Ansprechpartner: Dr. Burkhard Schmidt
Frustrated Magnetism: Exact Diagonalization and Spin Wave Studies
In magnetically frustrated compounds the pairwise exchange interactions of
spins cannot all be minimized simultaneously in any microscopic moment
configuration. This may arise already in the case of nearest neighbor
interactions when the lattice has the property of geometric frustration
like, e.g. trigonal, Kagome, checkerboard or pyrochlore type lattices.
Frustration can also arise through the competition of longer range
interactions even in simple structures like the two-dimensional (2D) square
lattice. At low temperatures there are basically two alternatives: quantum
fluctuations may select one of the degenerate states as the true magnetic
state (`order by disorder') or they may lead to an ordered quantum phase
with a new type of order parameter that is of the `hidden order' type, i.e.
it does not display a macroscopic modulation of the spin density.
In our research, we focus on the thermodynamic properties of frustrated
spin systems. A benchmarking example is the two-dimensional frustrated
Heisenberg model on a square lattice, showing, as a function of its
exchange parameters, a rich phase diagram of magnetically ordered and
As an example, the figure to the left shows the calculated heat capacity of this model as a function of frustration angle and
magnetic field strength. The white lines divide the three classical
ordered phases from each other. Quantum disorder effects show up as the
double-ridge shape (yellow and orange color coding) around the classical
phase transitions. [Clicking onto the figure will lead to a larger version.]
We use both exact diagonalization for finite clusters as well as analytical spin-wave methods. The eigensystems of the model Hamiltonians obtained from the exact-diagonalization data are used to directly evaluate arbitrary thermodynamic expectation values and related cumulants like the heat capacity (displayed above), magnetic susceptibility, or spin correlation functions. This method is called the finite-temperature Lanczos method.
|Dr. Burkhard Schmidt
||+49 (0)351 4646-2235
||+49 (0)351 4646-3232