Direct Determination of the Magnetic Ground State in the Square Lattice S  1=2 Antiferromagnet Li 2 VOSiO 4 A. Bombardi, 1 J. Rodriguez-Carvajal, 2 S. Di Matteo, 3,4 F. de Bergevin, 1 L. Paolasini, 1 P. Carretta, 5 P. Millet, 6 and R. Caciuffo 7 1 European Synchrotron Radiation Facility, BP 220, 38043 Grenoble Cedex 9, France 2 Laboratoire Le ´on Brillouin, CEA-SACLAY, 91191 Gif sur Yvette Cedex, France 3 Laboratori Nazionali di Frascati-INFN, via E. Fermi 40, I-00044 Frascati (Roma), Italy 4 Dipartimento di Fisica ‘‘E. Amaldi,’’ Universita ` di Roma III, via della Vasca Navale 84, I-00146 Roma, Italy 5 Istituto Nazionale per la Fisica della Materia and Dipartimento di Fisica, Universita ` di Pavia,Via Bassi 6, I-27100 Pavia, Italy 6 Centre d’Elaboration des Mate ´riaux et d’Etudes Structurales, CNRS, 31055 Toulouse Cedex, France. 7 Istituto Nazionale per la Fisica della Materia and Dipartimento di Fisica ed Ingegneria dei Materiali, Universita ` Politecnica delle Marche, Via Brecce Bianche, I-60131 Ancona, Italy (Received 15 December 2003; published 7 July 2004) Powder neutron diffraction and resonant x-ray scattering measurements from a single crystal have been performed to study the low-temperature state of the 2D frustrated, quantum-Heisenberg system Li 2 VOSiO 4 . Both techniques indicate a collinear antiferromagnetic ground state, with propagation vector k  1 2 1 2 0, and magnetic moments in the a-b plane. Contrary to previous reports, the ordered moment at 1.44 K, m  0:633 B , is very close to the value expected for the square lattice Heisenberg model ( ’ 0:6 B ). The magnetic order is three dimensional, with antiferromagnetic a-b layers stacked ferromagnetically along the c axis. Neither x-ray nor neutron diffraction shows evidence for a structural distortion between 1.6 and 10 K. DOI: 10.1103/PhysRevLett.93.027202 PACS numbers: 75.25.+z, 61.12.–q The phase diagram of two-dimensional (2D) frustrated quantum systems described by the Heisenberg Hamil- tonian on a square lattice has been the subject of a num- ber of theoretical analyses [1–3]. Thanks to the synthesis of several new compounds, such as VOMoO 4 [4], Pb 2 VOPO 4  2 [5], Li 2 VOGeO 4 [6], and Li 2 VOSiO 4 [6], theoretical predictions can now be explored experimen- tally. Such a recently disclosed opportunity renewed the interest toward the so-called J 1 -J 2 model, where J 1 and J 2 are the nearest- and the next-nearest-neighbor antiferro- magnetic exchange integrals. In this model, depending on the jJ 2 =J 1 j ratio, different situations can occur. For 0:35 jJ 2 =J 1 j 0:65 a spin liquid or dimer ground state is predicted. For jJ 2 =J 1 j 0:35 an antiferromagnetic or- der should develop, whereas for jJ 2 =J 1 j 0:65 the order- ing by the disorder mechanism [1,7,8] is expected to stabilize a twofold degenerate collinear order, with spins aligned ferromagnetically along the a axis and antiferro- magnetically along the b axis, or vice versa. Some theo- retical studies [1,2] suggested the possibility that such a twofold residual degeneracy leads to a finite-temperature Ising-like phase transition, with the chosen ground state being collinear or anticollinear [1]. However, coupling to the lattice may induce, as in the Jahn-Teller effect, a lattice distortion and remove the twofold degeneracy [9]. We explore such a scenario by making neutron powder- diffraction and resonant x-ray diffraction experiments on Li 2 VOSiO 4 , a system that has been proposed as a proto- type of frustrated 2D quantum (S  1=2) Heisenberg antiferromagnets, and one of the most studied among the new J 1 -J 2 systems [9–13]. Like its Ge based counter- part, Li 2 VOSiO 4 crystallizes in the tetragonal P4=nmm space group, with 2 f.u. per cell and room temperature lattice parameters a  6:36826  A and c  4:4491  A [6]. The magnetically active network of spin half V 4 ions is built up by layers of VO 5 square pyramids sharing corners with SiO 4 tetrahedra. The two V 4 ions occupy the positions  1 4 1 4 z and  3 4 3 4 1  z with z  0:5861. This structure suggests significant superexchange cou- pling both along the sides (J 1 ) and the diagonals (J 2 ) of the V 4 square lattice. Despite the small c value, the interlayer coupling should on the contrary be consider- ably weaker, so that Li 2 VOSiO 4 should be a good example of a 2D system belonging to the intermediate jJ 2 =J 1 j region. NMR, magnetization, specific heat, and muon spin rotation measurements on Li 2 VOSiO 4 [10,11] indicate that a collinear antiferromagnetic structure is established below 2.8 K, with magnetic moments lying in the a-b plane, J 2  J 1 ’ 8:21, and J 2 =J 1 ’ 1:11. The analysis of these experiments leads to a strongly reduced value for the ordered magnetic moment, mT ! 0’ 0:24 B , which is considerably smaller than that expected [14] for a nonfrustrated S  1=2 system on a 2D lattice (0:65 B ). Just above T N , 29 Si NMR results suggest the occurrence of a frustration-driven lattice distortion, which would relieve the degeneracy of the collinear ground state. More recently some doubts were raised [12,13] con- cerning the actual value of the ratio J 2 =J 1 , which was found ’ 12 from local density calculations. This result indicates that the system has a large J 2 , rather than being PHYSICAL REVIEW LETTERS week ending 9 JULY 2004 VOLUME 93, NUMBER 2 027202-1 0031-9007= 04=93(2)=027202(4)$22.50  2004 The American Physical Society 027202-1