Antiferromagnetic order in (Ga,Mn)N nanocrystals: A density functional theory study

We investigate the electronic and magnetic properties of (Ga,Mn)N nanocrystals using the density functional theory. We study both wurtzite and zinc-blende structures doped with one or two substitutional Mn impurities. For a single Mn dopant placed close to surface, the behavior of the empty Mn-induced state, hereafter referred to as "Mn hole", is different from bulk (Ga,Mn)N. The energy level corresponding to this off-center Mn hole lies within the nanocrystal gap near the conduction edge. For two Mn dopants, the most stable magnetic configuration is antiferromagnetic, and this was unexpected since (Ga,Mn)N bulk shows ferromagnetism in the ground state. The surprising antiferromagnetic alignment of two Mn spins is ascribed also to the holes linked to the Mn impurities located close to surface. Unlike Mn holes in (Ga,Mn)N bulk, these Mn holes in confined (Ga,Mn)N nanostructures do not contribute to the ferromagnetic alignment of the two Mn spins

Optical spin control in nanocrystalline magnetic nanoswitches

We investigate the optical properties of (Cd,Mn)Te quantum dots (QDs) by looking at the excitons as a function of the Mn impurities positions and their magnetic alignments. When doped with two Mn impurities, the Mn spins, aligned initially antiparallel in the ground state, have lower energy in the parallel configuration for the optically active spin-up exciton. Hence, the photoexcitation of the QD ground state with antiparallel Mn spins induces one of them to flip and they align parallel. This suggests that (Cd,Mn)Te QDs are suitable for spin-based operations handled by light

First-principles calculations of the magnetic properties of (Cd,Mn)Te nanocrystals

We investigate the electronic and magnetic properties of Mn-doped CdTe nanocrystals (NCs) with 2 nm in diameter which can be experimentally synthesized with Mn atoms inside. Using the density-functional theory, we consider two doping cases: NCs containing one or two Mn impurities. Although the Mn d peaks carry five up electrons in the dot, the local magnetic moment on the Mn site is 4.65 mu_B. It is smaller than 5 mu_B because of the sp-d hybridization between the localized 3d electrons of the Mn atoms and the s- and p-type valence states of the host compound. The sp-d hybridization induces small magnetic moments on the Mnnearest- neighbor Te sites, antiparallel to the Mn moment affecting the p-type valence states of the undoped dot, as usual for a kinetic-mediated exchange magnetic coupling. Furthermore, we calculate the parameters standing for the sp-d exchange interactions. Conduction N0\alpha and valence N0\beta are close to the experimental bulk values when the Mn impurities occupy bulklike NCs' central positions, and they tend to zero close to the surface. This behavior is further explained by an analysis of valence-band-edge states showing that symmetry breaking splits the states and in consequence reduces the exchange. For two Mn atoms in several positions, the valence edge states show a further departure from an interpretation based in a perturbative treatment. We also calculate the d-d exchange interactions |Jdd| between Mn spins. The largest |Jdd| value is also for Mn atoms on bulklike central sites; in comparison with the experimental d-d exchange constant in bulk Cd0.95Mn0.05Te, it is four times smaller

Multivector Field Formulation of Hamiltonian Field Theories: Equations and Symmetries

We state the intrinsic form of the Hamiltonian equations of first-order Classical Field theories in three equivalent geometrical ways: using multivector fields, jet fields and connections. Thus, these equations are given in a form similar to that in which the Hamiltonian equations of mechanics are usually given. Then, using multivector fields, we study several aspects of these equations, such as the existence and non-uniqueness of solutions, and the integrability problem. In particular, these problems are analyzed for the case of Hamiltonian systems defined in a submanifold of the multimomentum bundle. Furthermore, the existence of first integrals of these Hamiltonian equations is considered, and the relation between {\sl Cartan-Noether symmetries} and {\sl general symmetries} of the system is discussed. Noether's theorem is also stated in this context, both the ``classical'' version and its generalization to include higher-order Cartan-Noether symmetries. Finally, the equivalence between the Lagrangian and Hamiltonian formalisms is also discussed.Comment: Some minor mistakes are corrected. Bibliography is updated. To be published in J. Phys. A: Mathematical and Genera

On the k-Symplectic, k-Cosymplectic and Multisymplectic Formalisms of Classical Field Theories

The objective of this work is twofold: First, we analyze the relation between the k-cosymplectic and the k-symplectic Hamiltonian and Lagrangian formalisms in classical field theories. In particular, we prove the equivalence between k-symplectic field theories and the so-called autonomous k-cosymplectic field theories, extending in this way the description of the symplectic formalism of autonomous systems as a particular case of the cosymplectic formalism in non-autonomous mechanics. Furthermore, we clarify some aspects of the geometric character of the solutions to the Hamilton-de Donder-Weyl and the Euler-Lagrange equations in these formalisms. Second, we study the equivalence between k-cosymplectic and a particular kind of multisymplectic Hamiltonian and Lagrangian field theories (those where the configuration bundle of the theory is trivial).Comment: 25 page

Invariant Forms and Automorphisms of Locally Homogeneous Multisymplectic Manifolds

It is shown that the geometry of locally homogeneous multisymplectic manifolds (that is, smooth manifolds equipped with a closed nondegenerate form of degree > 1, which is locally homogeneous of degree k with respect to a local Euler field) is characterized by their automorphisms. Thus, locally homogeneous multisymplectic manifolds extend the family of classical geometries possessing a similar property: symplectic, volume and contact. The proof of the first result relies on the characterization of invariant differential forms with respect to the graded Lie algebra of infinitesimal automorphisms, and on the study of the local properties of Hamiltonian vector fields on locally multisymplectic manifolds. In particular it is proved that the group of multisymplectic diffeomorphisms acts (strongly locally) transitively on the manifold. It is also shown that the graded Lie algebra of infinitesimal automorphisms of a locally homogeneous multisymplectic manifold characterizes their multisymplectic diffeomorphisms.Comment: 25 p.; LaTeX file. The paper has been partially rewritten. Some terminology has been changed. The proof of some theorems and lemmas have been revised. The title and the abstract are slightly modified. An appendix is added. The bibliography is update

Non-standard connections in classical mechanics

In the jet-bundle description of first-order classical field theories there are some elements, such as the lagrangian energy and the construction of the hamiltonian formalism, which require the prior choice of a connection. Bearing these facts in mind, we analyze the situation in the jet-bundle description of time-dependent classical mechanics. So we prove that this connection-dependence also occurs in this case, although it is usually hidden by the use of the ``natural'' connection given by the trivial bundle structure of the phase spaces in consideration. However, we also prove that this dependence is dynamically irrelevant, except where the dynamical variation of the energy is concerned. In addition, the relationship between first integrals and connections is shown for a large enough class of lagrangians.Comment: 17 pages, Latex fil