Pyrochlore Antiferromagnet: A Three-Dimensional Quantum Spin Liquid

Abstract

The quantum pyrochlore antiferromagnet is studied by perturbative expansions and exact diagonalization of small clusters. We find that the ground state is a spin-liquid state: The spin-spin correlation functions decay exponentially with distance and the correlation length never exceeds the interatomic distance. The calculated magnetic neutron diffraction cross section is in very good agreement with experiments performed on Y(Sc)Mn2. The low energy excitations are singlet-singlet ones, with a finite spin gap. PACS number(s): 75.10. Jm, 75.50.Ee, Since Anderson proposed the resonant valence bond (RVB) wave function for the triangular lattice 1 , there has been a lot of attention focused on frustrated lattices, because they might have a spin-liquid-like ground state in two-or three-dimensional lattices. The frustrated systems can be classified into two different categories: structurally disordered systems and periodic lattices. Among the last one the ground state of the S = 1 2 quantum Heisenberg antiferromagnet on the kagomé and pyrochlore lattices is expected to be a quantum spin liquid (QSL). The common point of these two lattices is the high degree of frustration as they both belong to the class of the "fully frustrated lattices." The classical mean field description indicates a pathological spectrum with an infinite number of zero energy modes which prevents any magnetic phase transition and produces an extensive zero temperature entropy 2-4 . The classical critical properties are nonuniversal for both systems 5 . The pyrochlore lattice consists of a 3D arrangement of corner sharing tetrahedra (Fig. 1). All compounds which crystallize in the pyrochlore structure exhibit unusual magnetic properties: Two of them, FeF 3 and NH 4 Fe 2+ Fe 3+ F 6 6 , are known to have a noncollinear long range ordered magnetic structure at low temperature; the other compounds do not undergo any phase transition, but many of them behave as spin glasses, although there is no structural disorder at all. It is remarkable that frustration in a periodic lattice may give rise to ageing and irreversibility so that a conpound such as Y 2 Mo 2 O 7 has been considered as a "topological spin glass" 3,7 . The problem of ordering in the pyrochlore lattice was initiated by Anderson 8 who predicted that only long range interactions are able to stabilize a Néel-like ground state. More recently, mean field studies 9 have confirmed these predictions; from classical Monte Carlo calculations 5,10,11 it was concluded that this system does not order down to zero temperature, but any constraint will induce magnetic ordering 12 . FIG. 1.Description of the pyrochlore lattice as an fcc lattice of tetrahedra. Solid lines connect sites interacting with exchange J, dashed lines with exchange J ′ .The only attempt to describe the quantum S = 1 2Heisenberg antiferromagnet on the pyrochlore lattice has been done by Harris et al. 13 who studied the stability of a dimer-type order parameter and showed that quantum fluctuations play a crucial role. In this Letter, ...

Structural properties of the geometrically frustrated pyrochloreTb2Ti2OHan1, Gardner2, Booth3 2004Phys. Rev. B503320View full textAdd to dashboardCite

“…6 However, since any amount of lattice disorder can precipitate a spin-glass phase, 7 geometrically-frustrated systems that do not magnetically order to the lowest temperatures are extremely rare. 8 This situation has inhibited experimental studies that attempt to isolate the effects of frustration. For instance, lattice imperfections in several geometrically frustrated systems are thought to relieve the frustration allowing the system to freeze.…”

Spin correlations in the dipolar pyrochlore antiferromagnet Gd2Sn2O7

“…The presence of many states of similarly low energy suppresses conventional magnetic order below the Curie-Weiss temperature θ CW that defines the net strength of magnetic interactions. A canonical model that remains disordered at all temperatures contains only antiferromagnetic nearest-neighbour interactions on the pyrochlore lattice, yielding a classical spin-liquid ground state [9,10]. In most real materials, however, long-range magnetic order occurs at a measurable temperature T N , partially relieving this frustration.…”

Spin frustration and magnetic exchange in cobalt aluminum oxide spinels

“…1 The inability to satisfy simultaneously all pairwise interactions between spins results either in a spin-glass state for structurally disordered magnets 2 or in a dynamic liquid ground state 3 in magnets with topological constraints yielding exotic ordered phases, like, for example, spin-ice. 4,5 Magnetic ABB 2 X 4 spinels recently have attracted much attention because of strong frustration effects.…”