37 research outputs found
Dynamic spin Jahn-Teller effect in small magnetic clusters
Abstract.: We study the effect of spin-phonon coupling in small magnetic clusters, concentrating on a S=1/2 ring of 4 spins coupled antiferromagnetically. If the phonons are treated as classical variables, there is a critical value of the spin-phonon coupling above which a static distortion occurs. This is a good approximation if the zero point energy is small compared to the energy gain due to the distortion, which is true for large exchange interactions compared to the phonon energy (J≫ħω). In the opposite limit, one can integrate out the phonon degrees of freedom and get an effective spin Hamiltonian. Using exact diagonalizations to include the quantum nature of both spins and phonons, we obtain the spectrum in the whole range of parameters and explicit the crossover between the classical and quantum regimes. We then establish quantitatively the limits of validity of two widely used approaches (one in the quantum and one in the classical limits) and show that they are quite poor for small magnetic clusters. We also show that upon reducing ħω/J the first excitation of a 4-site cluster becomes a singlet, a result that could be relevant for Cu2Te2O5Br
Ordering in the pyrochlore antiferromagnet due to Dzyaloshinsky-Moriya interactions
The Heisenberg nearest neighbour antiferromagnet on the pyrochlore (3D)
lattice is highly frustrated and does not order at low temperature where
spin-spin correlations remain short ranged. Dzyaloshinsky-Moriya interactions
(DMI) may be present in pyrochlore compounds as is shown, and the consequences
of such interactions on the magnetic properties are investigated through mean
field approximation and monte carlo simulations. It is found that DMI (if
present) tremendously change the low temperature behaviour of the system. At a
temperature of the order of the DMI a phase transition to a long range ordered
state takes place. The ordered magnetic structures are explicited for the
different possible DMI which are introduced on the basis of symmetry arguments.
The relevance of such a scenario for pyrochlore compounds in which an ordered
magnetic structure is observed experimentally is dicussed
Dzyaloshinski-Moriya interactions in the kagome lattice
The kagom\'e lattice exhibits peculiar magnetic properties due to its
strongly frustated cristallographic structure, based on corner sharing
triangles. For nearest neighbour antiferromagnetic Heisenberg interactions
there is no Neel ordering at zero temperature both for quantum and classical s
pins. We show that, due to the peculiar structure, antisymmetric
Dzyaloshinsky-Moriya interactions ()
are present in this latt ice. In order to derive microscopically this
interaction we consider a set of localized d-electronic states. For classical
spins systems, we then study the phase diagram (T, D/J) through mean field
approximation and Monte-Carlo simulations and show that the antisymmetric
interaction drives this system to ordered states as soon as this interaction is
non zero. This mechanism could be involved to explain the magnetic structure of
Fe-jarosites.Comment: 4 pages, 2 figures. Presented at SCES 200
A study of long range order in certain two-dimensional frustrated lattices
We have studied the Heisenberg antiferromagnets on two-dimensional frustrated
lattices, triangular and kagome lattices using linear spin-wave theory. A
collinear ground state ordering is possible if one of the three bonds in each
triangular plaquette of the lattice becomes weaker or frustrated. We study
spiral order in the Heisenberg model along with Dzyaloshinskii-Moriya (DM)
interaction and in the presence of a magnetic field. The quantum corrections to
the ground state energy and sublattice magnetization are calculated
analytically in the case of triangular lattice with nearesr-neighbour
interaction. The corrections depend on the DM interaction strength and the
magnetic field. We find that the DM interaction stabilizes the long-range
order, reducing the effect of quantum fluctuations. Similar conclusions are
reached for the kagome lattice. We work out the linear spin-wave theory at
first with only nearest-neighbour (nn) terms for the kagome lattice. We find
that the nn interaction is not sufficient to remove the effects of low energy
fluctuations. The flat branch in the excitation spectrum becomes dispersive on
addition of furthet neighbour interactions. The ground state energy and the
excitation spectrum have been obtained for various cases.Comment: 18 pages, 9 figure
Dynamic spin Jahn-Teller effect in small magnetic clusters
We study the effect of spin-phonon coupling in small magnetic clusters,
concentrating on a S=1/2 ring of 4 spins coupled antiferromagnetically. If the
phonons are treated as classical variables, there is a critical value of the
spin-phonon coupling above which a static distortion occurs. This is a good
approximation if the zero point energy is small compared to the energy gain due
to the distortion, which is true for large exchange interactions compared to
the phonons energy (). In the opposite limit, one can
integrate out the phonon degrees of freedom and get an effective spin
hamiltonian. Using exact diagonalizations to include the quantum nature of both
spins and phonons, we obtain the spectrum in the whole range of parameters and
explicit the crossover between the classical and quantum regimes. We then
establish quantitatively the limits of validity of two widely used approaches
(one in the quantum and one in the classical limits) and show that they are
quite poor for small magnetic clusters. We also show that upon reducing
the first excitation of a 4-site cluster becomes a singlet, a
result that could be relevant for CuTeOBr
Spin-orbit effects in NaIrO, a hyper-kagom\'{e} lattice antiferromagnet
We consider spin-orbit coupling effects in NaIrO, a material in
which Ir spins form an hyper-kagom\'{e} lattice, a three-dimensional
network of corner-sharing triangles. We argue that both low temperature
thermodynamic measurements and the impurity susceptibility induced by dilute
substitution of Ti for Ir are suggestive of significant spin-orbit effects.
Because of uncertainties in the crystal-field parameters, we consider two
limits in which the spin-orbit coupling is either weak or strong compared to
the non-cubic atomic splittings. A semi-microscopic calculation of the exchange
Hamiltonian confirms that indeed large antisymmetric Dzyaloshinskii-Moriya (DM)
and/or symmetric exchange anisotropy may be present. In the strong spin-orbit
limit, the Ir-O-Ir superexchange contribution consists of unfrustrated strong
symmetric exchange anisotropy, and we suggest that spin-liquid behavior is
unlikely. In the weak spin-orbit limit, and for strong spin-orbit and direct
Ir-Ir exchange, the Hamiltonian consists of Heisenberg and DM interactions. The
DM coupling is parametrized by a three component DM vector (which must be
determined empirically). For a range of orientation of this vector, frustration
is relieved and an ordered state occurs. For other orientations, even the
classical ground states are very complex. We perform spin-wave and exact
diagonalization calculations which suggest the persistence of a quantum spin
liquid in the latter regime. Applications to NaIrO and broader
implications are discussed.Comment: 22 pages, 15 figures. submit to prb. New references are adde
Ising transition driven by frustration in a 2D classical model with SU(2) symmetry
We study the thermal properties of the classical antiferromagnetic Heisenberg
model with both nearest () and next-nearest () exchange couplings on
the square lattice by extensive Monte Carlo simulations. We show that, for
, thermal fluctuations give rise to an effective symmetry
leading to a {\it finite-temperature} phase transition. We provide strong
numerical evidence that this transition is in the 2D Ising universality class,
and that with an infinite slope when .Comment: 4 pages with 4 figure
Symmetry breaking due to Dzyaloshinsky-Moriya interactions in the kagome lattice
Due to the particular geometry of the kagom\'e lattice, it is shown that
antisymmetric Dzyaloshinsky-Moriya interactions are allowed and induce magnetic
ordering. The symmetry of the obtained low temperature magnetic phases are
studied through mean field approximation and classical Mont\'e Carlo
simulations. A phase diagram relating the geometry of the interaction and the
ordering temperature has been derived. The order of magnitude of the
anisotropies due to Dzyaloshinsky-Moriya interactions are more important than
in non-frustrated magnets, which enhances its appearance in real systems.
Application to the jarosites compounds is proposed. In particular, the low
temperature behaviors of the Fe and Cr-based jarosites are correctly described
by this model.Comment: 6 (revtex4) twocolumn pages, 6 .eps figures. Submitted to Phys. Rev.
High-field Phase Diagram and Spin Structure of Volborthite Cu3V2O7(OH)2/2H2O
We report results of 51V NMR experiments on a high-quality powder sample of
volborthite Cu3V2O7(OH)2/2H2O, a spin-1/2 Heisenberg antiferromagnet on a
distorted kagome lattice. Following the previous experiments in magnetic fields
below 12 T, the NMR measurements have been extended to higher fields up to
31 T. In addition to the two already known ordered phases (phases I and II), we
found a new high-field phase (phase III) above 25 T, at which a second
magnetization step has been observed. The transition from the paramagnetic
phase to the antiferromagnetic phase III occurs at 26 K, which is much higher
than the transition temperatures from the paramagnetic to the lower field
phases I (B < 4.5 T) and II (4.5 < B < 25 T). At low temperatures, two types of
the V sites are observed with different relaxation rates and line shapes in
phase III as well as in phase II. Our results indicate that both phases II and
III exhibit a heterogeneous spin state consisting of two spatially alternating
Cu spin systems, one of which exhibits anomalous spin fluctuations contrasting
with the other showing a conventional static order. The magnetization of the
latter system exhibits a sudden increase upon entering into phase III,
resulting in the second magnetization step at 26 T.We discuss the possible spin
structure in phase III.Comment: 9 pages, 12 figure
Toward Perfection: Kapellasite, Cu3Zn(OH)6Cl2, a New Model S = 1/2 Kagome Antiferromagnet
The search for the resonating valence bond (RVB) state continues to underpin
many areas of condensed matter research. The RVB is made from the dimerisation
of spins on different sites into fluctuating singlets, and was proposed by
Anderson to be the reference state from which the transition to BCS
superconductivity occurs. Little is known about the state experimentally, due
to the scarcity of model materials. Theoretical work has put forward the S =
1/2 kagome antiferromagnet (KAFM) as a good candidate for the realization of
the RVB state. In this paper we introduce a new model system, the S = 1/2 KAFM
Kapellasite, Cu3Zn(OH)6Cl2. We show that its crystal structure is a good
approximation to a 2-dimensional kagome antiferromagnet and that susceptibility
data indicate a collapse of the magnetic moment below T = 25 K that is
compatible with the spins condensing into the non-magnetic RVB state.Comment: Communication, 3 pages, 3 figure