Influence of crystalline boundaries on spin- and charge-density waves in chromium

Abstract

Using theSn Mossbauer eKect we show that the crystalline boundaries have a profound in-Buence on the shape of Mossbauer spectra. Based on the newly developed method of the harmonic analysis of the Mossbauer spectra, we analyze the measured spectra in terms of higher-order harmonics and reveal a relationship between the harmonics and the size of grains: the smaller the size, the greater the contribution of the harmonics, with the third-order one being negative and dominating. We also demonstrate that the present results support the up-to-date picture of the spin-density waves in the form of single Q domains.Chromium metal owes its scientific attraction to socalled spin-density waves (SDW's) which originate &om itinerant 8and d-like electrons, and demonstrate a variety of interesting properties (see Ref. 1 and references therein). Between the Neel temperature of Ttv = 311 K and the spin-Hip temperature of TsF = 123 K, SDW's are transversely polarized; i.e. , their wave vector Q is perpendicular to their polarization vector p. Below TSF the polarization is longitudinal, i.e. , Q~~p. SDW s are incommensurate with the periodicity of the lattice, i.e. , Q g -, a being the lattice constant.Theoretically, basic properties of SDW's can be explained in terms of the band structure of pure chromium and the Coulomb interaction between the electron and the hole surfaces is responsible for their existence. SDW's can be also described by the snoidal function or a series of odd harmonicspqi being an amplitude of the ith harmonic of the CDW and b a phase shift between the CDW's and the SDW's. According to a theoretical estimation, p2/po should be of the order of 10 -10 . A recent estimation based on an x-ray diffraction experiment yields for p2 the value where n = Q . r (r being the position vector).Experimentally, evidence of S3 was found from neutron diffraction and. Sn Mossbauer-effect experiments on single-crystal samples of chromium. Recently, the authors of the present paper found evidence of S5 and possibly of S7 &om the Sn Mossbauer spectrum registered at room temperature on a (110) face of chromium. s According to theory, the Coulomb interaction between the two hole surfaces induces a charge-density wave (CDW). As the CDW order parameter is proportional to the square of the SDW order parameter, CDW's can be described in terms of a series of even harmonics as follows: of 0.003 -0.02 electrons per atom and our analysis of the (110) face Cr~~9 Sn Mossbauer spectrum gives the value of 0.02 for the maximum amplitude of the CDW.It is also of interest in searching for SDW's to know the preferred relative orientation of SDW polarizations. A single SDW Q may have one or more SDW's with symmetry-equivalent wave vectors Q. For instance, in lead it has been found. that a cubic family of 12 SDW's is required in order to explain its various properties.A question arises whether various SDW's overlap with each other in certain regions of samples in which they exist. Theoretical calculations concerning the problem of such interference of ...

CEMS Evidence of the Presurface Zone Enhancement of the Spin-Density in Chromium

“…a different overall shape, 2. a much larger maximal hf field and 3. a single line contribution in its centre. tail stretching up to $20 T. The value of $13 T is more than twice as large as that found for the bulk chromium [11,12] and is similar to that recorded on the epitaxial Cr/Sn multilayers [10]. The best-fit spectral parameters of the spectrum shown in Fig.…”

“…A hyperfine magnetic field of 11-13 T was recorded which is twice as large as in a single crystal bulk Cr [11].…”

On Effect of Spin-Density Wave Parameters on Shape of119Sn Mössbauer Spectra

“…It enables to investigate the influence of various parameters characteristic of the SDW such as the sign and the magnitude of the higher-order harmonics, as well as the phase shift between the SDW and the lattice on the shape of the spectra and the related histograms of the hf field distributions. The procednre in its iterative version has been successfully applied to analyze various 119 Sn Mössbauer spectra recorded on various samples of chromium [8].…”

“…The reader is referred to our recent paper [8], where we give an evidence that the Mössbauer spectra of polycrystalline samples of chromium can be well described provided the higher-order harmonics are taken into account.…”

“…This has not only purely theoretical reasons, as in a real sample of a single-crystal chromium H3 > 0 and it amounts to 1.5%H1 [6], and in polycrystalline samples of chromium H3 < 0 and may reach ti 25%H [8], depending on the size of grains.…”