non-Kramers Doublet Ground State Research Articles

Well-Defined Crystal Field Splitting Schemes and Non-Kramers Doublet Ground States of f Electrons in PrT2Zn20 (T = Ir, Rh, and Ru)

Inelastic neutron scattering studies of Pr\(T_{2}\)Zn20 (\(T\) = Ir, Rh, and Ru) were carried out in order to reveal \(f\) electron states indispensable for the low-temperature properties of Pr\(T_{2}\)Zn20 associated with multipole degrees of freedom. Sharp excitation peaks, which are located within excitation energies of less than 10 meV, are attributed to crystal field splitting level schemes of \(4f^{2}\) in Pr3+ ions. Data of the Ir-based compound is explained by a non-Kramers doublet ground state in the local symmetry \(T_{d}\) for this system. Results of the Rh-based compound are explained by the scheme for the Pr-site local cubic symmetry \(T\) in the low-temperature structural phase, which is lower than \(T_{d}\). In the Ru-based compound, the doublet is split as a result of the loss of local cubic symmetry through structural transformation. These experimental results confirm the non-Kramers doublet ground state that causes the quadrupole ordering or orbital Kondo effect predicted for this series...

Basal-plane nonlinear susceptibility: A direct probe of the single-ion physics in URu2Si2

The microscopic nature of the hidden order state in URu${}_{2}$Si${}_{2}$ is dependent on the low-energy configurations of the uranium ions, and there is currently no consensus on whether it is predominantly $5{f}^{2}$ or $5{f}^{3}$. Here we show that measurement of the basal-plane nonlinear susceptibility can resolve this issue; its sign at low temperatures is a distinguishing factor. We calculate the linear and nonlinear susceptibilities for specific $5{f}^{2}$ and $5{f}^{3}$ crystal-field schemes that are consistent with current experiment. Because of its dual magnetic and orbital character, a ${\ensuremath{\Gamma}}_{5}$ magnetic non-Kramers doublet ground state of the U ion can be identified by ${\ensuremath{\chi}}_{1}^{c}(T)\ensuremath{\propto}{\ensuremath{\chi}}_{3}^{\ensuremath{\perp}}(T)$, where we have determined the constant of proportionality for URu${}_{2}$Si${}_{2}$.

Antiferro-Quadrupolar Ordering at the Lowest Temperature and Anisotropic Magnetic Field–Temperature Phase Diagram in the Cage Compound PrIr2Zn20

The cage compound PrIr 2 Zn 20 with the non-Kramers doublet ground state shows a phase transition at T Q ∼0.11 K. To investigate the origin of the phase transition, we have carried out ultrasonic measurements on single-crystalline samples. From the disappearance of electric quadrupole degrees of freedom at T Q and the negative sign of a quadrupole–quadrupole coupling constant, we clarified that the phase transition is antiferro-quadrupolar ordering at the lowest temperature ever measured. We also found anisotropic magnetic field H dependence and the re-entrant behavior of T Q ( H ) from the measurements in H parallel to the [100], [110], and [111] axes. The quadrupole Kondo effect interrupts the long-range quadrupole interaction at very low temperatures and thus lowers T Q . We first reported the rattling motion of Zn atoms at the 16 c site in the R T 2 Zn 20 system.

Low-Temperature Elastic Properties of Non-Kramers Doublet Compound PrMg3

We have investigated low-temperature elastic properties of PrMg3 with a non-Kramers Γ3 doublet ground state by using ultrasonic measurements under high field up to 18 T down to 20 mK. A softening of the elastic constant (C11–C12)/2 has been observed below 8 K due to the non-magnetic Γ3 doublet possessing electric quadrupole Ou and Ov with Γ3 symmetry and magnetic octupole Txyz with Γ2. This result appreciably is deviated from a theoretical fitting of the quadrupole susceptibility based on the crystal-electric-field levels below 800 mK. Furthermore, the (C11–C12)/2 shows strange magnetic dependence up to 18 T below 1.7 K, which are inconsistent with the theoretical results.

Low-temperature magnetization of PrMg3 with a Γ3 non-Kramers doublet ground state

Magnetization of a single crystal of cubic PrMg3 with a Γ3 non-Kramers doublet ground state has been examined at low temperatures down to 60 mK in fields up to 8.5 T. The 4f-electronic contribution of the magnetic susceptibility χ4f(T) is significantly enhanced over the expected Van-Vleck behavior and shows like temperature variation in a finite region 0.3 ≤ T ≤ 2.5 K. We argue that this enhancement in χ4f(T) originates from the Γ3 ground state and hybridization with conduction electrons. No such unusual temperature variation is observed in χ4f(T) of a tetragonal compound PrB2C2 which has a singlet ground state in the crystalline electric field level scheme.

Unusual Low-Temperature Magnetization of a Cubic Γ3 Non-Kramers Doublet Ground State Compound PrMg3-Evidence of a Hybridization Effect

Magnetizations of single crystals of cubic PrMg 3 with a Γ 3 non-Kramers doublet ground state have been examined at very low temperatures down to 60 mK in magnetic fields up to 8.5 T. No evidence of a long-range order is obtained. Instead, the magnetic susceptibility for both [001] and [111] directions continuously increases on cooling below 3 K where the system is well in the Van-Vleck paramagnetic regime, followed by a steep rise due to Pr nuclear Curie law below ∼0.2 K. Subtracting the nuclear contribution from the total magnetization yields a -log T (1≤ T ≤10 K) or a \(-\sqrt{T}\) (0.3 ≤ T ≤2.5 K) dependence of the 4 f -electronic susceptibility. We argue that a possible random site exchange effect in this Heusler type compound is not the origin of the unusual increase of the susceptibility. Our observations strongly suggest the presence of a hybridization effect between Pr 4 f and conduction electrons.

Elastic behavior around metal–insulator transition in PrRu 4P 12

Elastic properties of PrRu 4P 12 have been investigated by means of the ultrasonic measurement. A clear bend was observed in elastic constants C 11 , ( C 11 - C 12 ) / 2 and C 44 at metal–insulator transition temperature T MI of 62.3 K. Furthermore, C 11 , and ( C 11 - C 12 ) / 2 exhibits a pronounced elastic softening towards low temperature in the temperature range down to 1.5 K. This fact suggests strongly that Pr 3 + Γ 3 non-Kramers doublet ground state is realized in PrRu 4P 12 under the crystalline electric field (CEF) potential. This also suggests that an orbital degree of freedom still remains below T MI and a quadrupolar ordering has nothing to do with the metal–insulator transition. The elastic property and 4f ground state of Pr ions in this system will be discussed from the view point of CEF effect.

Magnetic Excitations in Heavy-Fermion Superconductor PrOs4Sb12

Magnetic excitations in a single crystal of heavy-fermion superconductor PrOs 4 Sb 12 have been studied by inelastic neutron scattering (INS) at low temperatures under high magnetic fields. The crystal field (CF) excitations at 0.7 meV observed in a previous INS study of a polycrystal sample were confirmed in this study on a single crystal. The observed excitations in the zero magnetic field soften around a wave vector (1,0,0), which is the modulation vector of the field-induced antiferro-quadrupolar ordering, suggesting the presence of quadrupolar instability. The observed field dependence of excitations is better reproduced in a singlet ground-state model rather than in a non-Kramers doublet ground-state model. In a high resolution experiment, furthermore, the change of the excitation spectra at (1,0,0) was observed on passing through the superconducting transition temperature, indicating that the excitation and the superconductivity are closely related in PrOs 4 Sb 12 .

High-field ultrasonic study on PrPtBi with non-Kramers doublet ground state

We have measured the elastic constants of PrPtBi single crystal with the cubic MgAgAs-type structure as functions of temperatures and magnetic fields. A remarkable softening of 10% in ( c 11− c 12)/2 was observed below 20 K with decreasing temperatures, while c 44 shows a monotonous increase. These behaviors are attributed to the crystal-field ground state non-Kramers doublet Γ 3. The enormous softening in ( c 11− c 12)/2 prefers a ferro-quadrupolar order of O 2 0 or O 2 2, which brings about a structural phase transition of cubic–tetragonal or cubic-orthorhombic. The magnetic field dependences of c 11 and ( c 11− c 12)/2 up to 25 T were explained qualitatively in terms of a quadrupolar susceptibility assuming the crystal-field level proposed by inelastic neutron scattering. Above 1.8 K the field dependence shows no clear indication of phase transition, which mean paramagnetic phase is stable above 1.8 K up to 25 T .

Non-Fermi-liquid behavior of impurity Anderson model with non-Kramers doublet ground state

We investigate the non-Fermi-liquid (NFL) behaviour of an impurity Anderson model which has an f 2 configuration subject to a tetragonal crystalline electric field (CEF), giving a ground state which is a non-Kramers doublet. The temperature dependence of the specific heat in a magnetic field is calculated. When the magnetic field is very weak, there are two peaks: one is a broad peak around 5 T*, where T* is the temperature at which the −ln T dependence of the magnetic susceptibility and the γ-coefficient of the specific heat, associated with the NFL behaviour, begins. The other peak is at very low temperatures and shows a release of the residual entropy which is expected from the NFL state of a two-channel type Kondo model.

Numerical Renormalization Group Study of Non-Fermi-Liquid State on Dilute Uranium Systems

We investigate the non-Fermi-liquid (NFL) behavior of the impurity Anderson model (IAM) with non-Kramers doublet ground state of the f$^2$ configuration under the tetragonal crystalline electric field (CEF). The low energy spectrum is explained by a combination of the NFL and the local-Fermi-liquid parts which are independent with each other. The NFL part of the spectrum has the same form to that of two-channel-Kondo model (TCKM). We have a parameter range that the IAM shows the $- \ln T$ divergence of the magnetic susceptibility together with the positive magneto resistance. We point out a possibility that the anomalous properties of U$_x$Th$_{1-x}$Ru$_2$Si$_2$ including the decreasing resistivity with decreasing temperature can be explained by the NFL scenario of the TCKM type. We also investigate an effect of the lowering of the crystal symmetry. It breaks the NFL behavior at around the temperature, $\delta /10$, where $\delta$ is the orthorhombic CEF splitting. The NFL behavior is still expected above the temperature, $\delta/10$.

Kondo screening of uranium in the dilute system (UxLa1-x)Ru2Si2.

Kondo screening is found in dilute uranium compounds (${\mathrm{U}}_{\mathit{x}}$${\mathrm{La}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$)${\mathrm{Ru}}_{2}$${\mathrm{Si}}_{2}$ (x\ensuremath{\leqslant}0.15). At high temperatures, the susceptibility with a large magnetic anisotropy is explained by the crystal field model with the non-Kramers doublet ground state. On the other hand, the low-temperature behaviors of the high-field magnetization, susceptibility, and specific heat are well described by the Kondo model. The \ensuremath{\gamma} value and Schottky anomaly are nearly the same as those observed for ${\mathrm{URu}}_{2}$${\mathrm{Si}}_{2}$. These results suggest that single-site Kondo screening is important for understanding the Fermi liquid state in ${\mathrm{URu}}_{2}$${\mathrm{Si}}_{2}$. \textcopyright{} 1996 The American Physical Society.

Possible Correlated-Electron Behavior from Quadrupolar Fluctuations in PrInAg2.

The temperature dependent magnetic susceptibility, specific heat, and electrical resistivity were measured on PrInA${\mathrm{g}}_{2}$. A broad peak, which is identified as a Kondo anomaly, is observed in the specific heat at $\ensuremath{\sim}0.4\mathrm{K}$ with a strongly enhanced linear contribution at lower temperatures. PrInA${\mathrm{g}}_{2}$ is a Pr-based heavy-fermion compound and has one of the largest known Sommerfeld coefficients of $\ensuremath{\sim}6.5\mathrm{J}/\mathrm{mol}{\mathrm{K}}^{2}$. A new type of nonmagnetic interaction between the conduction electrons and the non-Kramers doublet ground state of the ${\mathrm{Pr}}^{3+}$ ion may be responsible for this behavior. Related features are also observed in the susceptibility and resistivity.

Kondo Effect Due to Impurities with (5f)nConfiguration: Fermi Liquid Versus Non-Fermi Liquid

The Kondo effect due to U-type impurities is studied in connection with the stability of the Fermi liquid and the non-Fermi liquid. First, an effective exchange Hamiltonian in terms of irreducible tensor operators is derived for conduction electrons, which are coupled with plural 5 f electrons. It is based on the assumption of strong spin-orbit and Hund couplings. Second, a model for f 2 configuration placed in a tetragonal or hexagonal crystal field is studied by simplifying the internal structure as the non-Kramers doublet ground state and the first singlet excited state. The numerical renormalization group analysis shows that the singlet excited state plays an important role to stabilize the Fermi liquid over the non-Fermi liquid. Third, the difference of the Kondo effect is examined between non-Kramers doublet for f 2 and Kramers doublet for f 3 in the presence of the cubic crystal field. It is shown that for f 3 the Hund coupling reduces the channel number to one, while the situation is different for...

Simple model for coupled magnetic and quadrupolar instabilities in uranium heavy-fermion materials.

We present a mean-field calculation of the phase diagram of a simple model of localized moments, in the hexagonal uranium heavy-fermion compounds. The model considers a non-Kramers quadrupolar doublet ground state magnetically coupled with a singlet excited-state, favoring in-plane van-Vleck magnetism, as has been conjectured for UPt$_3$. The Hamiltonian which defines the model is Heisenberg like in both, magnetic and quadrupolar moments. Among our main results are: (i) for zero intersite quadrupolar coupling, the magnetic order is achieved by a first order transition above a critical intersite magnetic coupling value which becomes second order at higher coupling strengths. (ii) for finite intersite quadrupolar coupling, at temperatures below a second order quadrupolar ordering transition, the minimal magnetic coupling value is increased but (a) the magnetic ordering temperature is enhanced above this value, and (b) the ordering of first and second order transitions in the phase diagram is reversed.

Anomalies of magnetic and elastic properties of Jahn-Teller antiferromagnets

The properties of tetragonal crystals with sublattice of ions in degenerate non-Kramers doublet ground state are considered. In such system the magnetic and structural (quadrupole) orderings are competitive. For the situation, when strong magnetic correlations result in an antiferromagnetic phase transition, the effect of magnetic field, H ∥ c, on the crystal behaviour is examined. For some range of field and temperature values the phase is realized, where the magnetic order and the orthorhombic Jahn-Teller deformation coexist. The temperature and field dependences of magnetic moment and elastic constant possess anomalies at the boundaries and inside this phase.

Electron paramagnetic resonance of terbium in a zirconium fluoride glass

Electron paramagnetic resonance of trivalent terbium ions is reported in a glass based on zirconium fluoride at liquid helium temperatures and at frequencies in the range 9 to 30 GHz. The results are interpreted as arising from a nonKramers doublet ground state with g/sub ///=17.3+or-0.5, A/sub ///=0.209+or-0.001 cm-1 and with a zero-field-splitting parameter delta taking a continuous range of values from zero to at least 1.0 cm-1. A simple theoretical model is developed that satisfactorily reconstructs the essential features of the observed resonance spectra. It is concluded that terbium ions act as network formers. They occupy a relatively well defined type of site, similar to those found in crystalline hosts, with a dominant crystal-field term of axial symmetry but with a continuous range of small site-to-site variations.

Magnetic Ordering in Holmium Ethylsulfate below 215 mK

We report ac and dc susceptibility measurements of single crystals of the axial dipolar paramagnet Ho(C2H5SO4)3·9H2O between 10 mK and 1 K. This material has hexagonal symmetry, with a non-Kramers doublet ground state possessing a very anisotropic g factor, to which the Ising model might be expected to apply: g||=15.41, g⊥=0. An antiferromagnetic transition was observed at ∼215 mK. This is in marked contrast to two related compounds with Ising model interactions, Dy(C2H5SO4)3·9H2O and Tb(C2H5SO4)·9H2O, both of which order ferromagnetically. A possible reason for the difference is the hyperfine interaction, which is large in holmium.

Magnetic measurements on thulium nicotinate dihydrate

Magnetic susceptibility and optical absorption measurements, and EPR spectra at 20 MHz, and 8, 17 and 35 GHz, confirm the presence in thulium nicotinate dihydrate [Tm(C 5H 4NCO 2) 3(H 2O) 2] 2 of interacting dimers of Tm 3+ ions, each in a non-Kramers doublet ground state. The level corresponding to antiparallel spins lies 0.86(2) cm -1 above that of parallel spins.

The anomalous heat capacity of cerium magnesium nitrate

It has been demonstrated in several laboratories that the heat capacity of cerium magnesium nitrate is anomalous above 20 mK. The origin of the anomaly is unknown. We have measured the heat capacity of three samples of cerium magnesium nitrate from 0.15 to 0.6 K. The samples were: (a) from a cloudy region of a large single crystal grown from nominally 95% starting material, (b) from an optically clear region of the same single crystal, and (c) from a single crystal grown from 99.9% starting material. Within the scatter of the data the three heat capacity determinations showed the same anomaly as observed elsewhere; after subtracting an appropriate lattice contribution, the heat capacity above 0.1 K is more than twice that expected for a set of interacting magnetic dipoles on a regular lattice. The “cloudy sample versus clear sample” results ruled out crystal growth problems as the source of the anomaly. Chemical analysis by neutron activation analysis, mass spectrographic analysis, and optical absorption spectroscopy all showed the presence of approximately 0.06% praseodymium to cerium ratio in the two single crystals. The heat capacity arising from the hyperfine splitting of the non-Kramers doublet ground state of that concentration of praseodymium ions in cerium magnesium nitrate accounts for the heat capacity anomaly in magnitude and temperature dependence. No serious consequences are expected regarding the use of cerium magnesium nitrate as a primary thermometric substance.