The symmetry of magnetic quantum tunneling (MQT) has been studied in the prototype single molecule magnet (SMM) Mn12-acetate using a micro-Hall effect magnetometer and superconducting high field vector magnet system. An average crystal 4-fold symmetry is shown to be due to local molecular environments of 2-fold symmetry that are rotated by 90 degrees with respect to one another, confirming that...

Already Hermann Grassmann’s father Justus (1829, 1830) published two works on the geometrical description of crystals, influenced by the earlier works of C.S. Weiss (1780-1856) on three main crystal forces governing crystal formation. In his 1840 essay on the derivation of crystal shapes from the general law of crystal formation Hermann established the notion of a three-dimensional vectorial sy...

The relation between the notion of crystalline symmetry and characteristic time intervals when this symmetry could be observed is analyzed. Several time scales are shown to exist for a system of interacting particles. It is only when the observation time is much larger than the mesoscopic fluctuation time, the notion of crystalline symmetry becomes physically meaningful. The ideas are concretiz...

This manuscript has many predecessors. It is based on lectures and courses that repeatedly have been held since 1975 in Germany, Italy and France. Parts of this script were adopted from course scripts and other material by Hartmut B ¨ arnighausen (University of Karlsruhe). I am grateful to him for his generosity and for numerous discussions and suggestions.

Organisms can exert a remarkable degree of control over crystal growth. One way of achieving this is by the adsorption of specialized macromolecules on specific planes of the growing crystals. With continued growth of the crystal, the macromolecules are incorporated inside the crystal bulk. Their presence does not change the crystal structure, but creates discontinuities in the perfect lattice....

We have developed a biaxial-stress calorimeter for use at milli-Kelvin temperatures to study the nature of the double superconducting transition in single crystal UPt3. We suppress the basal-plane antiferromagnetism and merge the two transitions through c-axis stress, and then break the hexagonal symmetry of the basal plane in a regulated manner through stress along â. We recover a double super...

We report an extensive investigation of magnetic vortex lattice (VL) structures in single crystals of pure niobium with the magnetic field applied parallel to a fourfold symmetry axis, so as to induce frustration between the cubic crystal symmetry and hexagonal VL coordination expected in an isotropic situation. We observe new VL structures and phase transitions; all the VL phases observed (inc...