Crystal Electric Field Level Scheme Research Articles

Anisotropic magnetic and quadrupolar H−T phase diagram of CeRh2As2

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

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

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

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

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

Crystal electric field excitations in the quasicrystal approximantTbCd6studied by inelastic neutron scattering

We have performed inelastic neutron scattering measurements on powder samples of the quasicrystal approximant, ${\mathrm{TbCd}}_{6}$, grown using isotopically enriched $^{112}\mathrm{Cd}$. Both quasielastic scattering and distinct inelastic excitations were observed below 3 meV. The intensity of the quasielastic scattering measured in the paramagnetic phase diverges as ${T}_{\mathrm{N}}\ensuremath{\sim}22$ K is approached from above. The inelastic excitations, and their evolution with temperature, are well characterized by the leading term, ${B}_{2}^{0}{O}_{2}^{0}$, of the crystal electric field (CEF) level scheme for local pentagonal symmetry for the rare-earth ions [S. Jazbec et al., Phys. Rev. B 93, 054208 (2016)] indicating that the Tb moment is directed primarily along the unique local pseudofivefold axis of the Tsai-type clusters. We also find good agreement between the inverse susceptibility determined from magnetization measurements using a magnetically diluted ${\mathrm{Tb}}_{0.05}{\mathrm{Y}}_{0.95}{\mathrm{Cd}}_{6}$ sample and that calculated using the CEF level scheme determined from the neutron measurements.

Elastic anomalies of YbIrGe in magnetic fields

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

Magnetic Field–Temperature Phase Diagram of the Ferro-quadrupolar State and Crystal Electric Field Effect in UCu2Sn

The ternary uranium compound UCu 2 Sn shows a ferro-quadrupolar transition at T Q = 16 K originating from the ordering of the non-Kramers doublet Γ 5 ground state. To investigate the magnetic field–temperature phase diagram of the ferro-quadrupolar state in UCu 2 Sn, we measured elastic modulus C 66 at magnetic fields of up to 14 T. We found an anisotropic field dependence of T Q ( H ) in H ∥[\bar12\bar10], [0001], and [01\bar10]. We optimized the crystal electric field level scheme using C 66 under fields, magnetic susceptibility, and electronic entropy. The quadrupolar phase diagram is well reproduced by the obtained level scheme.

Magnetocrystalline anisotropy in RAu 2Ge 2 (R = La, Ce and Pr) single crystals

Anisotropic magnetic properties of single crystalline RAu 2Ge 2 (R=La, Ce and Pr) compounds are reported. LaAu 2Ge 2 exhibits a Pauli-paramagnetic behaviour whereas CeAu 2Ge 2 and PrAu 2Ge 2 show an antiferromagnetic ordering with Nèel temperatures T N = 13.5 and 9 K, respectively. The anisotropic magnetic response of Ce and Pr compounds establishes [0 0 1] as the easy axis of magnetization and a sharp spin-flip type metamagnetic transition is observed in the magnetic isotherms with H // [0 0 1]. The transport and magnetotransport behaviour of these compounds, in particular LaAu 2Ge 2, indicate an anisotropic Fermi surface. The magnetoresistivity of CeAu 2Ge 2 apparently reveals the presence of a residual Kondo interaction. A crystal electric field analysis of the anisotropic susceptibility in conjunction with the experimentally inferred Schottky heat capacity enables us to propose a crystal electric field level scheme for Ce and Pr compounds. For CeAu 2Ge 2 our values are in excellent agreement with the previous reports on neutron diffraction. The heat capacity data in LaAu 2Ge 2 show clearly the existence of Einstein contribution to the heat capacity.

Crystal field states in [formula omitted

Heavy fermion CeCu 4Al compound has been studied by inelastic neutron diffraction (INS), heat capacity and magnetic susceptibility measurements. A single Crystal Electric Field (CEF) peak has been detected in the INS spectra, which may be explained by a quasi-quartet state suggested by the analysis of the Schottky anomaly contributing to the magnetic part of the specific heat. The Kondo interactions have been included in the analysis of the magnetic part employing the simplified resonance level model. The resulting Kondo temperature of about 5–10 K is somewhat larger than in the previous studies. The magnetic susceptibility confirms the CEF level scheme of the type 0–93 K and provides the values of the CEF parameters.

Thomson scattering from the antiferroquadrupolar ordering phase in TmTe

On the basis of the recently established crystal electric field level scheme of Γ8 − Γ6 − Γ7, we investigate the Thomson scattering intensity of the superstructure reflections with h,k,l = 2n + 1 in the Γ3-type (O22, O02) antiferroquadrupolar (AFQ) ordering phase of TmTe. The intensities show strong dependence on G and the direction of the applied magnetic field H. These dependences on G and H similar to those found in the AFQ phase of CeB6, another AFQ material with Γ5-type (Oyz, Ozx, Oxy) order parameter having the Γ8 ground states, may provide us a useful tool to distinguish the component of the AFQ order of Γ3-type and Γ5-type.

Crystal electric field and quadrupole ordering in semiconducting PrPtBi

We prepared PrPtBi crystal by tungsten crucible and carried out inelastic neutron and thermal expansion experiments together with transport properties. The crystals show semiconducting properties both in electrical resistivity and Hall constant. As for crystal electric field (CEF), the results show that the CEF level scheme consists of non-Kramer's doublet Γ 3 ground state, a first excited state Γ 5 with an energy of 75 K, a second excited one Γ 4 with an energy of 116 K. Precise experiment of thermal expansion under the magnetic field suggests that the phase transition at 1.35 K is of a ferro-quadrupolar-type.

Crystal electric field excitations in CeAg1-xInxcompounds

The crystal electric field (CEF) levels of the Ce ions are investigated in the cubic phase of CeAg1-xInx for x=0.0, 0.05, 0.1, 0.2. The addition in In leaves the principle CEF level scheme ( Gamma 8 ground state, Gamma 7 first excited state) unchanged but causes a considerable broadening of the linewidth of the CEF transitions which is discussed in terms of a damping due to electron-hole excitations.

Investigation of the Crystal Field in PrNi5

AbstractInelastic slow‐neutron scattering experiments are made on polycrystalline samples of intermetallic compounds PrNi5 and LaNi5 over the temperature range 8 to 295 K. The peaks of the inelastic magnetic‐neutron—rare‐earth‐ion scattering resulting from the splitting of the ion ground state into a number of levels by the crystal electric field (CEF) of hexagonal symmetry are identified by temperature and angular dependence of resonance intensities and by comparing PrNi5 spectra with those of LaNi5. On the basis of an effective point charge model for the CEF Hamiltonian with four variable parameters, calculations are made and CEF level scheme is restored. Magnetic contributions to the temperature dependence of heat capacity and magnetic susceptibility of PrNi5 are calculated and compared with available experimental data.