VOLUME 73, NUMBER 26 PHYSICAL REVIEW LETTERS 26 DECEMaER 1994 Detailed Structure of a Charge-Density Wave in a Quenched Random Field J. D. Brock, A. C. Finnefrock, K. L. Ringland, and E. Sweetland School of Applied and Engineering Physics, Cornell University, Ithaca, New Vork 14853 (Received 26 July 1994) Using high resolution x-ray scattering, we have measured the structure of the Q~ charge-density wave in Ta-doped NbSe3. Detailed line shape analysis of the data demonstrates that two length scales are required to describe the phase-phase correlation function. Phase fluctuations with wavelengths less than a new length scale a are suppressed, and this a is identified with the amplitude coherence length. We find that $, = 34. 4 ~ 10. 3 A. Implications for the physical mechanisms responsible for pinning are discussed. PACS numbers: 78.70. Ck, 64.60.Cn, 71. 45.Lr During the past twenty years, the influence of random disorder on phase transitions has been studied extensively. Disorder can be formally described as randomness in either the interaction strength [1] or the field conjugate to the order parameter [2]. It is widely believed that a small amount of randomness in the interactions is irrelevant. Random fields, on the other hand, have dramatic consequences. In their seminal paper, Imry and Ma [2] suggested that a random field should cause the lower marginal dimensionality dz to rise from 2 to 4 for systems with continuous symmetry. Here, dz is the dimensionality below which the system cannot sustain long-range order (LRO) at finite temperatures [3]. This loss of LRO has been observed in a wide variety of systems. In particular, the structures of the charge-density waves (CDW's) found in the quasi-one-dimensional metal NbSe3 do not exhibit LRO [4,5]. For mathematical simplicity, the quenched random field is frequently assumed to be a time-independent random Gaussian variable satisfying (h(r)) = 0 and (h(r)h(r')) = n;hoB"(r — r'), where n, is the number density of impu- rity atoms and hp gives the strength of the pinning in- teraction. In the general case, scattering from a random structure is characterized by an exponentially decaying correlation function [6]. For the specific case of CDW systems, one expects an exponential decay of the correla- tions between static fluctuations in the phase of the CDW order parameter [7,8]. In this paper, we report the results of a detailed high resolution x-ray scattering study of the static phase correlations of the Q) CDW in Ta-doped NbSe3. The experiments clearly show that phase fluctuations with high spatial frequency components are suppressed; therefore, the destruction of LRO by the random field is suppressed on length scales less than =75 A. These results are explained using the standard Ginzburg-Landau phase Hamiltonian with a Gaussian random pinning field [7, 8]. This new length scale is then related directly to the amplitude coherence length. We conclude with a brief discussion of the implications for physical models of the pinning mechanism. The obvious way to study the interaction between a CDW and a quenched random distribution of impurity atoms is to dope crystals with impurities and study how the ordering varies with impurity concentration and type. Over the last decade a large number of such studies have been reported [9, 10]. Most of these studies have focused on NbSe3, which undergoes two independent Peierls transitions to CDW states at Tp, = 145 K and at Tp = 59 K. The most widely studied dopant has been Ta, which is isoelectronic with Nb. Experimentally [4,5], the structure of the Q( CDW in Ta-doped NbSe3 is quite well described by a Ginzburg- Landau field theory [11]. The effective Hamiltonian which describes the phase behavior of the Q( CDW at low temperatures can be written as [7] d x(t/t [g V@(x)] + tlrh(x)@(x)j, (1) where t/r is the amplitude of CDW order parameter, @(x) is the phase of the CDW order parameter, g is the amplitude coherence length, and h(x) is the quenched random field. Using A4, and the assumption that h(x) obeys Gaussian statistics, the phase-phase correlation function in three dimensions is [7,8] (e~(4(xi) — 4(x„)1) e — g(x~ — x2 d k n;hp g(x) = ' ( I — cos(k x) j, (2) 2m 4 t)'t k and L is the system size. At large separations, (e' &'"' 4'"' ) — e "' "') t where the correlation length is given by 8 = 32m$4t/r /n;ho. In order to provide a framework for discussing the experimental resu1ts, we first consider the consequences of random fields on the measured profiles. In an x-ray scattering experiment on a CD% system at low tempera- tures, the static structure factor S(q) is proportional to the spatial Fourier transform of the phase-phase correlation function [5]. Thus, at low temperatures S(q) exhibits Lorentzian squared fluctuations centered about the CD& satellite reflection positions. The experimentally measured profile is the convolution of S(q) with the resolution function of the diffractometer, 0031-9007/94/73(26)/3588(4)$06. 00 1994 The American Physical Society