Octupolar Components Research Articles

Pseudofermion functional renormalization group study of dipolar-octupolar pyrochlore magnets

Motivated by recent experiments on Ce2Zr2O7 that reveal a dynamic, liquidlike ground state, we study the nearest-neighbor XYZ Hamiltonian of dipolar-octupolar pyrochlore magnets with the pseudofermion functional renormalization group (PFFRG), which is numerically implemented by the software. Taking the interaction between the octupolar components to be dominant and antiferromagnetic, we map out the phase diagram demarcating the quantum disordered and magnetically ordered states. We identify four distinct phases, namely, the 0-flux and π-flux quantum spin ices and the all-in-all-out magnetic orders along the local z and x axes. We further use the static two-spin correlation output by the PFFRG algorithm to compute the polarized neutron scattering cross sections, which are able to capture several qualitative features observed experimentally, in the materially relevant parameter regime that stabilizes the π-flux quantum spin ice. Our results provide support for a quantum spin-liquid ground state in Ce2Zr2O7. Published by the American Physical Society 2024

Excitation of the σl_l = 90° resonance by the cavity rf accelerating fields

In rf linacs the longitudinal focalization is done by si-nusoidal forces and at high accelerating fields the zero-current longitudinal phase advance per longitudinal fo-cusing period σ0l_l can be high. The nonlinear compo-nents of the sinusoidal rf field (sextupolar, octupolar and higher order components) can then excite parametric resonances, including the 4th-order resonance (σl_l = 90°) when σ0l_l is higher than 90°, inducing strong longitudinal emittance growths and acceptance reductions. As pointed out in previous papers, the longitudinal beam dynamics is therefore complex, even when the space-charge forces are ignored. The parametric resonance excitation by the rf field is analyzed before discussing the additional effect of the space-charge forces, in particular to explain why the zero-current longitudinal phase advance per trans-verse focusing period σ0l_t is not a relevant parameter. Examples are given in the SPIRAL2 linac case.

Distinguishing dipolar and octupolar quantum spin ices using contrasting magnetostriction signatures

Recently there have been a number of experiments on Ce$_2$Zr$_2$O$_7$ and Ce$_2$Sn$_2$O$_7$, suggesting that these materials host a three-dimensional quantum spin liquid with emergent photons and fractionalized spinon excitations. However, the interpretation of the data to determine the precise nature of the quantum spin liquids is still under debate. The Kramers doublet in Ce$^{3+}$ local moment offers unusual pseudo-spin degrees of freedom as the $x$ and $z$ components transform as a dipole and $y$ component as an octupole. This leads to a variety of possible quantum spin liquid (or quantum spin ice) phases on the pyrochlore lattice of Ce$^{3+}$ moments. In this work, we theoretically propose that magnetostriction would be able to distinguish the dipolar (D-QSI) and octupolar (O-QSI) quantum spin ice, where the dipolar or octupolar components possess the respective spin ice correlations. We show that the magnetostriction in various configurations can be used as a selection rule to differentiate not only D-QSI and O-QSI, but also a number of competing broken symmetry states.

The Effect of Combined Magnetic Geometries on Thermally Driven Winds. II. Dipolar, Quadrupolar, and Octupolar Topologies

Abstract During the lifetime of Sun-like or low-mass stars a significant amount of angular momentum is removed through magnetized stellar winds. This process is often assumed to be governed by the dipolar component of the magnetic field. However, observed magnetic fields can host strong quadrupolar and/or octupolar components, which may influence the resulting spin-down torque on the star. In Paper I, we used the MHD code PLUTO to compute steady-state solutions for stellar winds containing a mixture of dipole and quadrupole geometries. We showed the combined winds to be more complex than a simple sum of winds with these individual components. This work follows the same method as Paper I, including the octupole geometry, which not only increases the field complexity but also, more fundamentally, looks for the first time at combining the same symmetry family of fields, with the field polarity of the dipole and octupole geometries reversing over the equator (unlike the symmetric quadrupole). We show, as in Paper I, that the lowest-order component typically dominates the spin-down torque. Specifically, the dipole component is the most significant in governing the spin-down torque for mixed geometries and under most conditions for real stars. We present a general torque formulation that includes the effects of complex, mixed fields, which predicts the torque for all the simulations to within 20% precision, and the majority to within ≈5%. This can be used as an input for rotational evolution calculations in cases where the individual magnetic components are known.

The effects of ion mass variation and domain size on octupolar out-of-plane magnetic field generation in collisionless magnetic reconnection

Graf von der Pahlen and Tsiklauri [Phys. Plasmas 21, 060705 (2014)] established that the generation of octupolar out-of-plane magnetic field structure in a stressed X-point collapse is due to ion currents. The field has a central region, comprising of the well-known quadrupolar field (quadrupolar components), as well as four additional poles of reversed polarity closer to the corners of the domain (octupolar components). In this extended work, the dependence of the octupolar structure on domain size and ion mass variation is investigated. Simulations show that the strength and spatial structure of the generated octupolar magnetic field is independent of ion to electron mass ratio; thus showing that ion currents play a significant role in out-of-plane magnetic structure generation in physically realistic scenarios. Simulations of different system sizes show that the width of the octupolar structure remains the same and has a spacial extent of the order of the ion inertial length. The width of the structure thus appears to be independent on boundary condition effects. The length of the octupolar structure, however, increases for greater domain sizes, prescribed by the external system size. This was found to be a consequence of the structure of the in-plane magnetic field in the outflow region halting the particle flow and thus terminating the in-plane currents that generate the out-of-plane field. The generation of octupolar magnetic field structure is also established in a tearing-mode reconnection scenario. The differences in the generation of the octupolar field and resulting qualitative differences between X-point collapse and tearing-mode are discussed.

Non-stationary dynamo and magnetospheric accretion processes of the classical T Tauri star V2129 Oph

We report here the first results of a multi-wavelength campaign focussing on magnetospheric accretion processes of the classical TTauri star (cTTS) V2129Oph. In this paper, we present spectropolarimetric observations collected in 2009 July with ESPaDOnS at the Canada-France-Hawaii Telescope (CFHT). Circularly polarised Zeeman signatures are clearly detected, both in photospheric absorption and accretion-powered emission lines, from time-series of which we reconstruct new maps of the magnetic field, photospheric brightness and accretion-powered emission at the surface of V2129Oph using our newest tomographic imaging tool - to be compared with those derived from our old 2005 June data set, reanalyzed in the exact same way. We find that in 2009 July, V2129Oph hosts octupolar & dipolar field components of about 2.1 & 0.9kG respectively, both tilted by about 20deg with respect to the rotation axis; we conclude that the large-scale magnetic topology changed significantly since 2005 June (when the octupole and dipole components were about 1.5 and 3 times weaker respectively), demonstrating that the field of V2129Oph is generated by a non-stationary dynamo. We also show that V2129Oph features a dark photospheric spot and a localised area of accretion-powered emission, both close to the main surface magnetic region (hosting fields of up to about 4kG in 2009 July). We finally obtain that the surface shear of V2129Oph is about half as strong as solar. From the fluxes of accretion-powered emission lines, we estimate that the observed average logarithmic accretion rate (in Msun/yr) at the surface of V2129Oph is -9.2+-0.3 at both epochs, peaking at -9.0 at magnetic maximum. It implies in particular that the radius at which the magnetic field of V2129Oph truncates the inner accretion disc is 0.93x and 0.50x the corotation radius in 2009 July and 2005 June respectively.

Theoretical study on the nonlinear optical properties of donor/acceptor-functionalized trigonal dehydrobenzoannulenes

The first hyperpolarizabilities β and ultraviolet spectra of two-dimensional charge transfer (2DCT) donor/acceptor-functionalized trigonal dehydrobenzoannulenes (compounds 2–7) have been calculated by using ab initio quantum chemistry methods. It is found that these multiple substituted chromophores possess large β values, where both diagonal and off-diagonal terms play important roles in β. This is different from the typical one-dimensional charge transfer (1DCT) compounds, where β is dominated by the diagonal terms. It is worth noting that a good nonlinearity-transparency trade-off is achieved for compounds 2–7 which exhibit larger β values coupled with enhanced transparency in the visible region. Moreover, the contributions of dipolar components to β are larger than that of octupolar components for compounds 2–7.

On the calculated first hyperpolarizability of substituted tri-cyclohexadien-2-yl-amines: Novel targets for experimental research

A new class of molecules, consisting of substituted cyclohexadien-2-yl-amines, is proposed as candidates for new materials with non-linear optical properties. The first hyperpolarizability tensor components for these molecules are calculated at the CPHF/6-31G**++, CPDFT/B3LYP/6-31G**++ and CPDFT/X3LYP/6-31G**++ levels. The results are analyzed in terms of the partition of the tensor into its dipolar and octupolar components. The molecules present calculated β components with values comparable to those of p-nitro-aniline, but with structural features that should result in materials with more than one axis of optical activity, and without the common pitfall of classic push–pull molecules, namely, the tendency to form centro-symmetric crystals. Calculated EFISH values, for future comparison with experimental data, are also presented.

χ(2) polarization induced in molecular glass of conjugated compound by all-optical poling

The paper presents the first report on χ(2) polarization induced in molecular glass of conjugated compound by all-optical poling. Transparent thin film of molecular glass of 1,4-bis[2-[4-[N,N-di(p-tolyl)amino]phenyl]vinyl]benzene (BTAPVB) was prepared using a spin-cast technique. Dipolar as well as octupolar components in BTAPVB contributed to the formation of photoinduced χ(2) polarization. Growth rate of χ(2) polarization has good linear relation with Eω4E2ω, which suggested that the simultaneous processes of two-photon (ω+2ω) and three-photon (ω+ω+ω) excitation on the same electronic level contributed to the formation of photoinduced χ(2) polarization.

New class of molecules predicted to exhibit non-linear optical properties

The search for materials with non-linear optical (NLO) properties has been the subject of intense research, due to their application in a wide range of technologies, such as optical computing and optical communication [1– 3]. Although several inorganic substances are known to exhibit NLO properties, macroscopic assemblies of organic molecules show great promise as new materials for building NLO devices, due to their fast response times [3]. Attempts at designing organic molecules with nonlinear optical activity have traditionally used the push– pull model, where an electron donor group is connected to an electron-acceptor group through a spacer. In order to facilitate charge transfer between the donor and the acceptor groups, the spacer is usually a conjugate, planar or quasi-planar system. Although molecules with reasonably large calculated hyperpolarizabilities (β and γ ) can be designed following this procedure, at the crystalline level, the property can be cancelled due to anti-parallel centrosymmetrical stacking of the molecules induced by their planarity. A well known example of the failure of the push–pull design model is p-nitro-aniline, which was expected to have a large (at least for that time’s standards) non-linear optical activity. Unfortunately, at the crystalline level the NLO activity vanishes. Some of the inconveniences of the 1-D π conjugated systems can be more or less circumvented by other arrangements such as 2-D shaped molecules or 3-D tetrahedral DA compounds [4, 5]. Recently, Barbosa and Nascimento [6] proposed a new approach, where a non-planar unit, with high electron affinity, is used as the acceptor, to which several donors can be linked. This new strategy presents two great advantages over the traditional push–pull model: first, the non-planarity of the central acceptor unit reduces the probability of forming a centro-symmetric crystal; second, by properly choosing the type and number of donor groups, one can design molecules in which the octupolar components of the β and γ tensors can be maximized, according to the proposal of Zyss et al. [7]. The advantages of octupolar crystalline structures over the dipolar ones have been extensively discussed by Zyss et al. [8]. Using this new approach several derivatives of C36 exhibiting large values of β have been designed [6]. However, since the chemistry of C36

Sound generation by coaxial collision of two vortex rings

Sound pressure fields generated by coaxial collisions of two vortex rings with equal/unequal strengths are simulated numerically. The axisymmetric, unsteady, compressible Navier–Stokes equations are solved by a finite difference method, not only for a near field but also for a far field. The sixth-order-accurate compact Padé scheme is used for spatial derivatives, together with the fourth-order-accurate Runge–Kutta scheme for time integration. The results show that the generation of sound is closely related to the change of direction of the vortex ring motion induced by the mutual interaction of the two vortex rings. For the case of equal strength (head-on collision), the change of direction is associated with stretching of the vortex rings. Generated sound waves consist of compression parts and rarefaction parts, and have a quadrupolar nature. For the case of unequal strengths, the two vortex rings pass through each other; the weaker vortex ring moves outside the stronger vortex ring which shows a loop motion. The number of generated waves depends on the relative strength of the two vortex rings. The sound pressure includes dipolar and octupolar components, in addition to monopolar and quadrupolar components which are observed for the case of a head-on collision.

Nonlinear optical properties of polyenoctupoles: a multipolar tensorial quantum analysis

This paper presents a theoretical analysis of the first-order hyperpolarizability properties ( β) of polyenic molecules of octupolar C 3h symmetry (polyenoctupoles), based on CNDO/S calculations, and interpreted in the frame of a tensorial formalism. One of the goals of this analysis is to dissect the hyperpolarizability components in such a way as to reveal interactions within the different subunits constituting the octupolar system. To this end, the polyenoctupole properties are compared to those of dipolar analogues having the same conjugation length m. The general laws obtained for 1D dipolar polyenes (linear variations of λ with m , exponential variations of β with m) are also verified for the polyenoctupoles. The theory also reveals that, for the same conjugation length, the polyenoctupoles should exhibit a better hyperpolarizability–absorption trade-off than the corresponding 1D polyenes. A multipolar tensorial analysis of the dipolar and octupolar components of β in 1D polyenes demonstrates that the nonlinear anisotropy ρ of the 1D polyenes effectively corresponds to ideal 1D chromophores, with a octupolar/dipolar ratio close to its theoretical value of 2/3 =0.82. Finally, the octupolar interaction concept is introduced within the frame of irreducible tensor representation. In this generally applicable representation, the β tensor of a multipolar system is dissected into two separate tensor components, one ( β A) representing the sum of the contributions of the individual dipole subunits, the other ( β I) reflecting interactions (charge transfer or Coulombic) between the dipole units constituting the multipole. The interaction term β I could be determined in magnitude and in direction in the irreducible J=3 space. In the C 3h octupoles considered in the present work, the octupolar interaction term β I is found negligible for the smallest molecules and becomes relatively important (up to 20–30% of β A) only for the octupoles having the largest size.

Finite field study on nonlinear optical properties of substituted ketene N, S-acetals

The nonlinear optical properties of title compounds calculated by AM1/finite field (AM1/FF) approach are discussed based on their crystal parameters. The origins of large molecular first hyperpolarizahilitiesβ and good transparency of the compounds are explained well through the aromatic character enhancement in the excited state and the short conjugation length in the ground state. Results show that the difference ofβ values obtained by two experimental methods (Solvatochromic and Hyper Rayleigh Scattering) is due to the molecular quasi-two-dimension character and the octupolar components’ contribution. The calculation has also demonstrated that the change ofγ xxx caused by different donor substituents is linearly related with the Hammett substituent constant σ+.

Vectorial and Octupolar Components of the First-Order Hyperpolarizability in Push-Pull Benzopyranic Series

Vectorial (weight 1) and octupolar (weight 3) components of the first-order hyperpolarizability are computed using the PM3/RHF/FF method following two different decomposition schemes. These calculations evidence the importance of the weight 3 component of the β tensor even in push-pull molecules. The β values, output from the two decomposition schemes, are different but show the same evolutionary trend within benzopyranic molecule series. The square root of a macroscopic square average quantity 〈β,〉2)1/2 (which is usually determined in elastic second-harmonic light scattering experiment) is then computed and compared to the norm of the molecular β cartesian tensor.