Magnetic dimerization in the frustrated spin ladder Li 2 Cu 2 O ( SO 4 ) 2
Résumé
The magnetic properties of Li 2 Cu 2 O(SO 4) 2 are investigated in the framework of density functional theory. In its high-temperature tetragonal structure, this compound appears as a rare material realization of a frustrated spin-1/2 two-leg ladder, where magnetic frustration arises from competing nearest and next-nearest interactions along the legs. Through a large magnetoelastic coupling, the triclinic distortion occurring around 125 K is shown to induce the formation of a staggered dimer structure, lifting most of the magnetic frustration. During the last few decades, a considerable effort has been devoted to the experimental and theoretical investigation of frustrated quantum antiferromagnets [1]. Among the different models studied as potential candidates in which new states of matter could occur, the frustrated S = 1/2 two-leg spin ladder has received considerable attention, as it combines low spin, low dimensionality, and magnetic frustration. The general Hamiltonian for this model can be written as H = J α=1,2 i S α,i · S α,i+1 + J ⊥ i S 1,i · S 2,i + J × i (S 1,i · S 2,i+1 + S 1,i+1 · S 2,i) + J 2 α=1,2 i S α,i · S α,i+2 , (1) where the index α distinguishes left and right legs, i labels rungs, and the S α,i are the S = 1/2 operators at the rung i on the α th leg of the ladder. J is the nearest-neighbor (NN) exchange coupling along the legs and J ⊥ the interleg coupling along the rungs. Frustration arises either through the next-nearest-neighbor (NNN) coupling along the legs J 2 or through the diagonal, interleg coupling J ×. In the absence of next-nearest-neighbor coupling (J 2 = 0), the phase diagram for this model was originally shown to consist of two parts: a Haldane and a rung-singlet phase [2–4]. It was later suggested that this picture might be incomplete and that an additional, intermediate dimerized phase could also occur [5,6]. Vekua and Honecker [7] further showed that the addition of sufficiently strong next-nearest-neighbor couplings along the legs (J 2 = 0) stabilizes additional columnar dimer and staggered dimer phases. A rich phase diagram thus emerges from this quasi-one-dimensional (quasi-1D) lattice model depending critically on the relative signs and strengths of the various exchange couplings. Unfortunately, only a very limited number of material systems can be considered as true realizations of frustrated S = 1/2 two-leg spin ladders and thus, provide experimental * guillaume.radtke@upmc.fr evidence to be confronted by these theoretical predictions. Whereas SrCu 2 O 3 [8] or Sr 14 Cu 24 O 41 [9,10] are prototypical realizations of nonfrustrated ladders, BiCu 2 PO 6 [11] might appear as one of the very rare examples of S = 1/2 frustrated spin ladder where the frustration arises only from NNN interactions along the legs [12]. In this Rapid Communication, we show that the newly synthesized compound Li 2 Cu 2 O(SO 4) 2 [13] is an actual realization of S = 1/2 frustrated two-leg spin ladder. Moreover, we demonstrate that the tetragonal to triclinic structural transition occurring around 125 K [14] leads to the emergence of a staggered S = 1/2 dimer structure, lifting most of the magnetic frustration. The crystal structure of Li 2 Cu 2 O(SO 4) 2 at room temperature is shown in Figs. 1(a) and 1(b). This compound crystallizes in a tetragonal structure, with space group P 4 2 /m where Cu 2+ ions occupy a slightly distorted square planar environment, as commonly observed for this strong Jahn-Teller ion. The resulting CuO 4 squares are grouped by two, sharing an edge to form Cu 2 O 6 platelets. These platelets are connected one to each other through an oxygen atom, after being rotated by 90 • under the effect of the 4 2 helical axis leading to infinite Cu 2 O 5 chains running along the c axis of the crystal [see Fig. 1(b)]. Tetrahedral SO 4 units further link every second platelet along the chains by sharing two oxygen ions with them. These chains are finally separated from each other by the Li + ions. From a magnetostructural perspective, dominant magnetic couplings should occur in this structure either through intra-[J ⊥ in Fig. 1(c)] or interplatelets (J = J ×) Cu-O-Cu superexchange mechanisms or through longer ranged interactions via the nonmagnetic bridging SO 4 units (J 2), as such polyanionic groups are known to be efficient media for magnetic interactions [15]. As additional interchain interactions are expected to be weak due to the absence of well-defined covalent superexchange paths, this compound should exhibit a strong quasi-1D character. Note that the resulting geometry for such an isolated chain maps exactly on a S = 1/2 frustrated two-leg ladder described by (1) in the special case where J = J × as illustrated in Fig. 1(d). Figure 2 shows the paramagnetic band structure and density of states (DOS) of Li 2 Cu 2 O(SO 4) 2 calculated close to the Fermi level. These density functional theory (DFT) 2469-9950/2017/96(18)/180406(5) 180406-1
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