Academic Press is an imprint of Elsevier 225 Wyman Street, Waltham, MA 02451, USA 525 B Street, Suite 1800, San Diego, CA 92101-4495, USA 125 London Wall, London EC2Y 5AS, UK The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, UK First edition 2015 Copyright © 2015, Elsevier Inc All rights reserved No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher Details on how to seek permission, further information about the Publisher’s permissions policies and our arrangements with organizations such as the Copyright Clearance Center and the Copyright Licensing Agency, can be found at our website: www.elsevier.com/permissions This book and the individual contributions contained in it are protected under copyright by the Publisher (other than as may be noted herein) Notices Knowledge and best practice in this field are constantly changing As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information, methods, compounds, or experiments described herein In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions, or ideas contained in the material herein ISBN: 978-0-12-803413-2 ISSN: 0081-1947 For information on all Academic Press publications visit our website at store.elsevier.com CONTRIBUTORS Numbers in parenthesis indicate the pages on which the authors’ contributions begin Ke Jiang (131) Center for Biofrontiers Institute, University of Colorado at Colorado Springs, Colorado Springs, Colorado, USA Hamid Kachkachi (301) PROMES, CNRS-UPR 8521, Universite´ de Perpignan Via Domitia, Rambla de la Thermodynamique—Tecnosud, Perpignan, France Jun-ichiro Kishine (1) Division of Natural and Environmental Sciences, The Open University of Japan, Chiba, Japan A.S Ovchinnikov (1) Institute of Natural Sciences, Ural Federal University, Ekaterinburg, Russia Anatoliy O Pinchuk (131) Center for Biofrontiers Institute, Department of Physics, University of Colorado at Colorado Springs, Colorado Springs, Colorado, USA Raymond C Rumpf (213) EM Lab, University of Texas at El Paso, El Paso, TX, USA David S Schmool (301) PROMES, CNRS-UPR 8521, Universite´ de Perpignan Via Domitia, Rambla de la Thermodynamique—Tecnosud, Perpignan, France vii PREFACE It is our great pleasure to present the 66th edition of Solid State Physics The vision statement for this series has not changed since its inception in 1955, and Solid State Physics continues to provide a “mechanism … whereby investigators and students can readily obtain a balanced view of the whole field.” What has changed is the field and its extent As noted in 1955, the knowledge in areas associated with solid state physics has grown enormously, and it is clear that boundaries have gone well beyond what was once, traditionally, understood as solid state Indeed, research on topics in materials physics, applied and basic, now requires expertise across a remarkably wide range of subjects and specialties It is for this reason that there exists an important need for up-to-date, compact reviews of topical areas The intention of these reviews is to provide a history and context for a topic that has matured sufficiently to warrant a guiding overview The topics reviewed in this volume illustrate the great breadth and diversity of modern research into materials and complex systems, while providing the reader with a context common to most physicists trained or working in condensed matter The editors and publishers hope that readers will find the introductions and overviews useful and of benefit both as summaries for workers in these fields, and as tutorials and explanations for those just entering ROBERT E CAMLEY AND ROBERT L STAMPS ix CHAPTER ONE Theory of Monoaxial Chiral Helimagnet Jun-ichiro Kishine*,1, A.S Ovchinnikov† *Division of Natural and Environmental Sciences, The Open University of Japan, Chiba, Japan † Institute of Natural Sciences, Ural Federal University, Ekaterinburg, Russia Corresponding author: e-mail address: kishine@ouj.ac.jp Contents Introduction Chiral Symmetry Breaking in Crystal and Chiral Helimagnetic Structure 2.1 Magnetic Representation of Chiral Helimagnetic Structure 2.2 Examples of Chiral Helimagnets 2.3 Microscopic Origins of the DM Interaction Helical and Conical Structures 3.1 Model 3.2 Helimagnetic Structure for Zero Magnetic Field 3.3 Conical Structure Under a Magnetic Field Parallel to the Chiral Axis 3.4 Helimagnon Spectrum Around the Conical State 3.5 Spin Resonance in the Conical State Chiral Soliton Lattice 4.1 Chiral Soliton Lattice Under a Magnetic Field Perpendicular to the Chiral Axis 4.2 Commensuration, Incommensuration, and Discommensuration 4.3 Elementary Excitations Around the CSL 4.4 Physical Origin of the Excitation Spectrum 4.5 Isolated Soliton Which Surfs Over the Background CSL Experimental Probes of Structure and Dynamics of the CSL 5.1 Transmission Electron Microscopy 5.2 Magnetic Neutron Scattering 5.3 Muon Spin Relaxation 5.4 Spin Resonance in the CSL State Sliding CSL Transport 6.1 Lagrangian for Sliding CSL 6.2 Collective Sliding Caused by a Time-Dependent Magnetic Field 6.3 Mass Transport Associated with the Sliding CSL Spin Motive Force 7.1 General Formalism 7.2 Spin Motive Force by the CSL Sliding Coupling of the CSL with Itinerant Electrons 8.1 Gauge Choice and One-Particle Spectrum Solid State Physics, Volume 66 ISSN 0081-1947 http://dx.doi.org/10.1016/bs.ssp.2015.05.001 # 2015 Elsevier Inc All rights reserved 6 11 12 12 14 15 16 20 21 21 26 27 33 33 35 35 38 41 45 48 48 50 55 65 65 71 73 73 Jun-ichiro Kishine and A.S Ovchinnikov 8.2 Current-Driven CSL Sliding in the Hopping Gauge 8.3 Magnetoresistance in the sd Gauge Confined CSL 9.1 Quantization of the CSL Period and Magnetization Jumps 9.2 Resonant Dynamics of Weakly Confined or Pinned CSL 10 Summary and Future Directions Acknowledgments Appendix A Brief Introduction to Jacobi Theta and Elliptic Functions Appendix B LAME Equation Appendix C Constrained Hamiltonian Dynamics Appendix D Computation of the Spin Accumulation in Nonequilibrium State References 77 89 97 97 103 106 109 110 112 117 120 124 INTRODUCTION Symmetry-broken states with incommensurate modulation have attracted considerable attention in condensed-matter physics Typical examples are charge- and spin-density waves in metals, magnetic structures in insulators, helicoidal structures in liquid crystals, and superconducting states with spatially nonuniform order parameters In spite of differences in microscopic origins, their physical properties are universally characterized by macroscopic phase coherence of the condensates and collective dynamics associated with them In particular, the condensates with multicomponent order parameters are of special importance, because they have orientational degrees of freedom in physical space Consequently, not only amplitude but phase of the order parameter can exhibit long-range order Typical example of such case is a helical magnetic structure (Fig 1), which is a main issue in this article The field of research on helimagnetic structure dates back to more than a half century ago Yoshimori [1], Kaplan [2], and Villain [3] interpreted an earlier report on magnetic structure of MnO2 [4] as a helimagnetic structure Since then, this field had been actively driven by neutron scattering measurements An early history of the field is well reviewed by Nagamiya [5] The microscopic origin of this class of helimagnets is the frustration among different superexchange interactions between localized spins or the Ruderman–Kittel–Kasuya–Yosida (RKKY) interactions mediated by conduction electrons Recently, the field of multiferroic materials has shed new light on the frustration-driven noncollinear magnetic structures [6] Theory of Monoaxial Chiral Helimagnet r o r ir M Figure Left- and right-handed helimagnetic structure On the other hand, Dzyaloshinskii [7] found another class of helimagnetic structures which are stabilized by the antisymmetric Dzyaloshinskii–Moriya (DM) interaction [8] The DM interaction originates from the relativistic spin–orbit interaction [9] and imprint an asymmetric electronic structure to the antisymmetric spin–spin interaction Dij ÁSi ÂSj between spins on sites i and j The constant vector Dij is called the DM vector The quantity χ ij ¼Si ÂSj is called the spin chirality which breaks chiral symmetry The term “chiral symmetry breaking” means that space inversion (P) symmetry is broken, but time reversal (T ) symmetry combined with any proper spatial rotation (R) is not broken, according to the definition of Laurence Barron [10] Actually χ ij is odd under the parity transformation P, but even under time reversal operation T When the DMvector Dij has a form Dij ¼ D^e with the D being constant and ^e being a unit vector along some crystallographic axis, competition between DM interaction and the isotropic ferromagnetic (FM) coupling J gives rise to a helical structure of spin magnetic moments Importantly, the direction of D determines whether spin magnetic moments rotate in a left- or right-handed manner along the helical axis, thus providing chirality to the given magnetic helix and creating a chiral helimagnetic (CHM) structure A necessary condition for this kind of DM vector to exist is that a magnetic crystal belongs to a chiral space group Gχ whose symmetry elements contain pure rotations only, i.e., 8g Gχ , det g ¼ The concept of chirality, Jun-ichiro Kishine and A.S Ovchinnikov originally meaning left- or right-handedness, plays an essential role in symmetry properties of nature at all length scales from elementary particles to biological systems In a helimagnetic structure realized in a chiral crystal, the degeneracy between the left- and right-handed helical structures, as shown in Fig 1, is lifted at the level of Hamiltonian The macroscopic DM interaction comes up in the Landau free energy as the Lifshitz invariant [7] Theoretical and experimental achievements on this topic up to early 1980s are well reviewed by Izyumov [11] Interestingly, Dzyaloshinskii’s work activated the research field of improper ferroelectricity where physical outcome of the Lifshitz invariant had been intensively studied [12, 13] Despite the apparent similarity of spin structures, the helimagnetic structures of Yoshimori’s type and Dzyaloshinskii’s types have profound difference in what level of chiral symmetry is broken In the Yoshimori type, chiral symmetry is not broken at the level of Hamiltonian, but the helimagnetic structure spontaneously breaks chiral symmetry On the other hand, in the Dzyaloshinskii’s (CHM) type, the Hamiltonian itself breaks chiral symmetry because of the DM interaction and the magnetic structure is forced to break the chiral symmetry An essential feature of the chiral helimagnetic structure is that the structure is protected by crystal chirality The symmetric helimagnet, however, does not have any macroscopic protectorate and is easily fragmented into multidomains In Fig 2, we summarize basic properties of symmetric and chiral helimagnets M–H curve Mechanism Symmetric (Yoshimori) Chiral (Dzyaloshinskii) M Continuum model Ferro Conical M Ferro Helical Fan Pitch angle = M Ferro Conical M Pitch angle = to n Soli Ferro la t e tic Figure Basic properties of symmetric and chiral helimagnets Spin wave Theory of Monoaxial Chiral Helimagnet This difference directly comes up in their magnetic structures under magnetic fields and elementary excitations In particular, a significant difference arises under a static magnetic field perpendicular to the helical axis The symmetric helimagnetic structure undergoes a discontinuous transition from a helimagnet structure to a fan structure and then continuously approaches the forced ferromagnetic configuration [5] On the other hand, in the chiral helimagnet, the ground state continuously evolves into a periodic array of the commensurate (C) and incommensurate (IC) domains This state, a main subject of this article, has several names, i.e., chiral soliton lattice (CSL), helicoid, or magnetic kink crystal (MKC) [7, 11] Throughout this article, we use the term chiral soliton lattice As the magnetic field strength increases, the spatial period of CSL increases and finally goes to infinity at the critical field strength This situation is depicted in Fig After almost a half century since the theoretical prediction [7], experimental observation of the CSL was achieved by Togawa et al in the hexagonal helimagnet CrNb3S6 [14] which has magnetic phase transition temperature A B C D E F Figure Formation of the chiral soliton lattice under a magnetic field applied perpendicular to the helical axis As the magnetic field strength increases from (A) Hx ¼ to (F) Hx ¼ Hxc , the spatial period of CSL increases and finally goes to infinity at the critical field strength Jun-ichiro Kishine and A.S Ovchinnikov TC ¼ 127 K and its helical pitch is 48 nm In this compound, ferromagnetic layers are coupled via interlayer weak exchange and DM interactions In this case, the formation of the CSL is observed by using Lorenz microscopy The spatial period of the stripe corresponds to the period of the CSL The magnetic field dependence of the period gives a clear evidence that a chiral helimagnetic structure under zero filed continuously evolves into the CSL and finally undergoes a continuous phase transition to commensurate forced-ferromagnetic state at a critical field strength Hc $ 2300 Oe The CSL has some special features to be noted (1) In the CSL state, the translational symmetry along the helical axis is spontaneously broken Therefore, the corresponding Goldstone mode becomes phonon like [7, 15] (2) The CSL state has infinite degeneracy associated with arbitrary choice of the center of mass position Consequently, the CSL can exhibit coherent sliding motion [16] (3) The CSL exerts a magnetic super-lattice potential on the conduction electrons coupled to the CSL This coupling may cause a magnetoresistance effect [17, 18] (4) Quantum spins carried by conduction electrons cause spin-transfer torque on the CSL [19] Here, we will review physical properties of the CSL from theoretical viewpoints The remaining part of the review will be divided into nine subsections In Section 2, we will describe the symmetry-based views on chiral helimagnetism In Section 3, we discuss helical and conical structures under a magnetic field parallel to the chiral axis In Section we will describe the ground state and elementary excitations associated with the CSL [feature (1) mentioned above] In Section 5, we will review some experimental probes of structure and dynamics of the CSL In Section 6, we review physical properties of the sliding CSL [feature (2)] and discuss a possible spin motive force driven by the sliding motion (Section 7) In Section 8, we discuss the coupling of the CSL with itinerant electrons [features (3) and (4)] In Section 9, we consider the case where the CSL is confined in a finite system Finally, we conclude and discuss the meaning of chirality in modern physics from broader viewpoints (Section 10) We will leave some supplementary or technical materials to appendices CHIRAL SYMMETRY BREAKING IN CRYSTAL AND CHIRAL HELIMAGNETIC STRUCTURE 2.1 Magnetic Representation of Chiral Helimagnetic Structure Quantum spin state for spin S ¼ 1/2 is described by a two-component spinor in SU(2) space, parameterized by polar angles, Theory of Monoaxial Chiral Helimagnet   ei=2 cos =2ị : j i ẳ + i=2 e sin ðθ=2Þ (1) Then, a spin operator as an observable is given by S^ ¼ S^ σ , where S ¼ ℏ=2 and σ^ denotes a Pauli spin operator and a corresponding spin polarization vector is written as an axial vector in O(3) space, S ¼ hχ jS^ jχ i ¼ S^ n, n ^ ¼ ðsinθ cosφ, sinθ sinφ,cos θÞ: (2) This classical axial vector enters a macroscopic Maxwell equations as a magnetic moment M ¼ ÀgμBS It is to be noted that whenever we talk about M, permutation symmetry, which is purely quantum, is totally lost and instead the parameters φ and θ have meaning as polar angles φ(r) and θ(r) tied to a spatial position r in O(3) space A purpose of magnetic representation theory is to classify possible ordering of the M vector as an order parameter The chiral helimagnetic structure is an incommensurate magnetic structure with a single propagation vector k ¼ (0,0,k) The chiral space group Gχ consists of the elements {gi} Among them, some elements leave the propagation vector k ¼ (0,0,k) invariant, i.e., these elements form the little group Gk The magnetic representation Γmag is written as Γmag ¼ Γperm  Γaxial, where Γperm and Γaxial represent the Wyckoff permutation representation and the axial vector representation, respectively [20] Then, Γmag is decomposed into the nonzero irreducible representations of Gk The incommensurate magnetic structure is determined by a “symmetry-adapted basis”of an axial vector space and the propagation Pvector k In a specific magnetic ion, the decomposition becomes Γmag ¼ i ni Γi , where Γi is the irreducible representations of Gk The chiral helimagnetic structure, ẩ ẫ M ặ ẳ Me1 cos kzị ặ Me2 sin kzị ẳ MRe e1 ầ ie2 Þeikz , (3) (+ and À signs correspond to left- and right-handed helix) requires real twodimensional or complex one-dimensional symmetry-adapted basis, e1 and e2 For these basis to exist, the group elements of Gk0 include three- (C3), four(C4), or sixfold (C6) rotations Therefore, among 65 chiral space groups whose elements are all proper rotations (for 8g G, det g ¼ 1), 52 space groups belonging to cubic, hexagonal, tetragonal, and trigonal crystal classes are eligible to accommodate the chiral helimagnetic structure This situation is depicted in Fig The cubic class is special because there are four C3 axes, although hexagonal, tetragonal, and trigonal crystals have only one principal axis In the latter case, a monoaxial helimagnetic structure as shown in Fig is 453 Author Index Wu, B., 142–143, 360 Wu, F., 175 Wu, J.C., 371 Wu, J.H., 279–281 Wu, L., 289 Wu, M., 392–393, 393f Wu, M.C., 289 Wu, Q., 146 Wu, Q.H., 283 Wu, R., 385–388 Wu, S.H., 164t Wu, W., 177 Wu, X., 173, 180 Wu, Y., 382 Wu, Y.-J., 134 Wu, Y.Q., 164t Wuestner, S., 216–217 Wysin, 316, 351–352 X Xi, J., 176–177 Xia, H., 180 Xia, Y., 132–133, 140–142, 141f, 146–147, 148f, 150, 152, 153t, 170t, 176–177, 183–184 Xiang, C., 173–174 Xiao, D., 65, 71 Xiao, F.S., 177–178 Xiao, J., 84–85 Xiao, J.C., 167 Xiao, X., 180–181 Xiao, Y., 166 Xie, A.J., 146 Xie, C., 173 Xie, J.P., 144, 146 Xie, X.S., 173–174 Xin, J., 146 Xing, B.G., 166 Xiong, Y., 141–142, 141f, 147, 148f, 152, 153t Xu, A.-W., 146 Xu, B.-B., 180–181 Xu, C.L., 164t Xu, G., 153t Xu, H., 151 Xu, K.H., 167 Xu, P.S., 177 Xu, S.Q., 148–150 Xu, X.H., 167 Xu, X.Y., 166 Xu, Y., 180 Xue, X.J., 164t Xue, Y.D., 167 Y Yablonovitch, E., 214–216 Yacaman, M.J., 146, 182 Yadav, A., 132–135, 146–147, 181–182 Yamada, S., 176–177 Yamamoto, K., 377 Yamamuro, S., 377 Yamanaka, M., 97, 181–182 Yamane, Y., 65 Yamashiki, N., 175 Yamashita, T., 8t Yamaura, J., 8t Yamazaki, T., 42–43 Yan, B., 133–134 Yan, M., 165–166, 166f Yanase, A., 12 Yanes, R., 326–327, 390–391 Yang, C.S., 163–165, 172–173 Yang, E.C., 397–398 Yang, G.L., 170t Yang, H., 150, 183–184 Yang, H.-Y., 281–282 Yang, J.K.W., 409 Yang, J.S., 371 Yang, L., 169–171 Yang, M.-J., 174 Yang, P., 147, 150–151, 151f, 170t, 182–183 Yang, Q., 177–178 Yang, S.A., 65, 71 Yang, T.Y., 144f, 145, 173 Yang, W.R., 164t Yang, W.S., 137–138 Yang, X.C., 145, 163–165, 168–169 Yang, Y., 133–134, 151 Yang, Z., 143–145, 153t Yannoni, C.S., 399–400 Yao, H., 145 Yao, J., 289 Yao, N., 307 Yariv, A., 224, 236, 289–290 Yasuoka, H., 42–43 Yawe, J.C., 168–169 454 Ye, J., 180 Yee, K.S., 262–264 Yeh, H.-I., 134, 144f, 145, 173 Yeh, P., 224, 236 Yguerabide, E.E., 134–135 Yguerabide, J., 134–135 Yi, G., 307–308 Yi, H., 380–381 Yi, S., 164t Yiagas, D.I., 348–349 Yin, H., 167 Yin, Y., 147, 148f, 152 Ying, J.Y., 144 Yin-Goen, Q., 169–171 Yip, H.Y., 146 Yngard, R.A., 135, 145 Yokobori, T., 8–9 Yokogawa, R., 170t Yong, K.-T., 165, 171–172, 172f, 174 Yonzon, C.R., 170t Yoo, S.M., 170t Yoon, H.C., 167 Yoon, I., 170t Yoon, K.Y., 182 Yoon, Y.-K., 180 Yoosaf, K., 167, 168f Yoshida, K., 164t Yoshida, Y., 8–9, 8t Yoshimori, A., Yoshimura, Y., 170t Yoshizawa, N., 169–171 You, C.C., 166, 168–169, 178–179 You, X.Y., 163–165 Youk, K.S., 164t Young, A.N., 169–171 Yu, C.X., 170t, 171–172 Yu, H.T., 170t Yu, J., 89, 173 Yu, J.C., 146 Yu, K.N., 181–182 Yu, N., 153t Yu, P., 163–165 Yu, R.Q., 170t Yu, S.H., 146, 153t Yu, T.B., 165–166 Yu, T.Y., 179 Yu, W.-Y., 181–182 Yu, X., 146, 165 Author Index Yu, Y., 140 Yu, Z.H., 173–174 Yuan, J.-M., 360 Yuan, Q., 153t Yun, S.-W., 169171 Z Zaăhres, H., 405–406 Zamani, A., 394–395 Zandvliet, H.J.W., 377–378 Zanella, M., 144f, 145, 173 Zangwill, A., 84–85 Zasadzinski, J.A., 177 Zborˇil, R., 145–146, 181–182 Zeller, R., 383–385 Zeng, H.B., 153t Zeng, S., 165 Zhan, Y.H., 177 Zhang, C.W., 143–144 Zhang, H.H., 140–141, 153t, 170t, 176–177 Zhang, J.G., 146, 148–150 Zhang, L., 146, 153t Zhang, M., 146, 177 Zhang, N., 167 Zhang, Q.F., 146 Zhang, R., 180–181 Zhang, S., 80, 89 Zhang, W., 159, 164t Zhang, X.E., 163–165, 170t Zhang, Y.F., 164t, 174, 180 Zhang, Z., 71, 175–176, 399–402 Zhang, Z.L., 409 Zhang, Z.P., 163–165 Zhang, Z.Y., 409 Zhao, B., 170t Zhao, H., 163–165 Zhao, J., 152–155 Zhao, L., 174 Zhao, S.Y., 151 Zhao, W.A., 166 Zhao, Y., 174, 176–177 Zharov, V.P., 175–177 Zheludev, A., 8–9 Zheng, H.R., 409 Zheng, J., 143–144, 148, 150, 173 Zheng, M., 140 Zheng, N.F., 153t 455 Author Index Zheng, P.C., 170t Zheng, W., 174 Zheng, Y.G., 144 Zhong, C.J., 138–139, 144–145, 144f Zhong, M.Y., 170t Zhou, B., 173 Zhou, C., 173 Zhou, H., 153t Zhou, W.H., 153t, 179 Zhou, X.Z., 170t, 309–310, 350–351 Zhou, Z.Y., 153t, 183–184, 249–250 Zhu, C.Z., 153t Zhu, D.B., 167 Zhu, F.Q., 371 Zhu, H., 175 Zhu, J., 174 Zhu, J.-G., 371 Zhu, N.N., 163–165 Zhu, X., 371 Zhu, Y., 37, 140, 152, 153t, 403 Zhuang, J., 153t Zhuang, X., 150 Zhukov, A.V., 378f, 379 Zhuo, L.H., 167 Zigler, A., 360 Zou, J.Z., 175 Zrig, S., 108 Zubarev, D.N., 90–91, 93–95, 333 Zueco, D., 336 Zuăger, O., 399400 Zukoski, C.F., 137138 zumer, S., 107–108 zˇutic´, I., 58, 106 Zweifel, D.A., 174 SUBJECT INDEX Note: Page numbers followed by “f ” indicate figures and “t ” indicate tables A Additive manufacturing (AM) technology, 217–219 AFM See Atomic force microscopy (AFM) Aharonov–Bohm expression, 35 American Society for Testing and Materials, 217–219 Anisotropic metamaterials 3D printed, 278–279, 278f binary grating, 273–275 cutoff frequency, 272–273 DSW, 281–283, 282f hyperbolic metamaterials, 283–284, 284f Maxwell’s equations curl equations, 219–220 dielectric tensor, 222, 223f divergence equations, 219–220 frequency-domain, 219–220 magnetoelectric coupling coefficients, 224 material magnetization, 220–221 material polarization, 220–221 permittivity and permeability tensors, 221–222 parallel polarization, 273–275 perpendicular polarization, 273–275 polarization manipulation, 283 ruled grating, 275–276, 275f sculpting near-fields, 279–281 square array of square rods, 278, 278f strength, 275 uniaxial lattice, 276 unit cells, 276–277, 277f Atomic force microscopy (AFM), 377378, 388389 B Baăcklund transformation, 3335, 34f Barkhausen effect, 97 Binder jetting, 217–219 Bolometer detection method, 405–406 Boltzmann and Gilbert relaxations, 84–85 Bragg gratings, 214–215, 289–290, 290f Bragg reflection, 93–97 Bragg scattering, 97 Brust–Schiffrin method, 138–139 C Chiral helimagnets DM interaction, microscopic origins of, 11–12, 12f examples, 2, 8–11, 8t magnetic representation, 6–8, 8f vs symmetric helimagnets, 4–5, 4f Chiral soliton lattice (CSL) Baăcklund transformation, 3335, 34f commensuration, 5, 5f, 26–27, 28f confinement effects (see Confined chiral soliton lattice) discommensuration, 26–27, 28f elementary excitations, 27–33, 28–29f, 31f Lame´ equation, 112–116 excitation spectrum, physical origin of, 33 incommensuration, 5, 5f, 26–27, 28f itinerant electrons (see Itinerant electrons–CSL coupling) magnetic field perpendicular to chiral axis, 21–26, 24f, 27f magnetic neutron scattering polarized elastic neutron scattering cross section, 38–39, 40–41f unpolarized elastic neutron scattering cross section, 40–41 muon spin rotation/relaxation asymmetry function, 41–42, 44 coordinate frame, 42–43, 43f equations of motion, 42 longitudinal field geometry, 44–45, 44f positive muon decays, 42 spin polarization, temporal dependence of, 43–44 457 458 Chiral soliton lattice (CSL) (Continued ) sliding motion (see Sliding CSL) spin resonance ESR spectrum, 45–46 Fourier coefficients, 45–46 incommensurate-to-commensurate (IC-C) phase transition, 47–48 Lame´ equation, 115–116 resonance energy level distribution, 46–47, 47f transmission electron microscopy Fresnel technique, 37–38 Heaviside’s step function, 36 magnetic phase shift, 35–37 magnetic vector potential, 35–37 signal spatial profile, 37–38, 38f Chiral symmetry breaking definition, 3, 6–12 helimagnetics (see Chiral helimagnets) Chromatic dispersion, 231, 232f Circular polarization (CP), 229–230 Citrate reduction method, 136, 137f Classical spin-wave theory, 329–331 Commensuration, 5, 5f, 26–27, 28f Confined chiral soliton lattice magnetization jumps, 97, 100–101, 103 spatial period quantization analytical magnetization curve, 100–103, 102f Barkhausen effect, 97 fixed boundary conditions, 97–99 ground state energy, 99–100, 99f lattice period, h-dependence of, 100, 101f magnetization curve, 100–101, 101f one-dimensional Hamiltonian, 97–98 phase angle, coordinate behavior of, 100, 100f weakly confined CSL resonant dynamics CSL sliding Lagrangian, 105–106 equation of motion (EOM), 105–106 pinning potential, 103–105 vs strong pinning, 105–106 Conical magnetic structure helimagnon spectrum, 16–20, 18f magnetic field parallel to chiral axis, 15, 15f spin resonance, 20–21, 22f Subject Index Constrained Hamiltonian dynamics, 117–120 CSL See Chiral soliton lattice (CSL) Cubic helimagnet, 7–8, 8f Curl equations, 219–220 D Dark-field microscopy, 171–172, 172f Delay-bandwidth product (DBP), 290–291 Dirac–Heisenberg model, 316 Directed energy deposition, 217–219 Discommensuration, 26–27, 28f Discrete dipole approximation (DDA) method, 156–158 Dispersion See Engineering dispersion Divergence equations, 219–220 DM interaction See Dzyaloshinskii–Moriya (DM) interaction D€ orring–Becker–Kittel mechanism, 49–50, 58–60 Drude model, 156 Drug delivery magnetic nanoparticles, 409 NMNs, 177–179 Dyakonov surface wave (DSW) anisotropic materials, 281–283, 282f Dzyaloshinskii–Moriya (DM) interaction, 3–4, 10–14, 30, 107 E Effective OSP (EOSP) approach, 326–328, 349–350, 349f Electrically anisotropic materials, 221 Electromagnetic band diagrams band gaps, 246–247 Bloch waves, 244–245 dispersion, 248 eigenvalue problems, 243–245 phase and group velocity, 247–248 photonic band diagrams, 243 transmission spectrum, 247 Electromagnetic waves complex exponentials, 226–227 LHI media, 225–226 magnetic field component, 226–227 Maxwell’s equations, 224–225 polarization, 229–230 refractive index, 226 459 Subject Index TE and TM, 230–231, 230f vector orientation, 228 wave equation, 225 wavelength, 227–228 Electron beam lithography, 364, 365f Engineering dispersion biaxial materials, 232–233 Bragg gratings, 289–290, 290f delay-bandwidth product, 290–291 optic axis, 232–233 phase matching, 288–289, 288f relation, 231–234 self-collimation IFC, 285–286, 285f lattice optimizing, 286 spatially variant, 287–288, 287f superprisms, 289 surface, 231–232, 234, 234f types, 231, 232f uniaxial materials, 233–234 Equation of motion (EOM) single magnetic nanoparticles, 334–336 weakly confined CSL resonant dynamics, 105–106 Euler–Lagrange–Rayleigh equations of motion, 51–52, 79 F FDFD method See Finite-difference frequency-domain (FDFD) method Ferromagnetic resonance (FMR) angular dependence of, 394–395, 396f Co nanoparticles, 398–399 EPR and micro-SQUID techniques, 397–398 general formalism, 336–338 measured vs simulated spectra, 394–395, 395f microwave spectroscopy, 391–392 Ni4 crystal, 397–398, 398f PMR, 394–395 VNA, 392–394, 393f XMCD measurements synchrotron sources, 382 Finite-difference frequency-domain (FDFD) method algorithm, 266–267 formulation, 262–264 scattered-field masking matrix, 266 (TF/SF) technique, 266 UPML, 261–262 Finite-size and surface effects, magnetic nanoparticles, 363–364 hysteresis and switching field, 351–352, 352f intrinsic properties, 350 magnetization profile, 354, 355f magnetization vs temperature and dc field, 353–354, 354f spin configuration and magnetic state, 350–351, 351f surface anisotropy, 353, 353f Fluorescent metal nanoclusters advantages, 135–136 AuNPs, 143–145, 144f silver nanomaterials, 148–150 FMR See Ferromagnetic resonance (FMR) Fokker–Planck equation (FPE), 335–336, 341–343 Fresnel technique, 37–38 Fused deposition modeling (FDM), 217–219 G Gilbert damping process, 50–54, 71–72, 82 Gold nanocages, 140–142 Gold nanoparticles (AuNPs) colorimetric sensing, 163–167, 164t, 166f dark-field microscopy, 171–172, 172f drug delivery systems, 177–179 FRET-based assay, 167–169, 168f laser ablation technique, 136 optical properties absorption/scattering ratios, 159–160 Mie theory, 162, 162t, 162f temperature change, 159–161, 161f photothermal conversion efficiency absorption/extinction ratios, 162, 162t vs diameter, 162, 162f heating effect, 159 temperature change vs laser power extinction, 160–161, 161f PTT, 175–177 SERS, 169–171 SPR absorption, 133–134 460 Subject Index Itinerant electrons–CSL coupling hopping gauge CSL sliding (see Sliding CSL) Hamiltonian, 75–76 Rashba effect, 75–76 transverse spin accumulation, 76 sd gauge Bragg scattering, 97 Hamiltonian, 73 insulating helicycloidal spin structure, 93 interaction effects, 73–75, 74f Jacobi theta and elliptic functions, 110–112 local SU(2) gauge transformation, 75 magnetic super-potential, 77, 89–92, 90f, 92f multivalued magnetoresistance, 93–97, 96f Gold nanoparticles (AuNPs) (Continued ) synthesis fluorescent nanoclusters, 143–145, 144f nanocages, 140–142, 141f nanorods, 139–140, 139f nanoshells, 142 nanowires, 142–143, 143f spherical nanoparticles, 136–139, 137–138f toxicity and environmental impact, 134 TPL microscopy, 174 Gold nanorods (AuNRs), 139–140, 174 Gold nanoshells (AuNSs), 134, 142 Gold nanowires (AuNWs), 142–143, 143f Gold–silver alloyed nanoparticles, 132–133, 132f Green dyadic method, 158–159 Green’s function, 333 Guided-mode resonance filters, 216–217 Gyrotropic materials, 224 J H Jacobi theta and elliptic functions, 110–112 Josephson junctions, 364 Heat-Assisted Magnetic Recording (HAMR) technology, 356 Heaviside’s step function, 36 Helical magnetic/helimagnetic structure chiral symmetry (see Chiral helimagnets) vs conical magnetic structure helimagnon spectrum, 16–20 magnetic field parallel to chiral axis, 15, 15f spin resonance, 20–21 CSL (see Chiral soliton lattice (CSL)) DM interaction, left-and right-handed structures, 3f symmetric vs chiral, 4–5, 4f Yoshimori’s type structures, zero magnetic field, 14, 15f Hexagonal helimagnet, 5–6, 8–9, 8f, 106 Holstein–Primakoff representation (HPR), 328–329 HPR See Holstein–Primakoff representation (HPR) Hyperbolic metamaterials, 283–284, 284f I Incommensuration, 5, 5f, 26–27, 28f Isofrequency contours (IFCs), 248–249 L Lagrangian equations sliding CSL collective dynamics, 48–50 D€ oring’s mechanism, 49–50 Galilean symmetry, 48 weakly confined sliding CSL, 105–106 Lame´ equation, 112–116 Landau–Lifshitz equation (LLE), 323, 334–338 Langreth’s method, 123–124 Laser ablation technique, 136 Left-hand circular polarization (LCP), 229–230 Ligand-protected method, 145 Linear polarization (LP), 229–230 Lorentz transmission electron microscopy (LTEM) application, 374 differential phase contrast (DPC) mode image, 375, 376f Fe3O4 nanoparticles, 377 Foucault and Fresnel modes, 375–376 Lorentz force, 373–374 magnetoresistance, 377 Subject Index schematic explanation, 374–375, 375f SmCo5 nanoparticles, 376 spatial resolution, 374 Lycurgus Cup, 132–133, 132f M Magnetically anisotropic materials, 221 Magnetic force microscopy (MFM) AFM, 377–378 bimodal phase shift image, 380–381, 381f cobalt cylinders, 377–378, 378f dc/ac mode operation, 379 magnetic thin films, schematic diagram of, 380–381, 380f STM, 377–378 Magnetic neutron scattering, CSL polarized elastic neutron scattering cross section, 38–39, 40–41f unpolarized elastic neutron scattering cross section, 40–41 Magnetic resonance force microscopy (MRFM) anharmonic modulation, 401 bolometer detection method, 405–406 detection sensitivity, 401, 403, 404f principal components, 400, 400f SThM-FMR, 403–404, 405f yttrium iron garnet studies, 401–402, 402f Magnetization jumps, 97, 100–101, 103 Magnetization switching, single magnetic nanoparticles exponential spin-wave instability, 360–362, 362f microwave-assisted reversal, 356–360, 357f, 359f Magnetoelectric coupling coefficients, 224 Many-spin problem (MSP) models boundary effects, 316–318 Dirac–Heisenberg model, 316 finite-size effects, 316–318 icosahedral particle, 314, 315f induced magnetization, 320 intrinsic magnetization, 320–321 magnetization field dependence, 321–322 NSA model, 319–320, 319f vs OSP model, 327 quasi-spherical particle, 314, 315f size regime for, 327, 327f 461 superparamagnetic relation, 321 surface spins, increasing number of, 314, 315f TSA model, 318–319, 318f uniaxial single-site anisotropy energy, 318 vector magnetization, 320 Mass transport, sliding CSL background spin current, 62–64 dissipationless spin current, 58–59 D€ orring–Becker–Kittel mechanism, 58–60 linear momentum and dynamical instability, 56–58 magnon current density, 59–62, 60–61f singular Lagrangian, Dirac’s prescription for, 55–56 Material extrusion, 217–219 Material jetting, 217–219 Maxwell’s electromagnetic equations curl equations, 219–220 dielectric tensor, 222, 223f divergence equations, 219–220 frequency-domain, 219–220 magnetoelectric coupling coefficients, 224 material magnetization, 220–221 material polarization, 220–221 Mie theory, 155–156 permittivity and permeability tensors, 221–222 Metal nanoparticles See Noble metal nanomaterials (NMNs) Metamaterials anisotropy (see Anisotropic metamaterials) definition, 214–215 MFM See Magnetic force microscopy (MFM) micro-SQUID See Superconducting quantum interference device (SQUID) Microwave spectroscopy, 391–392, 408 Mie theory, 155–156 Mixtures, definition of, 214–215 Monte Carlo (MC) simulations chiral helimagnet, 13 single magnetic nanoparticles, 338–340 MRFM See Magnetic resonance force microscopy (MRFM) 462 MSP models See Many-spin problem (MSP) models Muon spin rotation, CSL asymmetry function, 41–42, 44 coordinate frame, 42–43, 43f equations of motion, 42 longitudinal field geometry, 44–45, 44f positive muon decays, 42 spin polarization, temporal dependence of, 43–44 N Nanoscaled magnetic systems See Single magnetic nanoparticles nano-SQUID See Superconducting quantum interference device (SQUID) Ne´el–Brown models, 311–312, 341–343, 348–349, 369 Ne´el surface anisotropy (NSA) model, 319–320, 319f Negative refractive index metamaterials, 215–216 NMNs See Noble metal nanomaterials (NMNs) Noble metal nanomaterials (NMNs) antimicrobial agents, 181–182 AuNPs (see Gold nanoparticles (AuNPs)) catalytic applications, 182–184 drug delivery applications, 177–179 fluorescent nanoclusters, 135–136 laser deposition, 179–181, 179f, 181f optical imaging dark-field microscopy, 171–172, 172f fluorescence microscopy, 172–173 TPL microscopy, 173–174 optical properties analytical methods, 152–155 DDA method, 156–158 Mie theory, 155–156 numerical methods, 152–155 quasistatic approximation, 156 SPR, 152 PdNPs (see Palladium nanomaterials (PdNPs)) photothermal properties, 158–162 PtNPs (see Platinum nanomaterials (PtNPs)) Subject Index PTT, 175–177 silver (see Silver nanomaterials) synthetic routes, 133 Noble metal nanomaterials (NMNs) colorimetric sensing cells, 167 ions, 163, 164t oligonucleotides, 165 proteins, 165–166, 166f small organic molecules, 163–165 fluorescence quench-based sensing, 167–169, 168f SERS sensing, 169–171, 170t Noble metals, 133 Nonequilibrium statistical operator (NSO) approach, 93–95 Nonresonant metamaterials, 214–215 NSA model See Ne´el surface anisotropy (NSA) model O One-spin problem (OSP) models experimentalists preference, reasons for, 327–328 vs MSP model, 327 Ne´el–Brown model, 311–312 size regime for, 327, 327f SW model, 311–314, 314f Ordinary materials, 214–215 OSP models See One-spin problem (OSP) models P Palladium nanomaterials (PdNPs), 135 catalytic activities, 152 shape related synthetic routes, 152, 153t Parallel polarization, 230–231 PdNPs See Palladium nanomaterials (PdNPs) PEGylated AuNPs, 175 Periodic electromagnetic structures See Solid-state electromagnetics Perpendicular polarization, 230–231 Phase matching, 288–289, 288f Photonic crystals, 214–215 Photothermal therapy (PTT), 175–177 Pinned chiral soliton lattice, 103–106 Plane of incidence, 230–231 Subject Index Plane wave expansion method (PWEM), 253–257 algorithm, 260 Fourier space method, 254–255 matrix wave equation, 258 polarization, 258–260 Platinum nanomaterials (PtNPs) catalytic applications, 135, 150, 182–184 cuboctahedrons, 151, 151f fuel cells, 150, 183–184 nanocubes, 150, 151f octahedrons, 150, 151f synthesis, 150–151 TEM images, 151f Polarization electromagnetic waves, 229–230 TE and TM, 230–231, 230f Polarization dispersion, 231, 232f Polarized elastic neutron scattering, 38–39, 40–41f Powder bed fusion, 217–219 p-polarization, 230–231 Primitive translation vectors, 236–237, 237f PtNPs See Platinum nanomaterials (PtNPs) PTT See Photothermal therapy (PTT) PWEM See Plane wave expansion method (PWEM) Q Quantum spin-wave theory, 331–333 Quasistatic approximation, 156 R Rashba effect, 75–76 Resonant metamaterials, 214–217 Riccati–Bessel functions, 155–156 Right-hand circular polarization (RCP), 229–230 Ruderman–Kittel–Kasuya–Yosida (RKKY) interactions, 2, 12 S Scanning thermal microscopy ferromagnetic resonance (SThM-FMR), 403–404, 405f Scanning tunneling microscopy (STM), 377–378 Scattered-field masking matrix, 266 463 Schwinger–Keldysh formalism, 120–123 Seeded growth method, 138, 138f Self-collimating photonic crystals IFC, 285–286, 285f lattice optimizing, 286 spatially variant, 287–288, 287f Sheet lamination, 217–219 Silver nanomaterials antibacterial applications, 135, 181–182 drug delivery systems, 178–179 fabrication, 180–181 fluorescent nanoclusters, 148–150, 149f growth rate, 180 laser irradiation-induced photoreduction, 179–181, 179f nanobars, 147, 148f nanocubes, 147, 148f nanorice, 147, 148f nanorods and wires, 147, 148f optical activation, 178–179 shapes, 146–147 spherical nanoparticles (see Spherical nanoparticles) SPR, 134–135 synthesis controlled shapes, 146–147, 148f fluorescent nanoclusters, 148–150 spherical shapes, 145–146 Single magnetic nanoparticles vs bulk systems, 301–302 characterize measurement difficulties, 363 coarse-grained approach, 311 crossover approach, 322–328 equations of motion, 334–336 finite-size and surface effects, 363–364 hysteresis and switching field, 351–352, 352f intrinsic properties, 350 magnetization profile, 354, 355f magnetization vs temperature and dc field, 353–354, 354f spin configuration and magnetic state, 350–351, 351f surface anisotropy, 353, 353f FMR, 394–395, 396f angular dependence of, 394–395, 396f Co nanoparticles, 398–399 464 Single magnetic nanoparticles (Continued ) EPR and micro-SQUID techniques, 397–398 general formalism, 336–338 measured vs simulated spectra, 394–395, 395f microwave spectroscopy, 391–392 Ni4 crystal, 397–398, 398f PMR, 394–395 VNA, 392–394, 393f XMCD measurements, 398–399 LTEM application, 374 differential phase contrast (DPC) mode image, 375, 376f Fe3O4 nanoparticles, 377 Foucault and Fresnel modes, 375–376 Lorentz force, 373–374 magnetoresistance, 377 schematic explanation, 374–375, 375f SmCo5 nanoparticles, 376 spatial resolution, 374 macrospin approach experimentalists preference, reasons for, 327–328 vs MSP model, 327 Ne´el–Brown model, 311–312 size regime for, 327, 327f SW model, 311–314, 314f magnetic interactions, 363–364 magnetization switching exponential spin-wave instability, 360–362, 362f microwave-assisted reversal, 356–360, 357f, 359f many-spin approach (see Many-spin problem (MSP) models) MFM AFM, 377–378 bimodal phase shift image, 380–381, 381f cobalt cylinders, 377–378, 378f dc/ac mode operation, 379 magnetic thin films, schematic diagram of, 380–381, 380f STM, 377–378 micro-hall magnetometry advantages and disadvantages, 373 Subject Index central principle, 370–371 vs micro-SQUID measurements, 369–370 Ni nanoring hysteresis loop study, 371, 372f Ni pillar-shaped element hysteresis loop study, 371–372, 372f schematic illustration, 370–371, 371f spin-valve sensors, 373 Monte Carlo simulations, 338–340 MRFM anharmonic modulation, 401 bolometer detection method, 405–406 detection sensitivity, 401, 403, 404f principal components, 400, 400f SThM-FMR, 403–404, 405f yttrium iron garnet studies, 401–402, 402f relaxation rate energy barrier and, 340f EOSP approach, 349–350, 349f Langer’s approach, 346–347, 346f Ne´el–Brown models, 341–343, 348–349 Stoner–Wohlfarth model, 341–344, 348–349 superparamagnetism, 341 spin-wave theory classical spin waves, 329–331 HPR, 328–329 quantum theory, 331–333 SQUID blind method, 367 cobalt nanoparticle, 368–369, 368f cold mode method, 366, 367f difficulties, 365–366 electron beam lithography, 364, 365f Josephson junctions, 364 macroscopic quantum tunneling (MQT), 366 nanoparticle positioning, 365 Ne´el–Brown model, 369 Stoner–Wohlfarth model, 368–369, 369f switching current vs magnetization reversal, 312, 365–366 superparamagnetic effect, 328 Subject Index XMCD construction of, 385 orbital and spin magnetic moments, 385 principles, 383–385, 384f synchrotron sources, 382 XAS, 385, 386f X-PEEM Co nanoparticles, 388–389, 389f experimental setup, 382–383, 383f Fe nanoparticles, 388–391, 389f Landau flux closure structure, 385–388, 387f magnetic anisotropy energy, 390–391 spiral spin structure, 389–390, 390f vortex magnetic structure, 385–388 Sliding CSL Lagrangian collective dynamics, 48–50 D€ oring’s mechanism, 49–50 Galilean symmetry, 48 mass transport background spin current, 62–64 dissipationless spin current, 58–59 D€ orring–Becker–Kittel mechanism, 58–60 linear momentum and dynamical instability, 56–58 magnon current density, 59–62, 60–61f singular Lagrangian, Dirac’s prescription for, 55–56 SMF coherent motion, 65–71 general formalism, 65–71 one dimensional spatial modulation, 71–72, 72f time-dependent longitudinal field, 65, 65f types, 65 spin-torque transfer estimation band-splitting structure, 88, 89f Boltzmann and Gilbert relaxations, 84–85, 86f equations of motion, 78–82, 80f nonequilibrium state spin accumulation and depletion, 82–84, 85f sliding conductivity, 85–88, 87f 465 time-dependent magnetic field AC magnetic field, 53–54, 54f background spin current, 62–64 Dirac’s prescription, 55–64 D€ orring-Becker-Kittel mechanism, 59–60 equations of motion, 50–52 linear momentum and dynamical instability, 56–58 magnon current, 60–62 rapid switching, 52–53, 53f spin transport problem, 58–59 Solid-state electromagnetics anisotropy (see Anisotropic metamaterials) dispersion biaxial materials, 232–233 optic axis, 232–233 refractive indices, 233–234 relation, 231–234 surface, 231–232, 234, 234f types, 231, 232f uniaxial materials, 233–234 electromagnetic band diagrams band gaps, 246–247 Bloch waves, 244–245 dispersion, 248 eigenvalue problems, 243–245 phase and group velocity, 247–248 photonic band diagrams, 243 transmission spectrum, 247 electromagnetic waves complex exponentials, 226–227 LHI media, 225–226 magnetic field component, 226–227 Maxwell’s equations, 224–225 polarization, 229–230 refractive index, 226 TE and TM, 230–231, 230f vector orientation, 228 wave equation, 225 wavelength, 227–228 energy velocity, 236 group velocity, 235–236 IFCs, 248–249 math description amplitude function, 238–239 Bloch wave, 238–239, 239f Brillouin zone (IBZ), 241–242 466 Solid-state electromagnetics (Continued ) irreducible Brillouin zone (IBZ), 242–243, 243f primitive translation vectors, 236–237, 237f primitive unit cell, 237–238 reciprocal lattice vectors and direct lattice vectors, 239–241, 240–241f Wigner–Seitz primitive unit cell, 237–238, 238f Maxwell’s equations curl equations, 219–220 dielectric tensor, 222, 223f divergence equations, 219–220 frequency-domain, 219–220 magnetoelectric coupling coefficients, 224 material magnetization, 220–221 material polarization, 220–221 permittivity and permeability tensors, 221–222 numerical methods 2D lattice model, 252–254, 253–254f 3D lattice model, 252–254, 253–254f FDFD (see Finite-difference frequencydomain (FDFD) method) PWEM (see Plane wave expansion method (PWEM)) phase velocity, 234–235 spatially variant lattices, 249–250, 250f TO, 251–252 lattice bending, 250–251 synthesis, 267–271, 269f, 271–272f Spatial dispersion, 231, 232f, 248 Spatially variant anisotropic metamaterials (SVAMs) 1D planar gratings, 267 analog and binary lattice, 270, 271f grating phase, 267 grating vector, 267 grayscale unit cell, 270, 271f input and output parameters, 268–269, 269f sculpting near-fields, 279–281 truncation schemes, 270–272, 272f Spatial period quantization analytical magnetization curve, 100–103, 102f Subject Index Barkhausen effect, 97 fixed boundary conditions, 97–99 ground state energy, 99–100, 99f lattice period, h-dependence of, 100, 101f magnetization curve, 100–101, 101f one-dimensional Hamiltonian, 97–98 phase angle, coordinate behavior of, 100, 100f Spherical nanoparticles gold nanoparticles Brust-Schiffrin method, 138–139 citrate reduction, 136, 137f four-step growth mechanism, 137–138, 137f NIR region, 176 PTT, 175–176 seeded growth method, 138, 138f silver nanomaterials biological synthesis, 146 chemical reduction, 145 irradiation sources, 146 Tollens reaction, 145–146 Spin motive force (SMF), CSL coherent motion, 65–71 general formalism, 65–71 one dimensional spatial modulation, 71–72, 72f time-dependent longitudinal field, 65, 65f types, 65 Spin resonance, CSL ESR spectrum, 45–46 Fourier coefficients, 45–46 incommensurate-to-commensurate (IC-C) phase transition, 47–48 Lame´ equation, 115–116 resonance energy level distribution, 46–47, 47f Spin-torque transfer, sliding CSL band-splitting structure, 88, 89f Boltzmann and Gilbert relaxations, 84–85, 86f equations of motion, 78–82, 80f nonequilibrium state spin accumulation and depletion, 82–84, 85f Langreth’s method, 123–124 Schwinger–Keldysh formalism, 120–123 sliding conductivity, 85–88, 87f 467 Subject Index s-polarization, 230–231 SPR See Surface plasmon resonance (SPR) Stereolithography (SL), 217–219 SThM-FMR See Scanning thermal microscopy ferromagnetic resonance (SThM-FMR) STM See Scanning tunneling microscopy (STM) Stoner–Wohlfarth (SW) model, 311–314, 314f, 341–344, 348–349, 351, 368–369, 369f Superconducting quantum interference device (SQUID) blind method, 367 cobalt nanoparticle, 368–369, 368f cold mode method, 366, 367f difficulties, 365–366 electron beam lithography, 364, 365f Josephson junctions, 364 macroscopic quantum tunneling (MQT), 366 nanoparticle positioning, 365 Ne´el–Brown model, 369 Stoner–Wohlfarth model, 368–369, 369f switching current vs magnetization reversal, 312, 365–366 Superparamagnetism, 341 Superprisms, 289 Surface-enhanced Raman scattering (SERS), 169–171, 170t Surface plasmon resonance (SPR), 133, 152 SW model See Stoner–Wohlfarth (SW) model Symmetric helimagnets, 4–5, 4f T Template-based method, 144–145, 144f Tetragonal helimagnet, 7–8, 8f, 106 3D printing, 217–219 Time-dependent magnetic field, sliding CSL AC magnetic field, 53–54, 54f background spin current, 62–64 Dirac’s prescription, 55–64 D€ orring–Becker–Kittel mechanism, 59–60 equations of motion, 50–52 linear momentum and dynamical instability, 56–58 magnon current, 60–62 rapid switching, 52–53, 53f spin transport problem, 58–59 Tollens reaction, 145–146 Total-field/scattered-field (TF/SF) technique, 266 TPL microscopy See Two-photon luminescence (TPL) microscopy Transformation optics (TO), 251–252 Transmission electron microscopy, CSL Fresnel technique, 37–38 Heaviside’s step function, 36 magnetic phase shift, 35–37 magnetic vector potential, 35–37 signal spatial profile, 37–38, 38f Transverse spin accumulation, 76 Transverse surface anisotropy (TSA) model, 318–319, 318f Trigonal helimagnet, 7–8, 8f, 106 TSA model See Transverse surface anisotropy (TSA) model Two-photon luminescence (TPL) microscopy, 173–174 U Umklapp scattering, 77, 90–92 Uniaxial perfectly matched layer (UPML), 261–262 Unpolarized elastic neutron scattering, 40–41 V Vat photopolymerization, 217–219 Vector network analyzer ferromagnetic resonance (VNA-FMR), 392–394, 393f VNA-FMR See Vector network analyzer ferromagnetic resonance (VNAFMR) W Watson’s integral, 316–317 Weakly confined CSL resonant dynamics CSL sliding Lagrangian, 105–106 equation of motion (EOM), 105–106 pinning potential, 103–105 vs strong pinning, 105–106 468 Subject Index Co nanoparticles, 388–389, 389f experimental setup, 382–383, 383f Fe nanoparticles, 388–391, 389f Landau flux closure structure, 385–388, 387f magnetic anisotropy energy, 390–391 spiral spin structure, 389–390, 390f vortex magnetic structure, 385–388 Wigner–Seitz primitive unit cell, 237–238, 238f, 241–243 X XMCD See X-ray magnetic circular dichroism (XMCD) X-PEEM See X-ray photoemission electron microscopy (X-PEEM) X-ray magnetic circular dichroism (XMCD) construction of, 385 orbital and spin magnetic moments, 385 principles, 383–385, 384f synchrotron sources, 382 XAS, 385, 386f X-ray photoemission electron microscopy (X-PEEM) Y Yoshimori’s type structures, Z Zubarev’s method See Nonequilibrium statistical operator (NSO) approach ... our great pleasure to present the 66th edition of Solid State Physics The vision statement for this series has not changed since its inception in 1955, and Solid State Physics continues to provide... Coupling of the CSL with Itinerant Electrons 8.1 Gauge Choice and One-Particle Spectrum Solid State Physics, Volume 66 ISSN 0081-1947 http://dx.doi.org/10.1016/bs.ssp.2015.05.001 # 2015 Elsevier Inc... areas associated with solid state physics has grown enormously, and it is clear that boundaries have gone well beyond what was once, traditionally, understood as solid state Indeed, research