Spin-Driven Jahn-Teller Distortion in a Pyrochlore System

Abstract

The ground-state properties of the spin-1 antiferromagnetic Heisenberg model on the cornersharing tetrahedra, pyrochlore lattice, is investigated. By breaking up each spin into a pair of 1/2-spins, the problem is reduced to the equivalent one of the spin-1/2 tetrahedral network in analogy with the valence bond solid state in one dimension. The twofold degeneracy of the spin-singlets of a tetrahedron is lifted by a Jahn-Teller mechanism, leading to a cubic to tetragonal structural transition. It is proposed that the present mechanism is responsible for the phase transition observed in the spin-1 spinel compounds ZnV2O4 and MgV2O4. PACS numbers: 75.10.Jm, 75.40.Cx, 75.80.+q Geometrically frustrated spin systems have been a fascinating subject to study since the Anderson's pioneering work on classical spins with a disordered ground state [1]. The pyrochlore and the spinel compounds, both including the three-dimensional (3D) tetrahedral network sharing the vertexes, are the typical examples of such systems in nature. As recent theoretical progress on pyrochlore spin systems, it may be mentioned that the spin-1/2 antiferromagnetic (AF) Heisenberg model is shown to have a spin liquid ground state [2] and that, even for ferromagnetic Ising model, nontrivial effect of frustration leads to a newly found spin ice ground state [3]. In this letter, we investigate the ground-state properties of the spin-1 AF Heisenberg model on the pyrochlore lattice.We follow a general strategy of constructing effective variational wave functions, which approximately describe the low energy states in the same spirit as the resonating valence bond (RVB) [4] or the one-dimensional (1D) valence bond solid (VBS) approaches [5]. These simple pictures are of great use to understand essential physics of the systems in more intuitive way. Our simple scenario, where the low energy effective Hilbert space is assumed to adiabatically continue to the manifold of the product wave functions of the twofold degenerate spin-singlets at each tetrahedron, leads to a spontaneous breakdown of the lattice symmetry. This new effect of the magnetoelastic interaction in the pyrochlore spin system gives a consistent picture with the recent experimental results on the insulating spin-1 spinel compounds ZnV 2 O 4 andFirst, let us introduce the AF Heisenberg model on the pyrochlore lattice, Fig. 1, in two different but equivalent representations where the interactions are defined for the sets of bonds and tetrahedra, respectively,where S is the spin-1 operator and < i, j > denotes a nearest neighbor pair. The index k, numbered from 1 to N 4 , specifies a tetrahedron and S tot k represents the sum of the four spins on the k-th tetrahedron. For the present spinel compounds, we expect that the relatively small spin value makes the isotropic limit a good starting point. On the other hand, it is well known that there are strong anisotropies for some rare earth titanates [3]. To tackle this problem, we develop an analogous method with that of the VBS state, which captur...

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