Quantum fluctuations and phase transitions in antiferromagnetic spin configurations

Abstract

In this thesis we consider quantum fluctuations in the ground state energy of antiferromagnetic spin configurations, and phase transitions between these configurations. We use a Holstein-Primakoff transformation up to second order to transform our spin operators, and a Bogoliubov transformation to diagonalize the corresponding Hamiltonian. First we consider a Hamiltonian with Heisenberg-exchange interaction, a magnetic field and anisotropy, for which we investigated both the the antiferromagnetic phase and the spin-flop phase. For the antiferromagnetic phase we find that quantum fluctuations lower the ground state energy. For the spin-flop phase we find that quantum fluctuations lower the ground state energy even more, such that the phase transition point between these phases is shifted to a slightly lower strength of the magnetic field. Furthermore, this shifted phase transition is caused by ground state energies of the spin-flop phase that become complex, instead of an energy crossing. This energy takes on complex values due to imaginary eigenvalues for magnons, which correspond to exponentially increasing semi-classical spin waves.

Next we considered the Dzyaloshinskii-Moriya interaction (DMI) in one dimension, with the spiral phase it induces. We focused on the magnetic frustration of this phase due to anisotropy and the magnetic field. We used a superposition of two plane waves to describe the deviation due to this frustration, and minimized the ground state energy for their amplitudes numerically. By assuming only spirals of integer length and periodic boundary conditions, we constructed a semi-classical ground state phase diagram between the three mentioned phases. This phase diagram suggests a triple point between these phases when the DMI is zero, at the semi-classical phase transition point between the spin-flop phase and antiferromagnetic phase.