Spin Liquid Phase in the Pyrochlore Antiferromagnet

Correlation functions (CFs) of the classical Heisenberg antiferromagnet on the pyrochlore lattice are studied by solving exactly the infinite-component spin-vector model. % As in many Fully Frustrated Lattices, the constraint due to the minimization of the energy and the particular structure based on corner sharing tetrahedra both contribute to the creation of local degrees of freedom. % The resulting degeneracy destroys any magnetic order at all temperature and we obtain no sign of criticality, even at $T = 0$. % Calculated neutron scattering cross sections have their maxima beyond the first Brillouin Zone and reproduce experimental results obtained on Y(Sc)Mn$_2$ and CsCrNiF$_6$ as well as theoretical predictions previously obtained by classical Monte Carlo simulations. % Evidences for thermal and spatial decoupling of the magnetic modes are found so that the magnetic fluctuations in this system can be approximated by $S(q,T) \approx f(q) h(T)$.Comment: 6 pages (revtex two columns), 7 figures. Submitted to Canadian Journal of Physics for the Proceedings of the Higly Frustrated Magnetism 2000 Conference, Waterloo, Ontario, Canada, June 11-15, 200

Classical Spin Liquid Properties of the Infinite-Component Spin Vector Model on a Fully Frustrated Two Dimensional Lattice

Thermodynamic quantities and correlation functions (CFs) of the classical antiferromagnet on the checkerboard lattice are studied for the exactly solvable infinite-component spin-vector model, $D \to \infty$. In contrast to conventional two-dimensional magnets with continuous symmetry showing extended short-range order at distances smaller than the correlation length, $r \lesssim \xi_c \propto \exp(T^*/T)$, correlations in the checkerboard-lattice model decay already at the scale of the lattice spacing due to the strong degeneracy of the ground state characterized by a macroscopic number of strongly fluctuating local degrees of freedom. At low temperatures, spin CFs decay as $\propto 1/r^2$ in the range $a_0 \ll r \ll \xi_c \propto T^{-1/2}$, where $a_0$ is the lattice spacing. Analytical results for the principal thermodynamic quantities in our model are very similar with MC simulations, exact and analytical results for the classical Heisenberg model (D=3) on the pyrochlore lattice. This shows that the ground state of the infinite-component spin vector model on the checkerboard lattice is a classical spin liquid.Comment: 9 pages (epj-style, two columns), 7 figures. Version to be published in EPJ

Classical Spin Liquid: Exact Solution for the Infinite-Component Antiferromagnetic Model on the Kagom\'e Lattice

Thermodynamic quantities and correlation functions (CFs) of the classical antiferromagnet on the kagom\'e lattice are studied for the exactly solvable infinite-component spin-vector model, D \to \infty. In this limit, the critical coupling of fluctuations dies out and the critical behavior simplifies, but the effect of would be Goldstone modes preventing ordering at any nonzero temperature is properly accounted for. In contrast to conventional two-dimensional magnets with continuous symmetry showing extended short-range order at distances smaller than the correlation length, r < \xi_c \propto \exp(T^*/T), correlations in the kagom\'e-lattice model decay already at the scale of the lattice spacing due to the strong degeneracy of the ground state characterized by a macroscopic number of strongly fluctuating local degrees of freedom. At low temperatures, spin CFs decay as \propto 1/r^2 in the range a_0 << r << \xi_c \propto T^{-1/2}, where a_0 is the lattice spacing. Analytical results for the principal thermodynamic quantities in our model are in fairly good quantitative agreement with the MC simulations for the classical Heisenberg model, D=3. The neutron scattering cross section has its maxima beyond the first Brillouin zone; at T\to 0 it becomes nonanalytic but does not diverge at any q.Comment: 14 PR pages, 10 figures; Phys. Rev. B; Version 3: final published versio

Ising Like Order by Disorder In The Pyrochlore Antiferromagnet with Dzyaloshinskii-Moriya Interactions

It is shown that the mechanism of order out of disorder is at work in the antisymmetric pyrochlore antiferromagnet. Quantum as well as thermal fluctuations break the continuous degeneracy of the classical ground state manifold and reduce its symmetry to $\mathbb{Z}_3 \times \mathbb{Z}_2$. The role of anisotropic symmetric exchange is also investigated and we conclude that this discrete like ordering is robust with respect to these second order like interactions. The antisymmetric pyrochlore antiferromagnet is therefore expected to order at low temperatures, whatever the symmetry type of its interactions, in both the classical and semi classical limits.Comment: 6 pages. 9 figure

Semi-classical spin dynamics of the antiferromagnetic Heisenberg model on the kagome lattice

We investigate the dynamical properties of the classical antiferromagnetic Heisenberg model on the kagome lattice using a combination of Monte Carlo and molecular dynamics simulations. We find that frustration induces a distribution of timescales in the cooperative paramagnetic regime (i.e. far above the onset of coplanarity), as recently reported experimentally in deuterium jarosite. At lower temperature, when the coplanar correlations are well established, we show that the weath- ervane loop fluctuations control the system relaxation : the time distribution observed at higher temperatures splits into two distinct timescales associated with fluctuations in the plane and out of the plane of coplanarity. The temperature and wave vector dependences of these two components are qualitatively consistent with loops diffusing in the entropically dominated free energy landscape. Numerical results are discussed and compared with the $O(N)$ model and recent experiments for both classical and quantum realizations of the kagome magnets.Comment: 18 pages, 14 figure

Dynamically-Induced Frustration as a Route to a Quantum Spin Ice State in Tb2Ti2O7 via Virtual Crystal Field Excitations and Quantum Many-Body Effects

The Tb$_2$Ti$_2$O$_7$ pyrochlore magnetic material is attracting much attention for its {\em spin liquid} state, failing to develop long range order down to 50 mK despite a Curie-Weiss temperature $\theta_{\rm CW} \sim -14$ K. In this paper we reinvestigate the theoretical description of this material by considering a quantum model of independent tetrahedra to describe its low temperature properties. The naturally-tuned proximity of this system near a N\'eel to spin ice phase boundary allows for a resurgence of quantum fluctuation effects that lead to an important renormalization of its effective low energy spin Hamiltonian. As a result, Tb$_2$Ti$_2$O$_7$ is argued to be a {\em quantum spin ice}. We put forward an experimental test of this proposal using neutron scattering on a single crystal.Comment: 5 pages, 3 figures. Version 2 has a modified introduction. Figure 2b of version 1 (experimental neutron scattering has been removed. A proposal for an experimental test is now included accompanied by a new Figure (Fig. 3

XY checkerboard antiferromagnet in external field

Ordering by thermal fluctuations is studied for the classical XY antiferromagnet on a checkerboard lattice in zero and finite magnetic fields by means of analytical and Monte Carlo methods. The model exhibits a variety of novel broken symmetries including states with nematic ordering in zero field and with triatic order parameter at high fields.Comment: 6 page

Proposal to recover an extensive ground state degeneracy in a two-dimensional square array of nanomagnets

We investigate numerically the micromagnetic properties and the low-energy physics of an artificial square spin system in which the nanomagnets are physically connected at the lattice vertices. Micromagnetic simulations reveal that the energy stored at the vertex sites strongly depends on the type of magnetic domain wall formed by the four connected nanomagnets. As a consequence, the energy gap between the vertex types can be partially modified by varying the geometrical parameters of the nanomagnets, such as their width and thickness. Based on the energy levels given by the micromagnetic simulations, we compute the thermodynamic properties of the corresponding spin models using Monte Carlo simulations. We found two regimes, both being characterized by an extensive ground state manifold, in sharp contrast with similar lattices with disconnected nanomagnets. For narrow and thin nanomagnets, low-energy spin configurations consist of independent ferromagnetic straight lines crossing the whole lattice. The ground state manifold is thus highly degenerate, although this degeneracy is subdominant. In the limit of thick and wide nanomagnets, our findings suggest that the celebrated square ice model may be fabricated experimentally from a simple square lattice of connected elements. These results show that the micromagnetic nature of artificial spin systems involves another degree of freedom that can be finely tuned to explore strongly correlated disordered magnetic states of matter.Comment: 6 pages, 5 figure

Spin liquid correlations in Nd-langasite anisotropic Kagom\'e antiferromagnet

Dynamical magnetic correlations in the geometrically frustrated Nd$\_3$Ga$\_5$SiO$\_{14}$ compound were probed by inelastic neutron scattering on a single crystal. A scattering signal with a ring shape distribution in reciprocal space and unprecedented dispersive features was discovered. Comparison with calculated static magnetic scattering from models of correlated spins suggests that the observed phase is a spin liquid inherent to an antiferromagnetic kagom\'e-like lattice of anisotropic Nd moments.Comment: 4 page

Finite size effects in ferromagnetic 3He nano-clusters

International audience3He adsorbed on Graphite enables to create model 2D ferromagnetic Heisenberg systems. The exchange énergies are of the order of 2mK, typical sizes on the order of a thousand spins. By adding 4He (which is non magnetic) to the system, one can tune the effective size of one ferromagnetic domain. Up to now, the theoretical tools available did not allow a quantitative understanding of themagnetism of these clusters. For the first time, "engineered" ferromagnetic nano-clusters are compared to accurate theoretical models in order to understand the finite size effects. The experimental magnetization of a cluster of about 16 spins is compared to exact diagonalization and Monte-Carlo simulations based on the Heisenberg Hamiltonian