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Formulas are derived that express the contributions of the electric quadrupole-quadrupole and dipole-octupole forces, respectively, to the dispersion energy of two unexcited molecules possessing axial symmetry. The formulas are valid in situations where the optical dispersion curve of each molecule is adequately characterized by a pair of resonance frequencies.
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The pyrochlore magnet Ce 2 Zr 2 O 7 has attracted much attention as a quantum spin ice candidate whose novelty derives in part from the dipolar-octupolar nature of the Ce 3+ pseudospin-1/2 degrees of freedom it possesses. We report heat capacity measurements on single crystal samples of Ce 2 Zr 2 O 7 down to T~0.1K in a magnetic field along the [$1,\bar{1},0$] direction. These measurements show that the broad hump in the zero-field heat capacity moves higher in temperature with increasing field strength and is split into two separate humps by the [$1,\bar{1},0$] magnetic field at ~2T. These separate features are due to the decomposition of the pyrochlore lattice into effectively decoupled chains for fields in this direction: One set of chains (α chains) is polarized by the field while the other (β chains) remains free. This situation is similar to that observed in the classical spin ices Ho 2 Ti 2 O 7 and Dy 2 Ti 2 O 7 , but with the twist that here the strong transverse exchange interactions produce substantial quantum effects. Our theoretical modeling suggests that the β chains are close to a critical state, with nearly-gapless excitations. We also report elastic and inelastic neutron scattering measurements on single crystal Ce 2 Zr 2 O 7 in [$1,\bar{1},0$] and [0,0,1] magnetic fields at temperatures down to T=0.03K. The elastic scattering behaves consistently with the formation of independent chains for a [$1,\bar{1},0$] field, while the [0,0,1] field produces a single field-induced elastic magnetic Bragg peak at (0,2,0) and equivalent wavevectors, indicating a polarized spin ice state for fields above ~3T. For both [$1,\bar{1},0$] and [0,0,1] magnetic fields, our inelastic neutron scattering results show an approximately dispersionless continuum of scattering that increases in both energy and intensity with increasing field strength. By modeling the complete set of experimental data using numerical linked cluster and semiclassical molecular dynamics calculations, we demonstrate the dominantly multipolar nature of the exchange interactions in Ce 2 Zr 2 O 7 and the smallness of the parameter θ, which controls the mixing between dipolar and octupolar degrees of freedom. Finally, these results support previous estimates of the microscopic exchange parameters and place strong constraints on the theoretical description of this prominent spin ice candidate.
The Ce 3+ pseudospin-1/2 degrees of freedom in Ce 2 Zr 2 O 7 possess both dipolar and octupolar character which enables the possibility of novel quantum spin liquid ground states in this material. In this study, we report muon spin relaxation and rotation (μSR) measurements on single-crystal samples of Ce 2 Zr 2 O 7 in zero magnetic field and in magnetic fields directed along the [1, $\overline{1}$, 0] and [1, 1, 1] crystallographic directions, and for magnetic fields directed both longitudinal and transverse to the direction of muon polarization. Our zero-field results show no signs of magnetic ordering or spin freezing, consistent with earlier zero-field μSR measurements on a powder sample of Ce 2 Zr 2 O 7 , and also with the expectations for a quantum spin ice. However, we measure a more gentle relaxation rate for Ce 2 Zr 2 O 7 in zero field at low temperatures than was previously reported. This difference in relaxation rate is likely due to the low oxidation and, correspondingly, the high stoichiometry of our singlecrystal samples. Longitudinal field measurements confirm that the magnetic dipole moments in Ce 2 Zr 2 O 7 remain dynamic at T = 0.1 K on the microsecond timescale. For both [1, $\overline{1}$, 0] and [1, 1, 1] magnetic fields, our μSR Knight shift measurements show a field-induced leveling off of the magnetic susceptibility at low temperature which is qualitatively consistent with corresponding calculations using the numerical-linked-cluster method in combination with recent estimates for the nearest-neighbor exchange parameters of Ce 2 Zr 2 O 7 .
The lifetime of the 2 + and 9 – , 11 – , 13 – , 15 – states in the neutron-deficient 110 Te was measured for the first time using the recoil distance Doppler shift technique. The reported value of the reduced transition probability B(E2; $0$$^{+}_{g.s}$ → 2 + ) = 4.3(8) × 10 3 e 2 fm 4 supports the systematic for even-mass Te isotopes and was interpreted in the framework of the large-scale shell model and cranked shell model calculations. The measured reduced transition probabilities in the negative-parity yrast band revealed the upward trend towards the high spins. Furthermore, the enhanced collectivity is discussed in terms of the tilted axis cranking approach and the symmetry configuration mixing method with the Gogny D1S interaction.
Here, in this erratum to our publication, [Phys. Rev. C 62,044303 (2000)], we report the corrections to the previous level scheme of 147,151 Pr and the physical influence of those changes and other typos in the original paper.
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The phenomenon of reflection-asymmetric nuclear shapes is relevant to nuclear stability, nuclear spectroscopy, nuclear decays and fission, and the search for new physics beyond the standard model. Global surveys of ground-state octupole deformation, performed with a limited number of models, suggest that the number of pear-shaped isotopes is fairly limited across the nuclear landscape. Here, we carry out a global analysis of ground-state octupole deformations for particle-bound even-even nuclei with Z ≤ 110 and N ≤ 210 using nuclear density functional theory (DFT) with several nonrelativistic and covariant energy density functionals. In this way, we can identify the best candidates for reflection-asymmetric shapes. The calculations are performed in the frameworks of axial reflection-asymmetric Hartree-Fock-Bogoliubov theory and relativistic Hartree-Bogoliubov theory using DFT solvers employing harmonic oscillator basis expansion. We consider five Skyrme and four covariant energy density functionals. We predict several regions of ground-state octupole deformation. In addition to the “traditional” regions of neutron-deficient actinide nuclei around 224 Ra and neutron-rich lanthanides around 146 Ba, we identified vast regions of reflection-asymmetric shapes in very neutron-rich nuclei around 200 Gd and 288 Pu, as well as in several nuclei around 112 Ba. Our analysis suggests several promising candidates with stable ground-state octupole deformation, primarily in the neutron-deficient actinide region, that can be reached experimentally. Detailed comparison between Skyrme and covariant models is performed. Octupole shapes predicted in this study are consistent with the current experimental information. This work can serve as the starting point of a systematic search for parity doublets in odd-mass and odd-odd nuclei, which will be of interest in the context of new physics searches.
In this paper, the averaged Hamiltonian of a nonrestricted hierarchical triple system truncated at the third order is investigated. First, each secular resonant term is studied. For the well-studied secular quadrupole theory, it is analytically reformulated in a different manner in our work. The resonance width is numerically determined and displayed on the √(1−e{sub 1}{sup 2})−√(1−e{sub 2}{sup 2}) plane (also denoted as the e-tilde {sub 1}− e-tilde {sub 2} plane). In terms of the octupole terms, we show that for a near-planar configuration of the system, considerable variations of both the eccentricities of the inner and outer orbits can be generated by a single resonant term. The resonance width for every secular resonant angle from the octupole terms is also numerically determined and displayed on the e-tilde {sub 1}− e-tilde {sub 2} plane. The results show that an orbit flip with a near-perpendicular initial mutual inclination is possible for each secular resonance. By displaying the resonance widths of different resonant terms on the same e-tilde {sub 1}− e-tilde {sub 2} plane, we intuitively show the overlap of different secular resonances. Then, the full averaged Hamiltonian with both quadrupole and octupole terms is investigated using the Poincaré surface of section, with a special focus on the orbit flip. For the cases we exploited, we find that the near-planar flip of the inner orbit can be either regular or chaotic while the outer orbit flip is generally chaotic.
Antiferromagnetic (AFM) materials are attracting tremendous attention due to their spintronic applications and associated novel topological phenomena. However, detecting and identifying the spin configurations in AFM materials are quite challenging due to the absence of net magnetization. Herein, we report the practicality of utilizing the planar Hall effect (PHE) to detect and distinguish “cluster magnetic multipoles” in AFM Nd 2 Ir 2 O 7 (NIO-227) fully strained films. By imposing compressive strain on the spin structure of NIO-227, we artificially induced cluster magnetic multipoles, namely dipoles and A 2 - and T 1 -octupoles. Importantly, under magnetic field rotation, each magnetic multipole exhibits distinctive harmonics of the PHE oscillation. Moreover, the planar Hall conductivity has a nonlinear magnetic field dependence, which can be attributed to the magnetic response of the cluster magnetic octupoles. Our work provides a strategy for identifying cluster magnetic multipoles in AFM systems and would promote octupole-based AFM spintronics.
Quantum spin liquid (QSL) is a disordered state of quantum-mechanically entangled spins commonly arising from frustrated magnetic dipolar interactions. However, QSL in some pyrochlore magnets can also come from frustrated magnetic octupolar interactions. Although the key signature for both dipolar and octupolar interaction-driven QSL is the presence of a spin excitation continuum (spinons) arising from the spin quantum number fractionalization, an external magnetic field-induced ferromagnetic order will transform the spinons into conventional spin waves in a dipolar QSL. By contrast, in an octupole QSL, the spin waves carry octupole moments that do not couple, in the leading order, to an external magnetic field or to neutron moments but will contribute to the field dependence of the heat capacity. Here, in this study, we use neutron scattering to show that the application of a large external magnetic field to Ce 2 Zr 2 O 7 , an octupolar QSL candidate, induces an Anderson-Higgs transition by condensing the spinons into a static ferromagnetic ordered state with octupolar spin waves invisible to neutrons but contributing to the heat capacity. Our theoretical calculations also provide a microscopic, qualitative understanding for the presence of octupole scattering at large wave vectors in Ce 2 Sn 2 O 7 pyrochlore, and its absence in Ce 2 Zr 2 O 7 . Therefore, our results identify Ce 2 Zr 2 O 7 as a strong candidate for an octupolar U(1) QSL, establishing that frustrated magnetic octupolar interactions are responsible for QSL properties in Ce-based pyrochlore magnets.
The presence of nuclear ground states with stable reflection-asymmetric shapes is supported by rich experimental evidence. Theoretical surveys of odd-multipolarity deformations predict the existence of pear-shaped isotopes in several fairly localized regions of the nuclear landscape in the vicinity of near-lying single-particle shells with Δℓ = Δj = 3. We analyze the role of isoscalar, isovector, neutron-proton, neutron-neutron, and proton-proton multipole interaction energies in inducing the onset of reflection-asymmetric ground-state deformations. The calculations are performed in the framework of axial reflection-asymmetric Hartree-Fock-Bogoliubov theory using two Skyrme energy-density functionals and density-dependent pairing force. We show that reflection-asymmetric ground-state shapes of atomic nuclei are driven by the odd-multipolarity neutron-proton (or isoscalar) part of the nuclear interaction energy. This result is consistent with the particle-vibration picture, in which the main driver of octupole instability is the isoscalar octupole-octupole interaction giving rise to large E3 polarizability. The necessary condition for the appearance of localized regions of pear-shaped nuclei in the nuclear landscape is the presence of parity doublets involving Δℓ = Δj = 3 proton or neutron single-particle shells. This condition alone is, however, not sufficient to determine whether pear shapes actually appear, and, if so, what the corresponding reflection-asymmetric deformation energies are. The predicted small reflection-asymmetric deformation energies result from dramatic cancellations between even- and odd-multipolarity components of the nuclear binding energy.
Lead-208 is the heaviest known doubly magic nucleus and its structure is therefore of special interest. Despite this magicity, which acts to provide a strong restorative force toward sphericity, it is known to exhibit both strong octupole correlations and some of the strongest quadrupole collectivity observed in doubly magic systems. In this Letter, we employ state-of-the-art experimental equipment to conclusively demonstrate, through four Coulomb-excitation measurements, the presence of a large, negative, spectroscopic quadrupole moment for both the vibrational octupole 3$^{−}_{1}$ and quadrupole 2$^{+}_{1}$ state, indicative of a preference for prolate deformation of the states. The observed quadrupole moment is discussed in the context of the expected splitting of the 3 − ⊗3 − two-phonon states, due to the coupling of the quadrupole and octupole motion. These results are compared with theoretical values from three different methods, which are unable to reproduce both the sign and magnitude of this deformation. Thus, in spite of its well-studied nature, 208 Pb remains a puzzle for our understanding of nuclear structure.