Mapping of Critical Anisotropy on Spin Dynamics in a Frustrated Antiferromagnet

Alex Bunker, Kun Chen, David Paul Landau

Antonio S. T. Pires

Jozef Strečka, Lucia Čanová

The spin-1/2 Ising-Heisenberg model on the triangulated Kagomé (triangles-in-triangles) lattice is exactly solved by establishing a precise mapping correspondence to the simple spin-1/2 Ising model on Kagomé lattice. It is shown that the disordered spin liquid state, which otherwise occurs in the ground state of this frustrated spin system on assumption that there is a sufficiently strong antiferromagnetic intra-trimer interaction, is eliminated from the ground state by arbitrary but non-zero Dzyaloshinskii-Moriya anisotropy.

M. Drawid

Gang Chen

Motivated by the proposal of a topological quantum paramagnet in the diamond lattice antiferromagnet ${\mathrm{NiRh}}_{2}{\mathrm{O}}_{4}$, we propose a minimal model to describe the magnetic interaction and properties of the diamond material with spin-one local moments. Our model includes the first- and second-neighbor Heisenberg interactions as well as a local single-ion spin anisotropy that is allowed by the spin-one nature of the local moment and the tetragonal symmetry of the system. We point out that there exists a quantum phase transition from a trivial quantum paramagnet when single-ion spin anisotropy is dominant to the magnetic ordered states when the exchange is dominant. Due to the frustrated spin interaction, the magnetic excitation in the quantum paramagnetic state supports extensively degenerate band minima in the spectra. As the system approaches the transition, extensively degenerate bosonic modes become critical at the criticality, giving rise to unusual magnetic properties. Our phase diagram and experimental predictions for different phases provide a guideline for the identification of the ground state for ${\mathrm{NiRh}}_{2}{\mathrm{O}}_{4}$. Although our results are fundamentally different from the proposal for topological quantum paramagnets, they represent interesting possibilities for spin-one diamond lattice antiferromagnets.

S. Rufo

In this thesis we study spin systems in low dimension at zero temperature, analyzing their quantum phase transitions. In particular, we used a variational method and a linear spin wave theory for obtaining the approximate ground state. Firstly, we studied the order-disorder transitions of the quasi-one-dimensional isotropic antiferromagneticHeisenberg model of spin-1=2, dened on a square lattice with exchange interactions between nearest neighbors, J and J0. The latter interaction is responsible for onedimensional or two-dimensional behavior of the model namely, when it is zero and when it has a nonzero value, respectively. We obtained the staggered magnetizations of the antiferromagnetic and collinear antiferromagnetic phases. In the absence of exchange interactions between second neighbors, the collinear antiferromagnetic phase is obtained for J0 < 0. This model in the one-dimensional limit has a critical value for the ratio J0=J, where we have a phase transition of the order-disorder type. We founda critical value J0=J = 0, which corresponds to the value physically expected, and compare our results with the linear spin wave theory, that predicts a nonzero critical value. The variational method is also used in the study of the Heisenberg anisotropic model with frustration induced by the inclusion of exchange interactions between second neighbors J2. We renamed the exchange interactions of the rst neighbors J1 e J0 1 , so this model is known as J1 J0 1 J2. Furthermore, we include in this modelthe exchange anisotropy which follows the x and y components of the spin operators. Thus, the more general Hamiltonian presents the isotropic Heisenberg and Ising model limits for certain values of the anisotropy. With the goal to analyze the real role played by this anisotropy, we distinguish between rst and seconds neighbors by the labels 1and 2, respectively. We analyzed the staggered magnetization and the energies for the antiferromagnetic, collinear antiferromagnetic and quantum paramagnetic phase. From these analyzes, we observed quantum phase transitions for certain values of the exchange anisotropy and frustration parameter, the latter one given by the ratio J2=J1. The global phase diagram was also obtained for the cases where the rst and second neighbor exchange anisotropies are equal and where they dier from each other. In the rst case, we can observe the ordered phases, Néel and collinear antiferromagnetic, and between them a magnetically disordered phase. We checked the existence of a critical endpoint separating the three phases. In the second case, we note that the exchange anisotropy inuences the region of the disordered phase, aecting even the existence of the critical endpoint. Besides presenting, at certain intervals of the anisotropy, a behavior that was not expected a priori. We also analyze the quasi-one-dimensional behavior J01 ! 0, where the shape of the phase diagram is unchanged. We explore the degree of dimer formation via the dimerization parameter for some values of exchange anisotropy and obtain a higher degree of dimerization for the disordered phase in comparison with the ordered phases, as expected. We end this work with a generalization of the rst study without frustration in function only of the exchange anisotropy. As a challenge to the variational method, we study the more general J1 J0 1 J2 modelfor integer spin-1 without the exchange anisotropy and avoiding the unidimensional case. Dierent from what happens in the semi-integer spins case, we did not nd the disordered phase for integer spin S= 1. We note only a rst-order phase transition between the ordered phases. Finally, we return to the frustrated model with exchange anisotropies 1 and 2 to study the model from a perspective of linear spin wavetheory, in order to compare the results with those obtained via the variational method. A detailed analysis was performed based on the comparison between the two methods, which agreed qualitatively in all explored boundaries and even those behaviors that were not expected from the variational method were conrmed by the spin wave theory.This consistency of the results allowed us to get a dierent view of the role played by the exchange anisotropy when dierentiated for rst and second neighbors. If the anisotropies are considered equal they work only as a parameter that carries the model from the isotopic Heisenberg limit to the Ising model. However, when dierent, they promote disorder in the system.