Weak antiferromagnetism due to Dzyaloshinskii-Moriya interaction in Ba3_3Cu2_2O4_4Cl2_2

The antiferromagnetic insulating cuprate Ba$_3$Cu$_2$O$_4$Cl$_2$ contains folded CuO$_2$ chains with four magnetic copper ions ($S=1/2$) per unit cell. An underlying multiorbital Hubbard model is formulated and the superexchange theory is developed to derive an effective spin Hamiltonian for this cuprate. The resulting spin Hamiltonian involves a Dzyaloshinskii-Moriya term and a more weak symmetric anisotropic exchange term besides the isotropic exchange interaction. The corresponding Dzyaloshinskii-Moriya vectors of each magnetic Cu-Cu bond in the chain reveal a well defined spatial order. Both, the superexchange theory and the complementary group theoretical consideration, lead to the same conclusion on the character of this order. The analysis of the ground-state magnetic properties of the derived model leads to the prediction of an additional noncollinear modulation of the antiferromagnetic structure. This weak antiferromagnetism is restricted to one of the Cu sublattices.Comment: 13 pages, 1 table, 4 figure

Quantum magnetism in two dimensions: From semi-classical N\'eel order to magnetic disorder

This is a review of ground-state features of the s=1/2 Heisenberg antiferromagnet on two-dimensional lattices. A central issue is the interplay of lattice topology (e.g. coordination number, non-equivalent nearest-neighbor bonds, geometric frustration) and quantum fluctuations and their impact on possible long-range order. This article presents a unified summary of all 11 two-dimensional uniform Archimedean lattices which include e.g. the square, triangular and kagome lattice. We find that the ground state of the spin-1/2 Heisenberg antiferromagnet is likely to be semi-classically ordered in most cases. However, the interplay of geometric frustration and quantum fluctuations gives rise to a quantum paramagnetic ground state without semi-classical long-range order on two lattices which are precisely those among the 11 uniform Archimedean lattices with a highly degenerate ground state in the classical limit. The first one is the famous kagome lattice where many low-lying singlet excitations are known to arise in the spin gap. The second lattice is called star lattice and has a clear gap to all excitations. Modification of certain bonds leads to quantum phase transitions which are also discussed briefly. Furthermore, we discuss the magnetization process of the Heisenberg antiferromagnet on the 11 Archimedean lattices, focusing on anomalies like plateaus and a magnetization jump just below the saturation field. As an illustration we discuss the two-dimensional Shastry-Sutherland model which is used to describe SrCu2(BO3)2.Comment: This is now the complete 72-page preprint version of the 2004 review article. This version corrects two further typographic errors (three total with respect to the published version), see page 2 for detail

A quantum analogue of the first fundamental theorem of invariant theory

We establish a noncommutative analogue of the first fundamental theorem of classical invariant theory. For each quantum group associated with a classical Lie algebra, we construct a noncommutative associative algebra whose underlying vector space forms a module for the quantum group and whose algebraic structure is preserved by the quantum group action. The subspace of invariants is shown to form a subalgebra, which is finitely generated. We determine generators of this subalgebra of invariants and determine their commutation relations. In each case considered, the noncommutative modules we construct are flat deformations of their classical commutative analogues. Thus by taking the limit as $q\to 1$, our results imply the first fundamental theorem of classical invariant theory, and therefore generalise them to the noncommutative case.Comment: 44 pages, 3 figure

Development of biotissue training models for anastomotic suturing in pancreatic surgery

Background: Anastomotic suturing is the Achilles heel of pancreatic surgery. Especially in laparoscopic and robotically assisted surgery, the pancreatic anastomosis should first be trained outside the operating room. Realistic training models are therefore needed. Methods: Models of the pancreas, small bowel, stomach, bile duct, and a realistic training torso were developed for training of anastomoses in pancreatic surgery. Pancreas models with soft and hard tex-tures, small and large ducts were incrementally developed and evaluated. Experienced pancreatic sur-geons (n = 44) evaluated haptic realism, rigidity, fragility of tissues, and realism of suturing and knot tying. Results: In the iterative development process the pancreas models showed high haptic realism and highest realism in suturing (4.6 & PLUSMN; 0.7 and 4.9 & PLUSMN; 0.5 on 1-5 Likert scale, soft pancreas). The small bowel model showed highest haptic realism (4.8 & PLUSMN; 0.4) and optimal wall thickness (0.1 & PLUSMN; 0.4 on -2 to +2 Likert scale) and suturing behavior (0.1 & PLUSMN; 0.4). The bile duct models showed optimal wall thickness (0.3 & PLUSMN; 0.8 and 0.4 & PLUSMN; 0.8 on -2 to +2 Likert scale) and optimal tissue fragility (0 & PLUSMN; 0.9 and 0.3 & PLUSMN; 0.7). Conclusion: The biotissue training models showed high haptic realism and realistic suturing behavior. They are suitable for realistic training of anastomoses in pancreatic surgery which may improve patient outcomes.Surgical oncolog

Protostellar and cometary detections of organohalogens

Organohalogens, a class of molecules that contain at least one halogen atom bonded to carbon, are abundant on the Earth where they are mainly produced through industrial and biological processes1. Consequently, they have been proposed as biomarkers in the search for life on exoplanets2. Simple halogen hydrides have been detected in interstellar sources and in comets, but the presence and possible incorporation of more complex halogen-containing molecules such as organohalogens into planet-forming regions is uncertain3,4. Here we report the interstellar detection of two isotopologues of the organohalogen CH3Cl and put some constraints on CH3F in the gas surrounding the low-mass protostar IRAS 16293–2422, using the Atacama Large Millimeter/submillimeter Array (ALMA). We also find CH3Cl in the coma of comet 67P/Churyumov–Gerasimenko (67P/C-G) by using the Rosetta Orbiter Spectrometer for Ion and Neutral Analysis (ROSINA) instrument. The detections reveal an efficient pre-planetary formation pathway of organohalogens. Cometary impacts may deliver these species to young planets and should thus be included as a potential abiotical production source when interpreting future organohalogen detections in atmospheres of rocky planets.Stars and planetary systemsInterstellar matter and star formatio