Magnetoelectric and magnetoelastic phenomena correlated with a phase transition into noncollinear magnetic phase have been investigated for single crystals of CuFeO 2 with a frustrated triangular lattice. CuFeO 2 exhibits several long-wavelength magnetic structures related to the spin frustration, and it is found that finite electric polarization, namely inversion symmetry breaking, occurs with noncollinear but not at collinear magnetic phases. This result demonstrates that the noncollinear spin structure is a key role to induce electric polarization, and suggests that frustrated magnets which often favor noncollinear configurations can be plausible candidates for magnetoelectrics with strong magnetoelectric interaction. 75.30.Kz, 75.80.+q, 64.70.Rh
Many theories published in the last decade propose that either ordered or disordered local moments are present in elemental plutonium at low temperatures. We present new experimental data and review previous experimental results. None of the experiments provide any evidence for ordered or disordered magnetic moments (either static or dynamic) in plutonium at low temperatures, in either the α-or δ-phases. The experiments presented and discussed are magnetic susceptibility, electrical resistivity, NMR, specific heat, and both elastic and inelastic neutron scattering. Many recent calculations correctly predict experimentally observed atomic volumes, including that of δ-Pu. These calculations achieve observed densities by the localization of electrons, which then give rise to magnetic moments. However, localized magnetic moments have never been observed experimentally in Pu. A theory is needed that is in agreement with all the experimental observations. Two theories are discussed that might provide understanding of the ensemble of unusual properties of Pu, including the absence of experimental evidence for localized magnetic moments; an issue that has persisted for over 50 years.PACS index: 75; 75.25 +z; 75.20.En Paper to be submitted to Phys. Rev. B (11-Sept-04) I INTRODUCTIONIt has been known for many years that plutonium lies in the periodic table at a position where it is intermediate between itinerant-and localized-electron behavior. 1The elemental volumes of the 5f elements are shown in comparison to those of the elements in the 3d and 4f series in Fig. 1. The behavior of the early actinides (Th to Np) follows closely the contraction with increasing electron count that is systematically followed in all the d transition-metal series. At the beginning of the series each additional electron contributes to the cohesive energy of the solid, resulting in a decrease of volume until the shell is approximately half full. This characteristic of the early actinides, together with the absence of magnetic order, has been taken as a prima fascia case that the 5f electrons of these early actinide elements are itinerant. On the other hand, for the heavier actinide elements, there is an abrupt (at δ-Pu and Am) jump in the volume and very little change as the electron count is further increased. In comparison with the 4f elements, together with the presence of 2 ordered magnetism in Cm and the elements beyond (those that have been examined), this change in trend has been taken as evidence of localized behavior of the 5f electrons. If we accept this hypothesis, then it focuses a major interest on plutonium. Note that the volume change between α-Pu and Am is almost 50%, a staggering change in volume between two neighboring elements in the periodic table considering that the only change is to add one electron in the 5f shell. (Unlike the lanthanide elements Eu and Yb, which are both divalent in the normally trivalent lanthanide series, there is no indication of a straightforward valence change between Pu and Am)Plutoniu...
The discovery of the Dirac electron dispersion in graphene [1] led to the question of the Dirac cone stability with respect to interactions. Coulomb interactions between electrons were shown to induce a logarithmic renormalization of the Dirac dispersion. With a rapid expansion of the list of compounds and quasiparticle bands with linear band touching [2], the concept of bosonic Dirac materials has emerged. We consider a specific case of ferromagnets consisting of the Van der Waals-bonded stacks of honeycomb layers, e.g chromium trihalides CrX3 (X = F, Cl, Br and I), that display two spin wave modes with energy dispersion similar to that for the electrons in graphene. At the single particle level, these materials resemble their fermionic counterparts. However, how different particle statistics and interactions affect the stability of Dirac cones has yet to be determined. To address the role of interacting Dirac magnons, we expand the theory of ferromagnets beyond the standard Dyson theory [3, 4] to a case of non-Bravais honeycomb layers. We demonstrate that magnon-magnon interactions lead to a significant momentumdependent renormalization of the bare band structure in addition to strongly momentumdependent magnon lifetimes. We show that our theory qualitatively accounts for hitherto unexplained anomalies in a nearly half century old magnetic neutron scattering data for CrBr3 [5,6]. We also show that honeycomb ferromagnets display dispersive surface and edge states, unlike their electronic analogs.
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