Er2Ti2O7 has been suggested to be a realization of the frustrated 111 XY pyrochlore lattice antiferromagnet, for which theory predicts fluctuation-induced symmetry breaking in a highly degenerate ground state manifold. We present a theoretical analysis of the classical model compared to neutron scattering experiments on the real material, both below and above TN =1.173(2) K. The model correctly predicts the ordered magnetic structure, suggesting that the real system has order stabilized by zero-point quantum fluctuations that can be modelled by classical spin wave theory. However, the model fails to describe the excitations of the system, which show unusual features.PACS numbers: 28.20. Cz, 75.25.+z An important aspect of condensed matter is the separation of energy scales, such that the minimization of one set of interactions may result in the frustration of another. A paradigm is the frustrated antiferromagnet, in which the local magnetic couplings between ions are frustrated by the crystal symmetry that the ions adopt. However, a systematic study of the rare earth pyrochlore titanates R 2 Ti 2 O 7 has shown that local antiferromagnetic bond frustration is neither a necessary, nor a sufficient condition for magnetic frustration 1,2,3,4,5 . Rather, it arises from the interplay, in the context of the crystal symmetry, of the principal terms in the spin Hamiltonian. In the case of R 2 Ti 2 O 7 , the main terms are single-ion anisotropy, exchange and dipolar coupling. Depending on the balance of these factors, one observes spin ice behavior (R = Ho, Dy) 1,2,3 , spin liquid behavior (R = Tb) 4 , and dipole induced partial order (R = Gd)5 . Such behavior is best classified in terms of the dominant 111 single-ion anisotropy that arises from the trigonal crystal electric field (CEF) at the rare earth site. For example, whereas the Heisenberg antiferromagnet has a spin liquid ground state 6 , the 111 Ising (dipolar) ferromagnet has a spin ice ground state 1,3,7 . There is thus a clear motivation to study models based on other simple anisotropies and their realization in the titanate series. In this Letter we study one such model -the 111 XY model antiferromagnet 8 -and its realization Er 2 Ti 2 O 7 9,10,11,12 . We consider the Hamiltonian:where the classical spins, S i , populate a face centered cubic array of corner sharing tetrahedra: the pyrochlore lattice. The spins are confined to easy XY planes by a local d i = 111 anisotropy, D < 0, and are coupled antiferromagnetically by exchange J < 0. This model was first studied in Ref.8 , where a discrete, but macroscopically degenerate, set of ground states was identified. At finite temperature thermal fluctuations were found to select an ordered state by the mechanism that Villain called "order by disorder"13 and a first order phase transition was observed in numerical simulations. The propagation vector of the ordered state was found to be k = 0, 0, 0 (henceforth "k = 0"), but the basis vectors of the magnetic structure were not determined. We have recently discovere...

In this paper we show that ferromagnetism can be induced in pure TiO2 single crystals by oxygen ion irradiation. By combining x-ray diffraction, Raman-scattering, and electron spin resonance spectroscopy, a defect complex, i.e. Ti 3+ ions on the substitutional sites accompanied by oxygen vacancies, has been identified in irradiated TiO2. This kind of defect complex results in a local (TiO6−x) stretching Raman mode. We elucidate that Ti 3+ ions with one unpaired 3d electron provide the local magnetic moments.Recently, ferromagnetism has been observed in nonmagnetically doped, but defective oxides, including TiO 2 1,2,3,4 . This kind of observation challenges the conventional understanding of ferromagnetism, which is rather due to spin-split states or bands. Thus, one fundamental question must be answered: where are the moments located? Intensive theoretical work has been performed to understand the ferromagnetism in defective oxides 5,6,7 . In these papers, the triplet states of p-like electrons, located at cation or oxygen vacancies, yield the local moments, leading to a kind of ferromagnetism without the involvement of 3d electrons. Experimentally the ferromagnetism in undoped TiO 2 has been found to relate with oxygen vacancies (O V ) 2,3 , however, its mechanism remains unclear. It is worth to note that Ti 3+ ions with one 3d electron are usually generated in slightly reduced TiO 2 . When O is removed, the excess electrons are unpaired 8 . They can occupy the nearby localized Ti 3d orbit and therefore convert Ti 4+ ions to Ti 3+ ions. In a reduced rutile TiO 2 (110) surface, such a defect complex, Ti 3+ -O V , has been well studied by first-principles calculations 9,10 and experimentally by resonant photoelectron diffraction 11 . Therefore, experimental work is needed to clarify whether the magnetic moments in defective TiO 2 is due to unpaired 3d electrons localized on Ti 3+ ions.Ion irradiation is a non-equilibrium and reproducible method of inducing defects. Energetic ions displace atoms from their equilibrium lattice sites, thus creating mainly vacancies and interstitials. The amount of defects can be controlled by the ion fluence and energy. In this paper, we irradiated rutile TiO 2 single crystals with 2-MeV O ions, resulting in a projected range of 1.52 µm and a longitudinal straggling of 0.16 µm as calculated by SRIM code (The Stopping and Range of Ions in Matter) 12 . As a result of this irradiation, the formation of Ti/O vacancies/interstitials is expected 12 . We selected high-energy oxygen ions as projectiles to avoid the introduction of foreign elements. Moreover, from a ballistic point of view, the creation of oxygen vacancies is more efficient, e.g., by a factor of 1.5 larger than the Ti-vacancy creation. From SRIM calculations it is also evident that, at the given energy, the maximum atomic concentration of the implanted oxygen ions is by a factor of 500 smaller than the concentration of oxygen recoils. For the region of maximum defect creation, i.e., at the end of the ion range, those project...

A trinucleating cyclophane bearing three β-diketimine arms, and the corresponding iron(II) and manganese(II) complexes have been synthesized and characterized. The three metal ions are oriented towards the internal void space, and are coordinated by a N2Br2 donor set, in which a unique combination of μ(3), μ, and terminal coordination modes are observed for the halide donors.

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