Surface melting of electronic order in La${}_{0.5}$Sr${}_{1.5}$MnO${}_{4}$

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Surface melting of electronic order in La $_{0.5}$ Sr $_{1.5}$ MnO $_{4}$

S. B. Wilkins, X. Liu, Y. Wakabayashi, J.-W. Kim, P. J. Ryan, H. Zheng, J. F. Mitchell, and J. P. Hill

Phys. Rev. B 84, 165103 – Published 7 October 2011

Abstract

We report temperature-dependent surface x-ray scattering studies of the orbital ordered surface in La $_{0.5}$ Sr $_{1.5}$ MnO $_{4}$ . We find that as the bulk ordering temperature is approached from below the thickness of the interface between the electronically ordered and electronically disordered regions at the surface grows, though the bulk correlation length remains unchanged. Close to the transition, the surface is so rough that there is no well-defined electronic surface, despite the presence of bulk electronic order. That is, the electronic ordering at the surface has melted. Above the bulk transition, long-range ordering in the bulk is destroyed but finite-sized isotropic fluctuations persist, with a correlation length roughly equal to that of the low-temperature in-plane surface correlation length.

Received 8 September 2011

DOI:https://doi.org/10.1103/PhysRevB.84.165103

Authors & Affiliations

S. B. Wilkins¹, X. Liu¹, Y. Wakabayashi², J.-W. Kim³, P. J. Ryan³, H. Zheng⁴, J. F. Mitchell⁴, and J. P. Hill¹

¹Department of Condensed Matter Physics and Materials Science, Brookhaven National Laboratory, Upton, New York 11973-5000, USA
²Division of Materials Physics, Graduate School of Engineering Science, Osaka University, Toyonaka 560-8531, Japan
³Advanced Photon Source, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439, USA
⁴Division of Materials Science, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439, USA

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Vol. 84, Iss. 16 — 15 October 2011

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Images

Figure 1
(Top left) Simulated x-ray scattering in the (Q $_{x}$ ,Q $_{z}$ ) plane for a two-dimensional (2D) Lorentzian-squared function, with widths equal to those of the bulk orbital order reflection. (Bottom left) Line cuts at Q $_{z}$ = 0 (blue) and 0.28 Å $^{- 1}$ (red) through the simulated x-ray scattering intensity. (Top right) 2D intensity plot of the measured intensity for the orbital truncation rod in La $_{0.5}$ Sr $_{1.5}$ MnO $_{4}$ at 170 K obtained at Q $_{z} = 0.101, 0.127, 0.202$ , and $0.278$ Å $^{- 1}$ . The streak of scattering, elongated along $L$ due to the truncation of the orbital order by its surface, can clearly be seen. (Bottom right) Line cut at Q $_{z}$ = 0.28 Å $^{- 1}$ through the orbital truncation rod.Reuse & Permissions
Figure 2
(Top panel) Q $_{x}$ scans through the orbital truncation rod at 170 and 223.5 K (red circles and blue squares, respectively). Data taken at Q $_{z}$ = 0.1 Å $^{- 1}$ (top panel) and Q $_{z}$ = 0.28 Å $^{- 1}$ (bottom panel). The results of the fits to Eq. (1) are shown as solid lines.Reuse & Permissions
Figure 3
(Top panel) Calculation of the Q $_{z}$ dependence of the integrated intensity of the broad component for various values of the surface roughness $σ$ . (Bottom panel) Integrated intensity of the broad component as measured at several values of Q $_{z}$ along the orbital truncation rod and for several temperatures. In each case, the integrated intensity is scaled by Q $_{z}^{2}$ to emphasize the high Q $_{z}$ behavior. At temperatures approaching the bulk ordering temperature the measured integrated intensity increases faster with Q $_{z}$ , indicative of an increased surface roughness.Reuse & Permissions
Figure 4
(Top panel) Temperature dependence of the integrated intensity of the bulk orbital order superlattice reflection (red squares) measured at $L = 2$ , the integrated intensity of the sharp component of the orbital truncation rod measured at Q $_{z}$ = 0.13 Å $^{- 1}$ (blue circles), and the broad component measured at Q $_{z}$ = 0.2 Å $^{- 1}$ (magenta diamonds). (Middle panel) Temperature dependence of the correlation length as measured on the broad component of the orbital truncation rod at Q $_{z}$ = 0.2 Å $^{- 1}$ . (Bottom panel) Temperature dependence of the correlation lengths of the bulk orbital order superlattice reflection measured along the Q $_{z}$ and Q $_{x}$ directions (green circles and red squares, respectively) and the correlation length as measured on the broad component of the orbital truncation rod at Q $_{z}$ = 0.2 Å $^{- 1}$ .Reuse & Permissions
Figure 5
Schematic representation of the crystallographic surface, the orbital surface, and the orbitally ordered bulk for (a) $T ≪ T_{o o}$ , (b) $T \approx T_{o o}$ , and (c) $T ≫ T_{o o}$ . The size of the blue and yellow regions in the orbitally ordered bulk represents schematically the correlation length of the orbital order in the bulk. The roughness of the orbital surface is shown as the height variation of the shaded (blue and yellow) surface and the in-place correlation length by the size of the shaded surface regions. The relative size of the colored regions is physically correct, both within each temperature snapshot and from temperature to temperature, as determined from the x-ray scattering data analysis.Reuse & Permissions

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