Ground state properties of antiferromagnetic Heisenberg spin rings

Exact ground state properties of antiferromagnetic Heisenberg spin rings with isotropic next neighbour interaction are presented for various numbers of spin sites and spin quantum numbers. Earlier work by Peierls, Marshall, Lieb, Schultz and Mattis focused on bipartite lattices and is not applicable to rings with an odd number of spins. With the help of exact diagonalization methods we find a more general systematic behaviour which for instance relates the number of spin sites and the individual spin quantum numbers to the degeneracy of the ground state. These numerical findings all comply with rigorous proofs in the cases where a general analysis could be carried out. Therefore it can be plausibly conjectured that the ascertained properties hold for ground states of arbitrary antiferromagnetic Heisenberg spin rings.Comment: 13 pages, 5 figures, uses epsfig.sty, submitted to Phys. Rev. B. More information at http://www.physik.uni-osnabrueck.de/makrosysteme

Proton Spin Relaxation Induced by Quantum Tunneling in Fe8 Molecular Nanomagnet

The spin-lattice relaxation rate $T_{1}^{-1}$ and NMR spectra of $^1$H in single crystal molecular magnets of Fe8 have been measured down to 15 mK. The relaxation rate $T_1^{-1}$ shows a strong temperature dependence down to 400 mK. The relaxation is well explained in terms of the thermal transition of the iron state between the discreet energy levels of the total spin S=10. The relaxation time $T_1$ becomes temperature independent below 300 mK and is longer than 100 s. In this temperature region stepwise recovery of the $^1$H-NMR signal after saturation was observed depending on the return field of the sweep field. This phenomenon is attributed to resonant quantum tunneling at the fields where levels cross and is discussed in terms of the Landau-Zener transition.Comment: 13 pages, 5 figure

Heisenberg exchange parameters of molecular magnets from the high-temperature susceptibility expansion

We provide exact analytical expressions for the magnetic susceptibility function in the high temperature expansion for finite Heisenberg spin systems with an arbitrary coupling matrix, arbitrary single-spin quantum number, and arbitrary number of spins. The results can be used to determine unknown exchange parameters from zero-field magnetic susceptibility measurements without diagonalizing the system Hamiltonian. We demonstrate the possibility of reconstructing the exchange parameters from simulated data for two specific model systems. We examine the accuracy and stability of the proposed method.Comment: 13 pages, 7 figures, submitted to Phys. Rev.

Aeroacoustics research in Europe: The CEAS-ASC report on 2020 & 2021 highlights

The Council of European Aerospace Societies (CEAS) Aeroacoustics Specialists Committee (ASC) supports and promotes the interests of the scientific and industrial aeroacoustics community on a European scale and European aeronautics activities internationally. In this context, “aeroacoustics” encompasses all aerospace acoustics and related areas. Each year the committee highlights some of the research and development projects in Europe. Due the effects of the Covid 19 pandemic it was not possible to publish an edition in 2021 and so this paper is a report on highlights of aeroacoustics research in Europe in both 2020 and 2021, compiled from information provided to the ASC of the CEAS. In addition, during 2020 and 2021, a number of research programmes involving aeroacoustics were funded by the European Commission. Some of the highlights from these programmes are also summarized in this article. Enquiries concerning all contributions should be addressed to the authors who are given at the end of each subsection

High frequency resonant experiments in Fe8_8 molecular clusters

Precise resonant experiments on Fe$_{8}$ magnetic clusters have been conducted down to 1.2 K at various tranverse magnetic fields, using a cylindrical resonator cavity with 40 different frequencies between 37 GHz and 110 GHz. All the observed resonances for both single crystal and oriented powder, have been fitted by the eigenstates of the hamiltonian ${\cal H}=-DS_z^2+ES_x^2-g\mu_B{\bf H}\cdot {\bf S}$. We have identified the resonances corresponding to the coherent quantum oscillations for different orientations of spin S = 10.Comment: to appear in Phys.Rev. B (August 2000

Insights into the mechanism for gold catalysis: behaviour of gold(i) amide complexes in solution

We report the synthesis and activity of new mononuclear and dinuclear gold amide complexes . The dinuclear complexes and were characterised by single crystal X-ray analysis. We also report solution NMR and freezing point depression experiments to rationalise their behaviour in solution and question the de-ligation process invoked in gold catalysis

CSIDH on the surface

For primes p≡3mod4, we show that setting up CSIDH on the surface, i.e., using supersingular elliptic curves with endomorphism ring Z[(1+−p−−−√)/2], amounts to just a few sign switches in the underlying arithmetic. If p≡7mod8 then horizontal 2-isogenies can be used to help compute the class group action. The formulas we derive for these 2-isogenies are very efficient (they basically amount to a single exponentiation in Fp) and allow for a noticeable speed-up, e.g., our resulting CSURF-512 protocol runs about 5.68% faster than CSIDH-512. This improvement is completely orthogonal to all previous speed-ups, constant-time measures and construction of cryptographic primitives that have appeared in the literature so far. At the same time, moving to the surface gets rid of the redundant factor Z3 of the acting ideal-class group, which is present in the case of CSIDH and offers no extra security

Characterization of the S = 9 excited state in Fe8Br8 by Electron Paramagnetic Resonance

High Frequency electron paramagnetic resonance has been used to observe the magnetic dipole, $\Delta$ M$_s$ = $\pm$ 1, transitions in the $S = 9$ excited state of the single molecule magnet Fe$_8$Br$_8$. A Boltzmann analysis of the measured intensities locates it at 24 $\pm$ 2 K above the $S = 10$ ground state, while the line positions yield its magnetic parameters D = -0.27 K, E = $\pm$0.05 K, and B$_4^0$ = -1.3$\times$ 10$^{-6}$ K. D is thus smaller by 8% and E larger by 7% than for $S = 10$. The anisotropy barrier for $S = 9$ is estimated as 22 K,which is 25% smaller than that for $S = 10$ (29 K). These data also help assign the spin exchange constants(J's) and thus provide a basis for improved electronic structure calculations of Fe$_8$Br$_8$.Comment: 7 pages, Figs included in text, submitted to PR

Uniform bounds on complexity and transfer of global properties of Nash functions

We show that the complexity of semialgebraic sets and mappings can be used to parametrize Nash sets and mappings by Nash families. From this we deduce uniform bounds on the complexity of Nash functions that lead to first-order descriptions of many properties of Nash functions and a good behaviour under real closed field extension (e.g. primary decomposition). As a distinguished application, we derive the solution of the extension and global equations problems over arbitrary real closed fields, in particular over the field of real algebraic numbers. This last fact and a technique of change of base are used to prove that the Artin-Mazur description holds for abstract Nash functions on the real spectrum of any commutative ring, and solve extension and global equations in that abstract setting. To complete the view, we prove the idempotency of the real spectrum and an abstract version of the separation problem. We also discuss the conditions for the rings of abstract Nash functions to be noetherian

Calculating the energy spectra of magnetic molecules: application of real- and spin-space symmetries

The determination of the energy spectra of small spin systems as for instance given by magnetic molecules is a demanding numerical problem. In this work we review numerical approaches to diagonalize the Heisenberg Hamiltonian that employ symmetries; in particular we focus on the spin-rotational symmetry SU(2) in combination with point-group symmetries. With these methods one is able to block-diagonalize the Hamiltonian and thus to treat spin systems of unprecedented size. In addition it provides a spectroscopic labeling by irreducible representations that is helpful when interpreting transitions induced by Electron Paramagnetic Resonance (EPR), Nuclear Magnetic Resonance (NMR) or Inelastic Neutron Scattering (INS). It is our aim to provide the reader with detailed knowledge on how to set up such a diagonalization scheme.Comment: 29 pages, many figure