X-ray and neutron scattering

Abstract:

We report single-crystal x-ray-diffraction measurements on Na2Ti2Pn2O (Pn = As,Sb) which reveal a charge superstructure that appears below the density wave transitions previously observed in bulk data. From symmetry-constrained structure refinements we establish that the associated distortion mode can be described by two propagation vectors q1 = (1/2,0,l) and q2 = (0,1/2,l) with l = 0 (Sb) or l = 1/2 (As) and primarily involves in-plane displacements of the Ti atoms perpendicular to the Ti-O bonds.We also present angle-resolved photoemission spectroscopy measurements, which show band folding and backbending consistent with a density wave with the samewave-vectors q1 and q2 associated with Fermi-surface nesting, and muon-spin relaxation data, which show no indication of spin density wave order. The results provide direct evidence for phonon-assisted charge density wave order in Na2Ti2Pn2O and fully characterize a proximate ordered phase that could compete with superconductivity in doped BaTi2Sb2O.

Abstract:

In 1949, Forsbergh, Jr. reported spontaneous spatial ordering in the birefringence patterns seen in flux-grown BaTiO3 crystals under the transmission polarized light microscope [Phys. Rev. 76, 1187 (1949)]. Stunningly regular square-net arrays were often only found within a finite temperature window and could be induced on both heating and cooling, suggesting genuine thermodynamic stability. At the time, Forsbergh rationalized the patterns to have resulted from the impingement of ferroelastic domains, creating a complex tessellation of variously shaped domain packets. However, no direct evidence for the intricate microstructural arrangement proposed by Forsbergh has subsequently been found. Moreover, there are no robust thermodynamic arguments to explain the finite region of thermal stability, its occurrence just below the Curie temperature, and the apparent increase in entropy associated with the loss of the Forsbergh pattern on cooling. Despite decades of research on ferroelectrics, this ordering phenomenon and its thermodynamic origin have hence remained a mystery. In this paper, we reexamine the microstructure of flux-grown BaTiO3 crystals, which show Forsbergh birefringence patterns. Given an absence of any obvious arrays of domain polyhedra or even regular shapes of domain packets, we suggest an alternative origin for the Forsbergh pattern in which sheets of orthogonally oriented ferroelastic stripe domains simply overlay one another. We show explicitly that the Forsbergh birefringence pattern occurs if the periodicity of the stripe domains is above a critical value. Moreover, by considering well-established semiempirical models, we show that the significant domain coarsening needed to generate the Forsbergh birefringence is fully expected in a finite window below the Curie temperature. We hence present a much more straightforward rationalization of the Forsbergh pattern than that originally proposed in which exotic thermodynamic arguments are unnecessary