16 research outputs found
The Kagome Antiferromagnet with Defects: Satisfaction, Frustration, and Spin Folding in a Random Spin System
It is shown that site disorder induces noncoplanar states, competing with the
thermal selection of coplanar states, in the nearest neighbor, classical kagome
Heisenberg antiferromagnet (AFM). For weak disorder, it is found that the
ground state energy is the sum of energies of separately satisfied triangles of
spins. This implies that disorder does not induce conventional spin glass
behavior. A transformation is presented, mapping ground state spin
configurations onto a folded triangular sheet (a new kind of ``spin origami'')
which has conformations similar to those of tethered membranes.Comment: REVTEX, 11 pages + 3 pictures upon reques
Landau Expansion for the Kugel-Khomskii Hamiltonian
The Kugel-Khomskii (KK) Hamiltonian for the titanates describes spin and
orbital superexchange interactions between ions in an ideal perovskite
structure in which the three orbitals are degenerate in energy and
electron hopping is constrained by cubic site symmetry. In this paper we
implement a variational approach to mean-field theory in which each site, ,
has its own single-site density matrix \rhov(i), where , the
number of allowed single-particle states, is 6 (3 orbital times 2 spin states).
The variational free energy from this 35 parameter density matrix is shown to
exhibit the unusual symmetries noted previously which lead to a
wavevector-dependent susceptibility for spins in orbitals which is
dispersionless in the -direction. Thus, for the cubic KK model
itself, mean-field theory does not provide wavevector `selection', in agreement
with rigorous symmetry arguments. We consider the effect of including various
perturbations. When spin-orbit interactions are introduced, the susceptibility
has dispersion in all directions in -space, but the resulting
antiferromagnetic mean-field state is degenerate with respect to global
rotation of the staggered spin, implying that the spin-wave spectrum is
gapless. This possibly surprising conclusion is also consistent with rigorous
symmetry arguments. When next-nearest-neighbor hopping is included, staggered
moments of all orbitals appear, but the sum of these moments is zero, yielding
an exotic state with long-range order without long-range spin order. The effect
of a Hund's rule coupling of sufficient strength is to produce a state with
orbital order.Comment: 20 pages, 5 figures, submitted to Phys. Rev. B (2003
Order induced by dipolar interactions in a geometrically frustrated antiferromagnet
We study the classical Heisenberg model for spins on a pyrochlore lattice
interacting via long range dipole-dipole forces and nearest neighbor exchange.
Antiferromagnetic exchange alone is known not to induce ordering in this
system. We analyze low temperature order resulting from the combined
interactions, both by using a mean-field approach and by examining the energy
cost of fluctuations about an ordered state. We discuss behavior as a function
of the ratio of the dipolar and exchange interaction strengths and find two
types of ordered phase. We relate our results to the recent experimental work
and reproduce and extend the theoretical calculations on the pyrochlore
compound, GdTiO, by Raju \textit{et al.}, Phys. Rev. B {\bf 59},
14489 (1999).Comment: 5 pages, 5 figures, AMSLaTe
Site-Dilution-Induced Antiferromagnetic Long-Range Order in Two-Dimensional Spin-Gapped Heisenberg Antiferromagnet
Effects of the site dilution on spin-gapped Heisenberg antiferromagnets with
and S=1 on a square lattice are investigated by means of the quantum
Monte Carlo method. It is found that effective magnetic moments induced around
the diluted sites exhibit the antiferromagnetic long-range order in the medium
of spin-singlet pairs. Their microscopic structure is examined in detail and
important roles of the higher dimensionality than one on the phenomenon are
discussed.Comment: RevTeX, 4 pages, 6 figure
Green's function approach to the magnetic properties of the kagome antiferromagnet
The Heisenberg antiferromagnet is studied on the kagom\'e lattice by
using a Green's function method based on an appropriate decoupling of the
equations of motion. Thermodynamic properties as well as spin-spin correlation
functions are obtained and characterize this system as a two-dimensional
quantum spin liquid. Spin-spin correlation functions decay exponentially with
distance down to low temperature and the calculated missing entropy at T=0 is
found to be . Within the present scheme, the specific heat exhibits
a single peak structure and a dependence at low temperature.Comment: 6 (two-column revtex4) pages, 5 ps figures. Submitted to Phys. Rev.
Interplay of quantum and thermal fluctuations in a frustrated magnet
We demonstrate the presence of an extended critical phase in the transverse
field Ising magnet on the triangular lattice, in a regime where both thermal
and quantum fluctuations are important. We map out a complete phase diagram by
means of quantum Monte Carlo simulations, and find that the critical phase is
the result of thermal fluctuations destabilising an order established by the
quantum fluctuations. It is separated by two Kosterlitz-Thouless transitions
from the paramagnet on one hand and the quantum-fluctuation driven
three-sublattice ordered phase on the other. Our work provides further evidence
that the zero temperature quantum phase transition is in the 3d XY universality
class.Comment: 9 pages, revtex
Zero temperature phases of the frustrated J1-J2 antiferromagnetic spin-1/2 Heisenberg model on a simple cubic lattice
At zero temperature magnetic phases of the quantum spin-1/2 Heisenberg
antiferromagnet on a simple cubic lattice with competing first and second
neighbor exchanges (J1 and J2) is investigated using the non-linear spin wave
theory. We find existence of two phases: a two sublattice Neel phase for small
J2 (AF), and a collinear antiferromagnetic phase at large J2 (CAF). We obtain
the sublattice magnetizations and ground state energies for the two phases and
find that there exists a first order phase transition from the AF-phase to the
CAF-phase at the critical transition point, pc = 0.28. Our results for the
value of pc are in excellent agreement with results from Monte-Carlo
simulations and variational spin wave theory. We also show that the quartic 1/S
corrections due spin-wave interactions enhance the sublattice magnetization in
both the phases which causes the intermediate paramagnetic phase predicted from
linear spin wave theory to disappear.Comment: 19 pages, 4 figures, Fig. 1b modified, Appendix B text modifie
Bond order from disorder in the planar pyrochlore magnet
We study magnetic order in the Heisenberg antiferromagnet on the checkerboard
lattice, a two-dimensional version of the pyrochlore network with strong
geometric frustration. By employing the semiclassical (1/S) expansion we find
that quantum fluctuations of spins induce a long-range order that breaks the
four-fold rotational symmetry of the lattice. The ordered phase is a
valence-bond crystal. We discuss similarities and differences with the extreme
quantum case S = 1/2 and find a useful phenomenology to describe the
bond-ordered phases.Comment: Minor clarifications + reference to an informal introduction
cond-mat/030809
Quantum phase transitions and thermodynamic properties in highly anisotropic magnets
The systems exhibiting quantum phase transitions (QPT) are investigated
within the Ising model in the transverse field and Heisenberg model with
easy-plane single-site anisotropy. Near QPT a correspondence between parameters
of these models and of quantum phi^4 model is established. A scaling analysis
is performed for the ground-state properties. The influence of the external
longitudinal magnetic field on the ground-state properties is investigated, and
the corresponding magnetic susceptibility is calculated. Finite-temperature
properties are considered with the use of the scaling analysis for the
effective classical model proposed by Sachdev. Analytical results for the
ordering temperature and temperature dependences of the magnetization and
energy gap are obtained in the case of a small ground-state moment. The forms
of dependences of observable quantities on the bare splitting (or magnetic
field) and renormalized splitting turn out to be different. A comparison with
numerical calculations and experimental data on systems demonstrating magnetic
and structural transitions (e.g., into singlet state) is performed.Comment: 46 pages, RevTeX, 6 figure
Susceptibility and dilution effects of the kagome bi-layer geometrically frustrated network. A Ga-NMR study of SrCr_(9p)Ga_(12-9p)O_(19)
We present an extensive gallium NMR study of the geometrically frustrated
kagome bi-layer compound SrCr_(9p)Ga_(12-9p)O_(19) (Cr^3+, S=3/2) over a broad
Cr-concentration range (.72<p<.95). This allows us to probe locally the kagome
bi-layer susceptibility and separate the intrinsic properties due to the
geometric frustration from those related to the site dilution. Our major
findings are: 1) The intrinsic kagome bi-layer susceptibility exhibits a
maximum in temperature at 40-50 K and is robust to a dilution as high as ~20%.
The maximum reveals the development of short range antiferromagnetic
correlations; 2) At low-T, a highly dynamical state induces a strong wipe-out
of the NMR intensity, regardless of dilution; 3) The low-T upturn observed in
the macroscopic susceptibility is associated to paramagnetic defects which stem
from the dilution of the kagome bi-layer. The low-T analysis of the NMR
lineshape suggests that the defect can be associated with a staggered
spin-response to the vacancies on the kagome bi-layer. This, altogether with
the maximum in the kagome bi-layer susceptibility, is very similar to what is
observed in most low-dimensional antiferromagnetic correlated systems; 4) The
spin glass-like freezing observed at T_g=2-4 K is not driven by the
dilution-induced defects.Comment: 19 pages, 19 figures, revised version resubmitted to PRB Minor
modifications: Fig.11 and discussion in Sec.V on the NMR shif