Quantum Hall Ferromagnets: Induced Topological term and electromagnetic interactions

The $\nu = 1$ quantum Hall ground state in materials like GaAs is well known to be ferromagnetic in nature. The exchange part of the Coulomb interaction provides the necessary attractive force to align the electron spins spontaneously. The gapless Goldstone modes are the angular deviations of the magnetisation vector from its fixed ground state orientation. Furthermore, the system is known to support electrically charged spin skyrmion configurations. It has been claimed in the literature that these skyrmions are fermionic owing to an induced topological Hopf term in the effective action governing the Goldstone modes. However, objections have been raised against the method by which this term has been obtained from the microscopics of the system. In this article, we use the technique of the derivative expansion to derive, in an unambiguous manner, the effective action of the angular degrees of freedom, including the Hopf term. Furthermore, we have coupled perturbative electromagnetic fields to the microscopic fermionic system in order to study their effect on the spin excitations. We have obtained an elegant expression for the electromagnetic coupling of the angular variables describing these spin excitations.Comment: 23 pages, Plain TeX, no figure

DE MINIMIS NON CURAT LEX

An age-old maxim often applied but infrequently rationalized is that of de minimus non curat lex. In the recent case of Steve Anderson v. Mt. Clemens Pottery Company, the United States Supreme Court focused attention upon the doctrine by ruling that it should be applied in determining whether walking time and other preliminary activities constitute work for which employees are entitled to compensation under the Fair Labor Standards Act of 1938. The so-called portal-to-portal problems which have arisen as a result of the last mentioned ruling make timely a discussion of the origin, meaning, function and application of the maxim

Thermodynamic Phase Diagram of the Quantum Hall Skyrmion System

We numerically study the interacting quantum Hall skyrmion system based on the Chern-Simons action. By noticing that the action is invariant under global spin rotations in the spin space with respect to the magnetic field direction, we obtain the low-energy effective action for a many skyrmion system. Performing extensive molecular dynamics simulations, we establish the thermodynamic phase diagram for a many skyrmion system.Comment: 4 pages, RevTex, 2 postscript figure

Skyrmion Dynamics and NMR Line Shapes in QHE Ferromagnets

The low energy charged excitations in quantum Hall ferromagnets are topological defects in the spin orientation known as skyrmions. Recent experimental studies on nuclear magnetic resonance spectral line shapes in quantum well heterostructures show a transition from a motionally narrowed to a broader `frozen' line shape as the temperature is lowered at fixed filling factor. We present a skyrmion diffusion model that describes the experimental observations qualitatively and shows a time scale of $\sim 50 \mu{\rm sec}$ for the transport relaxation time of the skyrmions. The transition is characterized by an intermediate time regime that we demonstrate is weakly sensitive to the dynamics of the charged spin texture excitations and the sub-band electronic wave functions within our model. We also show that the spectral line shape is very sensitive to the nuclear polarization profile along the z-axis obtained through the optical pumping technique.Comment: 6 pages, 4 figure

Using Stories in Coach Education

The purpose of this paper is to illustrate how storied representations of research can be used as an effective pedagogical tool in coach education. During a series of continuing professional development seminars for professional golf coaches, we presented our research in the form of stories and poems which were created in an effort to evoke and communicate the lived experiences of elite professional golfers. Following these presentations, we obtained written responses to the stories from 53 experienced coaches who attended the seminars. Analysis of this data revealed three ways in which coaches responded to the stories: (i) questioning; (ii) summarising; and (iii) incorporating. We conclude that these responses illustrate the potential of storied forms of representation to enhance professional development through stimulating reflective practice and increasing understanding of holistic, person-centred approaches to coaching athletes in high-performance sport

Non-commutative field theory approach to two-dimensional vortex liquid system

We investigate the non-commutative (NC) field theory approach to the vortex liquid system restricted to the lowest Landau level (LLL) approximation. NC field theory effectively takes care of the phase space reduction of the LLL physics in a $\star$-product form and introduces a new gauge invariant form of a quartic potential of the order parameter in the Ginzburg-Landau (GL) free energy. This new quartic interaction coupling term has a non-trivial equivalence relation with that obtained by Br\'ezin, Nelson and Thiaville in the usual GL framework. The consequence of the equivalence is discussed.Comment: Add vortex lattice formation, more references, and one autho

Effective Crack-Propagation Resistance Under Monotonic And Cyclic Loading

Crack propagation under monotonic and cyclic loading was investigated in alumina-epoxy composite specimens, produced via a multi-step infiltration technique. Under monotonic loading, an increase in effective fracture toughness was observed, which was attributed to the development of a bridging zone behind the crack-tip. A similar increase in crack propagation resistance was observed under cyclic loading, though this was more difficult to quantify. This was achieved approximately using an adjustment based on the Paris-law relation. This adjustment approach is described in this paper, and is also applied to fatigue results for graded composite specimens, in which the increase in crack-growth resistance with crack-extension is accompanied by a spatial variation in intrinsic and extrinsic crack-growth resistance

Skyrme Crystal In A Two-Dimensional Electron Gas

The ground state of a two-dimensional electron gas at Landau level filling factors near $\nu =1$ is a Skyrme crystal with long range order in the positions and orientations of the topologically and electrically charged elementary excitations of the $\nu=1$ ferromagnetic ground state. The lowest energy Skyrme crystal is a square lattice with opposing postures for topological excitations on opposite sublattices. The filling factor dependence of the electron spin-polarization, calculated for the square lattice Skyrme crystal, is in excellent agreement with recent experiments.Comment: 3 pages, latex, 3 figures available upon request from [email protected]