Two-dimensional Magnetic Lattice Research Articles

Lattice of microtraps for ultracold atoms based on patterned magnetic films

We have realized a two-dimensional permanent magnetic lattice of Ioffe-Pritchard microtraps for ultracold atoms. The lattice is formed by a single $300\text{\ensuremath{-}}\mathrm{nm}$ magnetized layer of FePt, patterned using optical lithography. Our magnetic lattice consists of more than 15 000 tightly confining microtraps with a density of $1250\phantom{\rule{0.3em}{0ex}}\text{traps}∕{\mathrm{mm}}^{2}$. Simple analytical approximations for the magnetic fields produced by the lattice are used to derive relevant trap parameters. We load ultracold atoms into at least 30 lattice sites at a distance of approximately $10\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$ from the film surface. The present result is an important first step toward quantum information processing with neutral atoms in magnetic lattice potentials.

Permanent magnetic lattices for ultracold atoms and quantum degenerate gases

We propose the use of periodic arrays of permanent magnetic films for producing magnetic lattices of microtraps for confining, manipulating and controlling small clouds of ultracold atoms and quantum degenerate gases. Using analytical expressions and numerical calculations we show that periodic arrays of magnetic films can produce one-dimensional (1D) and two-dimensional (2D) magnetic lattices with non-zero potential minima, allowing ultracold atoms to be trapped without losses due to spin flips. In particular, we show that two crossed layers of periodic arrays of parallel rectangular magnets plus bias fields, or a single layer of periodic arrays of square-shaped magnets with three different thicknesses plus bias fields, can produce 2D magnetic lattices of microtraps having non-zero potential minima and controllable trap depth. For arrays with micron-scale periodicity, the magnetic microtraps can have very large trap depths (∼0.5 mK for the realistic parameters chosen for the 2D lattice) and very tight confinement.

Several Kinds of Aminoxyl Radicals and their Metal Ion Complexes

Recent results of magnetization, magnetic susceptibility and muon spin rotation/relaxation (μSR) measurements of some organic neutral radicals based on aminoxyl and their anion radical complexes with alkali and transition metal cations are reported. Ferromagnetic intermolecular interactions, coexistent with antiferromagnetic ones, in several carboxyaryl nitronyl nitroxide radicals are affected by inserting alkali metal ions, while the incorporation of transition metal ions result in complex behavior suggesting in part ferromagnetic interactions. Temperature dependence of spontaneous magnetization of TANOL suberate in the ordered state, obtained through the results of μSR measurements, is characteristic of a two-dimensional magnetic lattice, consistent with that of magnetic susceptibility above the ordering temperature.

Polarized neutron diffraction study of the extended honeycomb molecular network d20−P(C6D5)4MnFe(C2O4)3

The MII and MIII magnetic ions in the extended molecular network P(C6D5)4MnFe(C2O4)3 form a two-dimensional honeycomb magnetic lattice. The Mn2+ and Fe3+ ions alternate in the extended network which is formed by the oxalate (C2O4) ligands. These hexagonal layers are separated and charge compensated by large [P(C6D5)4]+ ions, positioned in between the honeycomb layers. P(C6D5)4MnFe(C2O4)3 orders magnetically at TN=27(1) K. A full neutron spin polarization study of the neutron scattering cross section has been carried out which allows the unambigious separation of the magnetic cross section from the total diffraction process. The magnetic structure can be described with the magnetic Shubnikov group R3c. The magnetic moments are antiferromagnetically aligned along the c axis while the Mn2+ and Fe3+ ions form an antiferromagnetic alignment on the honeycomb lattice.

The Phase Diagram and Dynamic Model of Thin Magnetic Film

Based on the located energy minimum, the magnetic states and the lowest energy barriers of two-dimensional magnetic square lattice and sandwiches with long-range dipole-dipole interactions, short-range exchange inter-actions and magnetic surface anisotropy have been calculated. The phase diagram and the transition from perpendicular to in-plane magnetization with varying temperature are presented. We also derive a time dependent decay equations of magnetization and obtain hysteresis at different temperature and measurement time.

AnSU(2) analogue of the Azbel-Hofstadter Hamiltonian

Motivated by the recent findings of Wiegmann-Zabrodin and Faddeev-Kashaev, concerning the appearance of the quantum symmetry in the problem of a Bloch electron on a two-dimensional magnetic lattice, we introduce a modification of the tight binding Azbel-Hofstadter Hamiltonian, that is a specific spin-S Euler top that can be considered as its `classical' analogue. The eigenvalue problem for the proposed model, in the coherent state representation, is described by the S-gap Lame equation and, thus, is completely solvable. We observe a striking similarity between the shapes of the spectra of the two models for various values of the spin S.

Molecular structure and single crystal EPR spectra of bis(L-Valinato)copper(II) monohydrate, Cu[H 2NCH(CH 3) 2CHCO 2] 2·H 2O

A magnetic-structural study of the title compound, Cu(L-Val) 2·H 2O, employing EPR spectroscopy and X-ray diffraction methods is presented. The complex crystallizes in the space group C2 with a = 21.314(5) A ̊ , b = 9.586(2) A ̊ , c = 7.417(2) A ̊ , β = 108.89(2)°, and Z=4. The Cu(II) ions, which are in a five-fold pyramidal coordination, with two valine molecules and a water oxygen (O w), are arranged in layers parallel to (100). Neighboring Cu(L-Val) 2·H 2O molecules in a layer are linked to each other by a net of O w-H…O and N-H…O hydrogen bonds. The single EPR line observed arises from the collapse of the resonances due to the two magnetically inequivalent Cu(II) ions in the lattice caused by the exchange interaction. The obtained g ⌈ = 2.254(1) and g ⊥ = 2.061(1) principal values of the molecular gyromagnetic tensor point to a d( x 2− y 2) orbital for the unpaired electron. The orientation of this orbital was also obtained from our EPR data. The angular variation of the resonance line width has contributions arising from the dipolar interaction modulated by exchange effects in a two-dimensional magnetic lattice, and from the incomplete collapse of the hyperfine structure. The EPR results are compared to those obtained in other copper amino acid complexes.

EPR of layered magnetic metal-amino acid salts. II. Cu(L-Met) 2

Single crystals of bis(L-methioninato)copper(II), Cu(L-Met) 2, were studied by EPR at 9.7 and 33.6 GHz, at 300 K. The position and the peak-to-peak linewidth of the single observed EPR line were measured in three perpendicular planes of the samples. This single resonance is due to the collapse of the resonances of the two magnetically inequivalent copper ions in the lattice caused by the exchange interaction. The components of the molecular g tensor for isolated copper ions were obtained using a model which assumes axial symmetry. The results indicate that the unpaired electron occupies the d( x 2 − y 2) orbital, and the orientation of the molecule obtained from the EPR data agrees with the crystallographic result. The linewidth data support a model which assumes exchange narrowing of the magnetic dipolar interaction in a two-dimensional magnetic lattice, an incomplete collapse of the hyperfine structure, and a frequency-dependent contribution in the planes where the g factors for the two sites of copper are different. An analysis of this latter contribution, allows to evaluate an exchange coupling constant | J′| = 0.10 K between inequivalent copper neighbors. Besides, the analysis of the hyperfine contribution to the linewidth gives | J| = 0.18 K for the average value of the exchange interaction of one copper ion with its six nearest neighbors within the layer. Concerning the possible superexchange paths between inequivalent copper ions, we suggest they can be of two types: the CuNH…OCu one, involving hydrogen bonds between equatorial nitrogens and equatorial oxygens, and the other consisting of CuOCOCu carboxylate bridges involving apical and equatorial oxygens. They are discussed in view of the experimental results.

Magnetic symmetry and crystal lattices

One-dimensional, two-dimensional and three-dimensional magnetic lattices have been derived making use of methods adopted by the authors in an earlier paper in deriving cystallographic magnetic point groups.