Quadrupolar Order Research Articles

Composite quadrupole order in ferroic and multiferroic materials

The formalism of composite and intertwined orders has been remarkably successful in discussing the complex phase diagrams of strongly correlated materials and high-$T_c$ superconductors. Here, we propose that composite orders are also realized in ferroelectric and ferromagnetic materials when lattice anisotropy is taken into account. This composite order emerges above the ferroic phase transition, and its type is determined by the easy axis of magnetization or polarization, respectively. In multiferroic materials, where polarization and magnetization are coupled, composites of both orders are possible. This formalism of composite orders naturally accounts for magnetoelectric monopole, toroidal, and quadrupole orders. More broadly, composite orders may explain precursor phenomena in incipient (multi)ferroic materials, arising at temperatures above the ferroic phase transition and potentially contributing to the characterization of currently hidden orders.

Strange-metal behavior without fine tuning in PrV2Al20

Strange-metal behavior observed in the praseodymium-based heavy-fermion material PrV2Al20 has been tentatively interpreted in the framework of proximity to a quantum critical point (QCP) associated with quadrupolar ordering. Here, we demonstrate that an alternative, natural explanation exists without invoking a QCP, in terms of the unconventional nature of the quadrupolar Kondo effect taking place in non-Kramers ions. Using a combination of density-functional theory calculations and analytical arguments, we construct a periodic Anderson model with realistic parameters to describe PrV2Al20. We solve the model using dynamical mean-field theory preserving the model symmetries and demonstrate the non-Fermi liquid strange-metal behavior stemming from the two-channel nature of the quadrupolar Kondo effect. Our calculations provide an explanation for the puzzling temperature dependence in the magnetic susceptibility and provide a basis for analyzing future photoemission experiments. Published by the American Physical Society 2024

Anisotropic magnetic and quadrupolar H−T phase diagram of CeRh2As2

The tetragonal heavy-fermion compound CeRh2As2 has intriguing low-temperature symmetry-breaking phases whose nature is unclear. The unconventional superconducting phase is complemented by other normal-state phases which presumably involve ordering of 4f electron multipoles supported by the Kramers doublets split by the tetragonal crystal electric field (CEF). The most striking aspect is the pronounced anisotropic H−T phase boundary for in-plane and out-of plane field directions. Using a localized 4f CEF model we demonstrate that its essential features can be understood as the result of competing low-field easy-plane magnetic order and field-induced quadrupolar order of xy type. We present calculations based on coupled multipole random phase approximation response function approach as well as molecular field treatment in the ordered regime. We use an analytical approach for a reduced quasiquartet model and numerical calculations for the complete CEF level scheme. We discuss the quantum critical properties as function of multipolar control parameters and explain the origin of a pronounced ac anisotropy of the H−T phase diagram. Finally, the field and temperature evolution of multipolar order parameters is derived and the high-field phase diagram is predicted. Published by the American Physical Society 2024

Quadrupolar radiation in de Sitter: displacement memory and Bondi metric

We obtain the closed form expression for the metric perturbation around de Sitter spacetime generated by a matter source below Hubble scale both in generalized harmonic gauge and in Bondi gauge up to quadrupolar order in the multipolar expansion, including both parities (i.e. both mass and current quadrupoles). We demonstrate that such a source causes a displacement memory effect close to future infinity that originates, in the even-parity sector, from a Λ-BMS transition between the two non-radiative regions of future infinity.

Inclination instability of circumbinary planets

ABSTRACT We analyse a tilt instability of the orbit of an outer planet in a two-planet circumbinary system that we recently reported. The binary is on an eccentric orbit and the inner circumbinary planet is on a circular polar orbit that causes the binary to undergo apsidal precession. The outer circumbinary planet is initially on a circular or eccentric orbit that is coplanar with respect to the binary. We apply a Hamiltonian in quadrupole order of the binary potential to show that the tilt instability is the result of a secular resonance in which the apsidal precession rate of the binary matches the nodal precession rate of the outer planet. A resonance is possible because the polar inner planet causes the apsidal precession of the binary to be retrograde. The outer planet periodically undergoes large tilt oscillations for which we analytically determine the initial evolution and maximum inclination. Following a typically relatively short adjustment phase, the tilt grows exponentially in time at a characteristic rate that is of order the absolute value of the binary apsidal precession rate. The analytic results agree well with numerical simulations. This instability is analogous to the Kozai–Lidov instability, but applied to a circumbinary object. The instability fails to operate if the binary mass ratio is too extreme. The instability occurs even if the outer planet is instead an object of stellar mass and involves tilt oscillations of the inner binary.

Extremely large magnetoresistance and anisotropic transport in the multipolar Kondo system PrTi2Al20

Multipolar Kondo systems offer unprecedented opportunities to design astonishing quantum phases and functionalities beyond spin-only descriptions. A model material platform of this kind is the cubic heavy fermion system PrT2Al20 (T=Ti, V), which hosts a nonmagnetic crystal-electric-field ground state and substantial Kondo entanglement of the local quadrupolar and octopolar moments with the conduction electron sea. Here, we explore the magnetoresistance (MR) and Hall effect of PrTi2Al20, which develops ferroquadrupolar (FQ) order below TQ∼2 K, and compare their behavior with that of the MR and Hall effect of the non-4f analog, LaTi2Al20. In the FQ ordered phase, PrTi2Al20 displays extremely large magnetoresistance (XMR) of ∼103%. The unsaturated, quasilinear field (B) dependence of the XMR violates Kohler's scaling and defies description based on carrier compensation alone. By comparing the MR and the Hall effect observed in PrTi2Al20 and LaTi2Al20, we conclude that the open-orbit topology on the electron-type Fermi surface sheet is key for the observed XMR. The low-temperature MR and the Hall resistivity in PrTi2Al20 display pronounced anisotropy in the [111] and [001] magnetic fields, which is absent in LaTi2Al20, suggesting that the transport anisotropy ties in with the anisotropic magnetic field response of the quadrupolar order parameter. Published by the American Physical Society 2024

Tailoring two-photon spontaneous emission: Framework and nanoantenna design for interference and directionality

We develop a framework that computes two-photon spontaneous emission (TPSE) spectra of a quantum emitter near an arbitrarily shaped nanostructure. The model considers the interaction up to the electric quadrupolar order, which is relevant for nanophotonic structures sustaining strongly confined fields that are used to enhance and to tailor spontaneous emission processes. Moreover, we consider interference effects between multipolar two-photon emission channels, for the first time to our knowledge. First, we show for a s → s transition of a hydrogen atom placed under a silver plasmonic nanodisk a substantial enhancement in the photon-pair emission rates by 5 and 11 orders of magnitude for the two-electric dipole (2ED) and two-electric quadrupole (2EQ) transitions, respectively. Then for the same emitter under a plasmonic graphene nanotriangle, we demonstrate a breakdown of the electric dipole approximation in the TPSE process where the interference between the 2ED and 2EQ transitions is important, as it increases the total rate by 63 %. Third, we explore platforms where entangled photons of different energy are emitted in the far-field in different directions. In the end, our framework is a complete tool to design emitters and nanostructures for the TPSE process, leading to a rich assortment of functional nanoantennas.

Berry-Curvature Engineering for Nonreciprocal Directional Dichroism in Two-Dimensional Antiferromagnets.

In two-dimensional antiferromagnets, we find that the mixed Berry curvature can be attributed as the geometrical origin of the nonreciprocal directional dichroism (NDD), which refers to the difference in light absorption between opposite propagation directions. This Berry curvature is closely related to the uniaxial strain in accordance with the symmetry constraint, leading to a highly tunable NDD, whose sign and strength can be tuned via strain direction. We choose the lattice model of MnBi_{2}Te_{4} as a concrete example. The coupling between mixed Berry curvature and strain also suggests the magnetic quadrupole of the Bloch wave packet as the macroscopic order parameter probed by the NDD in two dimensions, which is distinct from the multiferroic order P×M or the spin toroidal and quadrupole order within a unit cell in previous studies. Our work paves the way for the Berry-curvature engineering for optical nonreciprocity in two-dimensional antiferromagnets.

Quantum spin nematic phase in a square-lattice iridate.

Spin nematic is a magnetic analogue of classical liquid crystals, a fourth state of matter exhibiting characteristics of both liquid and solid1,2. Particularly intriguing is a valence-bond spin nematic3-5, in which spins are quantum entangled to form a multipolar order without breaking time-reversal symmetry, but its unambiguous experimental realization remains elusive. Here we establish a spin nematic phase in the square-lattice iridate Sr2IrO4, which approximately realizes a pseudospin one-half Heisenberg antiferromagnet in the strong spin-orbit coupling limit6-9. Upon cooling, the transition into the spin nematic phase at TC ≈ 263 K is marked by a divergence in the static spin quadrupole susceptibility extracted from our Raman spectra and concomitant emergence of a collective mode associated with the spontaneous breaking of rotational symmetries. The quadrupolar order persists in the antiferromagnetic phase below TN ≈ 230 K and becomes directly observable through its interference with the antiferromagnetic order in resonant X-ray diffraction, which allows us to uniquely determine its spatial structure. Further, we find using resonant inelastic X-ray scattering a complete breakdown of coherent magnon excitations at short-wavelength scales, suggesting a many-body quantum entanglement in the antiferromagnetic state10,11. Taken together, our results reveal a quantum order underlying the Néel antiferromagnet that is widely believed to be intimately connected to the mechanism of high-temperature superconductivity12,13.

Quadrupole anomalous Hall effect in magnetically induced electron nematic state

Berry phases in both momentum and real space cause transverse motion in itinerant electrons, manifesting various off-diagonal transport effect such anomalous and topological Hall effects. Although these Hall effects are isotropic within the plane perpendicular to the fictitious magnetic field, here, we report the manifestation of the anisotropic linear anomalous Hall effect (AHE) in the spinel oxide NiCo2O4 epitaxial film. The unconventional Hall effect indicates a quadrupole dependence on the in-plane current direction being added to the uniform AHE. Moreover, its sign can be manipulated just by magnetic-field cooling. The anisotropic effect is attributed to an electron nematic state originating from a deformed electronic state owing to an extended magnetic toroidal quadrupole and ferrimagnetic order.

Uniaxial Quadrupole Order in a Magnet With Strong Biquadratic Exchange

Abstract—It is shown that in a magnet with a sufficiently strong biquadratic exchange interaction (compared to bilinear exchange) and spin S 1, the temperature transition from a disordered paramagnetic state to the ground ferromagnetic state passes through an intermediate magnetically ordered phase—uniaxial quadrupole ordering. For a magnet with spin S = 3/2, a phase diagram of magnetic states was constructed in the region of large values of the biquadratic exchange and it was studied how the sequence of two phase transitions—“paramagnetic state–quadrupole state” and “quadrupole state–ferromagnetic state”—manifests itself in the temperature behavior of the magnetic heat capacity and the initial magnetic susceptibility.

Uniaxial Quadrupole Order in a Magnet with Strong Biquadratic Exchange

It is shown that the temperature transition from a disordered paramagnetic state to the ground ferromagnetic state in a magnet with sufficiently strong biquadratic exchange interaction (compared to bilinear exchange) and spin S > 1 passes through an intermediate magnetically ordered phase (uniaxial quadrupole ordering). For a magnet with spin S = 3/2, a phase diagram of magnetic states in the region of large values of the biquadratic exchange is constructed in the mean-field approximation and the influence of the sequence of two phase transitions (paramagnetic state−quadrupole state and quadrupole state–ferromagnetic state) on the temperature behavior of the magnetic heat capacity and the initial magnetic susceptibility is investigated.

Multipole couplings and resonance shifts in an array of dielectric particles at oblique incidence

In the present paper, we propose a coupled multipole model to treat the mutual interactions between nanoparticles aligned in a periodic array, which may be frequently encountered in designing metasurfaces and other functional electromagnetic structures. Our model is comprehensive in that it takes into account the electric and magnetic multipoles both up to the quadrupole order. Working under Cartesian coordinates, this model can readily give the multipole responses of the particles in an infinite array at both normal and oblique incidence. In particular, we work out the analytical expressions of the cross-multipole coupling tensors, which are much more complicated for oblique incidence than normal incidence. We invoke the Ewald method to efficiently and accurately calculate the involved lattice sum whose convergence is otherwise very slow. By quantifying the contributions from the various couplings, we are able to analyze the mechanisms of new resonances that emerge only at oblique incidence. As a prototypical example, we use this method to give physically clear explanations of and show flexible control on the resonance shifts of the multipoles of an array of silicon spheres. The power of this model makes it very promising for dealing with metasurfaces with extended areas or working at large numerical apertures.

Elastocaloric signatures of symmetric and antisymmetric strain-tuning of quadrupolar and magnetic phases in DyB2C2

The adiabatic elastocaloric effect measures the temperature change of a given system with strain and provides a thermodynamic probe of the entropic landscape in the temperature-strain space. Here, we demonstrate that the DC bias strain-dependence of AC elastocaloric effect allows decomposition of the latter into symmetric (rotation-symmetry-preserving) and antisymmetric (rotation-symmetry-breaking) strain channels, using a tetragonal [Formula: see text]-electron intermetallic DyB[Formula: see text]C[Formula: see text]-whose antiferroquadrupolar order breaks local fourfold rotational symmetries while globally remaining tetragonal-as a showcase example. We capture the strain evolution of its quadrupolar and magnetic phase transitions using both singularities in the elastocaloric coefficient and its jumps at the transitions, and the latter we show follows a modified Ehrenfest relation. We find that antisymmetric strain couples to the underlying order parameter in a biquadratic (linear-quadratic) manner in the antiferroquadrupolar (canted antiferromagnetic) phase, which are attributed to a preserved (broken) global tetragonal symmetry, respectively. The broken tetragonal symmetry in the magnetic phase is further evidenced by elastocaloric strain-hysteresis and optical birefringence. Additionally, within the staggered quadrupolar order, the observed elastocaloric response reflects a quadratic increase of entropy with antisymmetric strain, analogous to the role magnetic field plays for Ising antiferromagnetic orders by promoting pseudospin flips. Our results demonstrate AC elastocaloric effect as a compact and incisive thermodynamic probe into the coupling between electronic degrees of freedom and strain in free energy, which holds the potential for investigating and understanding the symmetry of a wide variety of ordered phases in broader classes of quantum materials.

Electronic origin of ferroic quadrupole moment under antiferroic quadrupole order and finite magnetic moment in Jeff=32 systems

We study the electronic origin of parasitic ferroic quadrupole moments in antiferroic quadrupole orders by extending a model studied in G. Chen et al., Phys. Rev. B 82, 174440 (2010) with the effective angular momentum ${J}_{\mathrm{eff}}=3/2$ quartet ground states. Taking into account the first crystalline-electric-field (CEF) excited doublet, cubic anisotropy in the quadrupole moments emerges, which leads to the induced ferroic quadrupole moments in the antiferroic quadrupolar phases. The hybridization with the CEF excited quartet states also causes finite magnetic moments compatible to the observed size of the effective moment in typical ${J}_{\mathrm{eff}}=3/2$ systems, as opposed to the naive expectation of vanishing moments in the ${J}_{\mathrm{eff}}=3/2$ systems. These results suggest the importance of the corrections arising from the high-energy CEF excited states in the ${J}_{\mathrm{eff}}=3/2$ systems.

Vibronic collapse of ordered quadrupolar ice in the pyrochlore magnet Tb2+xTi2−xO7+y

While the spin-liquid state in the frustrated pyrochlore ${\mathrm{Tb}}_{2+x}{\mathrm{Ti}}_{2\ensuremath{-}x}{\mathrm{O}}_{7+y}$ has been studied both experimentally and theoretically for more than two decades, a definite description of this unconventional state still needs to be achieved. Using synchrotron-based THz spectroscopy in combination with quantum numerical simulations, we highlight a significant link between two features: the existence of a quadrupolar order following an ice rule and the presence of strong magnetoelastic coupling in the form of hybridized ${\mathrm{Tb}}^{3+}$ crystal-field and phonon modes. The magnitude of this so-called vibronic process, which involves quadrupolar degrees of freedom, is significantly dependent on small off-stoichiometry $x$ and favors all-in--all-out-like correlations between quadrupoles. This mechanism competes with the long-range ordered quadrupolar ice, and for slightly different stoichiometry, is able to destabilize it.

Quadrupole partial orders and triple-q states on the face-centered cubic lattice

We study ${\mathrm{\ensuremath{\Gamma}}}_{3}$ quadrupole orders in a face-centered cubic lattice. The ${\mathrm{\ensuremath{\Gamma}}}_{3}$ quadrupole moments under cubic symmetry possess a unique cubic invariant in their free energy in the uniform ($\mathbf{q}=\mathbit{0}$) sector and the triple-$\mathbf{q}$ sector for the $X$ points $\mathbf{q}=(2\ensuremath{\pi},0,0),(0,2\ensuremath{\pi},0)$, and $(0,0,2\ensuremath{\pi})$. Competition between this cubic anisotropy and anisotropic quadrupole-quadrupole interactions causes a drastic impact on the phase diagram both in the ground state and at finite temperatures. We show details about the model construction and its properties, the phase diagram, and the mechanism of the various triple-$\mathbf{q}$ quadrupole orders reported in our preceding letter [J. Phys. Soc. Jpn. 90, 043701 (2021)]. By using a mean-field approach, we analyze a quadrupole exchange model that consists of a crystalline-electric field scheme with the ground-state ${\mathrm{\ensuremath{\Gamma}}}_{3}$ non-Kramers doublet and the excited singlet ${\mathrm{\ensuremath{\Gamma}}}_{1}$ state. We have found various triple-$\mathbf{q}$ orders in the four-sublattice mean-field approximation. A few partially ordered phases are stabilized in a wide range of parameter space and they have a higher transition temperature than single-$\mathbf{q}$ orders. With lowering temperature, there occur transitions from these partially ordered phases into further symmetry broken phases in which previously disordered sites acquire nonvanishing quadrupole moments. The identified phases in the mean-field approximation are further analyzed by a phenomenological Landau theory. This analysis reveals results qualitatively consistent with the mean-field results and also shows that the cubic invariant plays an important role for stabilizing the triple-$\mathbf{q}$ states. The present mechanism for the triple-$\mathbf{q}$ states also takes effect in systems with different types of quadrupoles, and we discuss its implications for recent experiments in a few $f$- and $d$-electron compounds.

Dipolar relaxation, conductivity, and polar order in AgCN.

By using dielectric spectroscopy in a broad range of temperatures and frequencies, we have investigated dipolar relaxations, the dc conductivity, and the possible occurrence of polar order in AgCN. The conductivity contributions dominate the dielectric response at elevated temperatures and low frequencies, most likely arising from the mobility of the small silver ions. In addition, we observe the dipolar relaxation dynamics of the dumbbell-shaped CN- ions, whose temperature dependence follows the Arrhenius behavior with a hindering barrier of 0.59eV (57 kJ/mol). It correlates well with a systematic development of the relaxation dynamics with the cation radius, previously observed in various alkali cyanides. By comparison with the latter, we conclude that AgCN does not exhibit a plastic high-temperature phase with free rotation of the cyanide ions. Instead, our results indicate that a phase with quadrupolar order, revealing dipolar head-to-tail disorder of the CN- ions, exists at elevated temperatures up to the decomposition temperature, which crosses over to long-range polar order of the CN dipole moments below about 475K. Dipole ordering was also reported for NaCN and KCN, and a comparison with these systems suggests a critical relaxation rate of 105-107Hz, marking the onset of dipolar order in the cyanides. The detected relaxation dynamics in this order-disorder type polar state points to glasslike freezing below about 195K of a fraction of non-ordered CN dipoles.

Accurate Prediction of Hall Mobilities in Two-Dimensional Materials through Gauge-Covariant Quadrupolar Contributions.

Despite considerable efforts, accurate computations of electron-phonon and carrier transport properties of low-dimensional materials from first principles have remained elusive. By building on recent advances in the description of long-range electrostatics, we develop a general approach to the calculation of electron-phonon couplings in two-dimensional materials. We show that the nonanalytic behavior of the electron-phonon matrix elements depends on the Wannier gauge, but that a missing Berry connection restores invariance to quadrupolar order. We showcase these contributions in a MoS_{2} monolayer, calculating intrinsic drift and Hall mobilities with precise Wannier interpolations. We also find that the contributions of dynamical quadrupoles to the scattering potential are essential, and that their neglect leads to errors of 23% and 76% in the room-temperature electron and hole Hall mobilities, respectively.

Near-continuous isotropic – nematic transition in compressed rod-like liquid crystal based nanocolloid

Landau-de Gennes mean-field model predicts the discontinuous transition for the isotropic – nematic (I-N) transition, associated with uniaxial ordering and a quadrupolar order parameter in three dimensions. This report shows pressure-related dielectric studies for rod-like nematogenic pentylcyanobiphenyl (5CB) and its nanocolloids with BaTiO3 nanoparticles. The scan of the dielectric constant revealed the near-continuous I-N phase transition in the compressed nanocolloid with a tiny amount of nanoparticles (x = 0.1%).For the nematic phase in 5CB and its x = 1% nanocolloid the enormous values of the dielectric constant and the bending–type, long-range pretransitional behavior were detected. The impact of prenematic fluctuations was also noted for the ionic-related contribution to dielectric permittivity in the isotropic liquid phase. For the high-frequency relaxation domain, this impact was tested for the primary relaxation time pressure evolution and the translational–orientational decoupling.