Magnetic Quantum States Research Articles

Time–energy distribution of photoelectron from atomic states with different magnetic quantum numbers in elliptically polarized laser fields

Abstract A Wigner-distribution-like (WDL) function based on the strong-field approximation (SFA) theory is used to investigate the ionization time of the photoelectron emitted from the initial states with different magnetic quantum number m in elliptically polarized electric fields. The saddle-point method is adopted for comparisons. For different m states, a discrepancy exists in the WDL distributions of the photoelectrons emitted in a direction close to the major axis of the laser field ellipse. Based on the saddle-point analysis, this discrepancy can be ascribed to the interference between electrons ionized from two tunneling instants. Our results show that the relationships between the tunneling instants and kinetic energy of photoelectrons are the same for different m initial states when the Coulomb potential is not considered. Our work sheds some light on the ionization-time information of electrons from different magnetic quantum states.

Spin-Resolved Magneto-Tunneling and Giant Anisotropic g-Factor in Broken Gap InAs-GaSb Core-Shell Nanowires.

We experimentally and computationally investigate the magneto-conductance across the radial heterojunction of InAs-GaSb core-shell nanowires under a magnetic field, B, up to 30 T and at temperatures in the range 4.2-200 K. The observed double-peak negative differential conductance markedly blue-shifts with increasing B. The doublet accounts for spin-polarized currents through the Zeeman split channels of the InAs (GaSb) conduction (valence) band and exhibits strong anisotropy with respect to B orientation and marked temperature dependence. Envelope function approximation and a semiclassical (WKB) approach allow to compute the magnetic quantum states of InAs and GaSb sections of the nanowire and to estimate the B-dependent tunneling current across the broken-gap interface. Disentangling different magneto-transport channels and a thermally activated valence-to-valence band transport current, we extract the g-factor from the spin-up and spin-down dI/dV branch dispersion, revealing a giant, strongly anisotropic g-factor in excess of 60 (100) for the radial (tilted) field configurations.

Mapping Orbital-Resolved Magnetism in Single Lanthanide Atoms.

Single lanthanide atoms and molecules are promising candidates for atomic data storage and quantum logic due to the long lifetime of their magnetic quantum states. Accessing and controlling these states through electrical transport requires precise knowledge of their electronic configuration at the level of individual atomic orbitals, especially of the outer shells involved in transport. However, no experimental techniques have so far shown the required sensitivity to probe single atoms with orbital selectivity. Here we resolve the magnetism of individual orbitals in Gd and Ho single atoms on MgO/Ag(100) by combining X-ray magnetic circular dichroism with multiplet calculations and density functional theory. In contrast to the usual assumption of bulk-like occupation of the different electronic shells, we establish a charge transfer mechanism leading to an unconventional singly ionized configuration. Our work identifies the role of the valence electrons in determining the quantum level structure and spin-dependent transport properties of lanthanide-based nanomagnets.

Frontispiece: Deconvolving Contributions to Decoherence in Molecular Electron Spin Qubits: A Dynamic Ligand Field Approach

Transition metal complexes have recently gained momentum as electron spin-based quantum bit (qubit) candidates due to their synthetic tunability and long achievable coherence times. The decoherence of magnetic quantum states imposes a limit on the use of these qubits for quantum information technologies, such as quantum computing, sensing, and communication. With rapid recent development in the field of molecular quantum information science, a variety of chemical design principles for prolonging coherence in molecular transition metal qubits have been proposed. To find out more, see the Minireview by R. G. Hadt et al. on page 9482.

Deconvolving Contributions to Decoherence in Molecular Electron Spin Qubits: A Dynamic Ligand Field Approach.

In the past decade, transition metal complexes have gained momentum as electron spin-based quantum bit (qubit) candidates due to their synthetic tunability and long achievable coherence times. The decoherence of magnetic quantum states imposes a limit on the use of these qubits for quantum information technologies, such as quantum computing, sensing, and communication. With rapid recent development in the field of molecular quantum information science, a variety of chemical design principles for prolonging coherence in molecular transition metal qubits have been proposed. Here the spin-spin, motional, and spin-phonon regimes of decoherence are delineated, outlining design principles for each. It is shown how dynamic ligand field models can provide insights into the intramolecular vibrational contributions in the spin-phonon decoherence regime. This minireview aims to inform the development of molecular quantum technologies tailored for different environments and conditions.

Quantum state manipulation of single atom magnets using the hyperfine interaction

The magnetic quantum states of holmium single atom magnets on MgO(100) have proven extremely robust when exposed to high magnetic fields and temperatures up to 35 K. Here we address the stability of Ho at small magnetic fields, where the hyperfine interaction creates several avoided level crossings. Using spin-polarized scanning tunneling microscopy, we demonstrate quantum state control via Landau-Zener tunneling and stable magnetization at zero field. Our observations indicate a total spin ground state of ${J}_{z}=\ifmmode\pm\else\textpm\fi{}8$. Combined quantum and classical control render Ho a promising qubit candidate.

Majorana fermions in the Kitaev quantum spin system α-RuCl3

α-RuCl3 has recently attracted great interest as a possible experimental realization of the Kitaev model. Neutron scattering measurements of a single crystal of this material reveal signatures of Majorana excitations, consistent with Kitaev’s predictions. Geometrical constraints to the electronic degrees of freedom within condensed-matter systems often give rise to topological quantum states of matter such as fractional quantum Hall states, topological insulators, and Weyl semimetals1,2,3. In magnetism, theoretical studies predict an entangled magnetic quantum state with topological ordering and fractionalized spin excitations, the quantum spin liquid4. In particular, the so-called Kitaev spin model5, consisting of a network of spins on a honeycomb lattice, is predicted to host Majorana fermions as its excitations. By means of a combination of specific heat measurements and inelastic neutron scattering experiments, we demonstrate the emergence of Majorana fermions in single crystals of α-RuCl3, an experimental realization of the Kitaev spin lattice. The specific heat data unveils a two-stage release of magnetic entropy that is characteristic of localized and itinerant Majorana fermions. The neutron scattering results corroborate this picture by revealing quasielastic excitations at low energies around the Brillouin zone centre and an hour-glass-like magnetic continuum at high energies. Our results confirm the presence of Majorana fermions in the Kitaev quantum spin liquid and provide an opportunity to build a unified conceptual framework for investigating fractionalized excitations in condensed matter1,6,7,8.

Coherent long-range magnetic bound states in a superconductor

The quantum coherent coupling of completely different degrees of freedom is a challenging path towards creating new functionalities for quantum electronics. Usually the antagonistic coupling between spins of magnetic impurities and superconductivity leads to the destruction of the superconducting order. Here we show that a localized classical spin of an iron atom immersed in a superconducting condensate can give rise to new kind of long range coherent magnetic quantum state. In addition to the well-known Shiba bound state present on top of an impurity we reveal the existence of a star shaped pattern which extends as far as 12 nm from the impurity location. This large spatial dispersion turns out to be related, in a non-trivial way, to the superconducting coherence length. Inside star branches we observed short scale interference fringes with a particle-hole asymmetry. Our theoretical approach captures these features and relates them to the electronic band structure and the Fermi wave length of the superconductor. The discovery of a directional long range effect implies that distant magnetic atoms could coherently interact leading to new topological superconducting phases with fascinating properties.

Investigation of state-selective cross-sections for excitation processes of the collisions of He2++ H(1s) in strong magnetic fields

Based on the excitation cross-sections in collisions of H(1s) atoms with He2+ obtained by using the classical trajectory Monte Carlo method, the state-selective cross-sections of excitation processes for different n and m, where n and m are the principal and magnetic quantum numbers respectively, are studied with the application of strong longitudinal and transverse magnetic fields. Meanwhile, the precise energy levels for atom H in strong magnetic fields are obtained by non-perturbative quantum method. It is found that there is some strong separation of the state-selective cross-sections among different magnetic quantum states. Such behaviors are related to the variation of the energy levels and the diamagnetic terms induced by the applied magnetic fields. The diamagnetic terms in transverse magnetic fields result in the rapid increase of the cross-sections for the state of negative m at 25keV/u, which is further indicated by the trajectory in this case. In some cases the decrease of the total excitation cross-sections is found to be due to the rise of the energy levels caused by the magnetic fields. The orbital angular momentum along the direction of the magnetic field is not conserved absolutely; this phenomenon is found also in the trajectories and agrees with our analysis.

Toroidal magnetic states in molecular wheels: Interplay between isotropic exchange interactions and local magnetic anisotropy

It is shown that magnetic quantum states characterized by a toroidal moment of the same order of magnitude as the routinely measured molecular magnetization can arise in molecular wheels from the interplay between isotropic exchange and on-site magnetic anisotropy. They represent the first example of noncollinear molecular N\'eel states whose coupling can be strongly quenched as function of the orientation of the local anisotropy axes.

Precise Measurements of Axial, Magnetron, Cyclotron, and Spin-Cyclotron-Beat Frequencies on an Isolated 1-meV Electron

A sensitive frequency-shift technique is employed to monitor the magnetic quantum state of a single electron stored in a compensated Penning trap. The electron sees a weak parabolic magnetic pseudopotential in addition to the electric well, which causes the axial oscillation frequency to have a slight magnetic quantum state dependence. Transitions at both the spin-cyclotron-beat (anomaly) frequency and the cyclotron frequency have been measured in the same environment to yield a magnetic anomaly ${a}_{e}=(1159652410\ifmmode\pm\else\textpm\fi{}200)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$.

Investigation of theAl27(α,p)Reaction by Cross-Section Fluctuation Studies

Cross sections for the reaction ${\mathrm{Al}}^{27}(\ensuremath{\alpha},p){\mathrm{Si}}^{30}$ have been measured with energy resolutions which, in the incoming alpha-particle channel, are finer than the energy width of the overlapping levels of the compound system ${\mathrm{P}}^{31}$. Fluctuations in these cross sections were analyzed for the coherence widths of this compound nucleus and for details of the reaction mechanism, such as the behavior of reaction amplitudes as shown by the form of the frequency distribution of the cross section, the independence of the reactions leading to the different magnetic substates, and the amounts of compound-nucleus and direct-interaction processes. Cross sections were measured at 11 angles between 0\ifmmode^\circ\else\textdegree\fi{} and 175\ifmmode^\circ\else\textdegree\fi{} and at 5-keV energy steps for energies between 5.8 and 8.6 MeV. Lack of a cross correlation between the yields of protons to the ground (${0}^{+}$) and first excited (${2}^{+}$) states of ${\mathrm{Si}}^{30}$ confirmed the expected overlapping of levels of the compound nucleus, which is a basic requirement of fluctuation analysis. The coherence width of the compound-nucleus ${\mathrm{P}}^{31}$ was found to increase from 8 to 18 keV over the range of excitation energy 14.7 to 17.1 MeV. At the back angles of 175\ifmmode^\circ\else\textdegree\fi{} and 170\ifmmode^\circ\else\textdegree\fi{} the frequency distributions of cross sections for protons to the ground state of ${\mathrm{Si}}^{30}$ agree with ${\ensuremath{\chi}}^{2}$ distributions with only slightly more than two effective degrees of freedom. This number corresponds to the slightly more than one effective magnetic substate allowed by angular-momentum properties near 180\ifmmode^\circ\else\textdegree\fi{}. This agreement substantiates cross-section fluctuation theory and indicates negligible direct interaction at these back angles. At 140\ifmmode^\circ\else\textdegree\fi{} and 160\ifmmode^\circ\else\textdegree\fi{} direct interactions were assumed still to be negligible, and then from the frequency distributions of cross sections the number of independent magnetic quantum states at these angles was found to be less than expected from an analysis based on angular-momentum properties and a Hauser-Feshbach calculation. This difference is a consequence of the small orbital angular momenta involved in the ($\ensuremath{\alpha},p$) reaction at these energies. These effective numbers of magnetic substates were used at the corresponding forward angles to determine the amounts of compound-nucleus and direct-interaction processes from fluctuations in cross sections. At the lowest energies of incident alpha particles the amount of direct interaction was too low to be determined with accuracy, but at the highest energies the maximum direct-interaction cross section was roughly equal to the compound-nucleus cross section. The direct-interaction cross section was found to vary with angle roughly as expected from distorted-wave Born-approximation calculations.

Low-Energy Expansion of the Scattering Amplitude for Long-Range Quadrupole Potentials

For static potentials which are proportional asymptotically to $\frac{q{P}_{2}(cos\ensuremath{\theta})}{{r}^{3}}$, the low-energy expansion of the scattering amplitude is found through terms of $O(k)$, using a modification of the method developed by Levy and Keller for central potentials. The resulting expansion to lowest order in $k$ is found to be $f(\ensuremath{\theta}, \ensuremath{\varphi})\ensuremath{\sim}\ensuremath{-}A+(\frac{q}{3}){P}_{2}({cos\ensuremath{\theta}}_{K})+O(k)$, where $A$ is the scattering length and ${\ensuremath{\theta}}_{K}$ is the coordinate of the momentum transfer vector. Applications are attempted first to electron-atom elastic scattering where results are somewhat more complicated than for the potentials above, secondly to transitions between magnetic quantum states of atoms caused by slow electrons.