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Metal oxide structure, crystal chemistry, and magnetic properties
Metal oxide structure, crystal chemistry, and magnetic properties
16
Vladimir V. Srdic´ 1, Zeljka Cvejic´ 2, Marija Milanovic´ 1, Goran Stojanovic´ 3 and Srdjan Rakic´ 2 1 Department of Materials Engineering, Faculty of Technology Novi Sad, University of Novi Sad, Novi Sad, Serbia, 2Department of Physics, Faculty of Sciences, University of Novi Sad, Novi Sad, Serbia, 3Department of Microelectronics, Faculty of Technical Sciences, University of Novi Sad, Novi Sad, Serbia
Magnetism is a force we experience every day without really being aware of it. The scientific interest in magnetism and magnetic oxides has been changed during years. The first magnetic material to be discovered was lodestone, which is better known today as magnetite (Fe3O4). The word magnet comes from the Greek word magnes, which itself may derive from the ancient colony of Magnesia (in Turkey) [1]. Magnetite was mined in Magnesia 2500 years ago. In its naturally occurring state lodestone is permanently magnetized and is the most magnetic mineral. The strange power of lodestone was well known in ancient times. Socrates (B400 BC) dangled iron rings beneath a piece of lodestone and found that the lodestone enabled the rings to attract other rings [1]. Even earlier (B2600 BC), a Chinese legend tells of the Emperor Hwang-ti being guided into battle through a dense fog by means of a small pivoting figure with a piece of lodestone embedded in its outstretched arm. The figure always pointed south and was probably the first compass. Commercial interest in ceramic magnets started in the early 1930s with a Japanese patent describing application of copper and cobalt ferrites. The first Golden age of magnetic oxides was the 1950s and the 1960s, when the ferrites were explored and their properties optimized. Discovery of the first family of ferromagnetic (FM) oxides with a higher magnetization than ferrimagnets also dates from this period. A new age for magnetic oxides recently started, where multifunctionality, control of defects, interfaces, and thin-film device structures are the new challenges.
16.1
Magnetic elements/ions
The macroscopic magnetic properties of materials are a consequence of magnetic moments associated with individual electrons (i.e., its orbital motion around the nucleus and spinning around the spin axis). Some of these concepts are relatively Magnetic, Ferroelectric, and Multiferroic Metal Oxides. DOI: http://dx.doi.org/10.1016/B978-0-12-811180-2.00016-5 Copyright © 2018 Elsevier Inc. All rights reserved.
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Magnetic, Ferroelectric, and Multiferroic Metal Oxides
complex and involve some quantum-mechanical principles, and will not be analyzed here. It is well known that in each individual atom, orbital moments of some electron pairs cancel each other; this also holds for the spin moments (i.e., an electron with spin-up will cancel the one with spin-down). The net magnetic moment, then, for an atom is just the sum of the magnetic moments of each of the constituent electrons, including both orbital and spin contributions, taking into account moment cancellation. The strength of spinorbit coupling is a key factor in determining the extent to which the orbital moment contributes to the magnetic properties and conversely, to what extent the spins interact with the lattice [2]. For an atom having completely filled electron shells or subshells, when all electrons are considered, there is a total cancellation of both orbital and spin moments. Thus, materials composed of atoms (or ions) having completely filled electron shells are not capable of being permanently magnetized. From this point of view transitional elements with the unfilled inner shells (while electrons occupying outer shells participate in chemical bonding) are responsible for a variety of magnetic properties because of the magnetic moments carried by their unpaired spins. The types of magnetism include diamagnetism, paramagnetism, and ferromagnetism (in addition, antiferromagnetism and ferrimagnetism are considered to be subclasses of ferromagnetism). All materials exhibit at least one of these types, and their behavior depends on the response of electron and atomic magnetic dipoles to the application of an externally applied magnetic field. Thus, most of the elements in the periodic table are diamagnetic and paramagnetic (Fig. 16.1), but exceptions are some d- and f-elements (transitional metals) from which most magnetic effects originate [3]. Characteristics of the d-elements are d-orbitals with up to five pairs of electrons and a relatively small difference in the energy of the different d-orbital electrons. This causes the number of electrons participating in chemical bonding to vary and results
Figure 16.1 Magnetic behavior of elements in the periodic table.
Metal oxide structure, crystal chemistry, and magnetic properties
315
in the same element exhibiting two or more oxidation states. The 3d-elements important for magnetism are iron, cobalt, and nickel, which are FM; and chromium, which is antiferromagnetic (AFM). Their ions, together with some ions of other d-elements (such as Fe21, Fe31, Co21, Ni21, Mn21, Mn31, Cr21, Cr31, V21, and V31) have high magnetic moments capable of producing strong spontaneous magnetism, when they are in sufficient densities, which allows exchange coupling to order magnetically as ferro-, ferri-, or antiferromagnets. However, the ions of the first two 3d-elements (Sc and Ti) are generally paramagnetic. The ions from 4d- and 5d-groups resemble the 3d-series in magnetic properties and can be used as alternatives for them in certain cases. However, in general these ions have not attracted much interest for their magnetic properties because their compounds do not exhibit strong spontaneous magnetic properties. The second most important transition group from a magnetic standpoint has an unfilled 4f-shell. The f-orbitals can contain up to seven pairs of electrons that are less chemically active, causing high chemical similarity between f-elements. They are generally paramagnetic and only gadolinium shows FM behavior. An important distinction between the 4f-ions and those of the 3d-ion group is the shielding of the 4f-shell inside the 5s and 5p outer shells of the xenon core. In other words, the magnetically active electrons are buried inside the xenon core and are therefore shielded from electrostatic fields of the molecular environment. As a result, the ions act largely independent of one another, even in highly concentrated compounds, and are generally paramagnetic because the multiple lobes of the 4f-orbital wave functions do not extend far enough for covalent bonding and magnetic exchange to be significant [2].
16.2
Magnetic oxides
Oxides are ionic compounds where small, highly charged metal cations are embedded in a lattice of oxygen anions. The O22 has its stable 2p6 closed-shell configura˚ . The oxide crystal structure is based on a tion with an ionic radius rO 5 1.40 A close-pack array of oxygen anions, with metal cations occupying interstitial sites. The close-packed arrays are usually face-centered-cubic and hexagonal-close packed. They both accommodate smaller metal cations in octahedral and tetrahedral interstices. The smaller one is the tetrahedral site with four oxygen neighbors, which can accommodate, without distortion, a spherical cation of radius ˚ . The larger one is the octahedral site with six oxygen neighbors that rtet 5 0.32 A ˚ . There are two tetrahecan accommodate a spherical cation of radius roct 5 0.58 A dral interstices and one octahedral interstice for each oxygen in dense-packed lattices, so that only a fraction of them can ever be filled. The ionic radii of common 3d-cations and others that may be incorporated in oxide structures are listed in Table 16.1. Due to the small size the tetrahedral site can accommodate only smaller cations (Mg21, Zn21, Al21, Fe31, or Si41) with some distortion of the tetragonal ˚ ) can occupy the octahedral sites (Fig. 16.2), site. The larger cations (0.550.70 A 21 while the cations such as Sr or La31, having ionic radii comparable to that of
Table 16.1
Ionic radii of cations in oxides
4-fold coordination
˚] d [A
6-fold coordination
˚] d [A
6-fold coordination
˚] d [A
12-fold coordination
˚] d [A
Mg21 Zn21 Al31 Fe31 Si41
0.53 0.60 0.42 0.52 0.40
Cr41 Mn41 Al31 Mn21 Fe21 Co21 Ni21
0.55 0.53 0.54 0.83 0.78 (0.61) 0.75 (0.65) 0.69
Ti31 V31 Cr31 Mn31 Fe31 Co31 Ni31
0.67 0.64 0.62 0.65 0.64 0.61 (0.56) 0.60
Ca21 Sr21 Ba21 Pb21 Y31 La31 Gd31
1.34 1.44 1.61 1.49 1.19 1.36 1.22
Values in brackets indicate a low-spin state.
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Figure 16.2 Octahedral site in a cubic symmetry (A) and its common distortions (B, C, D) [2].
oxygen, are incorporated within a 12-fold oxygen coordination [3]. Distortion of the lattice (Fig. 16.2) and presence of a variety of structural defects such as point defects (oxygen or metal vacancies and metal interstities) are usually following the incorporation of different cations in structure of metal oxides [2].
16.3
Magnetism of magnetic oxides
The magnetism of free atoms and ions can be associated with angular momentum. The electron has an intrinsic spin angular momentum s and intrinsic magnetic moment μs that can be expressed as μs 5 2 s μB/h , where μB 5 1/ 2 e h /me is the Bohr magneton. This quantity is the fundamental unit of atomic-scale magnetism. If a spinless electron is orbiting a nucleus in a state of angular momentum l, it behaves like a current loop with a magnetic moment μs 5 l μB/h . When electron spin and orbital angular momentum are taken into account, the magnetic moment of each electron in an isolated atom becomes μe 5 (2 s 1 l) μB/h . The Zeeman Hamiltonian for the electron in magnetic field B is represented by: HZ 52μ B 5
μB ðlz 1 2sz Þ ¯h
(16.1)
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Magnetic, Ferroelectric, and Multiferroic Metal Oxides
with the B-field taken along with the z-direction. The total magnetic moment for an N-electron atom becomes: μe 5
N μB X 2 ð2si 1 li Þ or ¯h i51
μ 5 2 ð2S 1 LÞ
μB ¯h
(16.2)
where S5
N X
si
and
i51
L5
N X
li
(16.3)
i51
S and L are total spin and orbital angular momentum, respectively. If J represents total angular momentum (i.e., J 5 S 1 L), the previous equation for total magnetic moment can be written as μ 5 (J 1 L) μB/h . The total magnetic moment of the ion or atom is then μ 5 g μB J, where Lande’s g-factor is given by: gL 5 1 1
J ðJ 1 1Þ 1 SðS 1 1Þ 2 LðL 1 1Þ 2J ðJ 1 1Þ
(16.4)
The Zeeman and spinorbit interaction are represented, respectively, by the Hamiltonians: HZ 5 2μ B 5
μB ðLz 1 2Sz Þ B ¯h
and
Hso 5 2λ L~ S~
(16.5)
Where λ is constant, L~ is the total orbital angular momentum, S~ is the spin angular momentum, and B-field is taken along with z-direction. For a free atom or ion, the angular momentum and spin of each electron is arranged according to the semiempirical Hund’s rules. Following these simple rules, it is then possible to calculate the magnetic moment without resorting to any particular knowledge of the individual atomic species for nearly all atoms. If we have a multielectron ion, the angular momentum of any filled (1s, 2s, 2p, 3s, 3p. . .) orbital is zero, because both the spin and orbital moments cancel each other. The net magnetic moment of atoms arises from unpaired electrons (Table 16.2). When the ions are placed in a crystalline environment of oxygen neighbors there are some drastic changes. For 3d- and 4d-ions crystalfield interaction is stronger than spinorbit interaction. For 4f-ions the crystal field is screened by the large filled 5s- and 5p-shells and it can influence on Hamiltonians only as a perturbation correction. For 3d-ions J is not a good quantum number, and from a magnetic viewpoint the 3d-ions may be represented as spin-only ions. The quenching of the orbital angular momentum in 3d-metal solids is due to the interaction of the d-orbitals with the crystal field formed by oxygen atoms. The crystal field leads to quenching by favoring the formation of superposition states with zero net magnetic moment.
Table 16.2
The ground state and magnetic moments for 3d ions [4]
Arrangements of electron in d-orbitals
T
S
L
J
gL
µJ/µB 5 gJ[J(J 1 1)]1/2
µS/µB 5 2[S(S 1 1)]1/2
3d1Ti31 V41 3d2V31 Cr41 3d3Cr31 Mn41 3d4Cr21 Mn31 3d5Mn21 Fe31 3d6Fe21 Co31 3d7Co21 Ni31 3d8Ni21 Co11 3d9Cu21 Ni11
2
1/2 1 3/2 2 5/2 2 3/2 1 1/2
2 3 3 2 0 2 3 3 2
3/2 2 3/2 0 5/2 4 9/2 4 5/2
4/5 2/3 2/5 2 3/2 4/3 5/4 6/5
1.55 1.63 0.77 0 5.92 6.70 6.54 5.59 3.55
1.73 2.83 3.87 4.90 5.92 4.90 3.87 2.83 1.73
m m m m m km km km km
m m m m m km km km
D3/2 F2 4 F3/2 5 D0 6 S5/2 5 D4 4 F9/2 3 F4 2 D5/2 3
m m m m m km km
m m m m m km
m m m m m
320
Magnetic, Ferroelectric, and Multiferroic Metal Oxides
In order to explain how the crystal field influence magnetic properties of metal oxides we can start with the one-electron model [5,6], which is good approximation for d1, d4, d6, and d9-ions. Depending on the type of the crystalline coordination of the metal ions (cubic, tetrahedral, octahedral coordination), d-orbitals are splitting in a different way (Fig. 16.3). For example, the splitting of d-orbitals is reversed in octahedral and in tetrahedral coordination. At octahedral sites t2g (dxy, dyz, and dxz)
Figure 16.3 Schematic crystal field splitting and occupations of Co and Fe 3d-electrons in tetrahedral and octahedral coordination environments and energy levels of the d-orbitals common stereochemistries. (A) Co (II) tetrahedral d7; (B) Co (III) octahedral d9; (C) Fe (III) tetrahedral d5; (D) Fe (II) octahedral d9.
Metal oxide structure, crystal chemistry, and magnetic properties
321
orbitals have lower energy compared to energy of eg (dx2-y2, dz2) orbitals. The magnitude of ligand field effect Δoct is of the order 1 eV. Contrary, the t2g orbitals at tetrahedral sites are those that possess the higher energy in the ligand field. It should be noted that the Jahn-Teller effect is strong for d4- and d9-ions in octahedral coordination (Mn21, Cu21) and for d1- and d6-ions in tetrahedral coordination (V41, Co31). In the one-electron model, orbitals with the lowest energy are filled first, in a way that five k (spin-down) lie above the five m (spin-up) by amount JH (the on-site exchange energy B1.5 eV). The low-spin state is observed at ions for which the values of Δoct is higher than the values of JH. In that case t2g orbitals filled before eg orbitals. The low-spin state, for example for the Co21 ion, is S 5 1/2 and the high-spin state is S 5 3/2. Exchange interaction is a symmetry-constrained Coulomb interaction that has the effect of coupling electronic spins. Intraionic exchange, also known as JH or Hund’s first rule exchange, couples electrons in partially filled orbitals in a way to maximize the total spin. This further means that the m orbitals are filled first, before beginning to fill the k orbitals. If the energy splitting caused by the crystal field is higher than the intraionic exchange, the ion enters in a low-spin state. The Heisenberg interaction (direct exchange) is described by Hamiltonian moments: HZ 5 2
1 ^ Sj ^ Jij Si ¯h
(16.6)
and is often used to describe the interaction between individual moments. If Jij is positive, the parallel alignment is favored and material is FM. If Jij is negative, the spin orientation is antiparallel and material is AFM. In this case the moments align when the overall moment is zero. There are many possible AFM alignments. If the magnitudes of the moments in an antiferromagnet are not equal (nonzero net magnetization), the material is known as a ferrimagnet. The mechanism that causes the order alignment is strong and temperature-dependent. Direct exchange is a consequence of the Pauli exclusion principle. Consider two atoms, each with a single electron. When the atoms are close enough, their orbitals interact, electrons can move between the atoms, and according to the Pauli principle the total wave function must be antisymmetric. Having in mind that the symmetry of the total wave function is a product of the spatial wave function and spin wave function, one of them must be antisymmetric. An antisymmetric spatial wave function lowers the Coulomb energy of the system, which favors a FM (symmetric) spin wave function. Indirect (super) exchange is responsible for the AFM order in metal oxides such as NiO, CaMnO3, and Fe2O3. The 3d-orbitals of transition metal ion overlap with the p-orbitals of the oxygen. This overlap stabilizes an AFM coupling between the 3d-orbitals if the angle between metal and bridging oxygen is close to 180 degrees. The coupling becomes FM if the angle decreases toward 90 degrees. The occupancy and degeneracy of 3d-orbitals determine the strength and sign of superexchange, and possible cases are given in the GoodenoughKanamari rules (later
322
Magnetic, Ferroelectric, and Multiferroic Metal Oxides
reformulated by Anderson) [7,8]. Superexchange interactions occur in insulators and make use of nonmagnetic ions to assist spin interactions between two magnetic ions. Also, this type of magnetic interaction is more commonly AFM than FM. RudermanKittelKasuyaYosida (RKKY) exchange and superexchange both involve spin interactions accommodated by intermediate atoms. RKKY exchange occurs in metals, where the medium for the exchange interactions is the conduction electrons. The strength and sign of RKKY interaction varies with the distance, so it causes FM or AFM ordering. Double exchange involves the transfer of an electron between two magnetic ions with different valences, and leads to metallic FM properties. For this type of magnetic interaction a mixed-valence configuration is required as in the case in mixedvalance manganite (La1xAxMnO3, A 5 Ba, Ca, Sr). Electrons from an oxygen orbital can hop to a Mn41 ion, and its vacant orbital then can be filled by an electron from Mn31. The electron has moved between the neighboring metal ions, retaining its spin. The electron movement from one ion to another is “easier” when spin direction does not have to be changed (Hund’s rules). Another well-known double-exchange pair is Fe31 and Fe21 ions. As Table 16.2 shows, Fe31 ion has md5 configuration, and d-orbital is half-filled with spin parallel alignment. Fe21 has six electrons and the sixth kd electron is placed at the bottom of a t2g band (if the ion is octahedrally coordinated by oxygen) from where it can jump directly from one d5 ion to another. There is clearly a difference between superexchange and double exchange. In a superexchange the occupancy of d orbital of two metal ions remains the same, so electrons are not actually moving between two metal ions. In double exchange electrons are hopping between ions of different valance states via the intermediate oxygen. The antisymmetric part of exchange interaction between spins, characterized by a vector parameter D and called DzyaloshinskiiMoriya interaction, is given by: HDM 5 2D
X ^ 3 SjÞ ^ ðSi
(16.7)
i;j
It gives rise to canted antiferromagnetismin iron oxides [9,10]. AFM iron oxides possessing weak ferromagnetism, such as iron rare-earth orthoferrites RFeO3 (R represents rare-earth element) and hematite α-Fe2O3, are natural candidates for observing superexchange interactions. The presence of the DzyaloshinskiiMoriya antisymmetric exchange interaction leads to a slight canting of the spins from the antiparallel orientation by an angle of 0.51 degrees.
16.3.1 Magnetism of metal-oxide nanoparticles The magnetic properties of nanomaterials such as the Curie (TC) or Ne´el (TN) temperatures, and the coercivity field (HC), can be significantly different than those of a bulk specimen [11]. It is well-known fact that a bulk FM material is composed of
Metal oxide structure, crystal chemistry, and magnetic properties
323
small regions called magnetic domains. The formation and orientation of these magnetic domains are the result of the balance of several energy terms: the exchange energy, magnetocrystalline anisotropy, and the magnetostatic (or dipolar) energy [12]. The first term, exchange energy, tries to align all magnetic moments in the same direction. The second one, magnetocrystalline anisotropy, tries to orient magnetic moments along specific directions, while the third term, magnetostatic energy, tries to eliminate the magnetization in the material. In each domain the magnetic moments of atoms are aligned in one direction giving a net magnetization of each domain. The directions of magnetizations of the domains are different. The net magnetization is obtained by adding the magnetization of individual domains. It was found that magnetic domains in FM material have a minimum critical size (B100 nm), below which the magnetic material cannot split up further into domains and are called single-domain particles [13,14]. Thus, super paramagnetism emerges when the system is composed of small particles called independent crystallites (Fig. 16.4). Since the particles are small, the direction of each magnetic moment is not rigidly confined. The crystalline anisotropy energy decreases as the size of the crystallite is reduced, and as a consequence of that each crystallite magnetic moment is relatively free to move between any of the easy axes in response to an applied field. When the applied field is removed, the thermal effects rapidly destabilize any overall moment and the material starts to act like a paramagnetic. The regime of paramagnetic behavior extends from the Curie (or Ne´el) temperature down to the so-called blocking temperature TB. Thus in the superparamagnetic state, the magnetic nanoparticles behaves as a paramagnetic atom with a giant spin. At temperatures below the blocking temperature, the thermal effect becomes small and cannot cause fluctuations in the orientations of the magnetic moments of the nanoparticles; in fact they freeze in random orientations. The blocking temperature can be estimated using dc magnetization measurements. These measurements involve the measurement of magnetization as a function of temperature in two different states. The first state is called the zero-field-cooled (ZFC) state, and the
Figure 16.4 Superparamagnetic, single-domain, and multidomain magnetic regime as a function of particle size.
324
Magnetic, Ferroelectric, and Multiferroic Metal Oxides
Figure 16.5 Temperature dependence of magnetization of In-doped ZnFe2O4 obtained in zero-field cooled (ZFC) and field cooled (FC) conditions [16].
second is called the field-cooled (FC) state. The value of the blocking temperature depends on the particle size, effective anizotropy constant, applied field, and experimental measurement time. The shape of the magnetization versus temperature plots in the ZFC and FC measurements can provide qualitative information about the size distribution and the strength of interaction among the particles in the sample (Fig. 16.5) [15,16]. It should be noted that due to the fine size effect in nanomaterials, the existence of randomly oriented uncompensated surface spins, the existence of canted spins and the existence of a spin-glass-like behavior of the surface spins can significantly affect magnetic behavior of metal oxides [1719]. The total magnetization of the nanoparticle is thought to be composed of two components: a component due to the surface spins and a component due to the core of the particle. Thus, the magnetization of the magnetic nanoparticles can be modeled via a coreshell (or coresurface) magnetic model leading to another type of magnetic interaction at the interface between the core and the shell. In nanoparticles of AFM or ferrimagnetic (FIM) materials, this interaction occurs at the interface between the FM surface and the AFM (or FIM) core. The coreshell interaction is called the exchange bias or exchange coupling [20]. The exchange coupling provides an additional magnetic anisotropy to help align the ferromagnetic spins in certain directions. The exchange coupling is known to vanish above a critical temperature called the blocking temperature, but no satisfactory understanding of this interaction at the microscopic level exists. In order to obtain a satisfactory understanding of the theory of exchange bias, it is essential to understand the atomic interface structure [21].
Metal oxide structure, crystal chemistry, and magnetic properties
16.4
325
Representative structures of magnetic oxides
The most valuable structures in magnetic oxides regarding their magnetic behavior are spinel, garnet, and magnetoplumbite structure. These structures will be explained in brief in following sections.
16.4.1 Spinel structure Spinel structure most often occurs in ferrites and other binary oxides with a general chemical formula AB2O4, where usually Fe31 (ferrite) is at the position B, but also some other transition metals Cr31, Mn31, and so on. The position A is filled with a divalent cation such as Mn21, Fe21, Co21, Ni21, Cu21, Zn21, or Mg21, or sometimes with the monovalent lithium cation (Li1) or even vacancies, as long as these absences of positive charge are compensated for by additional trivalent iron cations (Fe31). The oxygen anions (O22) adopt a close-packed cubic crystal structure, while metal cations occupy two different interstitial sites: tetrahedral and octahedral. The spinel lattice cell is composed of 8 formula units that contain 32 oxygen anions, 8 tetrahedrally coordinated cations (A sublattice), and 16 cations in octahedral sites (B sublattice). The antiparallel alignment and incomplete cancellation of magnetic spins between the two sublattices A and B leads to a permanent magnetic moment (Fig. 16.6) [22,23]. The well-known ferrite that belongs to the spinel group is mineral magnetite, Fe3O4. Fe3O4 has a cubic inverse spinel structure that consists of a cubic closepacked array of oxide ions, where all the Fe21 ions occupy half of the octahedral sites and the Fe31 are split evenly across the remaining octahedral sites and the tetrahedral sites, leading to ferrimagnetism. In magnetite, the Fe21 ions may be partly or fully replaced by other divalent ions (Co, Mn, Zn, etc.), thus creating a
Figure 16.6 Unit cell and ferromagnetic ordering in spinel ferrites.
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Magnetic, Ferroelectric, and Multiferroic Metal Oxides
whole spectrum of magnetic interactions. The magnetic properties of spinels are highly sensitive to the cation distribution between two sublattices and these properties are a complex function of the total chemical composition, stoichiometry, the substitution degree of foreign ions, and inversion parameter. Weather a foreign cation substitutes for A-site or B-site iron depends upon the relative sitepreference energies. Of the ions with partially filled d-shells, crystalline fields give a strong B-site preference to ions with d3, low-spin d5 or d6, or high-spin d8 configurations. Solute cations that can replace Fe31 ions for the tetrahedral sites include Cu1, Mg21, Zn21, Cd21, Mn21, Co21, Ga31, In31, Si41, Ge41, and so on [24]. Control of cation composition and inversion is essential for spinel properties [22,25]. Substitution on A-sites: The divalent cations such as Zn21 and Cd21have a strong preference for tetrahedral A-site in spinel. Therefore, bulk ZnFe2O4 is a paramagnet that has a normal spinel structure and becomes antiferromagnetic at TN 5 10 K. However, when prepared in the form of nanoparticles, ZnFe2O4 shows some degree of inversion and different kinds of magnetic ordering connected with it [26,27]. Trivalent cations could reside at tetrahedral sites, but substitution in complete solid solution range is difficult to find. Substitution with Ga31 has shown that it is possible to place Ga31 ions only on A-sites for x , 0.3 [8]. Substitution of In31 in ZnFe2O4 gives an even smaller compositional range (x # 0.15) for exclusive A-site substitution [26,28]. These substitutions have a profound impact on magnetic properties. For example, the saturation magnetization of spinel ferrites can be greatly enhanced by partial substitution of ZnFe2O4 for NiFe2O4 or MnFe2O4. The zinc cations prefer tetrahedral coordination and force additional Fe31 onto the octahedral sites. This results in less cancellation of spins and greater saturation magnetization. Substitution on B-sites: Substitution exclusively on B-sites can be achieved with ions having formal valence ranging from I to VI [8]. FIM NiFe2O4 is a good example of the complete inverse spinel with Ni21 ions placed onto a B-site, and Fe ions distributed between tetrahedral and octahedral sites. Large cations, such as some of the rare-earth ions (e.g., Y31), almost exclusively reside on octahedral sites [23,29,30]. Substitution on both A- and B-sites: Magnesium and manganese ferrites are good examples of mixed spinel structures where substitution for iron may result in a distribution of the cations on both A- and B-sites. The physical properties of the mixed spinel structures obtained in such way vary strongly with temperature.
16.4.2 Garnet structure The structure of garnets is a cubic structure, with a general chemical formula of A3B2 (XO4)3 (A 5 Ca, Mg, Y, La, or rare earth; B 5 Al, Fe, Ga, Ge, Mn, Ni, or V; X 5 Si, Ge, Al). The A cations are placed on dodecahedral C-sites, B cations on octahedral A-sites, and X cations on tetrahedral D-sites [31] (Fig. 16.7). The most important and widely studied magnetic garnet is yttrium-iron garnet (YIG), which has the formula Y3Fe5O12, where five Fe31 ions occupy two octahedral and three
Metal oxide structure, crystal chemistry, and magnetic properties
327
Figure 16.7 Structure of an ideal garnet with a general chemical formula of A3B2(XO4)3 and illustration of the cation coordination.
tetrahedral sites, and the Y31 ions are surrounded by eight oxygen ions. The YIG unit cell is composed of 8 formula units with 160 atoms. The net magnetic moment in YIG arises from an uneven contribution from antiparallel spins; the magnetic moments of the a- and d-ions are aligned antiparallel as are those of the c- and d-ions (Fig. 16.7B). By substituting specific sites with rare-earth elements, for example, interesting magnetic properties can be obtained. Other ions of the lanthanide group can be used generously in the c-sublattice to form what amounts to a distinct set of FIM compounds. Because the ionic spins that are introduced to the c-sublattice exchange couple to the iron in the d- and a-sublattices, a wide variety of thermomagnetic, magnetoelastic, microwave, and optical properties can be created in these rare-earth iron garnets.
16.4.3 Magnetoplumbite structure Hexagonal ferrites adopt magnetoplumbite structure, which is similar to the inverse spinel but with hexagonal symmetry instead of cubic. The general formula of magnetoplumbite structure can be written as AB12O19, in which A is a divalent metal ion, such as Ba21, Pb21, or Sr21, and B is a trivalent metal ion, such as Al31, Ga31, Cr31, or Fe31. The hexagonal ferrites are all FIM materials, and their magnetic properties are intrinsically linked to their crystalline structures [32]. There are many structural forms of hexagonal ferrites such as W, X, Y, or Z type, but only M structure of hexaferrites are technically important. Barium hexaferrite (BaO 6Fe2O3) is one of the most important M-type hexaferrite magnetic materials. The crystal structure of BaFe12O19 is shown in Fig. 16.8. It can be described by a periodically stacking sequence of two basic building blocks, S and R, along the c-axis, where an asterisk indicates rotation of the blocks by 180 degrees [33]. The Fe31 ions occupy three different sites in this structure: octahedral and tetrahedral in S block and bipyramidal sites in R block [34]. Large divalent ions, such as Ba21, Pb21, or Sr21 replace an oxygen atom in R block.
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Magnetic, Ferroelectric, and Multiferroic Metal Oxides
Figure 16.8 (A) Stacking sequence in M-type hexaferrite BaFe12O19, (B) crystal structure corresponding SR layers in barium hexaferrite BaFe12O19.
16.4.4 Other common structures in magnetic oxides Besides the already-mentioned structures, magnetic oxides can adopt structures such as halite, corundum, rutile, perovskite, pyrochlore, and wurzite. These structures will be briefly explained. Halite. The halite structure can be regarded as two interpenetrating face-centered cubic sublattices, with cations and anions alternating along [100] directions. Cations are octahedrally coordinated by anions and vice versa. Since there is only one type of cation, located in crystallographically equivalent positions, in these simple oxides, in accordance with the stoichiometric composition, ferrimagnetism cannot appear. However, fundamentally ferromagnetism is possible, but it has been found only in europium oxide, EuO. Typically magnetic moments are arranged in antiferromagnetic ordering, and in a set of planes (111) cations, situated in the same plane, have parallel magnetic moments and those in adjacent planes, antiparallel magnetic moments (Fig. 16.9A). The symmetry of these “magnetic structures” is no longer cubic, since the direction [111] is perpendicular to the set of planes with ordered magnetic moments and is not equivalent to the other three directions of the space diagonals of an elementary cube. Consequently, the occurrence of antiferromagnetism is accompanied by a distortion of the structure, which reduces the symmetry to rhombohedral (MnO, FeO, NiO) or to tetragonal (CoO). The real reason for these strains is exhibited in the fact that the ions are placed in such positions in which the exchange forces, as well as other interactions, are enhanced and accordingly, the free energy decreases. In the case of the rhombohedral distortion, the decrease of the free energy is achieved by reducing or increasing the distance between adjacent planes (111). If a portion of cations of a simple oxide, such as NiO, is substituted by other cations, such as Li1cations, then the location of cations
Metal oxide structure, crystal chemistry, and magnetic properties
329
Figure 16.9 Structures of (A) NiO, (B) α-Fe2O3, (C) CrO2, and (D) perovskite (La,Ca)MnO3.
in adjacent planes (111) is often the same as the arrangement of the magnetic moments. The result is a type of layered sublattice (i.e., a structure), which in principle allows the emergence of ferrimagnetism. Just like the antiferromagnetic ordering of the magnetic moments, the ordering of cations often changes the symmetry of the crystal. Corundum. In corundum structure, the oxygen atoms form a slightly distorted hexagonal close packing in which two-thirds of the octahedral interstices are occupied by metal ions. Hematite, α-Fe2O3, is a well-known magnetic oxide with corundum structure in its most common form (Fig. 16.9B) [35]. Since the cations in the corundum structure are mainly located in equivalent positions, in simple oxides of trivalent transition elements ferrimagnetism cannot occur. α-Fe2O3 and Cr2O3 compounds are indeed antiferromagnetic, whereby weak ferromagnetism is superimposed on the antiferromagnetism of the former. The structure of ilmenite, which is the most common in compositions of type ABO3, is virtually identical to the structure of corundum and differs from it only by a regular arrangement of ions A and B (in ilmenite, FeTiO3, half of the Fe atoms are replaced by Ti). For this reason it is enough to consider the simpler structure of corundum, although oxides with the structure of ilmenite are more important because of their magnetic properties.
330
Magnetic, Ferroelectric, and Multiferroic Metal Oxides
Rutile. Rutile structure can be regarded as a distorted hexagonal close-packed oxygen array, where cations occupy one-half of the octahedral interstices. This structure has CrO2 (Fig. 16.9C). The Cr41 ions are located at the corners of the unit cell and there is a distorted CrO6 octahedron in the center of the structure (Fig. 16.9C). Doped CrO2 represents one of the most important ferromagnets used as magnetic media. Perovskite. In the basic perovskite (ABO3) unit cell, A designates a large cation site with 12-fold dodecahedral oxygen coordination, often occupied by a trivalent member of the lanthanide (rare-earth) series, and B is an octahedral site that harbors ions of the 3d transition series. Variations of the A31B31O3 compounds, such as A21B41O3, also occur (the original compound from which the term perovskite was coined is diamagnetic Ca21Ti41O3), as well as solid solutions of multiple cations in each type of site that maintain the required 61 total cation charge. The most frequently encountered example of a B41 compound is the ferroelectric Ba21Ti41O3 with its relatives Sr21Ti41O3, Ca21Ti41O3, and Pb21Ti41O3, in which the Ti41ion is d0 and therefore diamagnetic. The perovskite structure has two nonequivalent cationic sublattices, thus if both sublattices are formed by magnetic ions, FIM ordering of the magnetic moments is possible. Typical examples are AFeO3 (A 5 Bi, Ho, Er, etc.). This situation is more complicated than with spinels because the exchange interaction within the sublattice B is in most cases much stronger than the exchange interactions AB and AA. Consequently, magnetic ordering appears in the sublattice B often, even at high temperatures. Depending on the type and valence of the ions, this ordering can be antiferromagnetic, ferromagnetic, or FIM. Ferrimagnetism occurs when planes are perpendicular to the directions [111] or [001], or are alternately occupied by ions of different elements, or by ions of the same element but with different valences. Another interesting magnetic oxide with perovskite structure is LaMnO3, which has been the subject of detailed investigations regarding its crystallography and magnetic behavior, particularly when Sr21 or Ca21 ions are blended with La31 in the A-sites to create a mixture of Mn31 and Mn41 ions in the B sublattice in (La,Ca)MnO3 (Fig. 16.9D).
References [1] C.C. Baryy, N.M. Grant, Ceramic Materials, Science and Engineering, Springer, 2007. [2] G.F. Dionne, Magnetic Oxides, Springer, New York Dordrecht Heidelberg London, 2009. [3] R. Skomski, J.M.D. Coey, Permanent Magnetism, Condensed Matter Physics, Institute of Physics Publishing, Bristol, 1999. [4] S. Krupicka, Elements of Theoretical Magnetism, Lincoln, UK, 1968. [5] R.G. Burns, Intervalence transitions in mixed-valence minerals of iron and titanium, Annu. Rev. Earth Planet. Sci. 9 (1981) 345383. [6] I. Chamritski, G. Burns, Infrared- and Raman-active phonons of magnetite, maghemite, and hematite: a computer simulation and spectroscopic study, J. Phys. Chem. B 109 (2005) 49654968.
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[7] P. Anderson, Magnetism, Academic Press, New York, 1963. [8] J. Goodenough, Magnetism and the Chemical Bond, John Wiley And Sons, New YorkLondon, 1963. [9] I.E. Dzyaloshinskii, A thermodynamic theory of “weak” ferromagnetism of antiferromagnetics, J. Phys. Chem. Solids 4 (1958) 241255. [10] T. Moriya, Anisotropic superexchange interaction and weak ferromagnetism, Phys. Rev. 120 (1960) 9198. [11] A.P. Guimara˜es, Principles of Nanomagnetism, Springer, Berlin/Heidelberg, Germany, 2009. [12] G. Bertotti, Hysterisis in Magnetism: For Physicists, Materials Scientists and Engineers, Academic Press-Elsevier, Waltham, MA, USA, 1998. [13] S. Mørup, M.F. Hansen, C. Frandsen, Magnetic nanoparticles, in: G. Scholes, G. Wiederrecht, D. Andrews (Eds.), Comprehensive Nanoscience and Technology, Elsevier, Amsterdam, The Netherlands, 2011, pp. 437491. [14] A.G. Kolhatkar, A.C. Jamison, D. Litvinov, R.C. Willson, T.R. Lee, Tuning the magnetic properties of nanoparticles, Int. J. Mol. Sci. 14 (8) (2013) 1597716009. [15] Z. Cvejic, B. Antic, A. Kremenovic, S. Rakic, G.F. Goya, H.R. Rechenberg, et al., Influence of heavy rare earth ions substitution on microstructure and magnetism of nanocrystalline magnetite, J. Alloys Compd. 472 (1-2) (2009) 571575. [16] M. Maletin, E.G. Moshopoulou, V.V. Srdi´c, Magnetic properties of ZnFe2O4 and In-doped ZnFe2O4 nanoparticles, Phys. Status Solidi A 205 (8) (2008) 18311834. [17] R. Kodama, A. Berkowitz, E. McNiff, S. Foner, Surface spin disorder in NiFe2O4 nanoparticles, Phys. Rev. Lett. 77 (1996) 394397. [18] R. Kodama, A. Berkowitz, Atomic-scale magnetic modeling of oxide nanoparticles, Phys. Rev. B. 59 (1999) 63216336. [19] S. Mørup, E. Brok, C. Frandsen, Spin structures in magnetic nanoparticles, J. Nanomater. (2013) (2013) Article ID 720629, 8 pages. [20] J. Nogue´sa, J. Sorta, V. Langlaisb, V. Skumryeva, S. Surin˜achb, J.S. Mun˜ozb, et al., Exchange bias in nanostructures, Phys. Rep. 422 (2005) 65117. [21] M. Kiwi, Exchange bias theory, J. Magn. Magn. Mater. 234 (2001) 584595. ˇ Cveji´c Ph.D., Thesis, Faculty of Sciences, University of Novi Sad, Serbia, 2008. [22] Z. [23] M. Vucinic-Vasic, E.S. Bozin, L. Bessais, G. Stojanovic, U. Kozmidis-Luburic, M. Abeykoon, et al., Thermal evolution of cationdistribution/crystallite size and their correlation with the magnetic state of Yb-substituted zinc ferrite nanoparticles, J. Phys. Chem. C 117 (2013) 1235812365. [24] C. Gleitzer, J.B. Goodenough, Mixed-valence iron oxides, Cation Ordering and Electron Transfer Structure and Bonding, vol. 61, Springer, Berlin, Heidelberg, 1985, pp. 176. [25] M. Milanovi´c Ph.D., Thesis, Faculty of Technology, University of Novi Sad, Serbia, 2010. [26] G. Stojanovi´c, V.V. Srdi´c, M. Maletin, Electrical properties of yttrium-doped Zn and NiZn ferrites, Phys, Status Solidi A 205 (10) (2008) 24642468. ˇ Cveji´c, E. Ðurði´c, G. Ivkovi´c Ivandeki´c, B. Bajac, P. Postolache, L. Mitoseriu, [27] Z. et al., The effect of annealing on microstructure and cation distribution of NiFe2O4, J. Alloys Compd. 649 (2015) 12311238. [28] A. Lakshman, K.H. Rao, R.G. Mendiratta, Magnetic properties of In31 and Cr31 substituted MgMn ferrites, J. Magn. Magn. Mater. 250 (2002) 9297. [29] M. Milanovi´c, K. Giannakopoulos, L. Nikolic, E. Devlin, D. Stamopoulos, E.G. Moshopoulou, et al., Structure and magnetic properties of Zn12xInxFe2O4 and
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ZnYxFe22xO4 nanoparticles prepared by coprecipitation, Ceram. Int. 37 (2011) 32353242. Z. Cveji´c, S. Rapaji´c, S. Raki´c, S. Jankov, S. Skuban, V.V. Srdi´c, Conductivity and dielectric behaviour of indium substituted zinc ferrites prepared by coprecipitation method, Phys.Scripta 90 (2015) 095802. V. Thangadurai, S. Narayanan, D. Pinzaru, Garnet-type solid-state fast Li ion conductors for Li batteries: critical review, Chem. Soc. Rev. 43 (2014) 47144727. R.C. Pullar, Hexagonal ferrites: a review of the synthesis, properties and applications of hexaferrite ceramics, Prog. Mater. Sci. 57 (2012) 11911334. A. Moitra, S. Kim, S.-G. Kim, S.C. Erwin, Y.-K. Hong, J. Park, Defect formation energy and magnetic properties of aluminum-substituted M-type barium hexaferrite, Comput. Condens. Matter 1 (2014) 4550. S.-P. Shen, J.-C. Wu, J.-D. Song, X.-F. Sun, Y.-F. Yang, Y.-S. Chai, et al., Quantum electric-dipole liquid on a triangular lattice, Nat. Commun. 7 (2016) 10569. N.Y. Dzade, A. Roldan, N.H. de Leeuw, A density functional theory study of the adsorption of benzene on hematite (α-Fe2O3) surfaces, Minerals 4 (1) (2014) 89115.
16
Vladimir V. Srdic´ 1, Zeljka Cvejic´ 2, Marija Milanovic´ 1, Goran Stojanovic´ 3 and Srdjan Rakic´ 2 1 Department of Materials Engineering, Faculty of Technology Novi Sad, University of Novi Sad, Novi Sad, Serbia, 2Department of Physics, Faculty of Sciences, University of Novi Sad, Novi Sad, Serbia, 3Department of Microelectronics, Faculty of Technical Sciences, University of Novi Sad, Novi Sad, Serbia
Magnetism is a force we experience every day without really being aware of it. The scientific interest in magnetism and magnetic oxides has been changed during years. The first magnetic material to be discovered was lodestone, which is better known today as magnetite (Fe3O4). The word magnet comes from the Greek word magnes, which itself may derive from the ancient colony of Magnesia (in Turkey) [1]. Magnetite was mined in Magnesia 2500 years ago. In its naturally occurring state lodestone is permanently magnetized and is the most magnetic mineral. The strange power of lodestone was well known in ancient times. Socrates (B400 BC) dangled iron rings beneath a piece of lodestone and found that the lodestone enabled the rings to attract other rings [1]. Even earlier (B2600 BC), a Chinese legend tells of the Emperor Hwang-ti being guided into battle through a dense fog by means of a small pivoting figure with a piece of lodestone embedded in its outstretched arm. The figure always pointed south and was probably the first compass. Commercial interest in ceramic magnets started in the early 1930s with a Japanese patent describing application of copper and cobalt ferrites. The first Golden age of magnetic oxides was the 1950s and the 1960s, when the ferrites were explored and their properties optimized. Discovery of the first family of ferromagnetic (FM) oxides with a higher magnetization than ferrimagnets also dates from this period. A new age for magnetic oxides recently started, where multifunctionality, control of defects, interfaces, and thin-film device structures are the new challenges.
16.1
Magnetic elements/ions
The macroscopic magnetic properties of materials are a consequence of magnetic moments associated with individual electrons (i.e., its orbital motion around the nucleus and spinning around the spin axis). Some of these concepts are relatively Magnetic, Ferroelectric, and Multiferroic Metal Oxides. DOI: http://dx.doi.org/10.1016/B978-0-12-811180-2.00016-5 Copyright © 2018 Elsevier Inc. All rights reserved.
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complex and involve some quantum-mechanical principles, and will not be analyzed here. It is well known that in each individual atom, orbital moments of some electron pairs cancel each other; this also holds for the spin moments (i.e., an electron with spin-up will cancel the one with spin-down). The net magnetic moment, then, for an atom is just the sum of the magnetic moments of each of the constituent electrons, including both orbital and spin contributions, taking into account moment cancellation. The strength of spinorbit coupling is a key factor in determining the extent to which the orbital moment contributes to the magnetic properties and conversely, to what extent the spins interact with the lattice [2]. For an atom having completely filled electron shells or subshells, when all electrons are considered, there is a total cancellation of both orbital and spin moments. Thus, materials composed of atoms (or ions) having completely filled electron shells are not capable of being permanently magnetized. From this point of view transitional elements with the unfilled inner shells (while electrons occupying outer shells participate in chemical bonding) are responsible for a variety of magnetic properties because of the magnetic moments carried by their unpaired spins. The types of magnetism include diamagnetism, paramagnetism, and ferromagnetism (in addition, antiferromagnetism and ferrimagnetism are considered to be subclasses of ferromagnetism). All materials exhibit at least one of these types, and their behavior depends on the response of electron and atomic magnetic dipoles to the application of an externally applied magnetic field. Thus, most of the elements in the periodic table are diamagnetic and paramagnetic (Fig. 16.1), but exceptions are some d- and f-elements (transitional metals) from which most magnetic effects originate [3]. Characteristics of the d-elements are d-orbitals with up to five pairs of electrons and a relatively small difference in the energy of the different d-orbital electrons. This causes the number of electrons participating in chemical bonding to vary and results
Figure 16.1 Magnetic behavior of elements in the periodic table.
Metal oxide structure, crystal chemistry, and magnetic properties
315
in the same element exhibiting two or more oxidation states. The 3d-elements important for magnetism are iron, cobalt, and nickel, which are FM; and chromium, which is antiferromagnetic (AFM). Their ions, together with some ions of other d-elements (such as Fe21, Fe31, Co21, Ni21, Mn21, Mn31, Cr21, Cr31, V21, and V31) have high magnetic moments capable of producing strong spontaneous magnetism, when they are in sufficient densities, which allows exchange coupling to order magnetically as ferro-, ferri-, or antiferromagnets. However, the ions of the first two 3d-elements (Sc and Ti) are generally paramagnetic. The ions from 4d- and 5d-groups resemble the 3d-series in magnetic properties and can be used as alternatives for them in certain cases. However, in general these ions have not attracted much interest for their magnetic properties because their compounds do not exhibit strong spontaneous magnetic properties. The second most important transition group from a magnetic standpoint has an unfilled 4f-shell. The f-orbitals can contain up to seven pairs of electrons that are less chemically active, causing high chemical similarity between f-elements. They are generally paramagnetic and only gadolinium shows FM behavior. An important distinction between the 4f-ions and those of the 3d-ion group is the shielding of the 4f-shell inside the 5s and 5p outer shells of the xenon core. In other words, the magnetically active electrons are buried inside the xenon core and are therefore shielded from electrostatic fields of the molecular environment. As a result, the ions act largely independent of one another, even in highly concentrated compounds, and are generally paramagnetic because the multiple lobes of the 4f-orbital wave functions do not extend far enough for covalent bonding and magnetic exchange to be significant [2].
16.2
Magnetic oxides
Oxides are ionic compounds where small, highly charged metal cations are embedded in a lattice of oxygen anions. The O22 has its stable 2p6 closed-shell configura˚ . The oxide crystal structure is based on a tion with an ionic radius rO 5 1.40 A close-pack array of oxygen anions, with metal cations occupying interstitial sites. The close-packed arrays are usually face-centered-cubic and hexagonal-close packed. They both accommodate smaller metal cations in octahedral and tetrahedral interstices. The smaller one is the tetrahedral site with four oxygen neighbors, which can accommodate, without distortion, a spherical cation of radius ˚ . The larger one is the octahedral site with six oxygen neighbors that rtet 5 0.32 A ˚ . There are two tetrahecan accommodate a spherical cation of radius roct 5 0.58 A dral interstices and one octahedral interstice for each oxygen in dense-packed lattices, so that only a fraction of them can ever be filled. The ionic radii of common 3d-cations and others that may be incorporated in oxide structures are listed in Table 16.1. Due to the small size the tetrahedral site can accommodate only smaller cations (Mg21, Zn21, Al21, Fe31, or Si41) with some distortion of the tetragonal ˚ ) can occupy the octahedral sites (Fig. 16.2), site. The larger cations (0.550.70 A 21 while the cations such as Sr or La31, having ionic radii comparable to that of
Table 16.1
Ionic radii of cations in oxides
4-fold coordination
˚] d [A
6-fold coordination
˚] d [A
6-fold coordination
˚] d [A
12-fold coordination
˚] d [A
Mg21 Zn21 Al31 Fe31 Si41
0.53 0.60 0.42 0.52 0.40
Cr41 Mn41 Al31 Mn21 Fe21 Co21 Ni21
0.55 0.53 0.54 0.83 0.78 (0.61) 0.75 (0.65) 0.69
Ti31 V31 Cr31 Mn31 Fe31 Co31 Ni31
0.67 0.64 0.62 0.65 0.64 0.61 (0.56) 0.60
Ca21 Sr21 Ba21 Pb21 Y31 La31 Gd31
1.34 1.44 1.61 1.49 1.19 1.36 1.22
Values in brackets indicate a low-spin state.
Metal oxide structure, crystal chemistry, and magnetic properties
317
Figure 16.2 Octahedral site in a cubic symmetry (A) and its common distortions (B, C, D) [2].
oxygen, are incorporated within a 12-fold oxygen coordination [3]. Distortion of the lattice (Fig. 16.2) and presence of a variety of structural defects such as point defects (oxygen or metal vacancies and metal interstities) are usually following the incorporation of different cations in structure of metal oxides [2].
16.3
Magnetism of magnetic oxides
The magnetism of free atoms and ions can be associated with angular momentum. The electron has an intrinsic spin angular momentum s and intrinsic magnetic moment μs that can be expressed as μs 5 2 s μB/h , where μB 5 1/ 2 e h /me is the Bohr magneton. This quantity is the fundamental unit of atomic-scale magnetism. If a spinless electron is orbiting a nucleus in a state of angular momentum l, it behaves like a current loop with a magnetic moment μs 5 l μB/h . When electron spin and orbital angular momentum are taken into account, the magnetic moment of each electron in an isolated atom becomes μe 5 (2 s 1 l) μB/h . The Zeeman Hamiltonian for the electron in magnetic field B is represented by: HZ 52μ B 5
μB ðlz 1 2sz Þ ¯h
(16.1)
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Magnetic, Ferroelectric, and Multiferroic Metal Oxides
with the B-field taken along with the z-direction. The total magnetic moment for an N-electron atom becomes: μe 5
N μB X 2 ð2si 1 li Þ or ¯h i51
μ 5 2 ð2S 1 LÞ
μB ¯h
(16.2)
where S5
N X
si
and
i51
L5
N X
li
(16.3)
i51
S and L are total spin and orbital angular momentum, respectively. If J represents total angular momentum (i.e., J 5 S 1 L), the previous equation for total magnetic moment can be written as μ 5 (J 1 L) μB/h . The total magnetic moment of the ion or atom is then μ 5 g μB J, where Lande’s g-factor is given by: gL 5 1 1
J ðJ 1 1Þ 1 SðS 1 1Þ 2 LðL 1 1Þ 2J ðJ 1 1Þ
(16.4)
The Zeeman and spinorbit interaction are represented, respectively, by the Hamiltonians: HZ 5 2μ B 5
μB ðLz 1 2Sz Þ B ¯h
and
Hso 5 2λ L~ S~
(16.5)
Where λ is constant, L~ is the total orbital angular momentum, S~ is the spin angular momentum, and B-field is taken along with z-direction. For a free atom or ion, the angular momentum and spin of each electron is arranged according to the semiempirical Hund’s rules. Following these simple rules, it is then possible to calculate the magnetic moment without resorting to any particular knowledge of the individual atomic species for nearly all atoms. If we have a multielectron ion, the angular momentum of any filled (1s, 2s, 2p, 3s, 3p. . .) orbital is zero, because both the spin and orbital moments cancel each other. The net magnetic moment of atoms arises from unpaired electrons (Table 16.2). When the ions are placed in a crystalline environment of oxygen neighbors there are some drastic changes. For 3d- and 4d-ions crystalfield interaction is stronger than spinorbit interaction. For 4f-ions the crystal field is screened by the large filled 5s- and 5p-shells and it can influence on Hamiltonians only as a perturbation correction. For 3d-ions J is not a good quantum number, and from a magnetic viewpoint the 3d-ions may be represented as spin-only ions. The quenching of the orbital angular momentum in 3d-metal solids is due to the interaction of the d-orbitals with the crystal field formed by oxygen atoms. The crystal field leads to quenching by favoring the formation of superposition states with zero net magnetic moment.
Table 16.2
The ground state and magnetic moments for 3d ions [4]
Arrangements of electron in d-orbitals
T
S
L
J
gL
µJ/µB 5 gJ[J(J 1 1)]1/2
µS/µB 5 2[S(S 1 1)]1/2
3d1Ti31 V41 3d2V31 Cr41 3d3Cr31 Mn41 3d4Cr21 Mn31 3d5Mn21 Fe31 3d6Fe21 Co31 3d7Co21 Ni31 3d8Ni21 Co11 3d9Cu21 Ni11
2
1/2 1 3/2 2 5/2 2 3/2 1 1/2
2 3 3 2 0 2 3 3 2
3/2 2 3/2 0 5/2 4 9/2 4 5/2
4/5 2/3 2/5 2 3/2 4/3 5/4 6/5
1.55 1.63 0.77 0 5.92 6.70 6.54 5.59 3.55
1.73 2.83 3.87 4.90 5.92 4.90 3.87 2.83 1.73
m m m m m km km km km
m m m m m km km km
D3/2 F2 4 F3/2 5 D0 6 S5/2 5 D4 4 F9/2 3 F4 2 D5/2 3
m m m m m km km
m m m m m km
m m m m m
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Magnetic, Ferroelectric, and Multiferroic Metal Oxides
In order to explain how the crystal field influence magnetic properties of metal oxides we can start with the one-electron model [5,6], which is good approximation for d1, d4, d6, and d9-ions. Depending on the type of the crystalline coordination of the metal ions (cubic, tetrahedral, octahedral coordination), d-orbitals are splitting in a different way (Fig. 16.3). For example, the splitting of d-orbitals is reversed in octahedral and in tetrahedral coordination. At octahedral sites t2g (dxy, dyz, and dxz)
Figure 16.3 Schematic crystal field splitting and occupations of Co and Fe 3d-electrons in tetrahedral and octahedral coordination environments and energy levels of the d-orbitals common stereochemistries. (A) Co (II) tetrahedral d7; (B) Co (III) octahedral d9; (C) Fe (III) tetrahedral d5; (D) Fe (II) octahedral d9.
Metal oxide structure, crystal chemistry, and magnetic properties
321
orbitals have lower energy compared to energy of eg (dx2-y2, dz2) orbitals. The magnitude of ligand field effect Δoct is of the order 1 eV. Contrary, the t2g orbitals at tetrahedral sites are those that possess the higher energy in the ligand field. It should be noted that the Jahn-Teller effect is strong for d4- and d9-ions in octahedral coordination (Mn21, Cu21) and for d1- and d6-ions in tetrahedral coordination (V41, Co31). In the one-electron model, orbitals with the lowest energy are filled first, in a way that five k (spin-down) lie above the five m (spin-up) by amount JH (the on-site exchange energy B1.5 eV). The low-spin state is observed at ions for which the values of Δoct is higher than the values of JH. In that case t2g orbitals filled before eg orbitals. The low-spin state, for example for the Co21 ion, is S 5 1/2 and the high-spin state is S 5 3/2. Exchange interaction is a symmetry-constrained Coulomb interaction that has the effect of coupling electronic spins. Intraionic exchange, also known as JH or Hund’s first rule exchange, couples electrons in partially filled orbitals in a way to maximize the total spin. This further means that the m orbitals are filled first, before beginning to fill the k orbitals. If the energy splitting caused by the crystal field is higher than the intraionic exchange, the ion enters in a low-spin state. The Heisenberg interaction (direct exchange) is described by Hamiltonian moments: HZ 5 2
1 ^ Sj ^ Jij Si ¯h
(16.6)
and is often used to describe the interaction between individual moments. If Jij is positive, the parallel alignment is favored and material is FM. If Jij is negative, the spin orientation is antiparallel and material is AFM. In this case the moments align when the overall moment is zero. There are many possible AFM alignments. If the magnitudes of the moments in an antiferromagnet are not equal (nonzero net magnetization), the material is known as a ferrimagnet. The mechanism that causes the order alignment is strong and temperature-dependent. Direct exchange is a consequence of the Pauli exclusion principle. Consider two atoms, each with a single electron. When the atoms are close enough, their orbitals interact, electrons can move between the atoms, and according to the Pauli principle the total wave function must be antisymmetric. Having in mind that the symmetry of the total wave function is a product of the spatial wave function and spin wave function, one of them must be antisymmetric. An antisymmetric spatial wave function lowers the Coulomb energy of the system, which favors a FM (symmetric) spin wave function. Indirect (super) exchange is responsible for the AFM order in metal oxides such as NiO, CaMnO3, and Fe2O3. The 3d-orbitals of transition metal ion overlap with the p-orbitals of the oxygen. This overlap stabilizes an AFM coupling between the 3d-orbitals if the angle between metal and bridging oxygen is close to 180 degrees. The coupling becomes FM if the angle decreases toward 90 degrees. The occupancy and degeneracy of 3d-orbitals determine the strength and sign of superexchange, and possible cases are given in the GoodenoughKanamari rules (later
322
Magnetic, Ferroelectric, and Multiferroic Metal Oxides
reformulated by Anderson) [7,8]. Superexchange interactions occur in insulators and make use of nonmagnetic ions to assist spin interactions between two magnetic ions. Also, this type of magnetic interaction is more commonly AFM than FM. RudermanKittelKasuyaYosida (RKKY) exchange and superexchange both involve spin interactions accommodated by intermediate atoms. RKKY exchange occurs in metals, where the medium for the exchange interactions is the conduction electrons. The strength and sign of RKKY interaction varies with the distance, so it causes FM or AFM ordering. Double exchange involves the transfer of an electron between two magnetic ions with different valences, and leads to metallic FM properties. For this type of magnetic interaction a mixed-valence configuration is required as in the case in mixedvalance manganite (La1xAxMnO3, A 5 Ba, Ca, Sr). Electrons from an oxygen orbital can hop to a Mn41 ion, and its vacant orbital then can be filled by an electron from Mn31. The electron has moved between the neighboring metal ions, retaining its spin. The electron movement from one ion to another is “easier” when spin direction does not have to be changed (Hund’s rules). Another well-known double-exchange pair is Fe31 and Fe21 ions. As Table 16.2 shows, Fe31 ion has md5 configuration, and d-orbital is half-filled with spin parallel alignment. Fe21 has six electrons and the sixth kd electron is placed at the bottom of a t2g band (if the ion is octahedrally coordinated by oxygen) from where it can jump directly from one d5 ion to another. There is clearly a difference between superexchange and double exchange. In a superexchange the occupancy of d orbital of two metal ions remains the same, so electrons are not actually moving between two metal ions. In double exchange electrons are hopping between ions of different valance states via the intermediate oxygen. The antisymmetric part of exchange interaction between spins, characterized by a vector parameter D and called DzyaloshinskiiMoriya interaction, is given by: HDM 5 2D
X ^ 3 SjÞ ^ ðSi
(16.7)
i;j
It gives rise to canted antiferromagnetismin iron oxides [9,10]. AFM iron oxides possessing weak ferromagnetism, such as iron rare-earth orthoferrites RFeO3 (R represents rare-earth element) and hematite α-Fe2O3, are natural candidates for observing superexchange interactions. The presence of the DzyaloshinskiiMoriya antisymmetric exchange interaction leads to a slight canting of the spins from the antiparallel orientation by an angle of 0.51 degrees.
16.3.1 Magnetism of metal-oxide nanoparticles The magnetic properties of nanomaterials such as the Curie (TC) or Ne´el (TN) temperatures, and the coercivity field (HC), can be significantly different than those of a bulk specimen [11]. It is well-known fact that a bulk FM material is composed of
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small regions called magnetic domains. The formation and orientation of these magnetic domains are the result of the balance of several energy terms: the exchange energy, magnetocrystalline anisotropy, and the magnetostatic (or dipolar) energy [12]. The first term, exchange energy, tries to align all magnetic moments in the same direction. The second one, magnetocrystalline anisotropy, tries to orient magnetic moments along specific directions, while the third term, magnetostatic energy, tries to eliminate the magnetization in the material. In each domain the magnetic moments of atoms are aligned in one direction giving a net magnetization of each domain. The directions of magnetizations of the domains are different. The net magnetization is obtained by adding the magnetization of individual domains. It was found that magnetic domains in FM material have a minimum critical size (B100 nm), below which the magnetic material cannot split up further into domains and are called single-domain particles [13,14]. Thus, super paramagnetism emerges when the system is composed of small particles called independent crystallites (Fig. 16.4). Since the particles are small, the direction of each magnetic moment is not rigidly confined. The crystalline anisotropy energy decreases as the size of the crystallite is reduced, and as a consequence of that each crystallite magnetic moment is relatively free to move between any of the easy axes in response to an applied field. When the applied field is removed, the thermal effects rapidly destabilize any overall moment and the material starts to act like a paramagnetic. The regime of paramagnetic behavior extends from the Curie (or Ne´el) temperature down to the so-called blocking temperature TB. Thus in the superparamagnetic state, the magnetic nanoparticles behaves as a paramagnetic atom with a giant spin. At temperatures below the blocking temperature, the thermal effect becomes small and cannot cause fluctuations in the orientations of the magnetic moments of the nanoparticles; in fact they freeze in random orientations. The blocking temperature can be estimated using dc magnetization measurements. These measurements involve the measurement of magnetization as a function of temperature in two different states. The first state is called the zero-field-cooled (ZFC) state, and the
Figure 16.4 Superparamagnetic, single-domain, and multidomain magnetic regime as a function of particle size.
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Figure 16.5 Temperature dependence of magnetization of In-doped ZnFe2O4 obtained in zero-field cooled (ZFC) and field cooled (FC) conditions [16].
second is called the field-cooled (FC) state. The value of the blocking temperature depends on the particle size, effective anizotropy constant, applied field, and experimental measurement time. The shape of the magnetization versus temperature plots in the ZFC and FC measurements can provide qualitative information about the size distribution and the strength of interaction among the particles in the sample (Fig. 16.5) [15,16]. It should be noted that due to the fine size effect in nanomaterials, the existence of randomly oriented uncompensated surface spins, the existence of canted spins and the existence of a spin-glass-like behavior of the surface spins can significantly affect magnetic behavior of metal oxides [1719]. The total magnetization of the nanoparticle is thought to be composed of two components: a component due to the surface spins and a component due to the core of the particle. Thus, the magnetization of the magnetic nanoparticles can be modeled via a coreshell (or coresurface) magnetic model leading to another type of magnetic interaction at the interface between the core and the shell. In nanoparticles of AFM or ferrimagnetic (FIM) materials, this interaction occurs at the interface between the FM surface and the AFM (or FIM) core. The coreshell interaction is called the exchange bias or exchange coupling [20]. The exchange coupling provides an additional magnetic anisotropy to help align the ferromagnetic spins in certain directions. The exchange coupling is known to vanish above a critical temperature called the blocking temperature, but no satisfactory understanding of this interaction at the microscopic level exists. In order to obtain a satisfactory understanding of the theory of exchange bias, it is essential to understand the atomic interface structure [21].
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16.4
325
Representative structures of magnetic oxides
The most valuable structures in magnetic oxides regarding their magnetic behavior are spinel, garnet, and magnetoplumbite structure. These structures will be explained in brief in following sections.
16.4.1 Spinel structure Spinel structure most often occurs in ferrites and other binary oxides with a general chemical formula AB2O4, where usually Fe31 (ferrite) is at the position B, but also some other transition metals Cr31, Mn31, and so on. The position A is filled with a divalent cation such as Mn21, Fe21, Co21, Ni21, Cu21, Zn21, or Mg21, or sometimes with the monovalent lithium cation (Li1) or even vacancies, as long as these absences of positive charge are compensated for by additional trivalent iron cations (Fe31). The oxygen anions (O22) adopt a close-packed cubic crystal structure, while metal cations occupy two different interstitial sites: tetrahedral and octahedral. The spinel lattice cell is composed of 8 formula units that contain 32 oxygen anions, 8 tetrahedrally coordinated cations (A sublattice), and 16 cations in octahedral sites (B sublattice). The antiparallel alignment and incomplete cancellation of magnetic spins between the two sublattices A and B leads to a permanent magnetic moment (Fig. 16.6) [22,23]. The well-known ferrite that belongs to the spinel group is mineral magnetite, Fe3O4. Fe3O4 has a cubic inverse spinel structure that consists of a cubic closepacked array of oxide ions, where all the Fe21 ions occupy half of the octahedral sites and the Fe31 are split evenly across the remaining octahedral sites and the tetrahedral sites, leading to ferrimagnetism. In magnetite, the Fe21 ions may be partly or fully replaced by other divalent ions (Co, Mn, Zn, etc.), thus creating a
Figure 16.6 Unit cell and ferromagnetic ordering in spinel ferrites.
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whole spectrum of magnetic interactions. The magnetic properties of spinels are highly sensitive to the cation distribution between two sublattices and these properties are a complex function of the total chemical composition, stoichiometry, the substitution degree of foreign ions, and inversion parameter. Weather a foreign cation substitutes for A-site or B-site iron depends upon the relative sitepreference energies. Of the ions with partially filled d-shells, crystalline fields give a strong B-site preference to ions with d3, low-spin d5 or d6, or high-spin d8 configurations. Solute cations that can replace Fe31 ions for the tetrahedral sites include Cu1, Mg21, Zn21, Cd21, Mn21, Co21, Ga31, In31, Si41, Ge41, and so on [24]. Control of cation composition and inversion is essential for spinel properties [22,25]. Substitution on A-sites: The divalent cations such as Zn21 and Cd21have a strong preference for tetrahedral A-site in spinel. Therefore, bulk ZnFe2O4 is a paramagnet that has a normal spinel structure and becomes antiferromagnetic at TN 5 10 K. However, when prepared in the form of nanoparticles, ZnFe2O4 shows some degree of inversion and different kinds of magnetic ordering connected with it [26,27]. Trivalent cations could reside at tetrahedral sites, but substitution in complete solid solution range is difficult to find. Substitution with Ga31 has shown that it is possible to place Ga31 ions only on A-sites for x , 0.3 [8]. Substitution of In31 in ZnFe2O4 gives an even smaller compositional range (x # 0.15) for exclusive A-site substitution [26,28]. These substitutions have a profound impact on magnetic properties. For example, the saturation magnetization of spinel ferrites can be greatly enhanced by partial substitution of ZnFe2O4 for NiFe2O4 or MnFe2O4. The zinc cations prefer tetrahedral coordination and force additional Fe31 onto the octahedral sites. This results in less cancellation of spins and greater saturation magnetization. Substitution on B-sites: Substitution exclusively on B-sites can be achieved with ions having formal valence ranging from I to VI [8]. FIM NiFe2O4 is a good example of the complete inverse spinel with Ni21 ions placed onto a B-site, and Fe ions distributed between tetrahedral and octahedral sites. Large cations, such as some of the rare-earth ions (e.g., Y31), almost exclusively reside on octahedral sites [23,29,30]. Substitution on both A- and B-sites: Magnesium and manganese ferrites are good examples of mixed spinel structures where substitution for iron may result in a distribution of the cations on both A- and B-sites. The physical properties of the mixed spinel structures obtained in such way vary strongly with temperature.
16.4.2 Garnet structure The structure of garnets is a cubic structure, with a general chemical formula of A3B2 (XO4)3 (A 5 Ca, Mg, Y, La, or rare earth; B 5 Al, Fe, Ga, Ge, Mn, Ni, or V; X 5 Si, Ge, Al). The A cations are placed on dodecahedral C-sites, B cations on octahedral A-sites, and X cations on tetrahedral D-sites [31] (Fig. 16.7). The most important and widely studied magnetic garnet is yttrium-iron garnet (YIG), which has the formula Y3Fe5O12, where five Fe31 ions occupy two octahedral and three
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Figure 16.7 Structure of an ideal garnet with a general chemical formula of A3B2(XO4)3 and illustration of the cation coordination.
tetrahedral sites, and the Y31 ions are surrounded by eight oxygen ions. The YIG unit cell is composed of 8 formula units with 160 atoms. The net magnetic moment in YIG arises from an uneven contribution from antiparallel spins; the magnetic moments of the a- and d-ions are aligned antiparallel as are those of the c- and d-ions (Fig. 16.7B). By substituting specific sites with rare-earth elements, for example, interesting magnetic properties can be obtained. Other ions of the lanthanide group can be used generously in the c-sublattice to form what amounts to a distinct set of FIM compounds. Because the ionic spins that are introduced to the c-sublattice exchange couple to the iron in the d- and a-sublattices, a wide variety of thermomagnetic, magnetoelastic, microwave, and optical properties can be created in these rare-earth iron garnets.
16.4.3 Magnetoplumbite structure Hexagonal ferrites adopt magnetoplumbite structure, which is similar to the inverse spinel but with hexagonal symmetry instead of cubic. The general formula of magnetoplumbite structure can be written as AB12O19, in which A is a divalent metal ion, such as Ba21, Pb21, or Sr21, and B is a trivalent metal ion, such as Al31, Ga31, Cr31, or Fe31. The hexagonal ferrites are all FIM materials, and their magnetic properties are intrinsically linked to their crystalline structures [32]. There are many structural forms of hexagonal ferrites such as W, X, Y, or Z type, but only M structure of hexaferrites are technically important. Barium hexaferrite (BaO 6Fe2O3) is one of the most important M-type hexaferrite magnetic materials. The crystal structure of BaFe12O19 is shown in Fig. 16.8. It can be described by a periodically stacking sequence of two basic building blocks, S and R, along the c-axis, where an asterisk indicates rotation of the blocks by 180 degrees [33]. The Fe31 ions occupy three different sites in this structure: octahedral and tetrahedral in S block and bipyramidal sites in R block [34]. Large divalent ions, such as Ba21, Pb21, or Sr21 replace an oxygen atom in R block.
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Figure 16.8 (A) Stacking sequence in M-type hexaferrite BaFe12O19, (B) crystal structure corresponding SR layers in barium hexaferrite BaFe12O19.
16.4.4 Other common structures in magnetic oxides Besides the already-mentioned structures, magnetic oxides can adopt structures such as halite, corundum, rutile, perovskite, pyrochlore, and wurzite. These structures will be briefly explained. Halite. The halite structure can be regarded as two interpenetrating face-centered cubic sublattices, with cations and anions alternating along [100] directions. Cations are octahedrally coordinated by anions and vice versa. Since there is only one type of cation, located in crystallographically equivalent positions, in these simple oxides, in accordance with the stoichiometric composition, ferrimagnetism cannot appear. However, fundamentally ferromagnetism is possible, but it has been found only in europium oxide, EuO. Typically magnetic moments are arranged in antiferromagnetic ordering, and in a set of planes (111) cations, situated in the same plane, have parallel magnetic moments and those in adjacent planes, antiparallel magnetic moments (Fig. 16.9A). The symmetry of these “magnetic structures” is no longer cubic, since the direction [111] is perpendicular to the set of planes with ordered magnetic moments and is not equivalent to the other three directions of the space diagonals of an elementary cube. Consequently, the occurrence of antiferromagnetism is accompanied by a distortion of the structure, which reduces the symmetry to rhombohedral (MnO, FeO, NiO) or to tetragonal (CoO). The real reason for these strains is exhibited in the fact that the ions are placed in such positions in which the exchange forces, as well as other interactions, are enhanced and accordingly, the free energy decreases. In the case of the rhombohedral distortion, the decrease of the free energy is achieved by reducing or increasing the distance between adjacent planes (111). If a portion of cations of a simple oxide, such as NiO, is substituted by other cations, such as Li1cations, then the location of cations
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Figure 16.9 Structures of (A) NiO, (B) α-Fe2O3, (C) CrO2, and (D) perovskite (La,Ca)MnO3.
in adjacent planes (111) is often the same as the arrangement of the magnetic moments. The result is a type of layered sublattice (i.e., a structure), which in principle allows the emergence of ferrimagnetism. Just like the antiferromagnetic ordering of the magnetic moments, the ordering of cations often changes the symmetry of the crystal. Corundum. In corundum structure, the oxygen atoms form a slightly distorted hexagonal close packing in which two-thirds of the octahedral interstices are occupied by metal ions. Hematite, α-Fe2O3, is a well-known magnetic oxide with corundum structure in its most common form (Fig. 16.9B) [35]. Since the cations in the corundum structure are mainly located in equivalent positions, in simple oxides of trivalent transition elements ferrimagnetism cannot occur. α-Fe2O3 and Cr2O3 compounds are indeed antiferromagnetic, whereby weak ferromagnetism is superimposed on the antiferromagnetism of the former. The structure of ilmenite, which is the most common in compositions of type ABO3, is virtually identical to the structure of corundum and differs from it only by a regular arrangement of ions A and B (in ilmenite, FeTiO3, half of the Fe atoms are replaced by Ti). For this reason it is enough to consider the simpler structure of corundum, although oxides with the structure of ilmenite are more important because of their magnetic properties.
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Rutile. Rutile structure can be regarded as a distorted hexagonal close-packed oxygen array, where cations occupy one-half of the octahedral interstices. This structure has CrO2 (Fig. 16.9C). The Cr41 ions are located at the corners of the unit cell and there is a distorted CrO6 octahedron in the center of the structure (Fig. 16.9C). Doped CrO2 represents one of the most important ferromagnets used as magnetic media. Perovskite. In the basic perovskite (ABO3) unit cell, A designates a large cation site with 12-fold dodecahedral oxygen coordination, often occupied by a trivalent member of the lanthanide (rare-earth) series, and B is an octahedral site that harbors ions of the 3d transition series. Variations of the A31B31O3 compounds, such as A21B41O3, also occur (the original compound from which the term perovskite was coined is diamagnetic Ca21Ti41O3), as well as solid solutions of multiple cations in each type of site that maintain the required 61 total cation charge. The most frequently encountered example of a B41 compound is the ferroelectric Ba21Ti41O3 with its relatives Sr21Ti41O3, Ca21Ti41O3, and Pb21Ti41O3, in which the Ti41ion is d0 and therefore diamagnetic. The perovskite structure has two nonequivalent cationic sublattices, thus if both sublattices are formed by magnetic ions, FIM ordering of the magnetic moments is possible. Typical examples are AFeO3 (A 5 Bi, Ho, Er, etc.). This situation is more complicated than with spinels because the exchange interaction within the sublattice B is in most cases much stronger than the exchange interactions AB and AA. Consequently, magnetic ordering appears in the sublattice B often, even at high temperatures. Depending on the type and valence of the ions, this ordering can be antiferromagnetic, ferromagnetic, or FIM. Ferrimagnetism occurs when planes are perpendicular to the directions [111] or [001], or are alternately occupied by ions of different elements, or by ions of the same element but with different valences. Another interesting magnetic oxide with perovskite structure is LaMnO3, which has been the subject of detailed investigations regarding its crystallography and magnetic behavior, particularly when Sr21 or Ca21 ions are blended with La31 in the A-sites to create a mixture of Mn31 and Mn41 ions in the B sublattice in (La,Ca)MnO3 (Fig. 16.9D).
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