Vanadium ladder compounds: From first principles to QMC

Ladder compounds with coupled chains of magnetically active ions (Cu or V) have recently been the focus of a large amount of experimental and theoretical work, due to their unusual properties. The topic of our project are vanadium ladder compounds, especially NaV2O5, in which spin, charge, and lattice degrees of freedom are of simultaneous importance, but insufficiently understood. NaV2O5 exhibits a phase transition (possibly two closely spaced ones) close to 35 K, with spatial ordering of the charges of V ions, and with a spin-Peierls-like transition which produces a gap in the spin excitations. The phase transition occurs due to an interplay of charge, spin, and lattice degrees of freedom. Despite recent progress, the origin of the transition(s) as well as the relevant properties of the compound are still very puzzling. It is widely assumed that these compounds can be described in terms of relatively simple models of solid state theory. However, adequate models are still lacking. One of the reasons is the complicated nonperturbative interplay of several degrees of freedom, for which known approximations appear to be insufficient. To get a deeper understanding we will take into account the coupling of charges and spins not only to each other but also to the lattice. We will combine advantages of two different techniques. First, we will determine the electronic structure of different kinds of V-based ladders by ab initio calculations. These calculations will allow us to get realistic parameters for the model analysis, to evaluate the electron-phonon and spin-phonon coupling, and to obtain results which can be compared to experimental properties related to the local electronic structure. Then we will perform Quantum Monte Carlo simulations to investigate the dynamics of the low-energy excitation and to obtain relevant experimentally measured characteristics like thermodynamical, magnetic, and optical properties of the V-based ladders. The model parameters will be taken from the first-principles calculations. The Quantum Monte Carlo approach is approximation-free and nonperturbative, and, therefore, is well suited for the investigation of models in a wide range of the parameters. As a result we can aim for a comprehensive theoretical picture of properties of the V-based ladders.

Ladder compounds are materials with very unusual properties. They consist mainly of one-dimensional ladder-like structures made up of magnetic atoms (e.g. copper or vanadium) and oxygen. In recent years they have been the object of many experimental and theoretical studies. In such materials, electric charges, magnetic moments (spins) and lattice vibrations can be important concurrently. They can strongly influence each other in their unusual properties. The compound sodium vanadate, for example, changes drastically below a temperature of about 35 Kelvin: strong lattice distortions occur, spatial order of charges, and strongly modified magnetic properties. This puzzling behavior has been studied intensely but had so far been insufficiently understood. The goal of our project has been a better understanding of such vanadium ladders, by using a combination of theoretical approaches which often stay apart . In "First Principles" Calculations we were able to calculate the local electronic structure, the properties of lattice fluctuations and their mutual interactions to a high precision from the crystal structures of the compounds. This enabled us to understand numerous experimental results like, e.g., optical properties and phonon-spectra. We were also able to predict new resonance phenomena in light scattering. Using the first-principles results we then extracted parameters for simplified effective models of the electronic structure and its coupling to lattice vibrations. Within these models we employed different, non-perturbative methods like the so-called Density Matrix Renormalization Group and Quantum Monte Carlo to calculate the effect of combined correlations of charges, spins and lattice fluctuations. In order to do so, we developed new methods and expanded and improved existing ones, in some cases reducing the computational effort required by several orders of magnitude. We succeeded in understanding, e.g., the low temperature phase of sodium vanadate in a much better way, which, as we showed, must be characterized by ordered structures of four neighboring ladders. The coupling of electrons to lattice fluctuations turned out to be decisive. The methods developed in this project and the successful combination of First Principles and model calculations will in the future be applicable to similarly complicated systems with many degrees of freedom, e.g. in connection with high temperature superconductors and related compounds.