Thermal Stability of the Magnetization in Perpendicularly Magnetized Thin Film Nanomagnets

Understanding the stability of thin film nanomagnets with perpendicular magnetic anisotropy (PMA) against thermally induced magnetization reversal is important when designing perpendicularly magnetized patterned media and magnetic random access memories. The leading-order dependence of magnetization reversal rates are governed by the energy barrier the system needs to surmount in order for reversal to proceed. In this paper we study the reversal dynamics of these systems and compute the relevant barriers using the string method of E, Vanden-Eijnden, and Ren. We find the reversal to be often spatially incoherent; that is, rather than the magnetization flipping as a rigid unit, reversal proceeds instead through a soliton-like domain wall sweeping through the system. We show that for square nanomagnetic elements the energy barrier increases with element size up to a critical length scale, beyond which the energy barrier is constant. For circular elements the energy barrier continues to increase indefinitely, albeit more slowly beyond a critical size. In both cases the energy barriers are smaller than those expected for coherent magnetization reversal.Comment: 5 pages, 4 Figure

Domain studies of CoCr with perpendicular anisotropy

R.F. Magnetron sputtered CoCr films (79/21 at%) with various thicknesses are magnetically characterized. The domain structure is observed by digitally enhanced Kerr microscopy and depends on the Hc/Hk values of the samples. For low and high coercivity films a comparison is made between the measured VSM hysteresis, domain period and a theoretical domain model. The domain shape is a function of the magnetic history of the sample and the bending created by the deposition process

Quantum Encodings in Spin Systems and Harmonic Oscillators

We show that higher-dimensional versions of qubits, or qudits, can be encoded into spin systems and into harmonic oscillators, yielding important advantages for quantum computation. Whereas qubit-based quantum computation is adequate for analyses of quantum vs classical computation, in practice qubits are often realized in higher-dimensional systems by truncating all but two levels, thereby reducing the size of the precious Hilbert space. We develop natural qudit gates for universal quantum computation, and exploit the entire accessible Hilbert space. Mathematically, we give representations of the generalized Pauli group for qudits in coupled spin systems and harmonic oscillators, and include analyses of the qubit and the infinite-dimensional limits.Comment: 4 pages, published versio

Evaluating the Role of Writing in the First and Second Year University Foreign Language Curriculum

Approaches to foreign language (FL) instruction have changed a great deal in the past fifty years, the most fundamental change being the shift from a focus solely on language form to a focus on communicative competence (CC). Although most FL instructors now appear to focus on CC in the teaching of speaking, they do not necessarily apply CC to writing in the same way. The study reported here attempts to describe the role currently played by writing in the first and second-year FL curriculum by detailing the methods used by 10 professors working at 7 different universities across the United States to teach FL writing in these courses. Results indicate that writing-to-learn activities make up a large majority of the writing methods used, but that learning-to-write activities that foster CC in writing have also been successfully integrated into the beginning FL curriculum