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In this dissertation we study the phases and phase transition properties of quantum ferromagnets and related magnetic materials. We first investigate the effects of an external magnetic field on the Goldstone mode of a helical magnet, such as MnSi. The field introduces a qualitatively new term into the dispersion relation of the Goldstone mode, which in turn changes the temperature dependences of the contributions of the Goldstone mode to thermodynamic and transport properties. We then study how the phase transition properties of quantum ferromagnets evolve with increasing quenched disorder. We find that there are three distinct regimes for different amounts of disorder. When the disorder is small enough, the quantum ferromagnetic phase transitions is generically of first order. If the disorder is in an intermediate region, the ferromagnetic phase transition is of second order and effectively characterized by mean-field critical exponents. If the disorder is strong enough the ferromagnetic phase transitions are continuous and are characterized by non-mean-field critical exponents.

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The interest in one dimensional (1D) magnetism has been strongly renewed with the synthesis of many magnetic compounds which exhibit a quasi one dimensional magnetic behaviour. One of the peculiarities of this 1D system is the absence of a long range magnetic ordered phase at any finite temperature for the ideal 1D system with short range interaction. Tetramethylammonium manganese chloride (CH3)4NMnCl3(TMMC) exhibits the properties of an ideal one dimensional antiferromagnets for temperature above 1 K, the transition to a three dimensional (3D) long range ordered state only occurs at 0.84K. In addition to its magnetic transition, TMMC exhibits structural phase transition due to the ordering of the tetramethylammonium (TMA) ions which makes also this compound very attractive from a lattice dynamical point of view. Structural phase transitions of tetramethylammonium manganese chloride (TMMC), tetramethylammonium manganese bromide (TMMB) and tetramethylammonium manganese chloride doped with 8% Cu (TMMC:Cu) of the hexagonal type compounds are investigated using the Brillouin scattering method. These crystals show pronounced acoustic anomalies in the region of the structural phase transition. The acoustic anomalies were observed by measuring sound velocity and hence the elastic constant can be deduced. The phase transition temperatures were observed at 129.6K and 388.6K (TMMC), 114.6K and 377.6K (TMMB) and at 108.6K and 359.6K (TMMC:Cu). The elastic constant at room temperature were C11 = 2.10 (TMMC) and C11 = 1.59 (TMMB) in units of 1010 Nm-2. The phase transition of these compounds were further investigated macroscopically using the Differential Scanning Calorimetry (DSC) method. Activation energies of TMMC, TMMC:Cu, TMMB and deuterated TMMB at the phase transition were determined using this method. The values are 70.612 kJ/mol (TMMC), 49.224 kJ/mol (TMMC:Cu), 51.747 kJ/mol (TMMB) and 69.909 kJ/mol (d12-TMMB). The elastic constant of the linear chain antiferromagnet CsNiCl3 and RbNiCl3 was also determined using the Brillouin scattering method. The room temperature measurements give C11 = 3.77 (3.71) and C33 = 5.62 (5.42) in units of 1010 Nm·2 for CsNiCl3 and RbNiCl3 respectively. The phonon dispersion curves at room temperature in the hexagonal CsFeBr3 have been studied using the inelastic neutron scattering technique. From the initial slope of the dispersion curve, the sound velocity was deduced which enable us to calculate the elastic constant of CsFeBr3 at room temperature. The values obtained are C11 = 7.33, C66 = 1.01, C33 = 2.58 and C44 = 0.56 in units of 1010 Nm·2.

We study dynamic phase transitions in the constant-volume and constant- pressure ensembles of two different systems: a one-dimensional system of diffusive hard particles and a three-dimensional glass-former of nearly-hard repulsive particles. The dynamic transitions are observed using ensembles of trajectories biased with respect to their dynamic activity, biasing to greater or lower activities than equilibrium allows us to sample different dynamic phases. We perform finite-size scaling of the transitions with respect to sys- tem size and observation time, and compare them to first-order phase tran- sitions. The two ensembles are not equivalent in the one-dimensional model. We compare our results to analytic predictions for diffusive systems in both the active and inactive phases, there are structural signatures for both dy- namic regimes. The active phases show hyperuniform ordering and the inac- tive regimes show jamming behaviour, local jamming in the constant-volume ensemble is achieved through phase separation. In the three-dimensional sys- tem we observe a dynamic transition to a glassy inactive phase, there is no obvious structural change and the structural relaxation time increases sig- nificantly. We take configurations from the active and inactive phases and subject them to a jamming protocol in order to compare the final density of the jammed packings. Previous work shows that the inactive phase of glass-forming systems have a different distribution of vibrational modes and a higher compressibility, this suggests that the jamming behaviour should differ between the two phases. We show that jammed packings generated from inactive configurations are denser than those generated from active configurations.

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