Crystal Field Singlet Ground State Research Articles

Crystal field interaction at the Tm 3+ site in TmCr 2Si 2

TmCr 2Si 2 is investigated using 169Tm-Mössbauer spectroscopy and specific heat measurements. The Tm sub-lattice is not magnetically ordered down to 2 K, in keeping with the observed singlet crystal field ground state. The fitted crystal field parameters are consistent with those determined elsewhere for isostructural HoCr 2Si 2 and indicate a deviation of the rank 6 parameters from the trend observed so far for the series RT 2Si 2 (R = rare earth, T = Fe, Co, Ni, Cu).

Interplay of Crystal Field Structures withf2Configuration to Heavy Fermions

We examine a relevance between characteristic of crystal field structures and heavily renormalized quasiparticle states in the $f^0$-$f^1$-$f^2$ Anderson lattice model. Using a slave-boson mean-field approximation, we find that for $f^2$ configurations two or three quasiparticle bands are formed near the Fermi level depending on the number of the relevant $f^1$ orbitals in the $f^2$ crystal field ground state. The inter-orbital correlations characterizing the crystal field ground state closely reflect in inter-band residual interactions among quasiparticles. Particularly in the case of a singlet crystal field ground state, resulting residual antiferromagnetic exchange interactions among the quasiparticles lead to an anomalous suppression of the quasiparticle contribution of the spin susceptibility, even though the quasiparticle mass is strongly enhanced.

Energy level crossing and high-field magnetization in HoVO4

The high-field magnetization, in fields up to 28T, and magnetic susceptibility were measured in HoVO4, which has a crystal-field singlet ground state. The temperature dependence of magnetic susceptibility exhibits Van Vleck behavior due to the non-magnetic ground state. An abrupt increase more than 8μB due to the level crossing of the non-magnetic ground state with the excited one, having the mainly Jz=−7, is observed in the magnetization process at the field of 11.5T along the [001]-axis. The magnetization processes along the three principal axes and the temperature dependence of magnetic susceptibility are well reproduced by the crystal-field energy level scheme previously reported.

Effect of Coulomb interaction on superconductivity for Van Vleck metals

For the Van Vleck metals, we study the effect of Coulomb interaction on the superconductivity mediated by the virtual excitation of the crystal-field singlet ground state. It is shown that the screened Coulomb interaction makes a small decrease of T c but leaves T c finite.

Effect of Crystalline Electric Field on Heavy Fermions : Fermi Liquid State withf2-Singlet Configuration

Fermi liquid description of heavy Fermions with the f 0 - f 1 - f 2 configuration is studied by using the slave boson technique. In particular, it is shown that a new type of Fermi liquid state is realized in the case where the f 2 configuration with a singlet crystal field ground state is predominant. Namely, the quasiparticle contribution χ qp to the magnetic susceptibility is not enhanced while the density of states of quasiparticle is enhanced producing the heavy Fermions. A relevance to an anomalously small reduction of the Knight shift across the superconducting transition observed in UPt 3 is discussed.

PrRu2Si2: A giant anisotropic induced magnet with a singlet crystal-field ground state

The magnetic properties of PrRu${}_{2}$Si${}_{2}$ have been investigated experimentally by specific heat, single-crystal magnetization, ${}^{141}$Pr M\ossbauer and muon spectroscopies, neutron powder diffraction, and inelastic neutron scattering, leading to the determination of its zero-field phase diagram and its crystal electric-field energy levels below 40 meV. PrRu${}_{2}$Si${}_{2}$ undergoes a magnetic phase transition at ${T}_{N}$ $\ensuremath{\simeq}$ 16 K to an axial incommensurate sine-wave magnetic structure characterized by a wave vector $\ensuremath{\tau}$ = (0.133, 0.133, 0), followed by a first-order phase transition at ${T}_{C}$ $\ensuremath{\simeq}$ 14.0 K to an axial ferromagnetic structure. The lowest crystal electric-field states are the two singlets $|{\ensuremath{\Gamma}}_{t1}^{(1)}〉$ and $|{\ensuremath{\Gamma}}_{t2}〉$ separated by 2.25 meV. The low-temperature properties are described by a Hamiltonian identical to that of an Ising system with a transverse magnetic field. Since the ratio of the exchange energy to the energy splitting between the singlets is sufficiently large, it exhibits spontaneous magnetization. The nature of the two singlet states explains the giant magnetic anisotropy. The random-phase approximation predicts the value of the high-field magnetization but yields a low-field magnetization too small by $\ensuremath{\sim}$ 15$%$. Possible application of our results to uranium intermetallic compounds is pointed out.

Structural, Mössbauer spectroscopic and magnetochemical investigations into EuPt 5, TmPt 5 and TmPt 3 synthesized from platinum and gaseous lanthanide

EuPt 5, TmPt 5, and TmPt 3 were prepared by reaction of the gaseous lanthanides with Pt at 1200, 1300, and 1500°C respectively. Structural investigations established that the former two crystallize in CaCu 5-type related superstructures, the details being still under investigation. 151Eu Mössbauer spectroscopy and magnetic susceptibility measurements revealed that EuPt 5 is a mixed-valent europium alloy containing both trivalent (Eu[4f 6]) and intermediate-valent Eu, the latter as a dynamic mixture of the [4f 6] and [4f 7] configurations. The magnetochemical analysis of TmPt 1 (AuCu 1-type structure) on the basis of a crystal field/molecular field model disclosed trivalent Tm[4f 12] with a singlet crystal field ground state and the absence of magnetic ordering (for T≥1.7K).

Superconductivity from magnetic order for Van Vleck metals

For Van Vleck metals such as Pr, it is shown in a previous paper that the indirect electron-electron interaction V, mediated by the virtual excitation of the crystal field singlet ground state through the s-f exchange interaction, can give rise to superconductivity. With increase of the s-f exchange interaction or the Van Vleck susceptibility, V increases and makes the superconducting transition temperature ${\mathrm{T}}_{\mathrm{c}}$ increase. Conversely, when V is beyond the critical value ${\mathrm{V}}_{\mathrm{M}}$, magnetic order appears at a finite temperature ${\mathrm{T}}_{\mathrm{M}}$. In this case, a problem arises in whether ${\mathrm{T}}_{\mathrm{c}}$ lies above or below ${\mathrm{T}}_{\mathrm{M}}$. This paper shows that, except for the very vicinity of ${\mathrm{V}}_{\mathrm{M}}$, the superconductivity appears below ${\mathrm{T}}_{\mathrm{M}}$ contrary to the conclusion of the BCS approximation. This is due to the depairing effect by the scattering of the conduction electrons accompanied by the excitation of the singlet ground state. The phase diagram is obtained by assuming the free electron band and the orthorhombic crystal field.

Superconductivity mediated by antiferromagnetic spin fluctuation for the Van Vleck metals

In the Van Vleck metals, a possibility of the superconductivity mediated by virtual excitation of the crystal field singlet ground state is studied in the case where antiferromagnetic spin fluctuation is dominant. It is shown that a finiteTc still exists for thed-wave pairing although the dynamical effect which brings about mass enhancement for the conduction electrons suppresses the pairing strongly.

Superconductivity in the Van Vleck metals.

In the Van Vleck metals such as Pr, an indirect interaction arises between the conduction electrons through the virtual excitation of the crystal-field singlet ground state. By solving the Eliashberg equations, it is shown that this effective interaction can bring about superconductivity in a way similar to the spin-fluctuation-mediated pairing due to the repulsive short-range interaction. For the free-electron band the triplet p-wave pairing is formed. Spin degeneracy of the triplet states is lifted by the crystal-field anisotropy to choose the highest ${\mathit{T}}_{\mathit{c}}$. The retardation effect brought by the effective interaction and the depairing effects due to the scattering of the conduction electrons by the crystal-field states are analyzed in detail. Of all these effects, it is the mass renormalization effect that strongly depresses ${\mathit{T}}_{\mathit{c}}$.

Pairing mediated by crystal-field state excitation

A new pairing mechanism is proposed for metals such as Pr that have a crystal-field singlet ground state for the 4f-electrons. It results from the electron-electron interaction mediated by virtual excitation of the singlet ground state. The Eliashberg equation is analyzed to estimate dynamical effects coming from the van Vleck susceptibility.

Pairing mechanism mediated by crystal-field excitation in van Vleck paramagnetic metals

We have shown so far that in van Vleck paramagnetic metals such as Pr indirect electron-electron interaction arises from virtual excitation of the crystal field singlet ground state. This effective interaction turns repulsive near the Fermi surface. We study the possible pairing mediated by the spin-fluctuation due to this repulsie interaction. For the conduction band where the conduction electron susceptibility takes a maximum at q=0, formal discussion can be made in parallel with the superfluidity in 3He. Among the spin triplet pairings crystal field anisotropy selects the most favorable state.

Electronic specific heat in metallic Van Vleck paramagnets.

Electronic specific heat due to virtual excitation of the crystal-field singlet ground state is studied by including higher-order processes, following the Doniach-Engelsberg-Brinkman theory. As the effective electron-electron interaction mediated by the excitation of the crystal-field states turns repulsive near the Fermi surface, correspondence with the Hubbard model is investigated. The specific heat is separated into a fermionlike term and a bosonlike term. The former has a T-linear contribution which corresponds to that in the Hubbard model. The bosonlike term corrects the Schottky-type contribution of individual crystal-field states by their collective modes. Numerical calculation is made in a simplified model for real substances to see the relative size of the fermion and boson terms in a magnetic field.

Low-temperature specific heat, AC susceptibility and magnetisation of the singlet ground-state compounds TmIr2 and TmRh2

We present low-temperature specific heat, AC susceptibility, magnetisation andresistivity experiments on the intermetallic Laves phase compounds TmIr2 and TmRh2. Theexperimental susceptibility data below 1 K, both in zero and non-zero magnetic field, showfor TmIr2 a transition to a completely diamagnetic state at 0.25 K, indicating the presenceof bulk superconductivity below that temperature. For TmRh2 it is found that this compoundhas a singlet crystal field ground state. TmRh2 undergoes a transition to a ferromagneticinduced moment ordered state at 0.4 K. Based on an analysis of the specific heat data for thetwo compounds, several possible sets of crystal field parameters are discussed. It appears tobe necessary to include the effect of a distortion from cubic symmetry in the Hamiltonian,which is consistent with available Mössbauer data.

Magnetic properties of the induced moment system TmNi 2

We present measurements of the ac susceptibility, magnetization, resistivity and specific heat of the intermetallic Laves phase compound TmNi 2. The specific heat of LuNi 2 is measured separately from 1.7 to 100 K, enabling an analysis of the magnetic specific heat of TmNi 2 over the temperature range 45 mK – 100 K. This material shows a ferromagnetic transition temperature of 1.1 K and a crystal field singlet ground state. Several sets of Hamiltonian parameters are discussed, taking into account the recently reported distortion from cubic symmetry in TmNi 2.

Unexpected magnetic behaviour in a singlet crystal field ground state induced by Tb 4f-instability

The magnetic susceptibility (χ) of Th1-xTbx alloys (with 5<x<55a/o Tb) in the range of 1 K<T<350K and the specific heat (forx=1.5a/o Tb) for 0.5<T<10 K were measured. A maximum in χ(T) was observed at a temperature which depends on concentration. The crystal field level scheme that fits the specific heat measurements shows two non-magnetic singlets as lowest levels. Such ambiguity is discussed within the framework of the 4f-Tb instability. The results are in agreement with the matrix superconductiveTc decrease. The contribution of the interconfigurational mixing on χ and the specific heat is also discussed.

Crystal-field effects in PrNi5: Comparison of calculations with experiments

In the intermetallic compound Pr${\mathrm{Ni}}_{5}$, exchange interactions between Pr ions are small enough in order not to disturb the crystal-field singlet ground state of the ${\mathrm{Pr}}^{3+}$ ion. The thermodynamic and magnetic properties are thus mainly determined by the crystal-field splitting. It is shown here that magnetic-susceptibility, specific-heat, and thermal-expansion data can be explained satisfactorily with one crystal-field Hamiltonian.

Thermodynamic properties of superconductors containing impurities in a crystal-field singlet ground state

Experimental results on superconducting and magnetic properties of ${\mathrm{La}}_{3}$In and ${\mathrm{La}}_{3}$Tl containing magnetic impurities are presented and discussed. From magnetic susceptibility and low-temperature specific heat we conclude that ${\mathrm{Pr}}^{3+}$ substituted for ${\mathrm{La}}^{3+}$ in these compounds is in a crystal-field singlet ground state; this also explains the characteristic behavior of the superconducting transition temperature as a function of the Pr concentration. The upper critical field of ${({\mathrm{La}}_{1\ensuremath{-}x}{\mathrm{Pr}}_{x})}_{3}$ In is limited by the mean exchange field due to the Pr ions which are polarized in the external magnetic field. At Pr concentrations higher than $x=0.90$ the system ${({\mathrm{La}}_{1\ensuremath{-}x}{\mathrm{Pr}}_{x})}_{3}$ In shows a transition to a self-polarized antiferromagnetic state at low temperatures.

Theory of collective magnetic excitations in strong crystal fields. II. Application toS=1singlet ground-state ferromagnet

The theory of collective magnetic excitations based upon the set of Green's functions of angular momentum spherical tensor operators is applied to the exchange-coupled ($S=1$) magnet with a singlet crystal-field ground state. The spin Hamiltonian is brought to an approximately diagonal form via a unitary transformation by a spin operator functional, the best single-site approximation being located variationally. This enables the set of equations of motion for the Green's tensor to be linearized by conventional techniques. The essential features of induced-moment systems are clarified and displayed in the theory and numerical calculations, respectively. In particular, soft-mode behaviors at the second-order phase transition to ferromagnetism, mode-mode interactions, and a lack of temperature dependence for the excitation energies except at small wave vectors are evident. The nature of the phase transition is examined in detail and a relationship between the divergence of the static susceptibility and the soft-mode behavior is derived from the unitary transformation to pseudospace.

Electronic properties of beryllides of the rare earth and some actinides

A magnetic study has been conducted of 17 beryllides of the form $M{\mathrm{Be}}_{13}$, $M$ being a rare earth, Th, U, and an alloy ${\mathrm{La}}_{0.75}$${\mathrm{Tm}}_{0.25}$. Specific-heat studies were also made for $M=\mathrm{L}\mathrm{a},\phantom{\rule{0ex}{0ex}}\mathrm{P}\mathrm{r},\phantom{\rule{0ex}{0ex}}\mathrm{S}\mathrm{m},\phantom{\rule{0ex}{0ex}}\mathrm{T}\mathrm{m},\phantom{\rule{0ex}{0ex}}\mathrm{L}\mathrm{u},\phantom{\rule{0ex}{0ex}}\mathrm{T}\mathrm{h},\phantom{\rule{0ex}{0ex}}\mathrm{a}\mathrm{n}\mathrm{d}\phantom{\rule{0ex}{0ex}}\mathrm{U}$. A thorough crystal-field analysis is presented for Pr${\mathrm{Be}}_{13}$, Tm${\mathrm{Be}}_{13}$, both ions being in a crystal-field singlet ground state, and the expected nuclear cooling and ordering behavior is also thoroughly discussed.