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arXiv:cond-mat/0407016v1 [cond-mat.str-el] 1 Jul 2004Competing Magnetic Phases on a “Kagom´ e Staircase”G. Lawes, 1 M. Kenzelmann, 2,3 N. Rogado, 4 K. H. Kim, 1,‡ G. A. Jorge, 1 R. J. Cava, 4 A. Aharony, 5O. Entin-Wohlman, 5 A. B. Harris, 6 T. Yildirim, 3 Q. Z. Huang, 3 S. Park, 3,7,§ C. Broholm, 2,3 and A. P. Ramirez 1,81Los Alamos National Laboratory, Los Alamos, NM 875442Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD 212183NIST Center for Neutron Research, Gaithersburg, MD 208994Department of Chemistry and Princeton Materials Institute, Princeton University, Princeton, NJ 085445School of Physics and Astronomy, Raymond and Beverly SacklerFaculty of Exact Sciences,Tel Aviv University, Tel Aviv 69978, Israel6Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA, 191047Department of Materials Science and Engineering,University of Maryland, College Park, MD 20742 and8Bell Labs, Lucent Technologies, 600 Mountain Avenue, Murray Hill, NJ 07974(Dated: February 2, 2008)We present thermodynamic and neutron data on Ni 3 V 2 O 8 , a spin-1 system on a kagom´ e staircase.The extreme degeneracy of the kagom´ e antiferromagnet is lifted to produce two incommensuratephases at f i nite T – one amplitude modulated, the other helical – plus a commensurate cantedantiferromagnet for T → 0. The H − T phase diagram is described by a model of competing f i rstand second neighbor interactions with smaller anisotropic terms. Ni 3 V 2 O 8 thus provides an elegantexample of order from sub-leading interactions in a highly frustrated system.PACS numbers: 75.10.Jm, 75.25.+z, 75.30.KzGeometrical magnetic frustration leads to unusual lowtemperature spin order and dynamics and presents newchallenges for the theoretical understanding of magneticsystems. Frustrated materials are often characterizedby triangle-based lattices and short-range antiferromag-netic (AF) interactions. 1 Of particular interest has beenmagnetism on the two-dimensional (2D) kagom´ e lattice,which consists of corner-sharing triangles. While theHeisenberg spin-1/2 model appears to have short rangespin correlations and a gap to free spinons, 2,3 the S → ∞classical model has N´ eel order with a√ 3 × √ 3 unit cellat temperature T = 0. 4 Materials that approximate thekagom´ e AF can be expected to lie close to a quantumcritical point, and indeed early work on the kagom´ e sys-tem SCGO exposed a spin liquid phase possessing a largefraction (15%) of the total spin entropy and short range√ 3× √ 3 order. 5,6Later work on jarosite systems showeddif f erent “q = 0” long range order apparently favored byinterlayer interactions. 7Here we study Ni 3 V 2 O 8 (NVO) in which the S =1 Ni 2+ spins form the orthorhombic kagom´ e staircasestructure shown in Fig. 1(a). 8 This structure has the co-ordination and two-dimensionality of the regular kagom´ elattice, but the kagom´ e planes are buckled. The systemis particularly attractive because its complex magneticphase diagram can be understood on the basis of an em-bellished kagom´ e spin hamiltonian. The model we intro-duce also applies to the isostructural compounds whereNi is replaced by Cu 9 or Co. 10 Although the symmetryof these compounds is the same as that of NVO, theirphase diagrams are very dif f erent. As indicated below,this dif f erence results from a small quantitative change inthe parameters which dictate how frustration is relieved.A previous study of the magneto-thermal response inpolycrystalline NVO revealed four zero f i eld phase tran-sitions with Θ W /T N > 5, where Θ W is the Weiss con-stant and T N the magnetic ordering temperature. 10 Inthis letter we report an unexpectedly rich anisotropicf i eld-temperature (H − T) phase diagram (Fig. 2), withhigh and low temperature incommensurate (IC) phases(HTI and LTI) and two commensurate (C and C’) spinstructures. These magnetic structures are determined vianeutron dif f raction. We also explain the salient featuresof NVO by a model, in which the spine (Ni s ) and cross-tie(Ni c ) spins interact via nearest neighbor (NN) and sec-ond nearest-neighbor (SNN) isotropic Heisenberg inter-actions. In addition, and consistent with crystal symme-try, it is necessary to take account of the Dzyaloshinskii-Moriya (DM) interaction and magnetic anisotropy.Symmetry is key to understanding the ordered phasesthat spring from the kagom´ e critical state in NVO. 11 Inthe presence of AF ordering on the spine sites, isotropicNN interactions produce zero mean f i eld on cross-tie sites.In this regard, NVO is reminiscent of Sr 2 Cu 3 O 4 Cl 2 12 andof some ”ladder” systems of recent interest. 13 However,the structural anisotropy of NVO induces interactionsnot usually considered in frustrated systems. First, be-cause the NiO 6 octahedra are edge-sharing, the NN Ni-O-Ni bond angle is close to 90 o so the NN and SNN Ni-Niinteractions are weak and similar in strength. Second,the symmetry of the crystal structure admits a DM in-teraction among the NN spine spins. 12 Third, anisotropicpseudo dipolar (PD) exchange interactions between spineand cross-tie spins induce both a uniform and a staggeredmoment on the cross-tie sites. 14 These interactions addto the usual isotropic NN super-exchange interaction toproduce the observed rich H − T phase diagram.Single crystals of NVO were grown from a BaO-V 2 O 5