We present a first principles LSDA+ U study of the magnetic coupling constants in the spinel magnets CoCr 2 O 4 and MnCr 2 O 4 . Our calculated coupling constants highlight the possible importance of AA interactions in spinel systems with magnetic ions on both A and B sites. Furthermore, we show that a careful analysis of the dependence of the magnetic coupling constants on the LSDA+ U parameters provides valuable insights in the underlying coupling mechanisms and allows to obtain a quantitative estimate of the magnetic coupling constants. We discuss in detail the capabilities and possible pitfalls of the LSDA+ U method in determining magnetic coupling constants in complex transition metal oxides.

A systematic ab initio study within the framework of the local-spin-density approximation including spinorbit coupling and an orbital-polarization term is performed for the spin and orbital moments and for the x-ray magnetic circular dichroism ͑XMCD͒ spectra in hcp Co, in a Pt supported and a free standing Co monolayer, and in a Pt supported and a free standing monatomic Co wire. When including the orbital-polarization term, the orbital moments increase drastically when going to lower dimensionality, and there is an increasing asymmetry between the L 2 and L 3 XMCD signals. It is shown that spin and orbital moments can be obtained with good accuracy from the XMCD spectra via the sum rules. The ͗T z ͘ term of the spin sum rule is surprisingly small for the wires, and the reason for this is discussed. DOI: 10.1103/PhysRevB.66.140407 PACS number͑s͒: 75.30.Ϫm, 75.90.ϩw The modern methods to prepare nanostructured systems made it possible to investigate the influence of dimensionality on the magnetic properties. A central question thereby is how the qualitative behavior will change when going from two-dimensional to one-dimensional systems because it has been predicted that there is no long-range magnetic order at finite temperature in infinitely extended one-dimensional systems with short-range magnetic interactions. In the past, several experimental investigations of monolayer nanostripes of Fe on vicinal surfaces of W ͑Refs. 1, 2͒ or Cu ͑Ref. 3͒ have been performed, with a stripe width down to 1-10 nm. Most recently, Gambardella et al. 4 succeeded in preparing a high density of parallel atomic chains along steps by growing Co on a high-purity Pt͑997͒ vicinal surface in a narrow temperature range. The magnetism of the Co wires was investigated 5 by the x-ray magnetic circular dichroism ͑XMCD͒. Below a blocking temperature a long-range magnetic ordering owing to the presence of anisotropy barriers was found on the time scale of the experiment. In Ref. 5 a simple model of exchange-coupled superparamagnetic clusters was applied ͑for a criticism of this model, see Ref. 6͒ to obtain the anisotropy energy from the shape of the magnetization curve above the blocking temperature and it appeared to be much larger than the one for a Co monolayer on Pt which, in turn, is much larger than the one of hcp Co. Accordingly, a large orbital moment of 0.68 B per Co atom was found, the highest value ever reported for a 3d itinerant electron system. So far, magnetism in quasi-one-dimensional systems was studied mainly in the insulating material CsNiF 3 , where the magnetic Ni ions are arranged along linear chains that are well separated from each other so that the interchain interaction is only 10 Ϫ3 or less of the intrachain interaction. Because of the one-dimensional character of this spin system and the easy-plane anisotropy, magnetic solitons play an important role in the dynamical and thermodynamical behavior which has been investigated by neutron-scattering experiments. 7 The discovery of magnetism in onedimensional metallic...

Phase inhomogeneity of otherwise chemically homogenous electronic systems is an essential ingredient leading to fascinating functional properties, such as high-Tc superconductivity in cuprates, colossal magnetoresistance in manganites and giant electrostriction in relaxors. In these materials distinct phases compete and can coexist owing to intertwined ordered parameters. Charge degrees of freedom play a fundamental role, although phase-separated ground states have been envisioned theoretically also for pure spin systems with geometrical frustration that serves as a source of phase competition. Here we report a paradigmatic magnetostructurally inhomogenous ground state of the geometrically frustrated α-NaMnO2 that stems from the system’s aspiration to remove magnetic degeneracy and is possible only due to the existence of near-degenerate crystal structures. Synchrotron X-ray diffraction, nuclear magnetic resonance and muon spin relaxation show that the spin configuration of a monoclinic phase is disrupted by magnetically short-range-ordered nanoscale triclinic regions, thus revealing a novel complex state of matter.

Electro-mechanical interactions between charged point defects and domain walls play a key role in the functional properties of bulk and thin-film ferroelectrics. While for perovskites the macroscopic implications of the ordering degree of defects on domain-wall pinning have been reported, atomistic details of these mechanisms remain unclear. Here, based on atomic and nanoscale analyses, we propose a pinning mechanism associated with conductive domain walls in BiFeO3, whose origin lies in the dynamic coupling of the p-type defects gathered in the domain-wall regions with domain-wall displacements under applied electric field. Moreover, we confirm that the degree of defect ordering at the walls, which affect the domain-wall conductivity, can be tuned by the cooling rate used during the annealing, allowing us to determine how this ordering affects the atomic structure of the walls. The results are useful in the design of the domain-wall architecture and dynamics for emerging nanoelectronic and bulk applications.