IOP PUBLISHING JOURNAL OF PHYSICS: CONDENSED MATTER J. Phys.: Condens. Matter 19 (2007) 145259 (4pp) doi:10.1088/0953-8984/19/14/145259 Crystal distortions in geometrically frustrated ACr 2 O 4 (A = Zn, Cd) S-H Lee 1 , G Gasparovic 2 , C Broholm 3 , M Matsuda 4 , J-H Chung 2 , Y J Kim 5 , H Ueda 6 , G Xu 7 , P Zschack 8 , K Kakurai 4 , H Takagi 9 , W Ratcliff 2 , T H Kim 10 and S-W Cheong 11 1 Department of Physics, University of Virginia, Charlottesville, VA 22904, USA 2 NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, MD 20899-8552, USA 3 Department of Physics and Astronomy, The Johns Hopkins University, Baltimore, MD 21218, USA 4 Advanced Science Research Center, Japan Atomic Energy Research Institute, Tokai, Ibaraki 319-1195, Japan 5 Department of Physics, University of Toronto, Toronto, ON, M5S 1A7, Canada 6 Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan 7 Neutron Scattering Group, Physics Department, Brookhaven National Laboratory, Upton, NY 11973-5000, USA 8 Frederick-Seitz Materials Research Lab, University of Illinois at Urbana-Champaign, IL 61801, USA 9 Graduate School of Frontier Science, University of Tokyo, Kashiwa, Chiba 277-8581, Japan 10 Department of Physics and Nanosciences, EWHA Womans University, Seoul 120-750, Korea 11 Department of Physics and Astronomy, Rutgers University, Piscataway, NJ 08854, USA E-mail: shlee@virginia.edu Received 24 October 2006 Published 23 March 2007 Online at stacks.iop.org/JPhysCM/19/145259 Abstract In this paper, we discuss neutron and synchrotron x-ray diffraction data obtained from single crystals of ACr 2 O 4 (A = Zn, Cd). The Cr spinels undergo three- dimensional spin-Peierls transitions at low temperatures that involve cubic-to- tetragonal lattice distortions and magnetic long-range ordering. Our results show that the magnetic structures selected by these systems are closely related to the lattice distortions that are undertaken. (Some figures in this article are in colour only in the electronic version) 1. Introduction Spin–lattice coupling has recently been found to be an effective mechanism for lifting frustration in geometrically frustrated Heisenberg antiferromagnets [1–3]. One of the best examples is ACr 2 O 4 (Zn, Cd) [1, 4] where the magnetic Cr 3+ ions form a network of corner- sharing tetrahedra [5, 6] (see figure 1(a)). A Cr 3+ ion has three unpaired electrons in the triply degenerate t 2g levels, and thus does not have orbital degeneracy [1, 7]. Due to the electronic 0953-8984/07/145259+04$30.00 © 2007 IOP Publishing Ltd Printed in the UK 1