| Pyrochlore antiferromagnet is one of the most studied examples of strongly-interacting systems. The conflict between the lattice geometry and the local spin correlations favored by their interactions precludes the simple Neel ordering and creates an extensive degeneracy of the classical ground state. This, in turn, renders the magnet susceptible to nominally small perturbations such as quantum fluctuations, anisotropies, and dipolar interactions.;Of particular interest is the classical Heisenberg spins on the pyrochlore lattice with exchange interactions restricted to the nearest neighbors. It has been demonstrated by analytical arguments and numerical simulations that the spin system remains disordered down to the lowest temperatures. In this thesis I study how magnetic ordering is induced by residual perturbations in such a system. Apart from the theoretical interest, the work presented in this thesis is mainly motivated by experimental observations of real materials. Three mechanisms of breaking the ground-state degeneracy are considered here: (1) order by distortion, (2) further-neighbor exchange interactions, and (3) the orbital degrees of freedom.;In the first part, we present a theoretical model describing the lattice distortion and incommensurate magnetic order in the compound CdCr2O 4, which belongs to a class of chromium spinels exhibiting the magnetoelastic phase transitions. The magnetic frustration is relieved through the spin-driven Jahn-Teller effect involving a phonon doublet with odd parity. The distortion stabilizes a collinear magnetic order with the propagation wavevector q = 2pi(0, 0, 1). The crystal structure becomes chiral due to the lack of inversion symmetry. The handedness is transferred to the magnetic system by the relativistic spin-orbit coupling: the collinear state is twisted into a long spiral with the spins in the ac plane and q shifted to 2pi(0, delta, 1), consistent with the experiments.;In the second part, we examine the effects of exchange interactions beyond the nearest neighbors. At the lowest temperatures, the magnet enters a ground state with long-range magnetic order, as predicted by the mean-field approach. More interestingly, through extensive Monte Carlo simulations, we discovered a partially ordered phase with collinear spins that is stable at intermediate temperatures for a ferromagnetic J2. In addition to a large nematic order parameter, this intermediate phase also exhibits a layered structure and a bond order that breaks the sublattice symmetry. Thermodynamic phase boundaries separating it from the fully disordered and magnetically ordered states scale as 1.87J2 S2 and 0.26J2 S2 in the limit of small J2 . The phase transitions are discontinuous. We analytically examine the stability of the collinear state and obtain a stability boundary T ∼ J22 /J1 in agreement with Monte Carlo simulations.;The last part of the thesis is devoted to orbitally degenerate pyrochlore antiferromagnets, with applications to vanadium spinels AV 2O4 (A = Zn, Cd, Mg, and Mn). We focus on the role of cooperative Jahn-Teller effect and attempt to provide a unifying picture for the structural distortion, orbital and magnetic orders in the ground state of vanadium spinels. We obtain an effective Jahn-Teller interaction between sublattice orbital orders by integrating out phonons with propagation wavevector q = 0. It is found that collinear state with predominantly ferro-orbital ordering, observed in spinel ZnV2O4, is favored by a distortion involving the oxygen phonons with Eg symmetry. On the other hand, the recently discovered orthogonal antiferromagnetic order in MnV2O4 is found to be stabilized by the softened rotational mode F1g of the oxygens. |
