Geometric and combinatorial realizations of crystal graphs

For irreducible integrable highest weight modules of the finite and affine Lie algebras of type A and D, we define an isomorphism between the geometric realization of the crystal graphs in terms of irreducible components of Nakajima quiver varieties and the combinatorial realizations in terms of Young tableaux and Young walls. For affine type A, we extend the Young wall construction to arbitrary level, describing a combinatorial realization of the crystals in terms of new objects which we call Young pyramids.Comment: 34 pages, 17 figures; v2: minor typos corrected; v3: corrections to section 8; v4: minor typos correcte

Coexistence of ferromagnetism and superconductivity near quantum phase transition: The Heisenberg- to Ising-type crossover

A microscopic mean-field theory of the phase coexistence between ferromagnetism and superconductivity in the weakly ferromagnetic itinerant electron system is constructed, while incorporating a realistic mechanism for superconducting pairing due to the exchange of critical spin fluctuations. The self-consistent solution of the resulting equations determines the superconducting transition temperature which is shown to depend strongly on the exchange splitting. The effect of phase crossover from isotropic (Heisenberg-like) to uniaxial (Ising-like) spin fluctuations near the quantum phase transition is analysed and the generic phase diagram is obtained. This scenario is then applied to the case of itinerant ferromagnet ZrZn2, which sheds light on the proposed phase diagram of this compound. Possible explanation of superconductivity in UGe2 is also discussed.Comment: 5 pages, 3 figure

A-site Randomness Effect on Structural and Physical Properties of Ba-based Perovskite Manganites

The discovery of novel structural and physical properties in the $A$-site ordered manganite $R$BaMn$_{2}$O$_{6}$ ($R$ = Y and rare earth elements) has demanded new comprehension about perovskite manganese oxides. In the present study, the $A$-site disordered form, $R_{0.5}$Ba$_{0.5}$MnO$_{3}$, has been investigated and compared with both $R$BaMn$_{2}$O$_{6}$ and $R_{0.5}A_{0.5}$MnO$_{3}$ ($A$: Sr, Ca) in the structures and electromagnetic properties. $R_{0.5}$Ba$_{0.5}$MnO$_{3}$ has a primitive cubic perovskite cell in the structure and magnetic glassy states are dominant as its ground state, in contrast to the ordinary disordered $R_{0.5}A_{0.5}$MnO$_{3}$ ($A$: Sr, Ca). In Pr-compounds with various degrees of Pr/Ba randomness at the $A$-sites, the $A$-site disorder gradually suppresses both ferromagnetic and A-type antiferromagnetic transitions and finally leads to a magnetic glassy state in Pr$_{0.5}$Ba$_{0.5}$MnO$_{3}$. A peculiar behavior, multi-step magnetization and resistivity change, has been observed in Pr$_{0.5}$Ba$_{0.5}$MnO$_{3}$. These properties could be closely related to any spatial heterogeneity caused by the random distribution of Ba$^{2 +}$ and $R^{3 +}$ with much different ionic radius.Comment: 9 pages, to be published in J. Phys. Soc. Jpn. 73 Aug. (2004

High-Energy Spin Dynamics in La1.69_{1.69}Sr0.31_{0.31}NiO4_4

We have mapped out the spin dynamics in a stripe-ordered nickelate, La$_{2-x}$Sr$_{x}$NiO$_{4}$ with $x \simeq 0.31$, using inelastic neutron scattering. We observe spin-wave excitations up to 80 meV emerging from the incommensurate magnetic peaks with an almost isotropic spin-velocity: $\hbar c_s\sim 0.32$ eV \AA, very similar to the velocity in the undoped, insulating parent compound, La$_{2}$NiO$_{4}$. We also discuss the similarities and differences of the inferred spin-excitation spectrum with those reported in superconducting high-$T_c$ cuprates.Comment: 4 figure

The Mean Ultraviolet Spectrum of a Representative Sample of Faint z~3 Lyman Alpha Emitters

We discuss the rest-frame ultraviolet emission line spectra of a large (~100) sample of low luminosity redshift z~3.1 Lyman alpha emitters (LAEs) drawn from a Subaru imaging survey in the SSA22 survey field. Our earlier work based on smaller samples indicated that such sources have high [OIII]/[OII] line ratios possibly arising from a hard ionising spectrum that may be typical of similar sources in the reionisation era. With optical spectra secured from VLT/VIMOS, we re-examine the nature of the ionising radiation in a larger sample using the strength of the high ionisation diagnostic emission lines of CIII]1909, CIV1549, HeII1640, and OIII]1661,1666 in various stacked subsets. Our analysis confirms earlier suggestions of a correlation between the strength of Ly-alpha and CIII] emission and we find similar trends with broad band UV luminosity and rest-frame UV colour. Using various diagnostic line ratios and our stellar photoionisation models, we determine both the gas phase metallicity and hardness of the ionisation spectrum characterised by xi_ion - the number of Lyman continuum photons per UV luminosity. We confirm our earlier suggestion that xi_ion is significantly larger for LAEs than for continuum-selected Lyman break galaxies, particularly for those LAEs with the faintest UV luminosities. We briefly discuss the implications for cosmic reionisation if the metal-poor intensely star-forming systems studied here are representative examples of those at much higher redshift.Comment: 15 pages, 9 figures. Accepted for publication in MNRA