Exchange bias and domain evolution at 10 nm scales

For a fixed 2 μm×2 μm area of a Co/Pt-CoO perpendicular exchange bias system we image the ferromagnetic (FM) domains for various applied fields with 10-nm resolution by magnetic force microscopy (MFM). Using quantitative MFM we measure the local areal density of pinned uncompensated spins (pinUCS) in the antiferromagnetic (AFM) CoO layer and correlate the FM domain structure with the UCS density. Larger applied fields drive the receding domains to areas of proportionally higher pinUCS aligned antiparallel to FM moments. The data confirm that the evolution of the FM domains is determined by the pinUCS in the AFM layer, and also present examples of frustration in the system.     

EPR study of erbium-impurity complexes in silicon

Electron paramagnetic resonance (EPR) measurements have been used to characterise Er complexes formed in FZ silicon by the implantation of erbium together with either oxygen or fluorine. The samples have a 2 μm thick layer containing 10¹⁹ Er/cm³ alone or in addition 3×10¹⁹ O/cm³, 10²⁰ O/cm³ or 10²⁰ F/cm³. Various post-implantation anneals were carried out. Several different erbium centres, which have either C_1h monoclinic or trigonal symmetry, are observed and the way in which the type of centre depends on the implantation and annealing conditions is reported.     

High coercivity sputtered Nd-Fe films with perpendicular anisotropy

Thin films of Nd-Fe prepared by rf sputtering are shown to exhibit marked perpendicular anisotropy. Hysteresis loops with a sqaureness ratio of essentially 1.0 with large coercivities and significant polar Kerr rotations are reported for films with 60 at% Nd.     

Index Theory, Gerbes, and Hamiltonian Quantization

We give an Atiyah-Patodi-Singer index theory construction of the bundle of fermionic Fock spaces parametrized by vector potentials in odd space dimensions and prove that this leads in a simple manner to the known Schwinger terms (Faddeev-Mickelsson cocycle) for the gauge group action. We relate the APS construction to the bundle gerbe approach discussed recently by Carey and Murray, including an explicit computation of the Dixmier-Douady class. An advantage of our method is that it can be applied whenever one has a form of the APS theorem at hand, as in the case of fermions in an external gravitational field. Received:     

Infinite dimensional groups and quantum field theory

This paper surveys recent work on representations of infinite dimensional groups and the connection with quantum field theory.     

Automorphisms of the canonical anticommutation relations and index theory

Let H be a complex Hilbert space, P₊ an orthogonal projection on H, and P_? the complementary projection. If $\text{G}$ is any symmetrically normed ideal in the ring of bounded operators on H, then we consider the group of unitary operators on H such that P₊UP_?and P_?UP₊ lie in $\text{G}$. When $\text{G}$ is the Hilbert-Schmidt class, these unitaries define automorphisms of the C¹-algebra $\text{b}$ of the canonical anticommutation relations over H which are implementable in the representation of $\text{b}$ determined by P_?. We investigate the structure of the group $\text{U}$, proving in particular that it has infinitely many connected components, $\text{U}$_k, labelled by the Fredholm index of P₊UP₊. The connected component of the identity, $\text{U}$₀, is generated by unitaries of the form exp(iA), with A self-adjoint and P₊AP_? in $\text{G}$. Finally we consider an application of these results to two dimensional field theory, showing in particular that the charge and chiral charge quantum numbers arise as the Fredholm indices of P_±UP_± for certain unitary U on L²($\text{R}$, $\text{C}$²)