Quadrupole Pairing Interaction Research Articles

Quadrupolar couplings and magnetic phase diagrams in tetragonal TmAu2

The occurrence of a quadrupolar ordering within the γ orthorhombic symmetry at 7 K in TmAu2 (MoSi2-type tetragonal structure) was recently discovered with properties closely reminiscent of the ones observed in isomorphous TmAg2. Both the magnetoelastic couplings and the quadrupolar pair interactions are here determined by means of third-order magnetic susceptibility and parastriction measurements. The existence of an antiferromagnetic ordering around 3 K in the quadrupolar phase leads to complex magnetic phase diagrams in the (H,T) plane, which have been established along the main crystallographic directions of the tetragonal cell and appear to result from the balance between magnetic and quadrupolar interactions.

Microscopic description of high-spin states: Quantum-number projections of the cranked Hartree-Fock-Bogoliubov self-consistent solution

Quantum-number projection is applied to generate exact eigenstates of angular momentum or of particle numbers from the self-consistent solution of the angular-momentum- and particle-number-constrained Hartree-Fock-Bogoliubov (CHFB) equation. Calculations are based on the symmetry-conserving microscopic Hamiltonian and the large single-particle space spanned by spherical Nilsson bases covering about 1.5 major shells for both protons and neutrons in the case of the yrast bands for ${}^{158,164,168}\mathrm{Er}$ and almost three major shells in the case of the superdeformed bands as well as g and s bands for ${}^{132}\mathrm{Ce}.$ The residual interaction is given by the monopole- and quadrupole-pairing interactions plus the quadrupole-quadrupole interaction. Symmetry properties of the Hamiltonian are fully taken into account through both stages of solving the CHFB equation and projections to reduce computational time substantially. A great mixture of angular momentum components requires the projection while particle-number projections become less important at high spins, especially along superdeformed bands with vanishingly small static gaps. It is shown that the angular momentum projection is effective to reproduce $K=0$ superdeformed levels appearing in the yrast band together with the g and s bands.

Nuclear shell model and interacting boson fermion approximation

Abstract The Interacting Boson-Fermion Model (IBFM) hamiltonian is derived starting from the shell-model interaction, by a straightforward extension of the Otsuka, Arima and Iachello mapping procedure to odd-mass systems. Employing a single j -shell model and identical many nucleon systems, systematic studies of spectra giving the comparison in the shell-model, SD pair truncated model and IBFM are carried out: (i) for various proportions of monopole pairing and Q · Q interactions which simulate vibrational-rotational transition; (ii) for a particular combination of these interactions together with the quadrupole pairing interaction, which conserves seniority.

Microscopic analysis of collective states in neutron-deficient doubly even xenon isotopes.

The low-lying collective states of xenon isotopes are studied by means of the boson expansion theory. The microscopic Hamiltonian is comprised of the self-consistent QQ interaction with higher-order (three- and four-body) terms, monopole- and quadrupole-pairing interactions in addition to the spherical limit of the Nilsson Hamiltonian. It is shown that the difficulty of weak strengths of the monopole-pairing interaction in this region, indicated by Rohozi\ifmmode \acute{n}\else \'{n}\fi{}ski et al., can be naturally remedied by including the quadrupole-pairing interactions.

Blocking effects at super-deformed shape

The strongly reduced blocking effect in the supper-deformed HgPb region is investigated by means of the cranked Strutinsky pairing and deformations selfconsistent Lipkin-Nogami approach including both monopole and quadrupole pairing interaction. The simultaneous reduction of monopole and quadrupole pair correlations due to blocking has opposite effect on the dynamical moments of inertia. This provides an additional cancellation mechanism that levels out the difference between odd and even nuclei.

Extended mean field description of deformed states in neutron deficient Cd- and Sn-nuclei

Extensions to the standard total routhian surface calculations are presented. The particle number symmetry is approximately restored using the Lipkin-Nogami method to avoid the well known problems of sharp pairing phase transitions, that are predicted by mean-field calculations in the vicinity of closed shells or in the high-spin regime. Secondly, the quadrupole pairing interaction is added to the standard seniority pairing to account for an improved treatment of particle-particle correlations. The method is applied to the analysis of collective rotational bands found in neutron deficient Cd, In, Sn, Sb and Te isotopes.

Anomalous crossing frequency in odd proton nuclei.

A generic explanation for the recently observed anomalous crossing frequencies in odd proton rare earth nuclei is given. As an example, the proton 1/2[541] band in $^{175}\mathrm{Ta}$ is discussed in detail by using the angular momentum projection theory. It is shown that the quadrupole pairing interaction is decisive in delaying the crossing point and the changes in crossing frequency along the isotope chain are due to the different neutron shell fillings.

Magnetic and elastic properties in the paramagnetic state of NdIn 3 antiferromagnet

The cubic AuCu 3 type system NdIn 3 exhibits complex magnetic structures at low temperature. Immediately below the Néel temperature, T N = 6 K, the spins assume a sine wave modulated arrangement; for 5.5 K > T > 4.7 K, the modulation tends towards a square wave. Finally, below 4.7 K, a simple commensurate structure is stabilized. We first confirm here the complex magnetic phase diagram by means of resistivity measurements. In order to quantitatively understand the low temperature properties, the crystalline electric field is determined by inelastic neutron spectroscopy. An extensive study of the magnetic, magnetoelastic and quadrupolar properties in the paramagnetic phase by magnetization, ultrasonic velocity and parastriction measurements is then presented. The values of one-ion magnetoelastic coefficients agree with previous determinations in isomorphous systems. Quadrupolar pair interactions are found to be positive for the tetragonal symmetry lowering mode, in agreement with the symmetry of collinear magnetic structures. However the only quadrupolar model fails to coherently describe the whole set of paramagnetic properties, in particular the third order magnetic susceptibility. The existence of two-ion magnetoelasticity is then discussed in relation to the ultrasonic velocity and parastriction results. The description of the magnetic phase diagrams will be reported elsewhere.

Quadrupolar ordering in tetragonal TmAg2.

The occurrence of a nonmagnetic transition at 5 K in ${\mathrm{TmAg}}_{2}$ (${\mathrm{MoSi}}_{2}$-type tetragonal symmetry) is analyzed as a ferroquadrupolar ordering within the orthorhombic \ensuremath{\gamma}-symmetry-lowering mode. The crystalline-electric-field parameters are obtained by inelastic-neutron-scattering and magnetic-susceptibility measurements. Both the magnetoelastic couplings and the quadrupolar pair interactions are then determined by third-order magnetic-susceptibility, parastriction, and ultrasonic-velocity experiments. The great coherency between these determinations allows us to understand completely the magnetic properties in both the orthorhombic and tetragonal phases. ${\mathrm{TmAg}}_{2}$ is then an archetype for compounds ruled by quadrupolar interactions.

Indirect multipolar interactions in rare-earth metals and alloys (abstract)

The presence of large quadrupolar interactions was observed in some rare-earth conducting systems such as DySb, TmCd, TmZn, DyZn.1 In this work, we present the results of an extensive ab initio calculation of the indirect pair interactions between rare-earth ions in transition metals arising from the polarization of the electric-multipole distribution of the conduction electrons. The effective Hamiltonian of the indirect quadrupolar pair interactions is constructed self-consistently, taking into consideration antishielding and band-structure effects in the system of conduction electrons, as well as the crystal field splitting of the rare-earth ion. Slater–Koster fits to first principles energy bands are employed to accurately account for the band-structure effects. The peculiarities of each intraband or interband contribution to the Fourier transforms of the indirect couplings as well as the role played by each type of the d electrons in the conduction band are investigated. The experimental data are discussed.2

Symmetry breaking of the galilean invariance in superfluid nuclei and its connection with quadrupole pairing interactions

Effects due to quadrupole-pairing interactions are analyzed in the context of a self-consistent symmetry-restoring mdoel. It is shown that the breaking of a multipole galilean invariance leads to results which are similar to the ones obtained by including quadrupole-pairing forces in the interaction among quasiparticle pairs. The model is applied to the description of low-lying quadrupole excitations in even-mass Sn-isotopes.

Quadrupolar properties and magnetic phase diagrams in PrB 6 hexaboride compound

The magnetoelastic and quadrupolar properties of the hexaboride compound PrB 6 are determined by measurements of the elastic constants, the parastriction and the third-order magnetic susceptibility. The magnetoelastic effects are sizeable only for the trigonal symmetry lowering mode. The quadrupolar pair interactions are negative in the paramagnetic phase in agreement with the multiaxial spin structure stabilized at low temperature by antiferroquadrupolar interactions. The quadrupolar couplings seem to coexist with additional terms. Spin fluctuations are in particular present above the Néel temperature. The quadrupolar interactions do not appear to be responsible for the first-order magnetic transition. The magnetic phase diagrams have been build for the three main crystallographic directions of the cubic cell. They exhibit at low field a transition from the double- k structure to the simple- k one, which was previously observed along the twofold axis by neutron diffraction. Only weak field-dependences of the Néel temperature and of the commensurate-incommensurate phase transition temperature have been observed.

Interplay of antiferromagnetic and antiferroquadrupolar interactions in DyAg and other rare earth intermetallic compounds

The study of the magnetoelasticity of the cubic (CsCl-type) rare earth intermetallic DyAg allows us to determine the strength of both the magnetoelastic coupling and the quadrupolar pair interactions. These latter ones are observed to be negative (antiferroquadrupolar type) for the tetragonal symmetry as well as for the trigonal one. They drive the magnetic structure to be triple- q at low temperature: the cubic magnetic cell consists of four pairs of ferromagnetic moments pointing along each of the treefold axes. At high temperature, it is replaced by a double- q structure, then, immediately below T N, by a modulated arrangement. The magnetization processes have been thoroughly studied along the three main axes in fields up to 40 T and compared with previous results in isomorphous DyCu and in the AuCu 3-type compound TmGa 3. The sequences under field of the different magnetic structures are identical and mainly determined by the crytalline electric field and the antiferroquadrupolar interactions. These 3 compounds do not set a peculiar case, but seem to belong to a larger family of cubic compounds with multiaxial structures governed by antiferroquadrupolar terms.

Interaction strengths in the interacting boson-fermion model.

Although a number of different types of boson-fermion interactions are possible in the interacting boson-fermion model, empirical results have shown that the exchange term is of cardinal importance. A recently constructed similarity transformation which reexpresses the Dyson boson images of the single-j shell fermion operators in terms of seniority bosons is used to confirm that the origin of the exchange term in spherical nuclei is linked to the quadrupole pairing interaction between identical nucleons. The relative importance of the exchange and direct boson-fermion interactions is also discussed and it is indicated that the direct term is essential for a complete description of that excited state which carries the j value of the shell.

Microscopic Description of Anharmonic Gamma-Vibrations by Means of the Selfconsistent-Collective-Coordinate Method. III

Properties of the anharmonic gamma-vibrations and their (N, Z)-dependence are investigated in a wide region of the rare-earth deformed nuclei. The effective Hamiltonian which contains, in addition to the monopole-pairing plus (doubly-stretched) quadrupole-quadrupole interactions, the quadrupole-pairing interaction and the effective three-body force is used in the microscopic calculation. Dynamical anharmonicity effects arising from the mode-mode couplings are analysed in detail in relation to these effective interactions. The couplings between the gamma-vibrations and the pairing rotations are also taken into account in order to recover the nucleon-number consevation. The numerical calculation indicates that the properties of the anharmonic gamma-vibrations significantly change from one nucleus to another reflecting the subshell structure near the Fermi surface. A characteristic (N, Z)-dependence of the double gamma-vibrational states is predicted for some Dy and Er isotopes.

Anisotropy in the paramagnetic phase of RAl2 cubic intermetallic compounds (R=Tb, Dy, and Er).

In this paper it is shown that the anisotropy in the paramagnetic phase is a useful characteristic when used to single out high-rank susceptibility tensor components in the paramagnetic regime of cubic crystals. Application of this technique to RAl/sub 2/ compounds (R = Tb,Dy,Er) allows the determination of longitudinal and transverse (in the form of linear combinations) fourth- and sixth-rank paramagnetic susceptibilities. The use of the fourth-rank longitudinal susceptibility allows quadrupolar pair interactions in these compounds to be probed.

Shell-model evidence for the exchange term in the interacting-boson-fermion Hamiltonian.

The shell-model origin of the exchange term in the interacting-boson-fermion Hamiltonian is studied. The quadrupole pairing interaction is shown to be the dominant source in and near spherical regions of the Periodic Table. The strength of this term calculated for the 0${g}_{9/2}$ orbit turns out to be in good agreement with the phenomenological fit.

Magnetic properties of equiatomic rare earth cadmium compounds

The magnetization processes obtained in monocrystalline samples are presented for the ferromagnetic compounds of the equiatomic rare earth cadmium series. They are discussed in terms of crystalline electric field and bilinear and quadrupolar pair interactions. A close similarity appears with the isomorphous series with zinc. The importance of quadrupolar interactions is emphasized. They are, for instance, strong enough in DyCd to enforce the fourfold axis as easy magnetization direction instead of the threefold one which would be driven by the only crystalline electric field. A discussion of the magnetic properties of dysprosium compounds having the CsCl-type structure is then given.

Magnetic and structural transitions in TmGa 3

We have established for TmGa 3 the occurrence of two close lying first-order transitions. The first transition at T Q = 4.29 K drives the compound to a distorted phase and the second one at T N = 4.26 K to an antiferromagnetic state. They are pushed apart markedly by an applied magnetic field. In the whole temperature range of the ordering we have observed a first-order field-induced metamagnetic transition along the 〈100〉 direction. The temperature variation of the reciprocal susceptibility gives magnetic Γ (5) 5 as the ground state. It is well known that the Γ 5 ground state of a Tm 3+ ion leads to a strong first-order structural transition in TmCd and TmZn intermetallics. Therefore we may assume that the structural transition in TmGa 3 has the same origin as in the compounds mentioned above. This transition is driven by quadrupolar pair interactions. The lattice follows the quadrupoles and distorts in such a way as to minimize the Jahn-Teller coupling energy.

Phase diagrams and magnetic excitations in holmium phosphide.

New neutron scattering studies were made on holmium phosphide (HoP) in order to resolve existing ambiguities. Neutron-diffraction investigations were performed on single-crystal and powdered samples of HoP in external fields up to 40 kOe as well as in zero field. In addition to obtaining phase diagrams, we have determined that the easy directions of magnetization are 〈100〉 in the ferromagnetic and paramagnetic states. Depending on the history of the samples, structural defects presumably of Schottky type tend to shorten the range of magnetic order. Inelastic neutron scattering was used to measure the magnetic excitation spectrum of HoP in the flopside phase. Four spin-wave branches were found which are almost independent of wave vector. The results are analyzed in terms of a mean-field Hamiltonian containing a crystal field and the effects of bilinear and quadrupolar pair interactions. On the basis of the resulting model parameters, we are able to explain the salient features of the magnetic behavior of HoP, in particular, the appearance of first the ferromagnetic and then the flopside phases, and the variations with fields of the paramagnetic-flopside transitions and the flopside-ferromagnetic transitions.