Okayama University  Faculty of Science  Department of Physics  RIIS  Harald O. Jeschke

A number of materials with interesting magnetic properties have been studied with special attention to lattice degrees of freedom. Some experience with the correct application of ab initio molecular dynamics to materials with transition metal centers has been collected. Careful preparation of structures was often a prerequisite of these investigations, either because materials that were not yet synthesized were investigated (see a) Cu₄Te₅O₁₂Br₄) or because the published structure lacked the precision necessary for precise DFT study (see b) azurite Cu₃(CO₃)₂(OH)₂). In most materials studied in this area, contact between the material and many body models was made by determination of effective Hamiltonian parameters via Nth order muffin tin orbital (NMTO) downfolding or tight binding (TB).

a) Coupled tetrahedra quantum spin systems Cu₄Te₅0₁₂Cl₄ and
Cu₄Te₅O₁₂Br₄

The family of oxyhalides which include Cu₂Te₂O₅X₂ (X=Br and Cl) and Cu₄Te₅O₁₂Cl₄ are quantum spin systems containing weakly coupled Cu₄²⁺ tetrahedra. The exchange interactions in the tetrahedra are geometrically frustrated, and thus small changes in the inter-tetrahedra couplings can lead to unconventional ground states. In particular, there is experimental evidence pointing to a closeness of the Cu₂Te₂O₅Br₂ system to a quantum critical point. While for the Cu₂Te₂O₅X₂-system the various intra- and intertetrahedral couplings have been determined by NMTO downfolding [1] and subsequently confirmed by neutron diffraction experiments [2], the present work addresses the changes in exchange couplings in Cu₄Te₅O₁₂Cl₄ with respect to Cu₂Te₂O₅Cl₂ due to the slightly changed arrangements of the Cu₄²⁺ tetrahedra in the crystal structure and the couplings that would be expected for the hypothetical, not yet synthesized system Cu₄Te₅O₁₂Br₄. The latter involved the determination of a likely crystal structure with the help of Car Parrinello molecular dynamics [3]. For Cu₄Te₅O₁₂Cl₄, we find that while the overall nature of the interaction remains the same as in Cu₂Te₂O₅Cl₂, the diagonal interaction between tetrahedra is strongly reduced while the out-of-plane interaction is strongly enhanced. The hypothetical Cu₄Te₅O₁₂Br₄ system shows in general stronger in-plane intertetrahedral couplings compared to the Cl system. These results are published in references [VSJ+07,RJV+07].

b) Diamond spin chain azurite Cu₃(CO₃)₂(OH)₂

Azurite has been intensely discussed since magnetic measurements found a 1/3 magnetization plateau [4]. The Cu²⁺ spins in azurite are arranged in a diamond chain formed by alternating Cu²⁺ dimers and monomers. Several experiments [4,5] and theoretical interpretations of experiments [6] have come to completely different sets of parameters for the underlying magnetic Hamiltonian. This dispute makes a first principle analysis of this material very interesting.

It turns out that the structural parameters have not been determined with sufficient precision, which leads to a failure of convergence of the FPLAPW calculation. Thus, we first carefully relax the light atom positions before extracting the low energy effective Hamiltonian parameters. These parameters are determined by a tight binding fit to the band structure as well as from energy differences between different spin configurations. The resulting picture for azurite compares well to experimental observations.