Impossibility of spontaneously rotating time crystals: a no-go theorem.

I present arguments indicating the impossibility of spontaneously rotating "quantum time crystals," as recently proposed by Frank Wilczek. In particular, I prove a "no-go theorem," rigorously ruling out the possibility of spontaneous ground-state (or thermal equilibrium) rotation for a broad class of systems.

Quantum geometric phase in Majorana's stellar representation: mapping onto a many-body Aharonov-Bohm phase.

The (Berry-Aharonov-Anandan) geometric phase acquired during a cyclic quantum evolution of finite-dimensional quantum systems is studied. It is shown that a pure quantum state in a (2J+1)-dimensional Hilbert space (or, equivalently, of a spin-J system) can be mapped onto the partition function of a gas of independent Dirac strings moving on a sphere and subject to the Coulomb repulsion of 2J fixed test charges (the Majorana stars) characterizing the quantum state. The geometric phase may be viewed as the Aharonov-Bohm phase acquired by the Majorana stars as they move through the gas of Dirac strings. Expressions for the geometric connection and curvature, for the metric tensor, as well as for the multipole moments (dipole, quadrupole, etc.), are given in terms of the Majorana stars. Finally, the geometric formulation of the quantum dynamics is presented and its application to systems with exotic ordering such as spin nematics is outlined.

Energies and lifetimes of magnons in complex ferromagnets: a first-principle study of Heusler alloys.

The energies and lifetimes of magnons in several Mn-based Heusler alloys are studied using linear response density functional theory. The number of the spin wave branches in Co(2)MnSi corresponds to the number of its magnetic sublattices in contrast with the NiMnSb case in which the induced Ni sublattice cannot support optical magnons. The half-metallicity of these systems results in long-living acoustic spin waves. The example of non-half-metallic Cu(2)MnAl shows that the hybridization with Stoner continuum leads not only to the damping of magnons but also to a renormalization of their energies.

Kondo effect in single atom contacts: the importance of the atomic geometry.

Co single atom junctions on copper surfaces are studied by scanning tunneling microscopy and ab initio calculations. The Kondo temperature of single cobalt atoms on the Cu(111) surface has been measured at various tip-sample distances ranging from tunneling to the point contact regime. The experiments show a constant Kondo temperature for a whole range of tip-substrate distances consistently with the predicted energy position of the spin-polarized d levels of Co. This is in striking difference to experiments on Co/Cu(100) junctions, where a substantial increase of the Kondo temperature has been found. Our calculations reveal that the different behavior of the Co adatoms on the two Cu surfaces originates from the interplay between the structural relaxations and the electronic properties in the near-contact regime.

Giant spin splitting through surface alloying.

The long-range ordered surface alloy Bi/Ag(111) is found to exhibit a giant spin splitting of its surface electronic structure due to spin-orbit coupling, as is determined by angle-resolved photoelectron spectroscopy. First-principles electronic structure calculations fully confirm the experimental findings. The effect is brought about by a strong in-plane gradient of the crystal potential in the surface layer, in interplay with the structural asymmetry due to the surface-potential barrier. As a result, the spin polarization of the surface states is considerably rotated out of the surface plane.

Berry phase, topology, and degeneracies in quantum nanomagnets.

A topological theory of the diabolical points (degeneracies) of quantum magnets is presented. Diabolical points are characterized by their diabolicity index, for which topological sum rules are derived. The paradox of the missing diabolical points for Fe8 molecular magnets is clarified. A new method is also developed to provide a simple interpretation, in terms of destructive interferences due to the Berry phase, of the complete set of diabolical points found in biaxial systems such as Fe8.

Nonquantized dirac monopoles and strings in the berry phase of anisotropic spin systems.

The Berry phase of an anisotropic spin system that is adiabatically rotated along a closed circuit C is investigated. It is shown that the Berry phase consists of two contributions: (i) a geometric contribution which can be interpreted as the flux through C of a nonquantized Dirac monopole, and (ii) a topological contribution which can be interpreted as the flux through C of a Dirac string carrying a nonquantized flux, i.e., a spin analogue of the Aharonov-Bohm effect. Various experimental consequences of this novel effect are discussed.