Low-Dimensional Magnetism PDF
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Low-Dimensional Magnetism Low-Dimensional Magnetism A.N. Vasiliev O.S. Volkova E.A. Zvereva M.M. Markina Translated from Russian by V.E. Riecansky CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2019 by CISP CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Printed on acid-free paper International Standard Book Number-13: 978-0-367-25535-0 (Hardback) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. 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Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Library of Congress Cataloging‑in‑Publication Data Names: Vasiliev, A. N. (Alexander N.), author. Title: Low-dimensional magnetism / A.N. Vasiliev [and three others]. Description: Boca Raton : CRC Press, Taylor & Francis Group, 2019. | Includes bibliographical references and index. Identifiers: LCCN 2019021450 | ISBN 9780367255350 (hardback : alk. paper) Subjects: LCSH: Magnetism. | Magnets. Classification: LCC QC753.2 .L69 2019 | DDC 620.1/1297--dc23 LC record available at https://lccn.loc.gov/2019021450 Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com Contents Introduction vii 1. Magnetic clusters 1 1.1. Dimers 1 1.1.1. Spin gap in cesium divanadate 3 1.1.2. Mineral urusovite 4 1.1.3. Copper trifluoroacetate 9 1.2. Trimers 15 1.2.1. Trimers of octahedra in rubidium–copper diphosphate 18 1.2.2. Trimer plaquettes in sodium–copper germanate 24 1.3. Tetramers 28 1.4. Bose–Einstein condensation of magnons 33 1.4.1. Pigment of the Han Dynasty 34 1.4.2. Barium–vanadium disilicate 35 2. Quasi-one dimensional magnetics 42 2.1. Homogeneous chain of half-integer spins 42 2.1.1. Rubidium–copper molybdate 44 2.1.2. Vanadyl diacetate 45 2.2. A homogeneous chain with competing interactions 54 2.2.1. Lithium–copper zirconate 56 2.2.2. Isostructural cuprates of lithium and sodium 58 2.2.3. Rubidium–copper–aluminium phosphate 66 2.2.4. Cesium–copper vanadium-diphosphate 72 2.2.5. Bismuth–iron selenite–oxochloride 78 2.3. Alternating chain of half-integer spins 83 2.4. A homogeneous chain of integer spins 88 2.5. Spin–Peierls transition 97 2.6. Orbital mechanism of dimerization of the spin chain 101 3. Spin ladders 106 3.1. Spin ladders with an odd number of legs: 106 3.2. Spin ladders with an even number of legs:a spin liquid with an energy gap in the spectrum of magnetic excitations 108 3.3. Charge mechanism of dimerization of the spin ladder 112 Contents 3.4. Combinations of spin chains and spin ladders 115 3.5. Frame structures 117 4. Quasi-two dimensional magnets with a square lattice 124 4.1. Quantum ground state 124 4.2. The Berezinsky–Kosterlitz–Thouless transition 126 4.3. Manganese chromate 129 5. Quasi-two dimensional magnetics with a triangular lattice 138 5.1. Geometrical frustration 138 5.1.1. Lithium–nickel tellurate 142 5.1.2. Barium–cobalt antimonide 147 5.1.3. Delafossites 149 5.2. BKT transition in two-dimensional magnetic materials with a triangular lattice 151 5.2.1. Chiral and non-chiral polymorphs of manganese antimonate 153 5.2.2. Lithium–iron antimonate 167 6. Quasi-two dimensional magnets with a honeycomb magnetic lattice 178 6.1. Frustration due to the competition of exchange interactions 178 6.2. Kitaev model 181 6.3. Experimental realization of Kitaev’s model 182 6.4. BKT transition in the honeycomb lattice 190 6.5. Antimonates and tellurates of transition metals 192 6.5.1. Nickel antimonates 201 6.5.2. Cobalt antimonates 211 7. Quasi-two-dimensional magnets with triangular motifs in the structure 219 7.1. Frustration of exchange interactions in the lattice of kagome and in diamond chains 219 7.1.1. Herbertsmithite and vésigniéite 221 7.1.2. The combination of kagome and triangular layers in quasi-2D cobaltites 223 7.1.3. Langasites 237 7.1.4. Dugganites 248 7.2. Plateau of magnetization in the lattice of diamond chains 257 7.3. Shastry–Sutherland lattice 266 7.4. Potassium carbonate–manganese vanadate 270 7.5. Sodium–nickel phosphate hydroxide 275 Conclusion 283 References 285 Index 301 Introduction The key to understanding the fundamental properties of matter is at low temperatures. Under the conditions where thermal oscillations do not conceal low-energy interactions, a field of quantum cooperative phenomena that have no analogs in classical physics opens up. It is these phenomena – superconductivity, exotic magnetism, spin and charge density waves, Bose–Einstein condensation – that are relevant in the physics of the condensed state. Most clearly, these effects are manifested in compounds where magnetoactive ions form objects or clusters of reduced dimensionality, such as dimers, chains, ladders and layers. The work on the study of the physical properties of new magnetic materials is aimed at understanding the most common effects and interactions that form the quantum ground states of matter. Quantum cooperative phenomena form a special branch of condensed matter physics. It is the quantum aspects in the behaviour of matter ‘quantum entanglement’, spin-polarized transport, exotic superconductivity – that are at the base or are supposed to be used in the most advanced technologies. Magnetism and superconductivity, considered antipodes for a long time, reveal common features in objects that were previously outside the field of view of theorists and experimenters. Actually, the detection of high-temperature superconductivity in complex oxides of transition metals, which initially are antiferromagnetic insulators, completely changed the vector of the development of solid state physics. Interest began to attract the so-called ‘new magnetic substances’, i.e., substances with a reduced dimensionality of the magnetic subsystem and the frustration of the exchange interaction. It became clear that in some of these systems the ground state of matter is the spin liquid, and the properties of this state and its elementary excitations are close to those of the electron liquid in superconductors. viii Introduction As a result of the investigation of the first high-temperature superconductors – copper-based complex oxides – it was found that along with the interaction of the conduction electrons with the lattice, an important part in the formation of the superconducting state belongs to the magnetic subsystem. New high-temperature superconductors – pnictides and iron chalcogenides – also exhibit unusual magnetic properties at high temperatures. This magnetism, unlike the ‘classical’ magnetism of iron, has a number of principal features, which explains its modern classification as ‘new magnetism’. Low-dimensional magnetism is most clearly manifested in frustrated systems, when the formation of the long- range magnetic order is difficult or impossible. In this case, the scale of the exchange magnetic interaction can turn out to be large not only at nitrogen but also at room temperature. In such a situation, magnetism and superconductivity not only compete but also ‘support’ each other. It is important to note that studies in the field of low-dimensional magnetism are aimed not only at increasing the functional characteristics of magnetic materials, but also form new directions in the physics of condensed matter. First of all, this is the physics of spin liquids, non-collinear and exotic magnetic structures, topological insulators, multiferroelectricity, and quantum superposition of states. The existing problems in the physics of low-dimensional magnetism are associated with the search for and improvement of the functional parameters of new magnetic compounds, bringing their characteristics in line with the requirements of innovative technologies. To achieve the stated goal, specific tasks are being solved worldwide in parallel to establish the dominant mechanisms of magnetic interaction, to determine the parameters of the exchange interaction in new magnetic materials. As a result of a comprehensive study of these materials, priority data were obtained on the main mechanism of the ground state formation, phase diagrams were constructed and the characteristics of the magnetic subsystem were determined in the formation of the long-range magnetic order. The obtained data stimulated the development of theoretical ideas about the structure of matter. In magnetic systems where one or several directions lack or have an infinitely small exchange magnetic interaction, the description of physical phenomena is possible only in the language of quantum mechanics. In the simplest case, such a system is two localized magnetic moments. To describe the exchange magnetic interaction in Introduction ix the dimer, the Hamiltonian proposed by Heisenberg in 1928 [1] and the total spin operators Ŝ and Ŝ for centres 1 and 2, formulated in 1 2 the work of Dirac and van Vleck in the 30s, were used [2]: HˆHeisenberg =−JSˆSˆ , 1 2 where J is the exchange interaction constant. An increase in the number of localized magnetic centres can lead to models of clusters, chains, ladders, two-dimensional layers. In many-particle systems, the Heisenberg Hamiltonian takes into account only the interactions between nearest neighbors 〈i,j〉: HˆHeisenberg =−∑J SˆSˆ . ij i j i,j To date, a number of theoretical models have been developed, taking into account the anisotropic terms of the exchange interaction and interactions with the next neighbours, which often leads to different solutions for the quantum ground state of low-dimensional systems. Of greatest interest are situations where it is possible to find experimental confirmation of predicted phenomena in real objects. Magnetism of compounds with reduced dimensionality of the spin subsystem – zero-dimensional 0D, one-dimensional 1D or two-dimensional 2D – is one of the most interesting and rapidly developing areas in the physics of condensed matter. In low- dimensional magnets, the quantum essence of matter manifests itself most clearly, and it becomes possible to observe a variety of quantum cooperative effects. In 1D, and even more so in the 2D situation, the influence of anisotropy and frustration increases significantly, which considerably complicates the mechanisms of achieving the quantum ground state and enriches the phase diversity on the magnetic phase diagram. A large number of new fascinating phenomena are observed in low-dimensional magnets, including cascades of spin-reorientation transitions, magnetization plateaux and instabilities induced by the magnetic field of the spin subsystem. Quasi-1D and quasi- 2D frustrated systems are often ordered into non-collinear, incommensurable and canted magnetic structures. Such spin states are often devoid of the inversion centre and can have a finite ferroelectric polarization.
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