5.1. Definition of magnetic materials
The symmetry concerns for magnetism are slightly more complex than those for ferroelectricity. Magnetic materials violate time reversal symmetry, but are invariant under spatial inversion, in other words, when magnetic moments are present in a crystal the antisymmetry operator must also be present. The 32 classical crystallographic point groups do not have the antisymmetry operator and hence cannot fully describe the symmetry of magnetic crystals. Symmetry analysis reveals 122 total magnetic space groups of which only 31 can support ferromagnetism [60,160]. A material is said to be a ferromagnet when there is long range, parallel alignment of the atomic moments resulting in a spontaneous net magnetization even in the absence of an external field. Ferromagnetic materials undergo a phase transition from a high-temperature phase that does not have a macroscopic magnetization (atomic moments are randomly aligned resulting in a paramagnetic phase) to a low-temperature phase that does.
Fig. 17. Ferroelectric memories. (a) Cross-sectional scanning electron microscopy image of an actual ferroelectric memory device. (b) Schematic illustration of the FeRAM module showing all the layers needed for the creation of this device. (c) Artist’s depiction of a FeRAM device, courtesy of Texas Instruments and Ramtron.
There are other types of magnetism including antiferromagnetism (atomic moments are aligned antiparallel) and ferrimagnetism (dipoles align antiparallel, but one subset of dipoles is larger than the other resulting in a net moment). The theory of magnetism is a rich field, the details of which are beyond the scope of this treatment, but is built upon the idea of the quantum mechanical exchange energy which causes electrons with parallel spins and therefore parallel moments to have lower energy then spins with antiparallel spin. Inherent to this concept is the presence of unpaired electrons in a material. Thus a requirement for magnetism in transition metals is a partially filled d (or f) orbital [62]. Magnetic materials find pervasive use in all walks of life, from information technologies (storage, sensing and communications) to health sciences (e.g., cancer treatment) and beyond.
5.2. Brief history of magnetic oxides
Unfortunately, a brief history of the role of oxide materials in the development of the greater field of magnetism is a rather difficult undertaking. In fact, the Greek philosopher Thales of Miletus, who was alive from approximately 634 to 546 BC, is thought to be the first person to describe magnetism after observing the attraction of iron by the mineral magnetite (Fe3O4). From that day forward, magnetic oxides were an essential key to the advances in many fields, including navigation, power production, and more. For a complete history of magnetism in materials see Ref.[161]. For the sake of brevity, we focus here solely on magnetic oxides. According to Pliny the Elder’s (23–79 AD) Historia Naturalis the name ‘‘magnet’’ came from a shepherd called Magnes, who likely originated from a town called Magnesia in the Greek Empire where nearby ore deposits were naturally magnetized and found that iron nailed shoes or iron-tipped canes stuck to the ground [162]. Beginning in the 1500s, the name lodestone (in old English ‘‘lode’’ is the word for lead) began being used to describe such iron-oxide (Fe3O4) based magnetic ore and also saw these materials make significant impact in the realm of navigation (although the earliest reports of lodestone-based direction pointers come from China between 221 and 206 BC and the earliest use of such pointers for navigation come from late 11th or early 12th century China and in Europe sometime in the late 12th century) [162]. Scholarly pursuit of the field of magnetism also began in 1269 when French crusader and scholar Peter Peregrinus (Pierre Pe`lerin de Maricourt) wrote a lengthy letter describing loadstone and how one could create useful devices from it. But real systematic studies of magnetism came only in 1600 with the publication of William Gilbert’s De Magnete – in which Gilbert proposed the presence of magnetic poles on the Earth which would only be confirmed in Carl Friedrich Gauss in 1835 [161]. Through 1819, only magnetization produced by lodestone was known, but the work of Hans Christian Oersted, Jean-Baptiste Biot, Felix Savart, and Andre´ Marie Ampe`re in the late
1700s and early 1800s lead to the delineation of classical electromagnetism and the work of Michael Faraday and James Clerk Maxwell to the field of modern magnetism[162].
The early 20th century saw much work on the development of an atom-based model for magnetic phenomena including the work of Pierre Weiss who introduced the theory of ferromagnetism based on a molecular field concept[163]and Paul Langevin who explained the ferromagnetic-paramagnetic transition observed by Pierre Curie. In 1928, Heisenberg formulated a spin-dependent model for the exchange interaction that allowed Weiss’ molecular field to be interpreted as having its origin in the exchange interaction [164] and marked the birth of modern magnetism theory. This, in turn, made it possible for the field of magnetic oxides to develop at a feverish pace. Of fundamental importance to this early work was a series of publications by Lois Ne´el who developed the idea of antiferromagnetism[165]. By the late 1950s a rapid expansion of technology, especially high-frequency devices, stimulated rapid research in ferromagnetic oxides and Smit and Wijn in their book on ferrites note that in 1959 the properties of magnetic oxides were better understood that the properties of metallic ferromagnets[166].
5.3. Common types of magnetism in transition metal oxides
Throughout the 20th century a number of fundamental ideas of coupling in oxide materials were developed that explained how indirect exchange – mediated through non-magnetic ions like oxygen – give rise to the effects seen in oxide materials including superexchange, double exchange, and RKKY coupling.
5.3.1. Superexchange
Superexchange gets its name from the fact that it extends the normally very short-range exchange interaction to a longer range [162]. The idea that exchange could be mediated by an intermediate, non-magnetic atom was put forth in 1934 [167]
and the theory was formally developed by Anderson in 1950[168].
Superexchange is an important effect in ionic solids where 3d and 2p orbitals of transition metals and oxygen or fluorine atoms interact and it describes, through a simple valence bonding argument, how antiferromagnetic ordering occurs. Fig. 18(a) shows a schematic illustration of the superexchange effect in LaMnO3. Each of the Mn3+ions contains four 3d electrons and when these atoms bond, with some degree of covalency, with a mediating O2anion the only way hybridization can take place is with the donation of electrons from the oxygen to the manganese ions. By Hund’s rule, the spin of the electron donated to the left Mn-ion must be the same as the spins in the Mn-ion, which leaves an electron of the opposite spin in the oxygen p-orbital to be donated to the right Mn-ion. By the same argument, this bonding can only take place if the spins of the right Mn-ion are opposite to the left Mn-ion. What occurs in the end is that the
Fig. 18. Magnetic coupling in oxides. Schematic illustrations of (a) superexchange, (b) double exchange, and (c) RKKY coupling.
oxygen-mediate bonding leads to a collective antiparallel spin alignment of nearest neighbor Mn-ions.
5.3.2. Double exchange
Double exchange, which was first proposed by Zener in 1951 [169], begins to change the nature of magnetic coupling in materials like LaMnO3if one dopes in materials like Sr or Ca on the La-site, creating a mixed valence compound. Double exchange describes the magneto-conductive properties of these mixed valence compounds and delineates the mechanism for hopping of an electron from one site to another through the mediating oxygen atom. Again, because the O2ion has full p-orbitals, the movement from one ion through O2to another ion is done in two steps. Let us explore this idea for the case of the widely studied oxide ferromagnet La0.7Sr0.3MnO3which has Mn3+and Mn4+ions (Fig. 18(b)). Assuming the ligand field is relatively small and we fill the 3d orbitals following Hund’s rules the Mn3+and Mn4+ions are filled with electrons as shown with the dark blue arrows. In such materials, electron conduction proceeds by this double step process by which one of the electrons on the Mn-sites jumps back and forth across the oxygen. The electron is thus delocalized over the entire M–O–M group and the metal atoms are said to be of mixed valency. This is aided by the fact that spin-flips are not allowed in electron hopping processes and thus it is more energetically favorable if the magnetic structure of the two Mn-ions is identical; therefore, ferromagnetic alignment of moments is achieved.
5.3.3. RKKY coupling
The final type of exchange we will discuss here is RKKY exchange. Unlike the previous two examples, RKKY exchange (named after the work of Ruderman and Kittel[170], Kasuya[171], and Yosida [172]) is not based on the relationship between bonding and magnetism, but instead is the concept that a local moment can induce a spin polarization in a surrounding conduction electron sea. Such studies showed that the spin polarization of the conduction electrons oscillates in sign as a function of distance from the localized moment and this spin information can be carried over relatively long distances (Fig. 18(c)). Such coupling has been proposed to explain coupling in dilute magnetic semiconductor systems where magnetic ions are too far apart to interact with each other directly and the sign of this coupling depends on the distance between magnetic ions.
5.4. Modern magnetic oxides
Since 1950 a number of magnetic oxides have dominated the landscape of solid state physics research. In this section we will investigate two of these systems: ferrites and manganites.
5.4.1. Ferrites
The ferrites include the entire family of Fe-containing oxides such as the spinels (AFe2O4), garnets (AFe5O12), hexaferrites (AFe12O19), and orthoferrites (RFeO3, where R is one or more of the rare-earth elements). In the past, ferrites have been used in applications as diverse as transformer cores[173]and microwave magnetic devices[174]to magneto-optic data storage materials [175]and flux guides and sensors[176]. In this section we will focus primarily on spinel ferrites as they have received much recent attention. The recent push with these materials has been to create high quality thin films of these complex materials to enable better understanding of structure–property relationships and to enable the creation of novel new devices based on the intriguing properties of these materials. Considerable effort has been undertaken to achieve bulk-like properties in ferrite thin films and because of the rather complex chemical nature of these
materials careful control of strain effects, growth conditions, and post-annealing treatments are needed to achieve high quality samples. In fact, recent theoretical studies of the spinal materials in particular point to the delicate nature of these materials as the electronic structure is strongly dependent on cationic order/
disorder in these materials[177]. In some cases, a half-metallic character is expect and this, combined with the high Curie temperatures of these materials, makes them of great interest as electrodes in magnetic tunnel junctions [178] and spintronic devices. Additionally, the spinel ferrites have become quite popular in the study of composite multiferroic heterostructures.
Here we will investigate briefly the work on epitaxial films of the materials Fe3O4, NiFe2O4, and CoFe2O4. For a detailed review of spinel ferrite thin films see Ref.[179].
5.4.1.1. Fe3O4. Fe3O4 or magnetite is one of the oldest known magnetic materials and has been extensively studied over the years[180], yet it has enjoyed a rejuvenation in interest driven by the possibility of utilizing the half-metallic nature of the material in magnetic multilayer devices. Band structure calculations suggest that the majority spin electrons in Fe3O4 are semicon-ducting with a sizable energy-gap and that the minority spins are metallic in nature [181]. Magnetite is the half-metal with the highest known Curie temperature (858 K). Fe3O4has also been studied because it undergoes an interesting first-order metal–
insulator phase transition known as the Verwey transition[182]
at 120 K where the Fe3O4undergoes a structural transition from cubic to monoclinic [183] structure that is accompanied by a dramatic increase in resistivity[184]and decrease in magnetic moment. Strong debate about the fundamental mechanisms for this transition are still ongoing – especially discussion of the localized or delocalized nature of 3d electrons in this system [162].
Driven by the desire to incorporate this material into magnetic devices, epitaxial growth of Fe3O4has been achieved on (0 0 1) MgO substrates using a wide variety of deposition techniques.
Pulsed laser deposition growth with substrate temperature between 200 and 500 8C has yielded good, bulk-like properties [185–190]. A comparison of magnetic properties for bulk Fe3O4
and various thin films is shown inFig. 19(a) and shows that careful attention must be given to materials synthesis to achieve bulk-like properties in these films. Detailed studies of magnetoresistance [187,191,192]as well as the study of magnetic devices, such as magnetic tunnel junctions based on Fe3O4 [193–196]have also been completed.
5.4.1.2. NiFe2O4. Nickel ferrite or NiFe2O4, unlike Fe3O4, has a sizeable gap in the majority spins and a smaller one in the minority spins resulting in an insulating state. Epitaxial films of NiFe2O4
have been grown via pulsed laser deposition on c-plane sapphire at 900 8C and high oxygen pressures[197]. Other routes to create high quality films of NiFe2O4 include the use of buffered spinel substrates[198]. Studies of such epitaxial films, however, revealed anomalous magnetic behavior including diminished magnetiza-tion and an anomalous approach to saturamagnetiza-tion for films grown in the range of 400–700 8C[199]. Over the years it has been shown that post-growth anneals at 1000 8C reduced the anomalous magnetic behavior of these NiFe2O4films (Fig. 19(b)). More recent investigations into ultrathin films of NiFe2O4 on SrTiO3 (0 0 1) substrates has shown that, under the appropriate growth conditions, epitaxial stabilization leads to the formation of a spinel phase with distinctly different magnetic and electronic properties – including magnetic moments that are enhanced by nearly 250% and metallic character – that results from an anomalous distribution of Fe and Ni cations among the A and B sites that occurs during non-equilibrium growth[200].
5.4.1.3. CoFe2O4. As is typically the case with these spinel ferrites, the properties of CoFe2O4 thin films were found to be quite different from bulk properties. Studies have found that the microstructure of the film significantly impacts the magnetic properties. Thin films have been grown on a wide array of substrates, including MgO (1 0 0)[201,202]and spinal structure substrates such as MgAl2O4(1 1 0) and CoCr2O4-buffered MgAl2O4
substrates which allowed researchers to create films free of anti-phase boundaries and led to the connection of cation distribution and lattice distortions to anomalous magnetic behavior [203].
More recently CoFe2O4has also been used a tunnel barrier layer in conjunction with a Fe3O4 electrode and interesting exchange spring magnet behavior arises at the interface between these two materials[204].
5.4.1.4. BaFe12O19. Barium hexaferrite is by far the most widely studied hexaferrite material. It is an attractive material for use in non-reciprocal devices that operate at microwave and millimeter wavelengths, it possesses a relatively high dielectric constant and a large uniaxial magnetocrystalline anisotropy. Thin films of BaFe12O19have been studied for nearly 30 years and have been grown via sputtering [205], metal-organic chemical vapor deposition[206], liquid phase epitaxy[207], pulsed laser deposi-tion[208,209]and more. The effect of epitaxial thin film strain on the structural and magnetic properties of BaFe12O19thin films has also been studied [210]. With appropriate thin film strain conditions and annealing procedures, narrow line widths of only 37 Oe were measured in ferromagnetic resonance (FMR)—the presence of strain was found to broaden the resonance absorption.
More recently, the most narrow FMR line-widths of only 27 Oe at 60.3 GHz have been measured in PLD grown films[211], exotic domain wall superconductivity has been observed in super-conductor-BaFe12O19heterostructures [212], epitaxial thin films have been achieved on SiC substrates[213], and much more. The hexaferrites continue to remain an exciting, technologically relevant materials system worthy of future study.
5.4.1.5. RFeO3. The rare-earth orthoferrites (RFeO3, including R = La, Nd, Sm, Gd, Dy, Er, Yb, and Y) have a crystalline structure which is close to that of the perovskites. In general the orthoferrites are antiferromagnetic due to the antiparallel alignment of the magnetic moments of the Fe sublattices; however, weak ferro-magnetism due to canting has been observed in some phases [214,215]. The rare-earth orthoferrites show strong uniaxial anisotropy and, beginning in the 1960s, were studied as candidate
materials for bubble memories[216]. Future development of these materials, however, was hindered because it was difficult to make high quality thin films of these materials. In the 1990s work on thin films of these materials accelerated as thin films of YFeO3[217], DyFeO3, GdFeO3, SmFeO3 [218], and others were produced. In recent years, interesting new properties have been reported in these materials, including relaxor-like dielectric behavior and weak ferromagnetism in YFeO3 materials[219]. In the end, the orthoferrites stand to experience a renewed period of interest as the search for magnetooptically active materials used in the near infrared that can be directly grown on Si or InP becomes increasingly important. The current standard materials, the garnets, possess a lattice parameter more than twice that of Si [220]rendering growth difficult.
5.4.2. Manganites
In the last 20 years, two classes of materials have defined and dominated the landscape of condensed matter physics study of oxide materials – high-temperature superconductivity in doped cuprates and, the focus of this section, colossal magnetoresistance (CMR) materials like doped manganites. As there exist a number of excellent and detailed reviews on CMR materials (see Refs.[221–
225]), and in the essence of space, we give here only a limited overview of these intriguing materials and thin film aspects of this rich field.
5.4.2.1. Manganite physics. Although present in many metal oxides, the manganite materials are especially interesting since they present large electronic correlations leading to a strong competition between lattice, charge, spin, and orbital degrees of freedom. These manganese-based perovskite oxides exhibit half-metallic character and CMR response rendering them as the ideal materials to develop novel concepts of oxide-electronic devices and for the study of fundamental physical interactions. Due to the close similarity between kinetic energy of charge carriers and Coulomb repulsion, tiny perturbations caused by small changes in temperature, magnetic or electric fields, strain and so forth may drastically modify the magnetic and transport properties of these materials.
5.4.2.2. Thin film manganites. In 1993, the modern rejuvenation of interest in manganite materials came with the discovery of the so-called CMR effect in thin films of La0.67Ca0.33MnO3 where a magnetoresistance effect gave rise to a change in resistance of the material 3 orders of magnitude larger than that observed in giant Fig. 19. Magnetism in spinel thin films. (a) Magnetization measured in the film plane for Fe3O4films grown on Si (1 0 0) and MgO (1 0 0) and (1 1 0). The crystallographic direction along which the field is applied is indicated beside each film in the figure. The magnetization axis is offset to facilitate observation of the high field data. (Adapted from Ref.[186].) (b) Magnetization of as-grown and post-annealed NiFe2O4thin films demonstrates the lengths to which on must go to achieve bulk-like properties in spinel films. (Adapted from Ref.[199].)
magnetoresistance (GMR) materials[226]. Since that time, thin film strain has been shown to be very important in determining the properties of manganite thin films.
Despite nearly 15 years of intensive study on these materials, continued research brings to light new insights on the physics of
Despite nearly 15 years of intensive study on these materials, continued research brings to light new insights on the physics of