Symmetry and magnetic structure determination: Developments in refinement techniques and examples

Group Theory techniques can aid greatly the determination of magnetic structures. The integration of their calculations into new and existing refinement programs is an ongoing development that will simplify and make more rigorous the analysis of experimental data. This paper presents an overview of the practical application of symmetry analysis to the determination of magnetic structures. Details are given of the different programs that perform these calculations and how refinements can be carried out using their results. Examples are presented that show how such analysis can be important in the interpretation of magnetic diffraction data, and to our reasoning of the causes for the observed ordering.Comment: Proceedings of ICNS 2001. To be published in Applied Physics

Conventional and unconventional orderings in the jarosites

The jarosites make up the most studied family of {\it kagom\'e} antiferromagnets. The flexibility of the structure to substitution of the A and B ions allows a wide range of compositions to be synthesised with the general formula AB3(SO4)2(OH)6 (A = Na$^+$, K$^+$, Ag$^+$, Rb$^+$, H3O$^+$, NH4$^+$, 1/2Ba$^{2+}$, and 1/2Pb$^{2+}$; B = Fe$^{3+}$, Cr$^{3+}$, and V$^{3+}$). Additional chemical tuning of the exchange between layers is also possible by substitution of the (SO4)$^{2-}$ groups by (SeO4)$^{2-}$ or (CrO4)$^{2-}$. Thus, a variety of S = 5/2, 3/2, and 1 systems can be engineered to allow study of the effects of frustration in both the classical and more quantum limits. Within this family both conventional long-ranged magnetic order and more exotic unconventional orderings have been found. This article reviews the different types of magnetic orderings that occur and examines some of the parameters that are their cause.Comment: Proceedings of the conterence "Highly Frustrated Magnetism 2000" . To be published in the Canadian Journal of Physic

Inelastic neutron scattering studies of the quantum frustrated magnet clinoatacamite, γ\gamma-Cu2(OD)3Cl, a proposed valence bond solid (VBS)

The frustrated magnet clinoatacamite, $\gamma$-Cu$_2$(OH)$_3$Cl, is attracting a lot of interest after suggestions that at low temperature it forms an exotic quantum state termed a Valence Bond Solid (VBS) made from dimerised Cu$^{2+}$ ($S=1/2$) spins.\cite{Lee_clinoatacamite} Key to the arguments surrounding this proposal were suggestions that the kagom\'e planes in the magnetic pyrochlore lattice of clinoatacamite are only weakly coupled, causing the system to behave as a quasi-2-dimensional magnet. This was reasoned from the near 95$^\circ$ angles made at the bridging oxygens that mediate exchange between the Cu ions that link the kagom\'e planes. Recent work pointed out that this exchange model is inappropriate for $\gamma$-Cu$_2$(OH)$_3$Cl, where the oxygen is present as a $\mu_3$-OH.\cite{Wills_JPC} Further, it used symmetry calculations and neutron powder diffraction to show that the low temperature magnetic structure ($T<6$ K) was canted and involved significant spin ordering on all the Cu$^{2+}$ spins, which is incompatible with the interpretation of simultaneous VBS and N\'eel ordering. Correspondingly, clinoatacamite is best considered a distorted pyrochlore magnet. In this report we show detailed inelastic neutron scattering spectra and revisit the responses of this frustrated quantum magnet.Comment: Proceedings of The International Conference on Highly Frustrated Magnetism 2008 (HFM2008

Toward Perfection: Kapellasite, Cu3Zn(OH)6Cl2, a New Model S = 1/2 Kagome Antiferromagnet

The search for the resonating valence bond (RVB) state continues to underpin many areas of condensed matter research. The RVB is made from the dimerisation of spins on different sites into fluctuating singlets, and was proposed by Anderson to be the reference state from which the transition to BCS superconductivity occurs. Little is known about the state experimentally, due to the scarcity of model materials. Theoretical work has put forward the S = 1/2 kagome antiferromagnet (KAFM) as a good candidate for the realization of the RVB state. In this paper we introduce a new model system, the S = 1/2 KAFM Kapellasite, Cu3Zn(OH)6Cl2. We show that its crystal structure is a good approximation to a 2-dimensional kagome antiferromagnet and that susceptibility data indicate a collapse of the magnetic moment below T = 25 K that is compatible with the spins condensing into the non-magnetic RVB state.Comment: Communication, 3 pages, 3 figure

On the adequacy of current empirical evaluations of formal models of categorization

Categorization is one of the fundamental building blocks of cognition, and the study of categorization is notable for the extent to which formal modeling has been a central and influential component of research. However, the field has seen a proliferation of noncomplementary models with little consensus on the relative adequacy of these accounts. Progress in assessing the relative adequacy of formal categorization models has, to date, been limited because (a) formal model comparisons are narrow in the number of models and phenomena considered and (b) models do not often clearly define their explanatory scope. Progress is further hampered by the practice of fitting models with arbitrarily variable parameters to each data set independently. Reviewing examples of good practice in the literature, we conclude that model comparisons are most fruitful when relative adequacy is assessed by comparing well-defined models on the basis of the number and proportion of irreversible, ordinal, penetrable successes (principles of minimal flexibility, breadth, good-enough precision, maximal simplicity, and psychological focus)

Machine learning of visual object categorization: an application of the SUSTAIN model

Formal models of categorization are psychological theories that try to describe the process of categorization in a lawful way, using the language of mathematics. Their mathematical formulation makes it possible for the models to generate precise, quantitative predictions. SUSTAIN (Love, Medin & Gureckis, 2004) is a powerful formal model of categorization that has been used to model a range of human experimental data, describing the process of categorization in terms of an adaptive clustering principle. Love et al. (2004) suggested a possible application of the model in the field of object recognition and categorization. The present study explores this possibility, investigating at the same time the utility of using a formal model of categorization in a typical machine learning task. The image categorization performance of SUSTAIN on a well-known image set is compared with that of a linear Support Vector Machine, confirming the capability of SUSTAIN to perform image categorization with a reasonable accuracy, even if at a rather high computational cost