process to 46 T in PrOs 4 P 12 .