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Muon spin relaxation investigation of frustrated antiferromagnetic pyrochlores A 2 B 2 O 7
Hyperfine Interactions, 1997
In a system where magnetic ions occupy the vertices of edge or corner sharing triangular units, the natural antiferromagnetic coupling between ions is geometrically frustrated. A wide variety of interesting magnetic behaviour has been observed in pyrochlores, where magnetic ions form a network of corner sharing tetrahedra. The low temperature spin dynamics of a number of pyrochlores A2B2O7 have been
Spin-liquid phase in the pyrochlore anti-ferromagnet
Canadian Journal of Physics, 2001
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)Mn2 and CsCrNiF6 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 ) ≈ f (q)h(T ).
Quantum Effects in a Half-Polarized Pyrochlore Antiferromagnet
Physical Review Letters, 2006
We study quantum effects in a spin-3/2 antiferromagnet on the pyrochlore lattice in an external magnetic field, focusing on the vicinity of a plateau in the magnetization at half the saturation value, observed in CdCr2O4 and HgCr2O4. Our theory, based on quantum fluctuations, predicts the existence of a symmetry-broken state on the plateau, even with only nearest-neighbor microscopic exchange. This symmetry broken state consists of a particular arrangement of spins polarized parallel and antiparallel to the field in a 3:1 ratio on each tetrahedron. It quadruples the lattice unit cell, and reduces the space group from F d3m to P 4332. We also predict that for fields just above the plateau, the low temperature phase has transverse spin order, describable as a Bose-Einstein condensate of magnons. Other comparisons to and suggestions for experiments are discussed.
Spin dilution in frustrated two-dimensional S=12 antiferromagnets on a square lattice
Physical Review B, 2005
7 Li and 29 Si NMR, µSR and magnetization measurements in Li2V1−xOTixSiO4, for 0 ≤ x ≤ 0.2, are presented. The x = 0 compound is a prototype of frustrated two-dimensional Heisenberg antiferromagnet on a square-lattice with competing nearest (J1) and next-nearest (J2) neighbour exchange interactions. Ti 4+ (S=0) for V 4+ (S=1/2) substitution yields the spin dilution of the antiferromagnetic layers. The analysis of the magnetization and of the nuclear spin-lattice relaxation rate shows that spin dilution not only reduces the spin-stiffness by a factor ≃ (1 − x) 2 , but also causes the decrease of the effective ratio J2(x)/J1(x). Moreover, the sublattice magnetization curves derived from zero-field µSR measurements in the collinear phase point out that, at variance with non-frustrated two-dimensional Heisenberg antiferromagnets, spin dilution affects the low-temperature staggered magnetization only to a minor extent. This observation is supported also by the x dependence of the collinear ordering temperature. The results obtained for the Ti doped samples are discussed in the light of the results previously obtained in the pure x = 0 compound and in non-frustrated two-dimensional Heisenberg antiferromagnets with spin-dilution.
Physical Review B, 2002
The stability of the disordered ground state of the classical Heisenberg pyrochlore antiferromagnet is studied within extensive Monte Carlo simulations by introducing an additional exchange interaction J ′ that interpolates between the pyrochlore lattice (J ′ = 0) and the face-centered cubic lattice (J ′ = J). It is found that for J ′ /J as low as J ′ /J ≥ 0.01, the system is long range ordered : the disordered ground state of the pyrochlore antiferromagnet is unstable when introducing very small deviations from the pure J ′ = 0 limit. Furthermore, it is found that the selected phase is a collinear state energetically greater than the incommensurate phase suggested by a mean field analysis. To our knowledge this is the first example where entropic selection prevails over the energetic one.
Magnetization plateaus of the quantum pyrochlore Heisenberg antiferromagnet
Physical Review B, 2019
We predict magnetisation plateaux ground states for S = 1/2 Heisenberg antiferromagnets on pyrochlore lattices by formulating arguments based on gauge and spin-parity transformations. We derive a twist operator appropriate to the pyrochlore lattice, and show that it is equivalent to a large gauge transformation. Invariance under this large gauge transformation indicates the sensitivity of the ground state to changes in boundary conditions. This leads to the formulation of an Oshikawa-Yamanaka-Affleck (OYA)-like criterion at finite external magnetic field, enabling the prediction of plateaux in the magnetisation versus field diagram. We also develop an analysis based on the spinparity operator, leading to a condition from which identical predictions are obtained of magnetisation plateaux ground states. Both analyses are based on the non-local nature of the transformations, and rely only on the symmetries of the Hamiltonian. This suggests that the plateaux ground states can possess properties arising from non-local entanglement between the spins. We also demonstrate that while a spin-lattice coupling stabilises plateaux in a system of quantum spins with antiferromagnetic exchange, it can compete with weak ferromagnetic spin exchange in leading to frustration-induced magnetisation plateaux.
Physical Review Letters, 2006
We study quantum effects in a spin-3/2 antiferromagnet on the pyrochlore lattice in an external magnetic field, focusing on the vicinity of a plateau in the magnetization at half the saturation value, observed in CdCr2O4 and HgCr2O4. Our theory, based on quantum fluctuations, predicts the existence of a symmetry-broken state on the plateau, even with only nearest-neighbor microscopic exchange. This symmetry broken state consists of a particular arrangement of spins polarized parallel and antiparallel to the field in a 3:1 ratio on each tetrahedron. It quadruples the lattice unit cell, and reduces the space group from F d3m to P 4332. We also predict that for fields just above the plateau, the low temperature phase has transverse spin order, describable as a Bose-Einstein condensate of magnons. Other comparisons to and suggestions for experiments are discussed.
Exact eigenstates and macroscopic magnetization jumps in strongly frustrated spin lattices
Journal of Physics: Condensed Matter, 2004
For a class of frustrated spin lattices including e.g. the 1D sawtooth chain, the 2D kagomé and checkerboard, as well as the 3D pyrochlore lattices we construct exact product eigenstates consisting of several independent, localized one-magnon states in a ferromagnetic background. Important geometrical elements of the relevant lattices are triangles being attached to polygons or lines. Then the magnons can be trapped on these polygons/lines. If the concentration of localized magnons is small they can be distributed randomly over the lattice. Increasing the number of localized magnons their distribution over the lattice becomes more and more regular and finally the magnons condensate in a crystal-like state. The physical relevance of these eigenstates emerges in high magnetic fields where they become groundstates of the system. As a result a macroscopic magnetization jump appears in the zero-temperature magnetization curve just below the saturation field. The height of the jump decreases with increasing spin quantum number and vanishes in the classical limit. Thus it is a true macroscopic quantum effect.