In this thesis we cover the dynamics of the macro magnetic transformations (spin avalanches) in crystals of molecular nanomagnets, also known as magnetic deflagration and detonation. Taking a single-molecule Hamiltonian, we calculate the dependence of Zeeman energy and the activation energy as a function of an external magnetic field at different angles relative to the easy axis of the crystal. Using quantum mechanical calculations, we show that the energy levels of the molecule exhibit complex behavior in presence of a transverse component of the magnetic field. For an arbitrarily aligned magnetic field, the energy levels do not arrange in a simple "double-well" manner. We extend existing theoretical models by generalizing the Zeeman energy for a wide range of magnetic fields and its different orientations. We obtain a new type of front instability in magnetization-switching media. Due to the dipole-dipole interaction between the molecules magnetic instability results to the front banding and change in the front propagation velocity. The magnetic instability has a universal physical nature similar to the Darrieus-Landau instability. The instability growth rate and the cutoff length are calculated for the spin avalanches in the crystals of nanomagnets. Finally, we investigate the internal structure of the magnetic detonation front. We calculate the continuous shock profile using the transport processes of the crystal such as thermal conduction and volume viscosity. Such an approach can be applied to any weak shock wave in solids. Zero volume viscosity leads to an isothermal jump, i.e., the temperature changes continuously while the pressure and the density experience discontinuity. The analysis has shown that the volume viscosity plays a major role in the formation of the detonation front.

Dans cette thèse, j’ai conçu un nouveau test de rupture adapté à l’étude des matériaux fragiles sur une grande gamme de vitesse de fissure. Il a été mis en œuvre sur le PMMA, permettant de caractériser la transition entre un régime de rupture à grande vitesse v>vc=15 mms-1 avec des faciès optiquement plats et un autre régime pour v<vc avec une rugosité caractérisée par des motifs triangulaires. L’étude de la déformation du front dans le plan moyen de fissuration montre que le matériau est plus tenace à l’intérieur de ces triangles qu’à l’extérieur. Qui plus est, ces triangles sont décorés par de petits motifs en forme de toit d’usine, caractéristiques de l’instabilité de fragmentation sous mode I+III. Pour comprendre l’émergence de ces formes, nous revisitons tout d’abord les modèles de fragmentation en supposant que l’énergie de rupture dépend du cisaillement comme Gc(KIII/KI)=GcI[1+ (KIII/KI)2]. Le seuil de fragmentation (KIII/KI)thc ainsi prédit décroit significativement, réconciliant théorie et expérience. Le motifs triangulaires permettant de mesurer le paramètre exp à partir de la déformée du front et le degré de cisaillement (KIII/KI)exp par l’inclinaison des facettes qui est compatible avec la valeur de seuil prédite (KIII/KI)thc. A partir des valeurs exp et (KIII/KI)thc ainsi déterminées, nous prédisons que les facettes dérivent le long du front avec un angle compatible avec celui formé par les triangles. Cette compréhension fine de ces motifs nous permet donc de mettre en relation la transition rugueuse observée dans le PMMA avec l’instabilité de fragmentation et ouvre de nouvelles perspectives pour la compréhension de motifs similaires dans d’autres matériaux. / During this PhD thesis, a new fracture test geometry is designed for the accurate measurement of the fracture properties of brittle solids, subsequently applied to study failure in PMMA. At high crack speeds, their fracture surfaces are optically smooth. But below vc = 15 mms-1, a transition to rough surfaces occurs through the formation of puzzling triangular patterns. These patterns lead to significant toughening of the material that reflects through the pinned shape of the crack front as it crosses triangles. In addition, these triangles are found to be decorated by faceted features reminiscent of the crack front fragmentation instability in mode I+III. Assuming a shear-dependent fracture energy Gc(KIII/KI) = GcI[1+ (KIII/KI)2] we theoretically predict a fragmentation threshold (KIII/KI)thc that can be as low as a few percent while earlier models (that assumes = 0) predict a much larger value, inconsistent with various experimental observations. Applied to our experiments, this model allows us to measure exp from the deformation amplitude of the pinned front and the amount of applied shear (KIII/KI)exp from the facet inclination which is found to be compatible with the theoretically predicted threshold (KIII/KI)thc . Using the values (KIII/KI)exp and exp thus determined, one finally predict a drift of the facets from the propagation direction accounting for the triangle angle observed experimentally. To conclude, our study shows that the roughening transition in PMMA is a signature of front fragmentation under mode I+III. As a result, deciphering the triangular patterns at the transition led to significant improvements in the understanding of this instability.