Magnetic Dipole Contributions Research Articles

Experimental observation of magnetic dimers in dilutedYb:YAlO3

We present a comprehensive experimental investigation of Yb magnetic dimers in Yb$_{0.04}$Y$_{0.96}$AlO$_3$, an Yb-doped Yttrium Aluminum Perovskite (YAP) YAlO$_3$ by means of specific heat, magnetization and high-resolution inelastic neutron scattering (INS) measurements. In our sample, the Yb ions are randomly distributed over the lattice and $\sim 7$\% of Yb ions form quantum dimers due to nearest-neighbor antiferromagnetic coupling along the $c$-axis. At zero field, the dimer formation manifests itself in an appearance of an inelastic peak at $\Delta \approx 0.2$~meV in the INS spectrum and a Schottky-like anomaly in the specific heat. The structure factor of the INS peak exhibits a cosine modulation along the $L$ direction, in agreement with the $c$-axis nearest-neighbor intra-dimer coupling. A careful fitting of the low-temperature specific heat shows that the excited state is a degenerate triplet, which indicates a surprisingly small anisotropy of the effective Yb-Yb exchange interaction despite the low crystal symmetry and anisotropic magnetic dipole contribution, in agreement with previous reports for the Yb parent compound, YbAlO$_3$ [arXiv:1904.11513, arXiv:1902.04112], and in contrast to Yb$_2$Pt$_2$Pb [arXiv:1606.01309, arXiv:1907.01067]. The obtained results are precisely reproduced by analytical calculations for the Yb dimers.

Rejecting the Majorana nature of dark matter with electron scattering experiments

Assuming that Dark Matter (DM) is made of fermions in the sub-GeV mass range with interactions dominated by electromagnetic moments of higher order, such as the electric and magnetic dipoles or the anapole moment, we show that direct detection experiments searching for atomic ionisation events in xenon targets can shed light on whether DM is a Dirac or Majorana particle. Specifically, we find that between about 45 (120) and 610 (1700) signal events are required to reject Majorana DM in favour of Dirac DM with a statistical significance corresponding to 3 (5) standard deviations. The exact number of DM signal events corresponding to a given significance depends on the relative size of the anapole, magnetic dipole and electric dipole contributions to the expected rate of DM-induced atomic ionisations under the Dirac hypothesis. Our conclusions are based on Monte Carlo simulations and the likelihood ratio test. While the use of asymptotic formulae for the latter is standard in many applications, here it requires a non-trivial extension to the case where one of the hypotheses lies on the boundary of the parameter space. Our results constitute a solid proof of concept about the possibility of using direct detection experiments to reject the Majorana DM hypothesis when the DM interactions are dominated by higher-order electromagnetic moments.

Comment on “Judd–Ofelt analysis of the Er3+ (4f11) absorption intensities in Er3+-doped garnets” [J. Appl. Phys. 93(5), 2602 (2003)

A previous paper [D. K. Sardar et al., J. Appl. Phys. 93(5), 2602 (2003)] has reported Judd–Ofelt (J–O) spectroscopic properties of Er3+ in garnets Y3Al5O12, Y3(Sc2Ga3)O12, and Gd3Ga5O12. In that paper, the possible magnetic-dipole contribution to the oscillator strength, which is non-zero for the 4I13/2 ↔ 4I15/2 (1.5 μm) transition of Er3+, has been erroneously omitted in their J–O calculation, resulting in incorrect results of relevant spectroscopic parameters. In this Comment, we point out the error, perform correct J–O analysis, and report correct results.

Numerical Study on Mie Resonances in Single GaAs Nanomembranes.

GaAs nanomembranes grown by selective area epitaxy are novel structures. The high refractive index of GaAs makes them good candidates for nanoantennas. We numerically studied the optical modal structure of the resonator. The nanomembrane geometry introduces a strong light-polarization dependence. The scattering is dominated by an electric dipole contribution for polarization along the nanomembrane long dimension and by a magnetic dipole contribution in the orthogonal direction. The dependence on the geometry of the resonances close to the GaAs band gap was modeled by a single coefficient. It describes the resonance shifts against up-to 40% changes in length, height, and width. We showed that the nanomembranes exhibited field enhancement, far-field directionality, and tunability with the GaAs band gap. All these elements confirm their great potential as nanoantennas.

The structure and radiative lifetimes of negative ions homologous to N−

Negative ions homologous to N− are interesting systems, since there are several bound terms within the ground configuration. The forbidden transitions between them, often dominated by the magnetic dipole contributions, are affected by term mixing—a relativistic effect. When increasing the nuclear charge in the homologous sequence of negative ions, this effect increases. In this paper we use systematic multiconfiguration Dirac–Hartree–Fock calculations to study these effects and predict affinities, level splittings and transition rates between bound states of N−, P−, As−, Sb− and Bi−. By monitoring the line strengths we are able to predict the deviation from the non-relativistic LS-coupled values for transitions between levels of the lowest 3P term. For Sb− the 1D term is also bound, and the prediction for the rates of its transition to the 3P-levels is a challenge for theory. For Bi− less is known experimentally and we analyze its structure and the relativistic contributions to it.

Light Scattering by a Dielectric Sphere: Perspectives on the Mie Resonances

Light scattering by a small spherical particle, a central topic for electromagnetic scattering theory, is here considered. In this short review, some of the basic features of its resonant scattering behavior are covered. First, a general physical picture is described by a full electrodynamic perspective, the Lorenz–Mie theory. The resonant spectrum of a dielectric sphere reveals the existence of two distinctive types of polarization enhancement: the plasmonic and the dielectric resonances. The corresponding electrostatic (Rayleigh) picture is analyzed and the polarizability of a homogeneous spherical inclusion is extracted. This description facilitates the identification of the first type of resonance, i.e., the localized surface plasmon (plasmonic) resonance, as a function of the permittivity. Moreover, the electrostatic picture is linked with the plasmon hybridization model through the case of a step-inhomogeneous structure, i.e., a core–shell sphere. The connections between the electrostatic and electrodynamic models are reviewed in the small size limit and details on size-induced aspects, such as the dynamic depolarization and the radiation reaction on a small sphere are exposed through the newly introduced Mie–Padé approximative perspective. The applicability of this approximation is further expanded including the second type of resonances, i.e., the dielectric resonances. For this type of resonances, the Mie–Padé approximation reveals the main character of the two different cases of resonances of either magnetic or electric origin. A unified picture is therefore described encompassing both plasmonic and dielectric resonances, and the resonant conditions of all three different types are extracted as functions of the permittivity and the size of the sphere. Lastly, the directional scattering behavior of the first two dielectric resonances is exposed in a simple manner, namely the Kerker conditions for maximum forward and backscattering between the first magnetic and electric dipole contributions of a dielectric sphere. The presented results address several prominent functional features, aiming at readers with either theoretical or applied interest for the scattering aspects of a resonant sphere.

Dispersive Optical Activity of (R)-Methylene Norbornene: Intrinsic Response and Solvation Effects.

The dispersive optical activity of a homoconjugated bicyclic diene, (R)-methylene norbornene (R-MNB), was interrogated under complementary vapor-phase and solution-phase conditions to elucidate the structural/electronic provenance of its unusual chiroptical signatures and to explore the marked influence of environmental perturbations. The intrinsic (isolated-molecule) values of specific rotation measured at 355 and 633 nm (1623.5 ± 5.5 and 390.4 ± 3.7 deg dm-1 (g/mL)-1) were found to be factors of 3.9 and 2.1 smaller in magnitude than analogous quantities obtained for the kindred enone, (R)-norbornenone (R-NBO), reflecting, in part, the loss of prominent magnetic-dipole contributions from the C═O moiety and the exclusion of electron delocalization from the oxygen lone pairs. The wavelength-resolved rotatory powers of R-MNB were enhanced dramatically (by ∼40% on average) upon dissolution in any of the four common solvents targeted by the present study (acetonitrile, di-n-butylether, cyclohexane, and chloroform), yet displayed only a slight dependence on the exact nature of the surrounding liquid (±2.7% variation from the mean at 589.3 nm). Quantum-chemical calculations built upon the linear-response frameworks of density-functional theory and coupled-cluster theory were enlisted to interpret experimental results, with the substantial effects incurred by nonspecific solvation phenomena being explored through use of polarizable continuum models and bulk property-response relationships. Aside from enumerating the varied quality of agreement attained between computational predictions and polarimetric measurements, these efforts have found that refractive-index correlations, akin to those embodied in the venerable (albeit often discounted) Lorentz local-field correction, afford a viable means of linking the chiroptical behavior of R-MNB across phases.

Near-infrared linewidth narrowing in plasmonic Fano-resonant metamaterials via tuning of multipole contributions

We report on an experimental and computational (multipole decomposition) study of Fano resonance modes in complementary near-IR plasmonic metamaterials. Resonance wavelengths and linewidths can be controlled by changing the symmetry of the unit cell so as to manipulate the balance among multipole contributions. In the present case, geometrically inverting one half of a four-slot (paired asymmetric double bar) unit cell design changes the relative magnitude of magnetic quadrupole and toroidal dipole contributions leading to the enhanced quality factor, figure of merit, and spectral tuning of the plasmonic Fano resonance.

Magnetic Dipole Scattering from Metallic Nanowire for Ultrasensitive Deflection Sensing.

It is generally believed that when a single metallic nanowire is sufficiently small, it scatters like a point electric dipole. We show theoretically when a metallic nanowire is placed inside specially designed beams, the magnetic dipole contribution along with the electric dipole resonance can lead to unidirectional scattering in the far field, fulfilling Kerker's condition. Remarkably, this far-field unidirectional scattering encodes information that is highly dependent on the nanowire's deflection at a scale much smaller than the wavelength. The special roles of small but essential magnetic response along with the plasmonic resonance are highlighted for this extreme sensitivity as compared with the dielectric counterpart. In addition, the same essential role of the magnetic dipole contribution is also presented for a very small metallic nanosphere.

Electric and Magnetic Dipole Strength at Low Energy.

A low-energy enhancement of radiative strength functions was deduced from recent experiments in several mass regions of nuclei, which is believed to impact considerably the calculated neutron capture rates. In this Letter we investigate the behavior of the low-energy γ-ray strength of the ^{44}Sc isotope, for the first time taking into account both electric and magnetic dipole contributions obtained coherently in the same theoretical approach. The calculations are performed using the large-scale shell-model framework in a full 1ℏω sd-pf-gds model space. Our results corroborate previous theoretical findings for the low-energy enhancement of the M1 strength but show quite different behavior for the E1 strength.

Orbital and spin moments in the ferromagnetic superconductor URhGe by x-ray magnetic circular dichroism

The ferromagnetic superconductor URhGe has been investigated by high field magnetic circular dichroism (XMCD) at the U ${M}_{4,5}$, Rh ${L}_{2,3}$, and Ge $K$ edges at 2.1 K and at applied fields up to 17 T. The XMCD performed at the ${M}_{4,5}$ absorption edges allows us to determine the spectroscopic branching ratio and the $5f$ electron contribution to the valence spin-orbit interaction. Combination with polarized neutron diffraction results allows us to derive the individual $\mathrm{U}$ orbital and spin moments and the magnetic-dipole contribution $\ensuremath{\langle}{T}_{z}\ensuremath{\rangle}$. There is no evidence for any change of the orbital-to-spin moment ratios across the spin reorientation transition at ${H}_{R}=12\phantom{\rule{0.16em}{0ex}}\mathrm{T}$, when the field is applied along the initial hard $b$ axis. We also confirm that the magnetism of URhGe is dominated by $\mathrm{U}$, with the contribution of Rh representing only about $10%$ of the macroscopic moment. The orbital and spin moments at the Rh site are found to be parallel to each other and parallel to the macroscopic magnetization, but an unexpectedly large orbital-to-spin moment ratio is observed. The XMCD at the Ge $K$ edge reveals the presence of a small induced Ge $4p$ orbital moment, parallel to the macroscopic magnetization. The results are discussed against predictions of the electronic band structure calculations by the density functional theory plus Coulomb $U$, including spin-orbit coupling $(\mathrm{DFT}+U+\mathrm{SOC})$.

Computational Design of Rare-Earth-Free Magnets with the Ti3Co5B2-Type Structure

The prolific Ti3Co5B2 structure type has produced exciting materials with tunable magnetic properties, ranging from soft magnetic Ti2FeRh5B2, to semihard magnetic Ti2FeRu4RhB2 and hard magnetic Sc2FeRu3Ir2B2. Density functional theory (DFT) was employed to investigate their spin–orbit coupling effect, spin exchange, and magnetic dipole–dipole interactions in order to understand their magnetic anisotropy and relate it to their various coercivities, with the objective of being able to predict new materials with large magnetic anisotropy. Our calculations show that the contribution of magnetic dipole–dipole interactions to the magnetocrystalline anisotropy energy (MAE) in Ti3Co5B2-type compounds is much weaker than the spin–orbit coupling effect, and Sc2FeRu3Ir2B2 has, by far, the largest MAE and strong intrachain and interchain Fe–Fe spin exchange coupling, thus confirming its hard magnetic properties. We then targeted materials containing the more earth-abundant and less expensive Co, instead of Rh, Ru or ...

Optical activity of chirally distorted nanocrystals

We develop a general theory of optical activity of semiconductor nanocrystals whose chirality is induced by a small perturbation of their otherwise achiral electronic subsystems. The optical activity is described using the quantum-mechanical expressions for the rotatory strengths and dissymmetry factors introduced by Rosenfeld. We show that the rotatory strengths of optically active transitions are decomposed on electric dipole and magnetic dipole contributions, which correspond to the electric dipole and magnetic dipole transitions between the unperturbed quantum states. Remarkably, while the two kinds of rotatory strengths are of the same order of magnitude, the corresponding dissymmetry factors can differ by a factor of 105. By maximizing the dissymmetry of magnetic dipole absorption one can significantly enhance the enantioselectivity in the interaction of semiconductor nanocrystals with circularly polarized light. This feature may advance chiral and analytical methods, which will benefit biophysics, chemistry, and pharmaceutical science. The developed theory is illustrated by an example of intraband transitions inside a semiconductor nanocuboid, whose rotatory strengths and dissymmetry factors are calculated analytically.

Resolving enantiomers using the optical angular momentum of twisted light.

Circular dichroism and optical rotation are crucial for the characterization of chiral molecules and are of importance to the study of pharmaceutical drugs, proteins, DNA, and many others. These techniques are based on the different interactions of enantiomers with circularly polarized components of plane wave light that carries spin angular momentum (SAM). For light carrying orbital angular momentum (OAM), for example, twisted or helical light, the consensus is that it cannot engage with the chirality of a molecular system as previous studies failed to demonstrate an interaction between optical OAM and chiral molecules. Using unique nanoparticle aggregates, we prove that optical OAM can engage with materials' chirality and discriminate between enantiomers. Further, theoretical results show that compared to circular dichroism, mainly based on magnetic dipole contributions, the OAM analog helical dichroism (HD) is critically dependent on fundamentally different chiral electric quadrupole contributions. Our work opens new venues to study chirality and can find application in sensing and chiral spectroscopy.

Measurement scheme and analysis for weak ground-state-hyperfine-transition moments through two-pathway coherent control

We report our detailed analysis of a table-top system for the measurement of the weak-force-induced electric dipole moment of a ground state hyperfine transition carried out in an atomic beam geometry. We describe an experimental configuration of conductors for application of orthogonal r.f. and static electric fields, with cavity enhancement of the r.f. field amplitude, that allows confinement of the r.f. field to a region in which the static fields are uniform and well-characterized. We carry out detailed numerical simulations of the field modes, and analyze the expected magnitude of statistical and systematic limits to the measurement of this transition amplitude in atomic cesium. The combination of an atomic beam with this configuration leads to strong suppression of magnetic dipole contributions to the atomic signal. The application of this technique to the measurement of extremely weak transition amplitudes in other atomic systems, especially alkali metals, seems very feasible.

Judd–Ofelt analysis of Tm3+ doped in CaSc2O4 ceramic samples

The Judd–Ofelt analysis is applied to light-scattering ceramic CaSc2O4 doped with Tm3+. The calibration of the Judd–Ofelt parameters is performed by two approaches: (i) using the known magnetic-dipole contribution to the transition intensity of 3H6→3H5; (ii) using the radiative lifetime of an energy level supposed to decay mainly radiatively (1G4 or 3F4). The following results were obtained: Ω2=1.55×10−20cm2; Ω4=1.71×10−20cm2; Ω6=0.98×10−20cm2, using the first approach; Ω2=1.70×10−20cm2, Ω4=1.84×10−20cm2, Ω6=1.13×10−20cm2 (calibration using 1G4); Ω2=1.57×10−20cm2, Ω4=1.70×10−20cm2, Ω6=1.04×10−20cm2 (calibration using 3F4). The obtained Judd–Ofelt parameters are used to calculate the radiative lifetimes and quantum efficiencies of several Tm3+ levels, spontaneous emission probabilities and branching ratios of various Tm3+ transitions. A fairly good agreement was obtained between the results of these methods.

Judd–Ofelt analysis of Tm3+ in La3Ga5.5Ta0.5O14 ceramic with granular structure

A Judd–Ofelt analysis was performed on a langatate (La3Ga5.5Ta0.5O14) translucent ceramic sample doped with 1 at% Tm3+. Due to the scattering of the transmitted light, the effective thickness of the sample is unknown and the absorption spectrum of Tm3+ in langatate ceramic sample is obtained in relative units. The absorption spectrum was calibrated using the magnetic-dipole contribution to the 3H6→3H5 transition. The Judd–Ofelt parameters obtained are: Ω2=2.65×10–20cm2, Ω4=0.80×10–20cm2, Ω6=1.86×10–20cm2. The electric-dipole and magnetic-dipole transition probabilities, radiative lifetimes and luminescence branching ratios were calculated. The calibration allowed the estimation of the ‘effective’ thickness of the ceramic sample which was approximately four times larger than the geometric thickness.

Hybrid DFT calculation ofFe57NMR resonances and orbital order in magnetite

The crystal structure and charge and orbital order of magnetite below the Verwey temperature are calculated using a first-principles hybrid density functional theory (DFT) method. The initial atomic positions in the crystal-structure calculation are those recently refined from x-ray diffraction data for the $Cc$ space-group unit cell [Senn, Wright, and Attfield, Nature (London) 481, 173 (2012)]. Fermi contact and magnetic dipolar contributions to hyperfine fields at $^{57}\mathrm{Fe}$ nuclei obtained from hybrid DFT calculations are used to obtain NMR resonance frequencies for magnetite for a range of external magnetic field directions in a relatively weak field. NMR frequencies from hybrid density functional theory calculations are compared to NMR data [M. Mizoguchi, J. Phys. Soc. Jpn. 70, 2333 (2001)] for a range of applied magnetic field directions. NMR resonance frequencies of $B$-site Fe ions show large relative variations with applied field direction owing to anisotropic hyperfine fields from charge and orbital ordered Fe $3d$ minority-spin electrons at those sites. Good agreement between computed and measured NMR resonance frequencies confirms the pattern of charge and orbital order obtained from calculations. The charge and orbital order of magne-tite in its low-temperature phase obtained from hybrid DFT calculations is analyzed in terms of one-electron bonds between Fe ions. The Verwey transition in magnetite therefore resembles Mott-Peierls transitions in vanadium oxides which undergo symmetry-breaking transitions owing to electron-pair bond formation.

Spin effects probed by Rayleigh X-ray scattering off hydrogenic ions

We study the polarization characteristics of X-ray photons scattered by hydrogenic atoms, based on the Dirac equation and second-order perturbation theory. The relativistic states used in calculations are obtained using the finite basis set method and expressed in terms of B-splines and B-polynomials. We derive general analytical expressions for the polarization-dependent total cross sections, which are applicable to any atom and ion, and evaluate them separately for linear and circular polarizations of photons. In particular, detailed calculations are performed for the integrated Stokes parameters of the scattered light for hydrogen as well as hydrogen-like neon and argon. For analyzing such integrated Stokes parameters, special attention is given to the electron–photon spin–spin interaction, which mostly stems from the magnetic-dipole contribution of the electron–photon interaction. Subsequently, we find an energy window for the selected targets in which such spin–spin interactions can be probed.

Quantifying and controlling the magnetic dipole contribution to1.5−μmlight emission in erbium-doped yttrium oxide

We experimentally quantify the contribution of magnetic dipole (MD) transitions to the near-infrared light emission from trivalent erbium-doped yttrium oxide (Er$^{3+}$:Y$_2$O$_3$). Using energy-momentum spectroscopy, we demonstrate that the $^4$I$_{13/2}{\to}^4$I$_{15/2}$ emission near 1.5 $\mu$m originates from nearly equal contributions of electric dipole (ED) and MD transitions that exhibit distinct emission spectra. We then show how these distinct spectra, together with the differing local density of optical states (LDOS) for ED and MD transitions, can be leveraged to control Er$^{3+}$ emission in structured environments. We demonstrate that far-field emission spectra can be tuned to resemble almost pure emission from either ED or MD transitions, and show that the observed spectral modifications can be accurately predicted from the measured ED and MD intrinsic emission rates.