Inhomogeneous ground state and the coexistence of two length scales near phase transitions in real solids

Abstract

Real crystals almost unavoidably contain a finite density of dislocations. We show that this generic type of long-range correlated disorder leads to a breakdown of the conventional scenario of critical behavior and standard renormalization group techniques based on the existence of a simple, homogeneous ground state. This breakdown is due to the appearance of an inhomogeneous ground state that changes the character of the phase transition to that of a percolative phenomenon. This scenario leads to a natural explanation for the appearance of two length scales in recent high resolution small-angle scattering experiments near magnetic and structural phase transitions. 64.60.Ak,75.10.NrThe modern theory of phase transitions (PTs) in pure and weakly disordered crystals is based on the scaling hypothesis and the renormalization group (RG). It has been confirmed by a large number of experiments and numerical simulations.Therefore, the results of some recent high resolution X-ray and neutron scattering experiments for various crystals near structural and magnetic PTs were quite unexpected [1]: in contrast to the predictions of conventional scaling theory two distinct large scales were observed. The temperature dependence of the smaller scale was found to be broadly consistent with the results of the conventional theory for the correlation scale of thermal fluctuations. Quite recently explicit experimental evidence for Verneuil grown samples of SrTiO 3 [2] confirmed earlier speculations that the second, larger scale is connected with the presence of defects in a very large region near the surface.All experiments that found two length scales used crystals which were considered to be of good quality. Nevertheless, surface preparation creates a significant density of defects in a surface layer with a thickness up to several µ [1-4]. Based on this observation, Altarelli et al. suggested [5] that most of the defects are actually dislocation dipoles which induce elastic strains with a pair correlator G(r) ∼ |r| −2 . They tried to explain the critical behavior (CB) in the disordered layer as that of the Weinrib-Halperin (WH) model [6]. The coexistence of two scales was then interpreted as a simple superposition effect, with scattering from the larger scale in the disordered layer (where the CB is governed by the WH fixed point) and from the smaller scale (corresponding to conventional CB) in the bulk of the sample. However, later experiments using very thin Holmium films found clear evidence that near the magnetic PT temperature both scales coexist in the same volume fraction of the sample [7].By construction, the conventional RG procedure is not able to explain the simultaneous existence of two length scales. Not only its detailed value and temperature dependence, but even the principal theoretical basis for the origin of the second length scale appears to be unclear.In this Letter we point out the shortcomings of the RG procedure for the treatment of systems with weak, but long-range (LR) correlated disorder, the generic sit...

Critical scattering of polarized neutrons in the invarFe65Ni35alloy

“…7 The local T C variations are described by a standard deviation of the transition temperature ⌬T C and by the characteristic correlation length R 0 ϳR d (͗T C ͘). The deduced parameters are ͗T C ͘ ϭ485Ϯ0.5 K, ⌬T C ϭ12.5Ϯ0.2 K, and R 0 Ϸ3ϫ10 3 Å.…”

“…On the other hand, attempts have been made to describe the experimental data in disordered systems using a scaling theory with a Gaussian distribution for the transition temperature. [3][4][5] Recently it was suggested 6,7 that the presence of spatial variations in T C is closely related to the enhancement of the large-scale fluctuations above T C .…”

“…Recently, the presence of two length scales above ͗T C ͘ was interpreted as a consequence of the large-scale disorder, which leads to local variations in T C . 6,7,10 These local T C variations are described by the average Curie temperature ͗T C ͘, its spread ⌬T C , and the characteristic size R 0 of the areas with different T C . In Refs.…”

“…In contrary, when R 0 ӷR c ( 1 ), the thermal fluctuations do not average out the local variations in T C that leads to a percolative ͑or inhomogeneous͒ scenario for the transition. 6,7 In a previous study we used the threedimensional ͑3D͒ neutron depolarization technique to investigate the large scale correlations near ͗T C ͘ in an invar Fe 70 Ni 30 alloy doped with 0.7 at. % carbon.…”

Magnetic phase transition in disordered Fe-Ni alloys studied by means of small-angle neutron scattering and three-dimensional analysis of the neutron depolarization

“…This is the percolative scenario of the phase transition in the disordered system. This concept received recently extensive development in the work of Korzhenevskii et al 6,7 where an explanation of the two scale length phenomenon was also given ͑see Refs. 1-4, and references therein͒.…”