Orbital ordering in the ferromagnetic insulator Cs2_2AgF4_4 from first principles

We found, using density-functional theory calculations within the generalized gradient approximation, that Cs$_2$AgF$_4$ is stabilized in the insulating orthorhombic phase rather than in the metallic tetragonal phase. The lattice distortion present in the orthorhombic phase corresponds to the $x^2-z^2$/$y^2-z^2$ hole-orbital ordering of the Ag$^{2+}$ $4d^9$ ions, and this orbital ordering leads to the observed ferromagnetism, as confirmed by the present total-energy calculations. This picture holds in the presence of moderate 4d-electron correlation. The results are compared with the picture of ferromagnetism based on the metallic tetragonal phase.Comment: 5 pages, 4 figures, 1 table; a few energy/moment entries in Table I are corrected due to a proper treatment of the Ag 4s semicore stat

HOMFLY polynomials, stable pairs and motivic Donaldson-Thomas invariants

Hilbert scheme topological invariants of plane curve singularities are identified to framed threefold stable pair invariants. As a result, the conjecture of Oblomkov and Shende on HOMFLY polynomials of links of plane curve singularities is given a Calabi-Yau threefold interpretation. The motivic Donaldson-Thomas theory developed by M. Kontsevich and the third author then yields natural motivic invariants for algebraic knots. This construction is motivated by previous work of V. Shende, C. Vafa and the first author on the large $N$ duality derivation of the above conjecture.Comment: 59 pages; v2 references added, minor corrections; v3: exposition improved, proofs expanded, results unchanged, to appear in Comm. Num. Th. Phy

Collinear factorization violation and effective field theory

The factorization of amplitudes into hard, soft and collinear parts is known to be violated in situations where incoming particles are collinear to outgoing ones. This result was first derived by studying limits where non-collinear particles become collinear. We show that through an effective field theory framework with Glauber operators, these factorization-violating effects can be reproduced from an amplitude that is factorized before the splitting occurs. We confirm results at one-loop, through single Glauber exchange, and at two-loops, through double Glauber exchange. To approach the calculation, we begin by reviewing the importance of Glauber scaling for factorization. We show that for any situation where initial state and final state particles are not collinear, the Glauber contribution is entirely contained in the soft contribution. The contributions coming from Glauber operators are necessarily non-analytic functions of external momentum, with the non-analyticity arising from the rapidity regulator. The non-analyticity is critical so that Glauber operators can both preserve factorization when it holds and produce factorization-violating effects when they are present.Comment: 55 Pages, 5 figure

Magnonic momentum transfer force on domain walls confined in space

Momentum transfer from incoming magnons to a Bloch domain wall is calculated using one dimensional continuum micromagnetic analysis. Due to the confinement of the wall in space, the dispersion relation of magnons is different from that of a single domain. This mismatch of dispersion relations can result in reflection of magnons upon incidence on the domain wall, whose direct consequence is a transfer of momentum between magnons and the domain wall. The corresponding counteraction force exerted on the wall can be used for the control of domain wall motion through magnonic linear momentum transfer, in analogy with the spin transfer torque induced by magnonic angular momentum transfer.Comment: 5 pages, 3 figure, published versio