Phase coexistence and pinning of charge density waves by interfaces in chromium

A. Singer, S. K. K. Patel, V. Uhlíř, R. Kukreja, A. Ulvestad, E. M. Dufresne, A. R. Sandy, E. E. Fullerton, and O. G. Shpyrko

Phys. Rev. B 94, 174110 – Published 16 November 2016

Abstract

We study the temperature dependence of the charge density wave (CDW) in a chromium thin film using x-ray diffraction. We exploit the interference between the CDW satellite peaks and Laue oscillations to determine the amplitude, the phase, and the period of the CDW. We find discrete half-integer periods of CDW in the film and switching of the number of periods by one upon cooling/heating with a thermal hysteresis of 20 K. The transition between different CDW periods occurs over a temperature range of 30 K, slightly larger than the width of the thermal hysteresis. A comparison with simulations shows that the phase transition occurs as a variation of the volume fraction of two distinct phases with well-defined periodicities. The phase of the CDW is constant for all temperatures, and we attribute it to strong pinning of the CDW by the mismatch-induced strain at the film-substrate interface.

Received 6 September 2016
Revised 22 October 2016

DOI:https://doi.org/10.1103/PhysRevB.94.174110

Physics Subject Headings (PhySH)

Antiferromagnetism Charge density waves

Interfaces Thin films

X-ray diffraction

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

A. Singer^1,*, S. K. K. Patel^1,2, V. Uhlíř², R. Kukreja^1,2, A. Ulvestad^1,†, E. M. Dufresne³, A. R. Sandy³, E. E. Fullerton², and O. G. Shpyrko¹

¹Department of Physics, University of California San Diego, La Jolla, California 92093, USA
²Center for Memory and Recording Research, University of California San Diego, La Jolla, California 92093, USA
³Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, USA

^*Email address: ansinger@ucsd.edu
^†Present address: Materials Science Division, Argonne National Laboratory, Lemont, Illinois 60439, USA.

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Vol. 94, Iss. 17 — 1 November 2016

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Images

Figure 1
(a) Sketch of the reciprocal space around the (002)-diffraction peak of Cr in the presence of a CDW. (b) X-ray reflectivity measurement of the Cr thin film with Cu K-α radiation. (Left inset) The φ rotation scan (right inset) and θ-2θ scan around the (011) peak (out of plane). In both insets, red dots show the data, and blue solid lines show Gaussian fits used to determine the peak widths. (c) A θ-2θ scan around the (002) peak recorded with synchrotron radiation at room temperature (red hexagons), 250 K (black squares), and 100 K (blue diamonds). Solid lines show theoretical fits to the data, and vertical dashed lines show the center of the Bragg peak. Inset: The corresponding lattice distortion or displacement; the curves are shifted vertically for better visibility.
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Figure 2
Fitting results of the data for different temperatures. The average lattice parameter (a), amplitude (b), number of periods (c), and phase (d) of the CDW. The black line in (b) shows a calculation of the CDW amplitude within the BCS theory based on the maximum observed CDW amplitude and a Neel temperature of 290 K. Uncertainties show 95% confidence intervals, and the error metric $χ^{2} = Σ {[lo g_{10} (I_{th}) - lo g_{10} (I_{\exp})]}^{2} / N$ , where summation over the fitted points N was used for fitting. The gray shaded area represents the transition region between fringe 7 and fringe 8.
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Figure 3
X-ray diffraction intensity around the CDW peak upon cooling. Low- $q$ (a) and high- $q$ (b) with respect to the Bragg peak are shown. Fringes as counted from the Bragg peak are indicated [see Fig. 1]. The intensities are shown on logarithmic scale. (c), (d) The intensity of fringe 7 (blue squares) and 8 (red circles) for low- $q$ (c) and high- $q$ (d). Filled (open) symbols show data collected with a cooling rate of 2 K/min (4 K/min). The gray shaded area represents the transition region between fringe 7 and fringe 8 and is approximately 30 K wide.
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Figure 4
Simulated diffraction patterns assuming abrupt (a), (b) and continuous (c), (d) phase transition between CDW phases with 7.5 and 8.5 periods. Calculations with a phase offset of $a_{4} = 3.8 rad$ (solid lines), and 3.8 + π/2 rad (dashed lines) are shown. The data from Figs. 3 and 3 are shown by shaded symbols for comparison. Blue (red) lines show intensity of fringe 7 (8). Simulations at low- $q$ (a), (c) and high- $q$ (b), (d) are shown. The insets show schematically the composition of the phases.
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