Abstract. We present theoretical procedure for estimating interchain exchange coupling J between antiferromagnetic spin-1/2 Heisenberg chains with frustration due to DzyaloshinskiiMoriya (DM) interaction characterized by DM vectors Dy which are uniform within each chain y, but staggered between adjacent chains, Dy ∼ (−1) y D. Under a magnetic field h D we obtain a field-temperature phase diagram which favorably agrees with the one experimentally observed. We then apply chain mean-field (CMF) technique to calculate interchain exchange J from the critical field hc at which the transition between the collinear spin-density wave and the cone states takes place. The CMF calculations are found to provide good physical description of the experimental measurements for the wide range of D/J .
IntroductionMany experimental realizations of Heisenberg spin chain materials have become available over recent years. Here we present comparative analysis of two new interesting materials -K 2 CuSO 4 Cl 2 and K 2 CuSO 4 Br 2 [1, 2] -which represent an interesting and novel case of Heisenberg spin chains with uniform Dzyaloshinskii-Moriya (DM) interactions.Both materials are believed to be described by the Hamiltonian (1) below and are characterized by a different set of parameters (J, D, J ), where J is the dominant intra-chain exchange, D is the DM interaction strength and J is the interchain spin exchange. Despite close structural similarity, the two materials are characterized by different h − T phase diagrams, as has been established by experiments in Prof. Zheludev's group in ETH [1][2][3]. That difference is attributed to the different D/J ratio -according to Ref.[1] DM interaction is relatively weak in K 2 CuSO 4 Cl 2 , so that D/J ∼ 1, while K 2 CuSO 4 Br 2 can be characterized as a strong DM material with D/J ∼ 10.As we describe below and show in more details elsewhere [4], large D/J ratio places Brbased material into a novel category of materials where interchain interaction between spins from adjacent chains is strongly frustrated by the uniform in-chain, but staggered between chains, DM interaction. This unique geometry of DM interactions makes K 2 CuSO 4 Br 2 somewhat similar to the honeycomb iridates family Li 2 IrO 3 an incommensurate magnetic order of which is characterized by unusual counter-rotating spirals on neighboring sublattices [5]. This kind of frustration requires theoretical re-evaluation of the kind and mechanism of the eventual two-(or, three-) dimensional magnetic order that develops in the system at sufficiently low temperature. Our work provides such an analysis.