Magnetic Octupole Moments Research Articles

Laser spectroscopy of 176Lu+

We perform high-resolution spectroscopy on Lu including the and clock transitions. Hyperfine structures and optical frequencies relative to the ground state of four low-lying excited states are given to a few tens of kHz resolution. This covers the most relevant transitions involved in clock operation with this isotope. Additionally, measurements of the hyperfine structure may provide access to higher order nuclear moments, specifically the magnetic octupole and electric hexadecapole moments.

Chiral Soliton Lattice Formation in Monoaxial Helimagnet Yb(Ni1−xCux)3Al9

Helical magnetic structures and its responses to external magnetic fields in Yb(Ni$_x$Cu$_{1-x}$)$_3$Al$_9$, with a chiral crystal structure of the space group $R32$, have been investigated by resonant X-ray diffraction. It is shown that the crystal chirality is reflected to the helicity of the magnetic structure by a one to one relationship, indicating that there exists an antisymmetric exchange interaction mediated via the conduction electrons. When a magnetic field is applied perpendicular to the helical axis ($c$ axis), the second harmonic peak of $(0, 0, 2q)$ develops with increasing the field. The third harmonic peak of $(0, 0, 3q)$ has also been observed for the $x$=0.06 sample. This result provides a strong evidence for the formation of a chiral magnetic soliton lattice state, a periodic array of the chiral twist of spins, which has been suggested by the characteristic magnetization curve. The helical ordering of magnetic octupole moments, accompanying with the magnetic dipole order, has also been detected.

John Gordon King

John Gordon King

Observation of the nuclear magnetic octupole moment of173Yb from precise measurements of the hyperfine structure in the3P2state

We measure hyperfine structure in the metastable ${{}^{3}P}_{2}$ state of ${}^{173}$Yb and extract the nuclear magnetic octupole moment. We populate the state using dipole-allowed transitions through the ${{}^{3}P}_{1}$ and ${{}^{3}S}_{1}$ states. We measure frequencies of hyperfine transitions of the ${{}^{3}P}_{2}\ensuremath{\rightarrow}{{}^{3}S}_{1}$ line at 770 nm using a Rb-stabilized ring cavity resonator with a precision of 200 kHz. Second-order corrections due to perturbations from the nearby ${{}^{3}P}_{1}$ and ${{}^{1}P}_{1}$ states are below 30 kHz. We obtain the hyperfine coefficients as $A=\ensuremath{-}742.11(2)$ MHz and $B=1339.2(2)$ MHz, which represent a two orders-of-magnitude improvement in precision, and $C=0.54(2)$ MHz. From atomic structure calculations, we obtain the nuclear moments quadrupole $Q=2.46(12)$ b and octupole $\ensuremath{\Omega}=\ensuremath{-}34.4(21)$ $\mathrm{b}\ifmmode\times\else\texttimes\fi{}{\ensuremath{\mu}}_{N}$.

Time-Reversal Symmetry Breaking and Consequent Physical Responses Induced by All-In-All-Out Type Magnetic Order on the Pyrochlore Lattice

The physical properties of pyrochlore compounds with the all-in-all-out type arrangement of magnetic moments are discussed. The magnetic order can be regarded as a ferroic order of magnetic octupole moments, which does not give rise to macroscopic magnetization but breaks the time-reversal symmetry. As a result of the time-reversal symmetry breaking, the magnetostriction, magnetocapacitance, Voigt magnetooptic effect, and magnetic susceptibility are expected to have a term linear to the external magnetic field. Another striking consequence of the magnetic order is the presence of spontaneous magnetization and scalar spin chirality on the most stable {111} surfaces. This may pave the way for unique surface magnetotransport phenomena.

Spectroscopy on a single trapped ^137Ba^+ ion for nuclear magnetic octupole moment determination

We present precision measurements of the hyperfine intervals in the 5D3/2 manifold of a single trapped Barium ion, 137 Ba+ . Measurements of the hyperfine intervals are made between mF = 0 sublevels over a range of magnetic fields allowing us to interpolate to the zero field values with an accuracy below a few Hz, an improvement on previous measurements by three orders of magnitude. Our results, in conjunction with theoretical calculations, provide a 30-fold reduction in the uncertainty of the magnetic dipole (A) and electric quadrupole (B) hyperfine constants. In addition, we obtain the magnetic octupole constant (C) with an accuracy below 0.1 Hz. This gives a subsequent determination of the nuclear magnetic octupole moment, {\Omega}, with an uncertainty of 1% limited almost completely by the accuracy of theoretical calculations. This constitutes the first observation of the octupole moment in 137 Ba+ and the most accurately determined octupole moment to date.

Neptunium multipoles and resonant x-ray Bragg diffraction by neptunium dioxide (NpO2)

The low-temperature ordered state of neptunium dioxide (NpO2) remains enigmatic. After decades of experimental and theoretical efforts, long-range order of a time-odd (magnetic) high-order atomic multipole moment is now generally considered to be the fundamental order parameter, the most likely candidate being a magnetic triakontadipole (rank 5). To date, however, direct experimental observation of the primary order parameter remains outstanding. In the light of new experimental findings, we re-examine the effect of crystal symmetry on the atomic multipoles and the resulting x-ray resonant scattering signature. Our simulations use the crystallographic point group (D3d), because corresponding magnetic groups , and are shown by us to be at odds with a wealth of experimental results. In addition to the previously observed (secondary) quadrupole order, we derive expressions for higher-order multipoles that might be observed in future experiments. In particular, magnetic octupole moments are predicted to contribute to Np M2,3 and L2,3 resonant scattering via E2–E2 events. The Lorentzian-squared lineshape observed at the M4 resonance is shown to be the result of the anisotropy of the 3p3/2 core levels. Quantitative comparison of our calculations to the measured data yields a core–hole width Γ = 2.60(7) eV and a core-state exchange energy eV.

Coherent excitation of the6S1/2to5D3/2electric-quadrupole transition in138Ba+

The electric dipole-forbidden, quadrupole 6S1/2 <-> 5D3/2 transition in Ba+ near 2051 nm, with a natural linewidth of 13 mHz, is attractive for potential observation of parity non-conservation, and also as a clock transition for a barium ion optical frequency standard. This transition also offers a direct means of populating the metastable 5D3/2 state to measure the nuclear magnetic octupole moment in the odd barium isotopes. Light from a diode-pumped, solid state Tm,Ho:YLF laser operating at 2051 nm is used to coherently drive this transition between resolved Zeeman levels in a single trapped 138Ba+ ion. The frequency of the laser is stabilized to a high finesse Fabry Perot cavity at 1025 nm after being frequency doubled. Rabi oscillations on this transition indicate a laser-ion coherence time of 3 ms, most likely limited by ambient magnetic field fluctuations.

Ring-Exchange Interaction in Doubly Degenerate Orbital System

Ring-exchange (RE) interaction in Mott insulator with doubly degenerate $e_g$ orbitals is studied. Hamiltonian for the RE interaction is derived by the perturbational calculation. A remarkably weak RE interaction destroys the orbital order caused by the order-by-fluctuation mechanism in the nearest-neighbor exchange-interaction model. A long range order of magnetic octupole moment, i.e. complex orbital wave functions, appears. Competition between octupole and quadrupole interactions strongly suppresses ordered moments.

Electric quadrupole and magnetic octupole moments of the light decuplet baryons within light cone QCD sum rules

The electric quadrupole and magnetic octupole moments of the light decuplet baryons are calculated in the framework of the light cone QCD sum rules. The obtained non-vanishing values for the electric quadrupole and magnetic octupole moments of these baryons show nonspherical charge distribution. The sign of electric quadrupole moment is positive for Ω−, Ξ∗−, Σ∗− and negative for Σ∗+, which correspond to the prolate and oblate charge distributions, respectively. A comparison of the obtained results with the predictions of non-covariant quark model which shows a good consistency between two approaches is also presented. Comparison of the obtained results on the multipole moments of the decuplet baryons containing strange quark with those of Δ baryons shows a large SU(3) flavor symmetry breaking.

Electromagnetic structure of decuplet baryons towards the chiral regime

The electromagnetic properties of the baryon decuplet are calculated in quenched QCD on a 20^3 x 40 lattice with a lattice spacing of 0.128 fm using the fat-link irrelevant clover (FLIC) fermion action with quark masses providing a pion mass as low as 300 MeV. Magnetic moments and charge radii are extracted from the electric and magnetic form factors for each individual quark sector. From these, the corresponding baryon properties are constructed. We present results for the higher order moments of the spin-3/2 baryons, including the electric quadrupole moment E2 and the magnetic octupole moment M3. The world's first determination of a non-zero M3 form factor for the Delta baryon is presented. With these results we provide a conclusive analysis which shows that decuplet baryons are deformed. We compare the decuplet baryon results from a similar lattice calculation of the octet baryons. We establish that the environment sensitivity is far less pronounced in the case of the decuplet baryons compared to that in the octet baryons. A surprising result is that the charge radii of the decuplet baryons are generally smaller than that of the octet baryons. The magnetic moment of the Delta^+ reveals a turn over in the low quark mass region, making it smaller than the proton magnetic moment. These results are consistent with the expectations of quenched chiral perturbation theory. A similar turn over is also noticed in the magnetic moment of the Sigma^*0, but not for Xi^* where only kaon loops can appear in quenched QCD. The electric quadrupole moment of the Omega^- baryon is positive when the negative charge factor is included, and is equal to 0.86 +- 0.12 x 10^-2 fm^2, indicating an oblate shape.

Electromagnetic structure of the lowest-lying decuplet resonances in covariant chiral perturbation theory

We present a calculation of the leading SU(3)-breaking $\mathcal{O}({p}^{3})$ corrections to the electromagnetic moments and charge radius of the lowest-lying decuplet resonances in covariant chiral perturbation theory. In particular, the magnetic dipole moment of the members of the decuplet is predicted fixing the only low-energy constant (LEC) present up to this order with the well-measured magnetic dipole moment of the ${\ensuremath{\Omega}}^{\ensuremath{-}}$. We predict ${\ensuremath{\mu}}_{\ensuremath{\Delta}}^{++}=6.04(13)$ and ${\ensuremath{\mu}}_{\ensuremath{\Delta}}^{+}=2.84(2)$, which agree well with the current experimental information. For the electric quadrupole moment and the charge radius, we use state-of-the-art lattice QCD results to determine the corresponding LECs, whereas for the magnetic octupole moment there is no unknown LEC up to the order considered here, and we obtain a pure prediction. We compare our results with those reported in large ${N}_{c}$, lattice QCD, heavy-baryon chiral perturbation theory, and other models.

Magnetic Field Induced4fOctupole inCeB6Probed by Resonant X-Ray Diffraction

A mysterious antiferroquadrupolar ordered phase of ${\mathrm{CeB}}_{6}$ is considered as originating from the ${T}_{xyz}$-type magnetic octupole moment in magnetic fields. By resonant x-ray diffraction, we have verified that the ${T}_{xyz}$-type octupole is indeed induced in the $4f$ orbital of Ce with a propagation vector $(\frac{1}{2},\frac{1}{2},\frac{1}{2})$, thereby supporting the theory. We observed an asymmetric field dependence of the intensity for an electric quadrupole ($E2$) resonance when the field was reversed and extracted a field dependence of the octupole by utilizing the interference with an electric dipole ($E1$) resonance. The result is in good agreement with that of the NMR-line splitting, which reflects the transferred hyperfine field at the boron nucleus from the anisotropic spin distribution of Ce with an ${O}_{xy}$-type quadrupole.

Electric quadrupole and magnetic octupole moments of the Δ

Using a covariant spectator constituent quark model we predict an electric quadrupole moment QΔ+=−0.043efm2 and a magnetic octupole moment OΔ+=−0.0035efm3 for the Δ+ excited state of the nucleon.

Magnetic dipole, electric quadrupole and magnetic octupole moments of the Δ baryons in light cone QCD sum rules

Due to the very short life time of the Δ baryons, a direct measurement on the electromagnetic moments of these systems is almost impossible in the experiment and can only be done indirectly. Although only for the magnetic dipole moments of Δ ++ and Δ + systems there are some experimental data, the theoretical, phenomenological and lattice calculations could play crucial role. In the present work, the magnetic dipole (μ Δ ), electric quadrupole (Q Δ ) and magnetic octupole (O Δ ) moments of these baryons are computed within the light cone QCD sum rules. The results are compared with the predictions of the other phenomenological approaches, lattice QCD and existing experimental data.

Observation of the nuclear magnetic octupole moment of 87Rb from spectroscopic measurements of hyperfine intervals

The magnetic octupole moment of 87Rb is determined from hyperfine intervals in the 5p 2P3/2 state measured by Ye et al. Opt. Lett. 21, 1280 (1996). Hyperfine constants A = 84.7189(22) MHz, B = 12.4942(43) MHz, and C = –0.12(09) kHz are obtained from the published measurements. The existence of a significant value for C indicates the presence of a nuclear magnetic octupole moment Ω. Combining the hyperfine constants with atomic structure calculations, we obtain Ω = –0.58(39) bμN. Second-order corrections arising from the interaction with the nearby 5p 2P1/2 state are found to be insignificant.PACS Nos.: 21.10.Ky, 32.10.Fn, 42.62.Fi

Baryon octupole moments⋆

We report on a calculation of higher electromagnetic multipole moments of baryons in a non-covariant quark model approach. The employed method is based on the underlying spin-flavor symmetry of the strong interaction and its breaking.We present results on magnetic octupole moments of decuplet baryons and discuss their implications.

Hyperfine structure of the metastableP32state of alkaline-earth-metal atoms as an accurate probe of nuclear magnetic octupole moments

Measuring the hyperfine structure (HFS) of long-lived ${^{3}P}_{2}$ states of divalent atoms may offer the opportunity of extracting relatively unexplored nuclear magnetic octupole and electric hexadecapole moments. Here, using relativistic many-body methods of atomic structure and the nuclear shell model, we evaluate the effect of these higher nuclear moments on the hyperfine structure. We find that the sensitivity of HFS interval measurements in $^{87}\text{S}\text{r}$ needed to reveal the perturbation caused by the nuclear octupole moment is on the order of kHz. The results of similar analyses for $^{9}\text{B}\text{e}$, $^{25}\text{M}\text{g}$, and $^{43}\text{C}\text{a}$ are also reported.

Microscopic aspects of multipole properties of filled skutterudites

We discuss low-temperature multipole states of Nd-based filled skutterudites by analyzing a multiorbital Anderson model with the use of a numerical renormalization group method. In order to determine the multipole state, we take a procedure to maximize the multipole susceptibility matrix. Then, it is found that the dominant multipole state is characterized by the mixture of 4u magnetic and 5u octupole moments. The secondary state is specified by 2u octupole. When we further take into account the coupling between f electrons in degenerate Γ 67 - ( e u ) orbitals and dynamical Jahn–Teller phonons with E g symmetry, quadrupole fluctuations become significant at low temperatures in the mixed multipole state with 4u magnetic and 5u octupole moments. Finally, we briefly discuss possible relevance of the present results to actual Nd-based filled skutterudite compounds.

Multipole Susceptibility of Multiorbital Anderson Model Coupled with Jahn–Teller Phonons

In order to clarify possible multipole states of Sm-based filled skutterudite compounds, we investigate multipole susceptibility of a multiorbital Anderson model dynamically coupled with Jahn–Teller phonons by using a numerical renormalization group method. Here we take a procedure to maximize the multipole susceptibility matrix to determine the multipole state. When the electron–phonon coupling term is simply ignored, it is found that the dominant multipole state is characterized by 2u octupole for the Γ 67 - quartet ground state, while the low-temperature phase is governed by magnetic fluctuations for the Γ 5 - doublet ground state. When we include the coupling between f electrons in degenerate Γ 67 - ( e u ) orbitals and Jahn–Teller phonons with E g symmetry, the mixed multipole state with 4u magnetic and 5u octupole moments is found to be dominant with significant 3g quadrupole fluctuations at low temperatures.