Irreducible tensor operator techniques and point-group symmetries for molecular magnetism
Final Report Abstract
I consider the project a great success. In detail we achieved the following: We successfully studied the frustrated three-leg ladder compound [(CuCl2tachH)3Cl]Cl2, which is a spin tube system that attracted broad interest since it is one of the very few spin tube systems at all and a very clean system in particular. We could demonstrate that this quasi one dimensional system behaves as a Luttinger liquid at low temperatures and can serve as a model system for spin-3/2 antiferromagnetic chains. We successfully compiled a detailed review article on the combined application of SU(2) and general point-group symmetries. It demonstrates with its examples that long-standing systems such as the ferric wheel Fe10 can finally be investigated in full detail and that the properties of interesting (yet fictitious) spin systems such as the spin cuboctahedra and icosahedra can be understood by inspecting the energy spectrum which is now resolved with respect to irreducible representations of the point group. This explains for instance the exact and near degeneracies in the spectrum of the icosahedron that lead to a very unusual specific heat function. We investigated several molecules synthesized by our collaborators, mainly from Manchester, Glasgow and Edinburgh. We also did develop a high performance version of the program. The scientific problem is to ease the enormous operating expense in calculating the so-called recoupling coefficients. Our research strategy is twofold. We try to reduce the number of numerical steps and we make use of highly parallelized numerics. Nevertheless, the problem of the evaluation of an enormous number of recoupling coefficients could not be solved completely. Meanwhile a bachelor student investigated special cases in his thesis. We plan to continue research along these lines. The low-lying spectrum of bipartite magnetic spin systems and maybe even frustrated ones can be described rather accurately by rotational bands, i.e. energy bands that depend quadratically on total spin S. It was conjectured that this approximation might be improved by considering superpositions of rotational band states. This is in principle correct for the ground state since the method is variational, but it is not clear how good the approximation for the low-lying gaps would be. Indeed, if ground and first excited state converge differently with the number of superimposed rotational bands it might very well be that the gaps develop not even monotonously. In a close collaboration with Dr. Andreas Läuchli of the MPI for Complex Systems, Dresden, Germany, we investigated this question, and indeed the convergence of gaps is cumbersome at least for the highly frustrated systems such as the icosidodecahedron. We gave up the idea to develop a public version of the program since at the present stage it is still far too complicated to allow easy usage. But we offer to everybody who is interested to perform the necessary calculations. Dr. Schnalle used his program to also investigate questions of magnetic transport in one-dimensional spin systems together with Dr. Robin Steinigeweg (TU Braunschweig).
Publications
- Condens. Matter Phys. 12, 331 (2009)
R. Schnalle, A. Läuchli, and J. Schnack
- in High Performance Computing in Science and Engeniering, Garching/Munich 2009, edited by S. Wagner, M. Steinmetz, A. Bode, and M. M. Müller (Springer, Heidelberg, 2010), Chap. Evaluation of Magnetic Spectra Using the Irreducible Tensor Operator Approach, pp. 575-588
J. Schnack and R. Schnalle
- Int. Rev. Phys. Chem. 29, 403 (2010)
R. Schnalle and J. Schnack
- Phys. Rev. E 82, 040103 (2010)
R. Steinigeweg and R. Schnalle
- Phys. Rev. Lett. 105, 037206 (2010)
N. B. Ivanov et al.
