A quite unusual diffuse scattering phenomenology was observed in the single-crystal X-ray diffraction pattern of cubic perovskite BMT ($mathrm{BaMg}_{1/3}mathrm{Ta}_{2/3}mathrm{O}_3$). The intensity of the scattering is parametrized as a set of cube-
like objects located at the centers of reciprocal space unit cells, resembling very broad and cubic-shaped (1/2,1/2,1/2)-satellites. BMT belongs to perovskites of formula AB$_{1/3}$B$_{2/3}$O$_{3}$ (A=Mg, B$=$Ta, B$=$Mg). The cubes of the intensity can be attributed to the partial correlations of the occupancies of the B site. The pair correlation function is the Fourier transform of the diffuse scattering intensity and the latters idealized form yields the unusual property of a power-law correlation decay with distance. Up to now this is observed only in a few exotic instances of magnetic order or nematic crystals. Therefore it cannot be classified as a short-range order phenomenon, as in most situations originating diffuse scattering. A Monte-Carlo search in configuration space yielded solutions that reproduce faithfully the observed diffuse scattering. Analysis of the results in terms of the electrostatic energy and the entropy point to this phase of BMT as a metastable state, kinetically locked, which could be the equilibrium state just below the melting point.
The structure of BaMg1/3Ta2/3O3 (BMT) has been studied using X-ray scattering. The phonons have been measured and the results are similar to those of other materials with the perovskite structure such as PbMg1/3Nb2/3O3 (PMN). The acoustic and lowest
energy optic branches were measured but it was not possible to measure the branches of higher energy, possibly this is because they largely consist of oxygen motions. High-resolution inelastic measurements also showed that the diffuse scattering was strictly elastic and not directly related to the phonon spectra. A diffuse scattering was observed in BMT near the (Hpm1/2, Kpm1/2, Lpm1/2) points in the Brillouin zone and this had a characteristic cube shape. This arises from ordering of the B-site ions in BMT. Additional experiments revealed a diffuse scattering in BMT similar in shape to Bragg reflections at wave-vectors of the form (Hpm1/3, Kpm1/3, Lpm1/3). Such reflections were also observed by Lufaso [Chem. Matt. 16 (2004) 2148] from powders and suggest that this structure of BMT consists of 4 differently oriented domains of a trigonal structure and results from a different ordering of the B-site ions from that responsible for the scattering at the (Hpm1/2, Kpm1/2, Lpm1/2) points. The results lead us to suggest that for BMT single crystals the bulk has the properties of a cubic perovskite, whereas the surface may have quite different structure from that of the bulk. This difference resembles the behaviour of cubic relaxors like PMN and PMN doped by PbTiO3, where significant surface effects have been reported.
We study spin liquid in the frustrated diamond lattice antiferromagnet CoAl2O4 by means of single crystal neutron scattering in zero and applied magnetic field. The magnetically ordered phase appearing below TN=8 K remains nonconventional down to 1.5
K. The magnetic Bragg peaks at the q=0 positions remain broad and their profiles have strong Lorentzian contribution. Additionally, they are connected by weak diffuse streaks along the <111> directions. These observations are explained within the spiral spin liquid model as short-range magnetic correlations of spirals populated at these finite temperatures, as the energy minimum around q=0 is flat and the energy of excited states with q=(111) is low. The agreement is only qualitative, leading us to suspect that microstructure effects are also important. Magnetic field significantly perturbs spin correlations. The 1.5 K static magnetic moment increases from 1.58 mB/Co at zero field to 2.08 mB/Co at 10 T, while the magnetic peaks, being still broad, acquire almost Gaussian profile. Spin excitations are rather conventional spin waves at zero field, resulting in the exchange parameters J1=0.92(1) meV, J2=0.101(2) meV and the anisotropy term D=-0.0089(2) meV for CoAl2O4. The application of a magnetic field leads to a pronounced broadening of the excitations at the zone center, which at 10 T appear gapless and nearly featureless.
The relaxor ferroelectric PbMg_1/3Ta_2/3O_3 was studied by single-crystal neutron and synchrotron x-ray diffraction and its detailed atomic structure has been modeled in terms of static Pb-displacements that lead to the formation of polar nanoregions
. Similar to the other members of the Pb-based relaxor family like PbMg_1/3Nb_2/3O_3 or PbZn_1/3Nb_2/3O_3 the diffuse scattering in the [H,0,0]/[0,K,0] scattering plane has a butterfly-shape around the (h,0,0) Bragg reflections and is transverse to the scattering vector for (h,h,0) peaks. In the [H,H,0]/[0,0,L] plane the diffuse scattering is elongated along the <1,1,2> directions and is transverse to the scattering vector for (h,h,h) reflections. We find that a model consisting of correlated Pb-displacements along the <1,1,1>-directions reproduces the main features of the diffuse scattering in PbMg_1/3Ta_2/3O_3 adequately when the correlation lengths between the Pb-ion displacement vectors are longest along the <1,1,1> and <1,-1,0> and shortest along <1,1,-2> directions.
Using neutron powder diffraction and Monte-Carlo simulations we show that a spin-liquid regime emerges at $all compositions in the diamond-lattice antiferromagnets Co(Al1-xCox)2O4. This spin-liquid regime induced by frustration due to the second-neig
hbour exchange coupling J2, is gradually superseded by antiferromagnetic collinear long-range order (k=0) at low temperatures. Upon substitution of Al3+ by Co3+ in the octahedral B-site the temperature range occupied by the spin-liquid regime narrows and TN increases. To explain the experimental observations we considered magnetic anisotropy D or third-neighbour exchange coupling J3 as degeneracy-breaking perturbations. We conclude that Co(Al1-xCox)2O4 is below the theoretical critical point J2/J1=1/8, and that magnetic anisotropy assists in selecting a collinear long-range ordered ground state, which becomes more stable with increasing x due to a higher efficiency of O-Co3+-O as an interaction path compared to O-Al3+-O.
