On the complexity of spinels: Magnetic, electronic, and polar ground states

Vladimir Tsurkan, Hans-Albrecht Krug von Nidda, Joachim Deisenhofer, Peter Lunkenheimer, Alois Loidl
2021 Physics reports  
This review aims to summarize more than 100 years of research on spinel compounds, mainly focusing on the progress in understanding their magnetic, electronic, and polar properties during the last two decades. Over the years, more than 200 different spinels, with the general formula AB2X4, were identified or synthesized in polycrystalline or single-crystalline form. Many spinel compounds are magnetic insulators or semiconductors; however, a number of spinel-type metals exists including
more » ... including superconductors and some rare examples of d-derived heavy-fermion compounds. In the early days, they gained importance as ferrimagnetic or even ferromagnetic insulators with relatively high saturation magnetization and high ordering temperatures, with magnetite being the first magnetic mineral known to mankind. From a technological point of view, spinel-type ferrites with the combination of high electrical resistance, large magnetization, and high magnetic ordering temperature made them promising candidates for many applications. However, spinels are also known as beautiful gemstones, with the famous "Black Prince's Ruby" in the front centre of the Imperial State Crown. In addition, spinels are important for the earth tectonics, and the detection of magnetite in a Martian meteorite even led to the speculation of life on Mars. However, most importantly in the perspective of this review, spinels played an outstanding role in the development of concepts of magnetism, in testing and verifying the fundamentals of magnetic exchange, in understanding orbital-ordering and chargeordering phenomena including metal-to-insulator transitions, in developing the concepts of magnetic frustration, in establishing the importance of spin-lattice coupling, and in many other aspects. The still mysterious Verwey transition in magnetite was one of the very first illuminating examples of this complexity, which results from the fact that some ions can exist in different valence states in spinels, even at a given sublattice. In addition, the A-site as well as the B-site cations in the spinel structure form lattices prone to strong frustration effects resulting in exotic ground-state properties. The A-site ions are arranged in a diamond lattice. This bipartite lattice shows highly unusual ground states due to bond-order frustration, with a strength depending on the ratio of inter-to intra-sublattice exchange interactions of the two interpenetrating face-centred cubic lattices. The occurrence of a spiral spin-liquid state in some spinels is an enlightening example. Very recently, even a meron (half-skyrmion) spin structure was identified in MnSc2S4 at moderate external magnetic fields. In case the A-site cation is J o u r n a l P r e -p r o o f Journal Pre-proof 2 Jahn-Teller active, additional entanglements of spin and orbital degrees of freedom appear, which can give rise to a spin-orbital liquid or an orbital glass state. In systems with such a strong entanglement, the occurrence of a new class of excitations -spinorbitons -has been reported. The B-site cations form a pyrochlore lattice, one of the strongest contenders of frustration in three dimensions. A highly degenerate ground state with residual zero-point entropy and short-range spin ordering according to the ice rules is one of the fascinating consequences, which is known already for more than 50 years. At low temperatures, in B-site spinels the occurrence of spin molecules has been reported, strongly coupled spin entities, e.g., hexamers, with accompanying exotic excitations. A spin-driven Jahn-Teller effect is a further possibility to release magnetic frustration. This phenomenon has been tested in detail in a variety of spinel compounds. In addition, in spinels with both cation lattices carrying magnetic moments, competing magnetic exchange interactions become important, yielding ground states like the timehonoured triangular Yafet-Kittel structure. Very recently, it was found that under external magnetic fields this triangular structure evolves into very complex spin orders, which can be mapped on spin super-liquid and spin super-solid phases. In addition, due to magnetic frustration, competing interactions, and coupling to the lattice, very robust magnetization plateaus appear in a variety of spinel compounds as function of an external magnetic field. Furthermore, spinels gained considerable importance in elucidating the complex physics driven by the interplay of spin, charge, orbital, and lattice degrees of freedom in materials with partly filled d shells. This entanglement of the internal degrees of freedom supports an exceptionally rich variety of phase transitions and complex ground states, in many cases with emerging functionalities. It also makes these materials extremely susceptible to temperature, pressure, or external magnetic and electric fields, an important prerequisite to realize technological applications. Finally, yet importantly, there exists a long-standing dispute about the possibility of a polar ground state in spinels, despite their reported overall cubic symmetry. Indeed, recently a number of multiferroic spinels were identified, including multiferroic spin super-liquid and spin super-solid phases. The spinels also belong to the rare examples of multiferroics, where vector chirality alone drives long-range ferroelectric order. In addition, a variety of spinel compounds were investigated up to very high pressures up to 40 GPa and in high magnetic fields up to 100 T, revealing complex (p,T) and (H,T)-phase diagrams. Corresponding author: alois.loidl@physik.uni-augsburg.de J o u r n a l P r e -p r o o f Journal Pre-proof 3 Keywords Spinel compounds, spinels, spinel thin films, magnetism, magnetic frustration, ferroelectricity, multiferroicity, metal-to-insulator transition, Jahn-Teller effect, heavyfermions, colossal magneto resistance Highlights  Ground-breaking concepts in magnetism were developed conceptually using spinel compounds  Spinels are prototypical examples of strongly frustrated magnets  Ferroelectricity and multiferroicity in spinels result from very different mechanisms  Spinels represent outstanding examples of metal-to-insulator transitions and charge order  Examples of well-established d-derived heavy-fermion behaviour J o u r n a l P r e -p r o o f Journal Pre-proof Acknowledgments 115 References 117 J o u r n a l P r e -p r o o f Journal Pre-proof J o u r n a l P r e -p r o o f Journal Pre-proof rubies, the most prominent example being the Black Prince's Ruby in the front centre of the British Imperial State crown, which later was identified as spinel ( Fig. 1) . In 1779 they were named by Jean Demeste, derived from the Latin word "spinella", which means little thorn and refers to their sharp octahedral crystal shapes. The determination of the crystal structure of spinels by Bragg [6] and independently by Nishikawa [7] was one of the very early accomplishments of crystal-structure analysis. The spinel structure is cubic with a large unit cell containing 8 formula units, e.g., 8 A, 16 B and 32 X atoms. In most cases the anions X can be approximated by cubic close packing, while the cations fill certain interstices as described above. Later it was found that in addition to the normal variant of the spinel structure AB2X4 and inverted structure of B(AB)X4 can exist, which was termed inverse spinel [8] . Due to their remarkable electrical and magnetic properties, spinels are of considerable technological interest, specifically due to the need of insulating or semiconducting ferromagnets. One should have in mind that permanent magnetism was first observed in lodestone, naturally magnetized pieces of the mineral magnetite, Fe3O4, which was also called the Magnesian stone, resulting in the nomenclature of the word magnetism. The development of models and theories of magnetism are closely related to magnetit, starting more than 2500 years ago. Early on it was recognized that lodestone can attract pieces of iron and the Greek philosopher Thales of Milet (625 -545 BC) probably provided the first scientific discussion of lodestone. About 585 B.C. he stated, as witnessed by Aristotle [9] that loadstone attracts iron because it has a soul. Since then, this material fascinated countless scientists. In ancient China a variety of compass needles were invented, either using southpointing chariots, two-wheeled vehicles that carried a movable pointer to indicate the south, no matter how the chariot turned, or south-pointing spoons (see Fig. 2 ). Each time the spoon manufactured from naturally occurring magnetite is spun on a non-magnetic plate, it comes to rest with its neck pointing south [10] . Even nowadays non-metallic ferromagnetic (FM) materials are rare and interestingly, many spinels are insulating ferrimagnets, in many cases with relatively high saturation magnetization and high magnetic-ordering temperatures. Hence, an early fundamental characterization of structural, electrical and magnetic properties of various spinels, which will be discussed later in this review, has been performed in the Natuurkundig Laboratorium of the J o u r n a l P r e -p r o o f Journal Pre-proof 7 N. V. Philips Gloeilampenfabrieken in the Netherlands. Before World War II, Verwey and coworkers performed the most pertinent work on spinel compounds, later on, in the early fifties, this work was continued by Gorter, Lotgering, Romeijn, and coworkers to name a few. Fig. 3. Life on Mars. Martian meteorite ALH84001 containing magnetite microcrystals. This meteorite was found in the Alan Hill ice field (Antarctica). It was speculated that these magnetite crystals were produced in ancient times by magneto-receptive Martian bacteria (see text). Image credit: NASA/JSC/Stanford University Spinels, in addition of being beautiful gemstones and utilized in early compass needles, probably are one of the most important classes of minerals concerning technological applications and an amazing variety of other aspects. Because of their multiple compositions, electron configurations, and valence states, spinels have demonstrated remarkable magnetic, optical, electrical, and catalytic properties. Potential applications of magnetic properties of spinels containing 3d magnetic ions like Fe, Co, Cr, or Ni, can be found in information technology, in biotechnology, and in applications for spintronic devices. Ferrites, which mainly are ceramic and composite spinel compounds, already play an important technological role because of their interesting electrical, magnetic, and dielectric properties. The combinations of high electrical resistivity, low eddy currents, low dielectric losses, high saturation magnetization, and high permeabilities, together with high Curie temperatures, good chemical stability, and mechanical compactness makes them extremely useful for applications such as rod antennas, electronic devices, sensors, memory devices, data storage, or tele-communication. The optical properties of transparent or semi-transparent spinels were utilized for photo-luminescence as well as for magneto-optical recording. Furthermore, the electrical characteristics of spinels have allowed their application in the field of energystorage materials, such as super-capacitors. In addition, they also have been widely used as electrodes in Li-ion batteries, and last not least, their controllable composition, structure, valence, and morphology have made them suitable as catalysts in a variety of chemical reactions. A detailed overview over possible applications of spinel compounds is given in Ref. [2] . Quite general, magnetic insulators are promising materials for spintronics, spincaloritronics, nonvolatile memories, and microwave applications. Magnetic insulating heterostructures in form of single crystalline thin films, grown on suitable substrates, are important and even critical for realizing quality interfaces for these applications. However, magnetic and insulating single crystalline materials with a Curie temperature well above room temperature are rare. In these introductory remarks, we tried to document that spinel ferrites J o u r n a l P r e -p r o o f Journal Pre-proof 8 constitute a class of materials that were recognized having significant potential for these applications and FM as well as ferrimagnetic (FiM) insulating spinel oxides were synthesized as thin films or heterostructures and were carefully characterized. To document this broad and important field of applications, we include a chapter dealing with synthesis and possible applications of spinel-derived thin films (Chapter 3.5.). An informative review on epitaxiallygrown spinel ferrite thin films has been provided earlier by Y. Suzuki [11] . Spinels are also of utmost importance for the earth tectonics: spinel compounds form the so-called transition region between the lower and the outer mantle of the earth structure, extending roughly from 450 to 600 km below the earth's surface, forming an important zone for seismic activities of the earth. In this regime of the earth's mantle, the spinel-olivine transition is important in driving the plate tectonics. Finally, spinels in form of magnetite or greigite are believed to act as magnetic receptors in magneto-receptive species, including honeybees, birds, sea turtles, salmons and a variety of phytoplankton and bacteria [12] . The identification of magnetite in the Martian meteorite ALH84001 (Fig. 3) , which was collected in the Antarctica in Alan Hills ice field, even led to the conclusion of life on mars [13] by correlating the found magnetite micro crystals with the activity of magneto-receptive bacteria. Regarding this Mars meteorite discovery, the possibility of life on mars was even mentioned in a press-release satement by US president Clinton on August 7, 1996. It should be noticed that scientifically this claim lateron was strongly challenged. During the past decades, magnetic nanoparticles have attracted continuous interest and were intensively explored and studied for both, basic research phenomena and potential applications in a variety of different fields ranging from data storage, energy storage, spintronics, and magneto-optical devices, to contrast agents for magnetic resonance imaging. Quite generally, they also are of interest in biomedicine in areas like medical diagnostics, drug delivery, and magneto-hyperthermia, in environmental purification, and in catalysis, to name a few. In first respect, nano-structured materials exhibit unique magnetic features depending on nanoscale size modulation and grain-boundary engineering. When compared to the bulk, nanomaterials are strongly dependent on the microcrystalline grain size and on distribution, thickness, and chemical constitution of the grain boundaries. In addition to grain size and size dispersion, materials engineering regarding core-shell design, shape, morphology, crystallinity, and surface decoration opens up a variety of prospects for potential application and innovation. Over the years, spinel-type ferrite nanoparticles played an important role, specifically with respect to cobalt ferrites and magnetite. The physics and chemistry of magnetic nanoparticles constitute an entire new research field on its own and it is impossible to review their synthesis, structural and magnetic characterization, and possible applications in this review, which mainly focuses on the basic principles of magnetism of mostly single-crystalline spinel compounds. The interested reader is referred to reviews on the importance of magnetic nanoparticles in general [14, 15, 16] and specifically on work dealing with spinel-type nanoparticles and nanocomposites [17, 18, 19, 20] , which only provide a very first look into this recent universe of nanoscience. Here we mainly will focus on magnetic, electric, and multiferroic (MF) properties of spinel compounds, where in the context of this work, multiferroicity denotes the coexistence of magnetic and polar order. As will be documented in the course of this work, the complex and partly exotic magnetism of many spinel compounds results from magnetic frustration and competing interactions. As mentioned above, the pyrochlore network formed by the B sites can give rise to strong magnetic frustration in three dimensions (3D) [21] . In the bipartite diamond lattice of the A sites, depending on the magnetic exchange interactions within or inbetween the two sublattices, again strong spin-frustration effects can occur [22] . The importance of frustration and competing interactions was recognized early on in studying the magnetic ground-state properties of spinels. In B-site spinels the magnetic moments occupy J o u r n a l P r e -p r o o f Journal Pre-proof 9 the corners of a pyrochlore lattice and are coupled by antiferromagnetic (AFM) exchange. In the seminal work on antiferromagnetism in spinels, Anderson [23] noticed that in such a lattice nearest-neighbour forces alone can never lead to long-range order. However, it is possible to achieve essentially perfect short-range order while maintaining a finite entropy. Down to the lowest temperatures, there will be residual zero-point entropy and Anderson noticed the closeness of this problem to the ice-rules developed by Pauling for hydrogen bonds in water. In spinels were both, A and B sites are occupied by magnetic moments exhibiting dominant AFM exchange between the A and B cations, Yafet and Kittel [24] predicted a resulting triangular spin structure, the famous Yafet-Kittel (YK) spin structure, which later indeed was identified in MnCr2S4 [25] . In the more recent past, it has been recognized that as function of an external magnetic field, the spin structure of this compound exhibits unusual magnetic states, like an ultra-robust magnetization plateau or a spin supersolid phase [26] . In a number of spinel compounds a variety of complex spin configurations driven by magnetic frustration, e.g., composite spin degrees of freedom forming spin loops in ZnCr2O4 [27] or the formation of a spin-spiral liquid state in MnSc2S4 [22, 28] , were identified. As will be documented in Chapter 3.2., also the orbital degrees of freedom play an important role in the physics of spinel compounds, ranging from the cooperative Jahn-Teller effect to an orbital-ordering driven dimensional reduction in spinel systems like MgTi2O4 or CuIr2S4. Such orbital effects are described in detail in a recent review by Khomskii and Streltsov [29 ]. In the late fifties and early sixties, the magnetism of spinels was important for developing theories predicting the ground state properties of Néel type, YK like, or spiral spin structures. In addition, spinel compounds gained considerable importance in elucidating the complex physics driven by the interplay of spin, charge, orbital, and lattice degrees of freedom in materials with partly filled d or f shells. This entanglement of the internal degrees of freedom supports an exceptionally rich variety of phase transitions and complex ground states, in many cases with emerging functionalities. It also makes these materials extremely susceptible to temperature, pressure, or external magnetic and electric fields an important prerequisite to achieve technological functionality. The first illuminating example of a strong entanglement of spin, charge, and lattice degrees of freedom was given by Verwey [30] by detecting a "mysterious" transition in magnetite close to 120 K, where the resistivity increases by two orders of magnitude. Despite enormous attempts in recent times, the microscopic nature of this metal-to-insulator transition (MIT), nowadays called Verwey transition, so far has not been completely unravelled. Other examples of the coupling of internal degrees of freedom in spinel compounds are, e.g., colossal magneto-resistance (CMR) effects in FeCr2S4 [31], the occurrence of multiferroicity in CdCr2S4 [32], CoCr2S4 [33], FeCr2S4 [34], and MnCr2S4 [35], structural phase transitions induced via a spin-Jahn-Teller effect [36,37,38] in a number of chromite spinels, and the formation of iridium octamers and spin dimerization at the charge ordering MIT in CuIr2S4 [39]. The complexity of the orbital physics in some of the spinel compounds is best documented by the observation of a spin-orbital-liquid (SOL) state in FeSc2S4 [40] and the report on the observation of an orbital glass in FeCr2S4 [41]. In this review, we mainly will summarize 20 years of research guided by the authors of this work. Of course, we always will refer to important results in the field: Since the crystallographic studies of Bragg [6] more than 100 years ago, outstanding solid-state researchers including a number of Nobel-prize winners have contributed to this fascinating spinel research important for physics, chemistry, material science, geology, and biology. There exist a number of reviews on spinel compounds. First, one has to mention the overview over structural, magnetic, and electrical properties of different classes of spinel compounds mainly published as Philips Research Reports and summarizing the detailed work performed in the Philips Research Laboratories, mainly by Romeijn [42, 43] , Gorter [44, 45, 46, 47, 48] , Lotgering [49, 50] and Blasse [51] . A review focusing on structural details of spinels was J o u r n a l P r e -p r o o f Journal Pre-proof 10 provided by Hill and coworkers [1]. Grimes [52] gave a short review with a specific look on their potential industrial applications. Takagi and Niitaka [53] described magnetic properties of spinels, mainly with respect to magnetic frustration effects. A review focusing on physicochemical aspects of spinels was published by Zhao et al. [2] and Liu et al. [54] summarized the possible use of spinel compounds as multivalent battery cathodes. J o u r n a l P r e -p r o o f Journal Pre-proof 11 2. General properties of spinel compounds Synthesis and single-crystal growth High-purity spinels can be synthesized in ceramic form and as single crystals by a variety of methods. Many of the preparation routes are given in the original literature cited in this review. A detailed summary of synthesis methods of spinel compounds is given in [2] . Here we only want to mention the extreme sensitivity of many physical properties on minor changes of impurities or defects introduced by the different synthesis routes. One illuminating example is FeSc2S4: There exist contrasting experimental results on spin and orbital order (OO) in this compound [40, 55, 56] . It was unambiguously shown that the magnetic order in some samples result from excess Fe forming a second phase corresponding to a vacancyordered iron sulphide with composition close to the 5C polytype of pyrrhotite (Fe9S10) [55] . It is also now well established that the growth of thio-spinels by chemical transport reaction using chlorine as transport agent, by minor substitution of chlorine ions for sulphur, results in an enhanced defect-induced conductivity and in distinct differences of magnetocapacitive effects. This has been documented in full detail comparing single crystals grown by chemical transport using chlorine as well as bromine as transport agents and comparing the results to stoichiometric ceramic samples [57]. Structural properties Compounds with the general formula AB2X4 having the same structure as the mineral MgAl2O4, which originally was referred to as red gemstone, are named normal spinels. Starting with the mineral spinel MgAl2O4 one easily can substitute Mg 2+ and Al 3+ with a wide range of cations with different valences. Hence, the general chemical formula for spinel compounds can be written as A 2+ B2 3+ X4 2− or A 4+ B2 2+ X4 2− where the A sites in most cases include ions with valence 2+ and 4+, while the B sites host divalent or trivalent cations. The anions X are oxygen or chalcogenide ions. Spinels with X = S usually are called thiospinels. Bragg [6] and Nishikawa [7] determined the spinel structure, which belongs to the space group Oh 7 ( 3 ) or number 227 in the International Tables. The "normal" spinel structure, which is reproduced from Ref. [58] and shown in Fig. 4 , is based on a cubic close-packed fcc structure of O 2− anions introducing two types of interstitial positions. There are 64 tetrahedral and 32 octahedral interstices, of which 8 respectively 16 are occupied by cations. The former is the A site, which is tetrahedrally coordinated, the latter correspond to the octahedral B sites. Each anion in the spinel structure is surrounded by one A and one B cation. The distribution of the cations, divalent and trivalent, among the two sites A, B may vary between normal spinel (e.g., divalent on A site, trivalent on B site) and inverse spinel (e.g., divalent and trivalent on B site, trivalent on A site). In the spinel structure, the cations occupy the special positions 8a and 16d. The anions occupy the general positions 32e, which for their complete description require an additional parameter, generally designated as fractional coordinate x (please note that in many publications the fractional coordinate is called u parameter, but in this review the symbol u is used as generalized exchange parameter), in oxide spinels sometimes known as the oxygen and in thiospinels known as the sulphur parameter. If the origin of the unit cell is taken at the centre of symmetry, then for x = 0.250 the anions form an exactly cubic closepacked array and define a regular tetrahedral coordination polyhedron about the 8a sites (point symmetry 43m) and a regular octahedron about the 16d sites (m3m). J o u r n a l P r e -p r o o f Journal Pre-proof J o u r n a l P r e -p r o o f Journal Pre-proof J o u r n a l P r e -p r o o f Journal Pre-proof With respect to the spinel compounds reviewed in this work, Fe 2+ at the tetrahedral A site is of prime importance. As outlined above, the energy-gain of a structural transition driven by orbital-ordering phenomena is small and hence the transition energies are low. In FeCr2S4 the JT transition appears at 10 K and can easily be identified via heat-capacity experiments or via ultrasound investigations [71] . In FeSc2S4, the JT energy is too low, OO is J o u r n a l P r e -p r o o f Journal Pre-proof T  = C / (T +  CW ) f = | CW | / T N paramagnet  CW  J S 2 J o u r n a l P r e -p r o o f Journal Pre-proof This effective exchange parameter u represents the relative strength of the two nearestneighbour BB and AB interactions multiplied by the appropriate spin values S. For u u0 = 8/9, the collinear Néel configuration, where all A-site spins are parallel to each other and antiparallel to the B-site moments, is the stable ground state. For u u0, it was shown that a J o u r n a l P r e -p r o o f Journal Pre-proof Later on, Ederer and Komelj [103] presented first-principle LSDA+U calculations of the magnetic coupling constants in the spinel magnets CoCr2O4 and MnCr2O4. One of the main conclusions of their work is that the coupling between the A-site cations, neglected in the classical LKDM theory, is of appreciable size in both compounds and definitely not J o u r n a l P r e -p r o o f Journal Pre-proof J o u r n a l P r e -p r o o f Journal Pre-proof J o u r n a l P r e -p r o o f Journal Pre-proof J o u r n a l P r e -p r o o f Journal Pre-proof J o u r n a l P r e -p r o o f Journal Pre-proof J o u r n a l P r e -p r o o f Journal Pre-proof J o u r n a l P r e -p r o o f Journal Pre-proof J o u r n a l P r e -p r o o f Journal Pre-proof J o u r n a l P r e -p r o o f Journal Pre-proof J o u r n a l P r e -p r o o f Journal Pre-proof Recently, the (H,T)-phase diagram of MnCr2S4 was investigated utilizing fielddependent sound velocity and pulsed magnetization experiments in external magnetic fields up to 60 T [26]. Some representative results are shown in Fig. 45 . In Fig. 45 (a) the fielddependence of the magnetization M as measured at 1.5 K is shown as blue solid line. After a strong increase of M due to domain-orientation effects below 1 T, M(H) reveals a continuous increase up to ~ 11 T, where obviously spin-reorientation occurs, visible via a significant change of slope (labelled Nr. 1). This field regime characterizes the YK phase, which obviously extends up to 11 T. On increasing magnetic fields, the angle between the J o u r n a l P r e -p r o o f Journal Pre-proof Staring with the pioneering work by Kondo et al. [422], a series of NMR experiments was published in LiV2O4, as well as in zinc and titanium doped samples, mainly utilizing 7 Li and 51 V line width, Knight shift, and spin-lattice relaxation [431, 432, 433, 434, 435, 436] . The temperature dependence of the linewidth usually is determined by an inhomogeneous broadening due to local magnetic fields and often can be taken as measure of homogeneity J o u r n a l P r e -p r o o f Journal Pre-proof J o u r n a l P r e -p r o o f Journal Pre-proof 116 and Zn based selenides, as compared to sulphide and oxide spinels was attributed to steric effects, which are proposed to be the driving force of the cubic-to-monoclinic transformation. J o u r n a l P r e -p r o o f Journal Pre-proof J o u r n a l P r e -p r o o f Journal Pre-proof J o u r n a l P r e -p r o o f Journal Pre-proof
doi:10.1016/j.physrep.2021.04.002 fatcat:eyzqdjztbfhihj5uiqd4vf66ym