EPR spectrum via entangled states for an Exchange-Coupled Dimer of Single-Molecule Magnets

Multi-high-frequency electron paramagnetic resonance(EPR) spectrum for a supermolecular dimer $[ Mn_4]_2$ of single-molecule magnets recently reported [S. Hill, R. S. Edwards, N. Aliaga-Alcalde and G. Christou(HEAC), Science 302, 1015 (2003)] is studied in terms of the perturbation method in which the high-order corrections to the level splittings of degenerate states are included. It is shown that the corresponding eigenvectors are composed of entangled states of two molecules. The EPR-peak positions are calculated in terms of the eigenstates at various frequencies. From the best fit of theoretical level splittings with the measured values we obtain the anisotropy constant and exchange coupling which are in agreement with the corresponding values of experimental observation. Our study confirms the prediction of HEAC that the two $Mn_4$ units within the dimer are coupled quantum mechanically by the antiferromagnetic exchange interaction and the supermolecular dimer behaviors in analogy with artificially fabricated quantum dots.Comment: 16 pages,2 figures, 2 table

A Hybrid Approach to Case Teaching

We structure case based teaching using a combination of computer-support echnology and in-class activities. We create and design an on-line learning tool, Case Study On-line (CSOL) that enables instructor to structure the delivery of teaching resources and set up assignment tasks in the system. The tool enables tasks to be set in a way that they can be completed sequentially, and learning resources can be accessed only when required by students. Upon submission of their assignments, students can promptly receive instructor’s explanations to the tasks. Follow up activities take place in class, with the objective to promote active learning. The tool was adopted over two semesters in an undergraduate economics course and surveys were conducted among the students to evaluate the effectiveness of the tool. The results of the survey were very positive, providing support to our belief that a system of well-designed case teaching delivery tool, together with classroom activities, is able to increase the level of students’ engagement and interest. The paper helps to address some concerns about teaching methods in undergraduate economics courses.Technologies-based Instruction, In-class Activities, Scaffolding, Active-based Learning