The transition metal spinel MgTi2O4 undergoes a metal-insulator transition on cooling below TM−I = 260 K. A sharp reduction of the magnetic susceptibility below TM−I suggests the onset of a magnetic singlet state. Using high-resolution synchrotron and neutron powder diffraction, we have solved the low-temperature crystal structure of MgTi2O4, which is found to contain dimers with short Ti-Ti distances (the locations of the spin singlets) alternating with long bonds to form helices. Band structure calculations based on hybrid exchange density functional theory show that, at low temperatures, MgTi2O4 is an orbitally ordered band insulator.The interest in geometrically frustrated systems can be traced back to the work of Linus Pauling [1] on the frozen disorder of crystalline ice. Frustration arises when geometrical constraints promote a locally degenerate ground state. In a periodic system with this local geometry, there exists a manifold of degenerate ground states, which may freeze on cooling forming ice or remain liquid down to the lowest temperatures due to quantum effects. A third possibility is that of a phase transition that lowers the local symmetry and lifts the degeneracy. In 1956, Anderson considered the ordering of charges or Ising spins on the Bsite network of the spinel structure [2]. Spinels have the general formula AB 2 X 4 , where A and B are metals and X is an anion. The B site forms a network of corner-sharing tetrahera, also known as the pyrochlore lattice, which is geometrically frustrated. It can be shown that Pauling's 'ice rules' are equivalent to antiferromagnetic coupling between the spins or to nearest-neighbor Coulomb repulsion between equal charges. Anderson concluded that the spinels should have large low-temperature residual magnetic or configurational entropy, similar to ice. Also, he interpreted the Verwey transition of magnetite (Fe 3 O 4 , a half-filled mixed-valence spinel) [2] as an example of degeneracy-lifting transition. Almost perfect realizations of the 'spin ice' concept were found much later in rareearth pyrochlores such as Ho 2 Ti 2 O 7 [3] One might in principle ask what would happen if the 'entities' (spins, charges, etc.) at the nodes of the pyrochlore lattice had the tendency to form pairs. It is well known, for example, that early transition metals in edge-or face-sharing octahedral coordination display strong cation-cation interaction, which often leads to dimerization and spin pairing [4]. The classic example of this behavior is VO 2 (rutile structure, V 4+ , 3d 1 , S = 1/2), which undergoes a metal-insulator transition at 340 K, associated with a structural transition from the high-temperature tetragonal structure to a monoclinic structure containing dimers with short V-V distances (2.65Å) [5]. The magnetic susceptibility shows Curie-Weiss behavior above T c and a nearly constant van Vleck-like contribution below T c , which is due to the formation of spin singlets associated with the V-V dimers. The rutile structure has a strong 1-dimensional character, due to ...

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The crystal and magnetic structure of strontium ferrite Sr 4 Fe 4 O 11 (SrFeO 2.75 ) has been investigated using neutron powder diffraction and magnetic susceptibility measurements over the temperature range 1.5-293 K and by Mössbauer spectroscopy at room temperature. Sr 4 Fe 4 O 11 is orthorhombic (symmetry group Cmmm) over the temperature range 1.5-293 K. Its crystal structure contains two iron sites occupied by trivalent and tetravalent iron. The trivalent magnetic moments order antiferromagnetically below T N = 232(4) K and the magnetic unit cell coincides with the chemical cell. The ordered moments are parallel to the b axis and the tetravalent iron moments form a magnetically frustrated sublattice. The extrapolated value of the Fe 3+ moment is 3.55(5) µ B at 0 K. The antiferromagnetic coupling occurs by the superexchange mechanism and is mediated by oxygen ions. There are no signs of long-range magnetic order in the tetravalent sublattice down to 1.5 K.