Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations 2001 X-ray resonant exchange scattering investigations of rare earth intermetallic compounds: TbNi2B2C, TbCu2Ge2, and GdAgSb2 Changyong Song Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/rtd Part of the Condensed Matter Physics Commons Recommended Citation Song, Changyong, "X-ray resonant exchange scattering investigations of rare earth intermetallic compounds: TbNi2B2C, TbCu2Ge2, and GdAgSb2 " (2001). Retrospective Theses and Dissertations. 456. https://lib.dr.iastate.edu/rtd/456 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Retrospective Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. 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Goldman Iowa State University Ames, Iowa 2001 UMI Number: 3003272 UMT UMI Microform 3003272 Copyright 2001 by Bell & Howell Information and Learning Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. Bell & Howell Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, Ml 48106-1346 ii Graduate College Iowa State University This is to certify that the Doctoral dissertation of Changyong Song has met the dissertation requirements of Iowa State University Signature was redacted for privacy. Committee Member Signature was redacted for privacy. Committee M mber Signature was redacted for privacy. Committee Signature was redacted for privacy. Committee Member Signature was redacted for privacy. Major Professor Signature was redacted for privacy. Signature was redacted for privacy. iii TABLE OF CONTENTS 1 INTRODUCTION 1 2 REVIEW OF X-RAY SCATTERING PROCESSES 5 Interaction Hamiltonian and Scattering Length 5 Scattering from the Resonant Process 6 Electric Dipole (El) Transitions 10 Electric Quadrupole (E2) Transitions 14 Nonresonant Scattering 18 Interference Scattering 19 3 PHENOMENOLOGICAL MAGNETIC INTERACTIONS IN RARE- EARTH INTERMETALLIC COMPOUNDS 22 The Rudermann-Kittel-Kasuya-Yoshida Interaction 23 Crystalline Electric Field Effects 25 Magneto-Elastic Interactions 30 4 MAGNETIC ORDERING IN TbNi2B2C 34 Survey of RNigBgC Compounds 34 In-House X-ray Diffraction Study of Structure Change 35 Synchrotron Magnetic X-ray Scattering Study of The Magnetic Structure in Orthrhombic Symmetry 42 Low-Temperature Study: Lock-in Transition 49 X-ray Magnetic Circular Dichroism Search for Weak Ferromagnetism 51 iv Spin Arrangements 60 5 OBSERVATION OF A SPIN REORIENTATION IN TbCu2Ge2 FROM RESONANT AND NONRESONANT X-RAY SCATTER­ ING 65 6 THE MAGNETIC STRUCTURE OF GdAgSb2 DETERMINED BY X-RAY RESONANT EXCHANGE SCATTERING 77 7 SUMMARY OF THE WORK 86 APPENDIX DERIVATIONS OF SCATTERING CROSS SECTION . 88 BIBLIOGRAPHY 97 ACKNOWLEDGMENTS 108 V LIST OF TABLES Table 3.1 Stevens operator equivalents used for tetragonal symmetry (from reference [1]) 27 Table 3.2 Factorization of J = 6 states satisfying closure relation for the CEF interaction of HCBF = + B\0\ + B\0\ + BgOg + 29 Table 3.3 Normalized, symmetrized strains for tetragonal symmetry (from reference [2]) 32 Table 3.4 Elastic constants in tetragonal symmetry (from reference [2]) . 32 Table 4.1 Peak positions extracted from fitting longitudinal scans taken at a temperature of 6.7 K using a Lorentzian line shape. The center of the two magnetic peaks, 1/2 • (0.3370+0.5904) = 0.4637, matches with the (2 0 0)orth position 46 vi LIST OF FIGURES Figure 2.1 The XRES process inside a magnetic ion. Excitation (broken green Une) and deexcitation (solid green line) processes of the core electron are shown simultaneously. The offset between spin up and down band is the exchange splitting 8 Figure 2.2 Scattering geometry with the scattering plane defined by the trace of incident and scattered x-ray beams 13 Figure 2.3 The resonance magnetic signal enhancement is simulated to demon­ strate the asymmetric peak shape contributed by the interference scattering. The intensity of the interference scattering chosen to be 1/6 of the resonant intensity. 20 Figure 4.1 Crystal structure of TbNi^BgC. Large gray circles represent rare earth Tb ions, black circles are C ions, medium size gray balls are Ni ions, and small gray balls show the B ions 36 Figure 4.2 Longitudinal scans through the (400) Bragg peak at selected tem­ peratures. The solid Unes are the results of least-square fits using two Gaussian line profiles. The dotted vertical line shows the po­ sition of (400) in the tetragonal structure 39 vii Figure 4.3 (a) The lattice parameters, a and 6, extracted from longitudinal scans of the (400) Bragg peak, (b) The order parameter, a/b — 1 of the lattice distortion. The solid line is a least-square fit to a power law, A(1 — T/Tn)20• The error bars close to the transition denote the indistinguishability of the two separate domains, (400) and (040), within the current experimental resolution limit, (c) The FWHM of transverse scan for the two different domains, (400) and (040). The solid lines are guide to the eye. The dotted vertical lines in (a), (b), and (c) locate the Tyv found in this work. 40 Figure 4.4 Energy profiles of the (200) charge Bragg peak, and the (2+r 0 0) magnetic satellite peak through the Lm absorption edge of Tb. 44 Figure 4.5 Longitudinal scan along [/i00] showing the split charge peaks, and the magnetic satellite peaks. As described in the text, the two magnetic satellites bracket the (200)orth rather than (020)orth implying magnetic moments are modulated along a*. Data were taken at 6.7 K, and the intensities of charge and magnetic peaks are arbitrarily rescaled 45 Figure 4.6 (a) Integrated intensities of magnetic satellites of (1+r 0 7) and (3—3r 0 7). Solid Unes are power-law fits as described in the text, (b) Orthorhombicity order parameter from the lattice distortion, a/b — 1. The solid Une represents a power-law fit. (c) The spin modulation wave vector with respect to the lattice parameter, a, in the orthorhombic symmetry 47 Figure 4.7 The modulation wave vector calculated from the (—1 + r07) and (—t08) peaks is displayed. Lock-in to the wave vector of 6/11 (broken horizontal Une) below 7 K is shown 51 viii Figure 4.8 Tb Lni-edge absorption (upper panel) and XMCD signal (lower panel) taken at T=3 K and H=4 kG for TbNigBgC. For both panels, circles show the averaged value from flipping the external field 55 Figure 4.9 The dichroic signals at external field of 500 G are plotted for several temperatures. The solid lines are fits to a Lorentzian line shape 56 Figure 4.10 The dichroic signal taken at 500 G is plotted with filled circles. The solid line is the bulk magnetization measurement data on the same powder sample at the same field. The scale for XMCD data is shown to the left while that for the SQUID data are shown to right 57 Figure 4.11 XMCD and SQUID magnetization data on TbNigBgC as a func­ tion of applied external field at a fixed temperature of 3.1 K. The scale for the XMCD data is shown to the left while the magnetic moment determined form the SQUID measurements is shown to the right. The smearing of the metamagnetic transitions arises from powder averaging 59 Figure 4.12 Spin arrangements satisfying the observed modulation wave vec­ tor are depicted in the projected basal plane. Circles displays the Tb ion and filled circles are introduced for the body-centered Tb ions. The broken line has a longer periodicity than the 6/11 lock in modulation 61 ix Figure 4.13 Upper panel shows the reciprocal lattice space scan along the (/i07), and the data were taken at 2 K. The lower panel displays the calculated integrated intensities of all the possible harmonics from the model in Fig. 4.12. The primary modulation of r is 6/11(^1 63 Figure 4.14 Order parameters from the integrated intensities of harmonics are shown. The solid lines are power-law fit as described in the text 64 Figure 5.1 Crystal structure of TbCugGeg.