Research

Quantum and classical magnetism

Magnetism is a fascinating physical phenomenon that was already known to ancient civilizations even though to understand it, we need quantum mechanics which is barely 100 years old. Today, magnetic materials, magnetic properties and technological applications are a huge endeavour. Many of our present technologies depend on magnetism, and with spintronics, magnonics, or spin orbitronics, there is great enthusiasm for and expectation of future technologies for computing, energy, cooling and numerous other applications. Our research is driven by the hope of discovery and fundamental understanding. Experimentally and theoretically, magnetic materials are interesting because of their complex phase diagrams as function of temperature, magnetic field and other parameters. Understanding phase diagrams is also crucial for exploring technological applications. We specialize in precise parametrization of magnetic materials which leads, via different kinds of manybody calculations, to precise predictions of phase diagrams and spectroscopic or thermodynamic quantities.

Recent examples

We apply methods of computational materials science to the study of complex magnetic materials. A special focus is the use of density functional theory methods to learn about the magnetic Hamiltonian governing natural and synthetic magnetic materials (so-called DFT energy mapping). This is a crucial link that connects experimentally measured magnetic properties on one side and quantum or classical manybody approaches for magnets on the other side to generate a deep understanding of magnetic phenomena.

• The molybdenum oxynitride pyrochlore Lu₂Mo₂O₅N₂ has been identified as a rare spin 1/2 pyrochlore magnet. It is a spin liquid even though there are significant nonzero longer range exchange interactions.[link]
• In breathing chromium spinels, the magnetic lattice is composed of small and large tetrahedra. In these materials with compositions like LiInCr₄O₈ or CuInCr₄Se₈, a fascinating proximity to various different classical spin liquids can be identified.[link]
• A toroidal moment appears as a higher order term in the multipole expansion of vortex-like arrangements of magnetic moments. In the ground state of BaCoSiO₄, a ferritoroidal state is realized, and the toroidal moment can easily be controlled by magnetic field. This rare phenomenon which might be useful for technologies beyond spintronics can be traced back to a surprising magnetic Hamiltonian via DFT energy mapping.[link]

Unconventional superconductivity

Our dream is to contribute both to fundamental understanding and to discovery of new classes of superconducting materials. One central idea is to use insight into magnetism to identify new unconventional superconductors. At the heart of our research is very close collaboration with experimental groups that synthesize and measure on new materials. Therefore, we work on methods that allow more realistic description of materials. we continuously aspire to refine computational and theoretical tools for the screening of material candidates.

Recent examples

In unconventional superconductors, the pairing of electrons leading to the property of superconductivity is due to a magnetic mechanism rather than to lattice vibrations. We use density functional theory in combination with spin fluctuation theory to understand how tuning parameters like pressure or doping can influence the superconducting transition temperature Tc. While this approach only considers very low energies close to the Fermi level, for some questions it is important to explore the magnetic interactions which involves large energy scales.

• In the organic charge transfer salt κ-(ET)₂Cu[N(CN)₂]Br, theory in combination with scanning tunneling spectroscopy can identify the superconducting order parameter as a mixture of s– and d-wave superconducting gaps leading to eight nodes.[link]
• In the iron based superconductor FeS, the occurrence of two superconducting transition temperature maxima (domes) as function of pressure can be traced back to the evolution of the Fermi surface. The appearance of additional Fermi surface features (a Lifshitz transition) is responsible for a sudden increase of Tc.[link]
• In titanium based superconductors like BaTi₂Sb₂O, we can explain the trends in the superconducting transition temperature with alkali doping using spin fluctuation theory while an explanation with a conventional pairing mechanism is unlikely.[link]

Development of Theoretical and Numerical Methods

Theoretical investigations as above require advanced numerical methods that enable precise treatment of electronic structures in solids and elaborate consideration of many-body effect. The list below shows examples we are developing/using for our investigations.

• Density functional theory (DFT) is a standard framework for electronic structure calculations. We are using energy mapping method that enables estimation of the effective
  exchange interactions between correlated electrons.
• Dynamical mean-field theory (DMFT) offers a practical way of taking account of strong correlations that lead to Mott insulating state and heavy-fermion states. In particular, DFT+DMFT framework is now an important extension of DFT to strongly correlated materials. We contribute to development of open-source software DCore.
• Feynman diagram technique is a fundamental way of incorporating correlation effect between electrons. It includes random phase approximation (RPA) and fluctuation exchange approximation (FLEX).
• Quantum Monte Carlo simulations provide unbias results that take strong correlations into account. In particular, continuous-time quantum Monte Carlo (CT-QMC) method is a powerful tool in obtaining solutions within DFT+DMFT framework.

Data-Science Approaches

in preparation