Master thesis defense by Estrid Buhl Naver

Simulations of anisotropy effects of classical spin dynamics in frustrated magnets at finite temperatures

Neutron scattering studies of Gd3Al5O12 (GAG), a frustrated material with a hyperkagomé lattice, have shown several low lying magnetic excitations. A theoretical description of these excitations is missing, as they cannot be modelled using conventional spin wave theory. Spin dynamics simulations can help understanding the cause of the excitations.

In this thesis we make use of an existing simulation program Copenhagen Langevin Spin Simulation Code (CLaSSiC), made to simulate Langevin spin dynamics. The single-ion anisotropy effect was implemented in the program and the physical parameters were validated both separately and in different combinations. These validations included both integration in spherical and Cartesian coordinates. The integration in spherical coordinates showed both instabilities and errors for simulations with finite temperature when compared to theory. The integration in Cartesian coordinates show results consistent with theoretical predictions, and using these we can accurately simulate the dynamics of any system of spins with nearest neighbour exchange interaction, single-spin anisotropy, applied magnetic field and temperature effects.

Two systems were simulated in order to compare to GAG, three spins in a triangle and $3\times3$ unit cells of a kagomé lattice, with various anisotropy directions and temperatures. These simulations used the same value for the exchange interaction as GAG with a similar temperature range as the neutron scattering studies. Simulating a hyperkagomé lattice would have taken too long with the current run time of the simulations.

The triangle with no anisotropy showed two excitation peaks, with one increasing in energy as a function of temperature, which shows a concrete example of the zero mode excitation at finite temperatures. The triangle with anisotropy in the local z-direction showed excitation peaks decreasing in energy as a function of temperature. The triangle with anisotropy in the local xy-plane had two excitations, the low energy excitation increasing in energy with temperature and the high energy excitation decreasing in energy with temperature.

The kagomé lattice with no anisotropy showed signs of propagating spin waves, with a dispersion that was difficult to make out due to the low q-resolution. The three kagomé simulations with anisotropies in the local z-axis, global z-axis and global xy-plane had energies constant in temperature. The kagomé lattice with anisotropy in the local xy-plane showed the energies changing as a function of temperature like for the triangle with anisotropy in the local xy-plane. In all the simulations with anisotropy the spin movements were confined by the anisotropy.

The shape of the excitation spectra for the triangle and the kagomé lattice with anisotropy in the local xy-plane both have two excitation peaks, with energies E=0.02 meV and E=0.11 meV for the triangle and E=0.03 meV and E=0.15 meV for the kagomé lattice. These are close to the energies of the excitation peaks INS1 and INS2 for GAG.

These simulations are a big step in the direction of understanding the excitations in GAG.