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Non-Collinear Magnetic Phases of a Triangular-Lattice Antiferromagnet and Doped CuFeO
We obtain the non-collinear ground states of a triangular-lattice
antiferromagnet with exchange interactions up to third nearest neighbors as a
function of the single-ion anisotropy . At a critical value of , the
collinear \uudd phase transforms into a complex non-collinear phase with
odd-order harmonics of the fundamental ordering wavevector \vQ . The observed
elastic peaks at 2\pi \vx -\vQ in both Al- and Ga- doped CuFeO are
explained by a "scalene" distortion of the triangular lattice produced by the
repulsion of neighboring oxygen atoms.Comment: 4 pages 3 figures, accepted for publication by Phys. Rev. B Rapid
communication
Exact Eigenfunctions of a Chaotic System
The interest in the properties of quantum systems, whose classical dynamics
are chaotic, derives from their abundance in nature. The spectrum of such
systems can be related, in the semiclassical approximation (SCA), to the
unstable classical periodic orbits, through Gutzwiller's trace formula. The
class of systems studied in this work, tiling billiards on the pseudo-sphere,
is special in this correspondence being exact, via Selberg's trace formula. In
this work, an exact expression for Green's function (GF) and the eigenfunctions
(EF) of tiling billiards on the pseudo-sphere, whose classical dynamics are
chaotic, is derived. GF is shown to be equal to the quotient of two infinite
sums over periodic orbits, where the denominator is the spectral determinant.
Such a result is known to be true for typical chaotic systems, in the leading
SCA. From the exact expression for GF, individual EF can be identified. In
order to obtain a SCA by finite series for the infinite sums encountered,
resummation by analytic continuation in was performed. The result is
similar to known results for EF of typical chaotic systems. The lowest EF of
the Hamiltonian were calculated with the help of the resulting formulae, and
compared with exact numerical results. A search for scars with the help of
analytical and numerical methods failed to find evidence for their existence.Comment: 53 pages LaTeX, 10 Postscript figure
Characterization of low-energy magnetic excitations in chromium
The low-energy excitations of Cr, i.e. the Fincher-Burke (FB) modes, have
been investigated in the transversely polarized spin-density-wave phase by
inelastic neutron scattering using a single-(Q+-) crystal with a propagation
vector (Q+-) parallel to [0,0,1]. The constant-momentum-transfer scans show
that the energy spectra consist of two components, namely dispersive FB modes
and an almost energy-independent cross section. Most remarkably, we find that
the spectrum of the FB modes exhibits one peak at 140 K near Q = (0,0,0.98) and
two peaks near Q = (0,0,1.02), respectively. This is surprising because Cr
crystallizes in a centro-symmetric bcc structure. The asymmetry of those energy
spectra decreases with increasing temperature. In addition, the observed
magnetic peak intensity is independent of Q suggesting a transfer of
spectral-weight between the upper and lower FB modes. The energy-independent
cross section is localized only between the incommensurate peaks and develops
rapidly with increasing temperature.Comment: 6 pages, 8 figure
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