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Magnetism and microstructure: the role of interfaces
PII: S1359-6454(99)00282-7
Acta mater. Vol. 47, Nos 15, pp. 4233±4244, 1999 Published by Elsevier Science Ltd On behalf of Acta Metallurgica Inc. Printed in Great Britain 1359-6454/99 $20.00 + 0.00
MAGNETISM AND MICROSTRUCTURE: THE ROLE OF INTERFACES KANNAN M. KRISHNAN Materials Sciences Division, National Center for Electron Microscopy, Lawrence Berkeley National Laboratory, University of California, Berkeley, CA 94720, U.S.A. AbstractÐThe role of microstructure in determining the magnetic properties of materials is introduced and the role of interfaces, including intergranular phases, is presented in the context of three dierent classes of materials exhibiting novel magnetic behavior. This includes perpendicular interface anisotropy in metallic multilayers, origin of coercivity in hard magnets and the role of interface roughening in giant magnetoresistive materials. It is demonstrated that in these systems the microstructure of the interfaces (structural and compositional roughness, compound formation, strain and defects) and intergranular coupling and/or isolation are the appropriate length scales that determine their magnetic and magnetotransport properties. This approach not only makes it possible to atomically engineer thin ®lms and nanostructures but also oers opportunities to elucidate the physics of magnetism and build new materials with unique properties. Published by Elsevier Science Ltd on behalf of Acta Metallurgica Inc.
1. INTRODUCTION
Tremendous progress has been made in the ®eld of magnetic materials research and technology over the past few years [1]. Superior properties and novel scienti®c questions arise due to our ability to either synthesize arti®cial structures or to tailor microstructures at the appropriate length scales. Microstructure is generally de®ned as the morphological arrangement of crystallites with similar or dierent phase constitutions and of the crystal defects. It is controlled by the processing, which in turn aects the phases present, their topology and their dispersion [2]. There are two key length scales that determine the magnetic behavior of materials. One is the characteristic length scale associated with the dimensional characteristics of the magnetic phenomenon under consideration. The second is the size of the microstructural feature of interest; here, we will speci®cally focus on the atomic scale, i.e. interfaces broadly de®ned to include intergranular phases. It is important to identify the range where these two length scales overlap, for it is there that novel properties and the phenomenon are usually observed. There are three principal magnetic interactions (e.g. Ref. [3])Ðexchange, magnetostatic or dipolar and magnetocrystallineÐand the interplay between them and the physical microstructure determines the magnetic properties of materials. The fundamental interaction giving rise to ferromagnetic behavior is the exchange interaction energy, Eij between neighboring spins (Si, Sj) such that Eij ÿ2Jij Si Sj . For ferromagnetic materials, Jij > 0 and favors parallel alignment of neighboring
spins. Note that Eij depends only on the relative orientations of neighboring spins and not on their relative position. Hence, the interaction is isotropic (amorphous magnets are a reality) and strong coupling across disordered and non-crystalline interfaces is possible. The physical extent of the exchange interaction, called the exchange correlation length, is of the order of the domain wall width (see below). In addition to the exchange interaction, all magnetic materials are in¯uenced by the long-range dipolar interactions. The magnetostatic energy (0kM2s =volume) associated with this dipolar interaction is a function of the shape (0 < k < 4p) and size of the object and is often minimized by the formation of regions of dierent magnetization directions or domains. However, the formation of domains is subject to the additional constraint imposed by an in-built preference in all crystals to be magnetized along certain preferred directions (or easy axes). This magnetocrystalline anisotropy, arising from the spin-orbit±lattice interaction, is phenomenologically de®ned in terms of a series expansions of the direction cosines of the magnetization direction where the constants are material parameters called anisotropy constants (K). For an unperturbed lattice, the competition between the quantum-mechanical exchange interaction (which favors parallel alignment of neighboring spins) and the magnetocrystalline anisotropy (which encourages rapid spin rotation for maximum alignment along the easy axes) determines the domain wall width, d. This wall width is de®ned by the energy minimum between these two competing terms and is a key material parameter given by
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1=2 A dp , K
g 2Kd,
Rc 0
g M2s
1
where A is the exchange integral (a modi®ed form of Jij incorporating the crystal structure). Values for d range from 2 to 3 nm for high anisotropy materials (such as the rare-earth based hard magnets) to 300 nm for magnetically soft nickel. Introduction of such a wall in the unperturbed magnetic lattice is tantamount to the introduction of a twist in the magnetization. The energy per unit area associated with the formation of a wall, g, is balanced with the magnetostatic energy. If the total energy can be minimized, domains are formed; if not each particle remains as a single domain and the critical size for a single domain particle, Rc, is another important materials parameter. The ``hardness'' of a magnet, characterized by the coercive ®eld, Hc required to annul the magnetization completely, is a function of the size of the grains (single domain particles or not). In addition, the presence of second phases and defects/impurities of the size of domain walls that can eectively pin them and impede their movement making domain reversals dicult also aect the coercivity. In summary, it can be argued that the key parameters (coercive ®eld, remanence, hysteresis loss, etc.) de®ning the hysteresis behavior of any magnetic material are essentially extrinsic parameters that can be controlled by the microstructure. In the following sections, three dierent classes of materials that are the focus of much recent research and where interfaces play a controlling role in de®ning the magnetic and magnetotransport properties are discussed.
oriented along the ®lm normal. In such cases, a perpendicular anisotropy in thin ®lms can be achieved by carefully selecting a ferromagnetic material that exhibits uniaxial anisotropy in the bulk, and grow it epitaxially (good lattice matching is important) on appropriate substrates such that the magnetization is along the ®lm normal. Moreover, the phase of interest should be thermodynamically stable in the bulk, and interdiusion as well as interface reactions should be a minimum [4]. Alternatively, for ultrathin ®lms and multilayers (tM < 01 nm), it has been suggested that the surface/interface anisotropy contribution, arising from a break in symmetry at the interface [5] and proportional to tÿ1 M , can overcome the shape anisotropy and result in a spontaneous magnetization perpendicular to the ®lm. In practice, an understanding of the origin of perpendicular anisotropy in such multilayers requires a careful evaluation of the evolution and control of their complex microstructure at the atomic scale [6, 7]. The discussion in this section highlights the role of interfaces in determining the perpendicular anisotropy of [Cox(AÊ)Pty(AÊ)]n, where n is the number of repeats, grown on GaAs (111) substrates with a Ag buer layer. Multilayer stacks (x 3 A , y 15 A , n 15) grown on a 200 AÊ silver buer layer show strong uniaxial magnetic anisotropy perpendicular to the surface whilst direct growth on GaAs resulted in a predominant in-plane component. Magnetic properties (B±H loops) measured from two such samples are shown in Fig. 1. The deposition of a Ag buer layer [Fig. 1(b)] enhances the crystalline quality of the multilayers and leads to better epitaxy.
2. INTERFACE ANISOTROPY IN THIN FILMS AND MULTILAYERS
For a ferromagnetic thin ®lm or multilayer the anisotropy energy, Ean, is written in terms of an eective anisotropy constant, Ke Ean Keff sin2 y
2
where Ke includes contributions from the demagnetizing ®eld or shape anisotropy, surface/interface anisotropy and volume magnetocrystalline anisotropy and is given by Keff ÿ2pM2s 2
Ks Kv tM
3
where Ms is the saturation magnetization, tM is the thickness of the individual magnetic layers and Ks (Kv) is the surface (volume) anisotropy constant. For thick ®lms (tM greater than a few nanometers, for transition metals), the shape anisotropy energy contribution is predominant and the magnetization lies in the plane of the ®lm. However, the volume magnetocrystalline anisotropy can dominate provided the material exhibits strong uniaxial anisotropy and is grown such that the easy axis is
Fig. 1. Magnetic properties (B±H loops) of the [Cox(AÊ)Pty(AÊ)]n multilayers grown (a) without and (b) with a Ag buer layer on GaAs(111) substrate.
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High resolution images from cross-section specimens of the sample with a Ag buer layer (Fig. 2) were recorded with electron beams parallel to the [110] axis of the GaAs substrate. A good epitaxial relationship between the GaAs substrate and the Ag buer layer is observed; the {111} planes of the Ag layer are parallel to the {111} planes of the GaAs substrates. However, twin related grains, 30± 40 nm in diameter, are present in all the components of the multilayer stack. These twins are generated either by the propagation of the twin boundaries in the Ag layer into the multilayers or by nucleation of twin-related Pt grains on the Ag buer surface [8]. Rotational Moire fringes with three times the Pt(111) spacing along the growth direction, due to superposition of these twin related grains are observed in both the Ag buer layer and the Co/Pt multilayer stack. Whilst these Moire fringes explain the observed contrast in the HREM images, neither the contrast in the high resolution
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micrographs, nor the spatial frequencies in the optical diractograms from the multilayer regions in the negatives, indicate the expected 1.83 nm periodicity. However, simulations of the HREM images using a graded composition for the Co interface layer indicate that, in spite of the large dierence in scattering factors for Co and Pt, high resolution electron micrographs will not resolve the interface layer if the probability of Co occupation in the interface layer is less than 40%. Low-angle re¯ectivity measurements in the form of y±2y scans (Fig. 3) clearly show the ®rst- and second-order satellites corresponding to a repeat period of 18.4 AÊ in the multilayer structures. Transverse rocking scans at two values of scattering angle, 2y, (a) at 28, and (b) at the position of the ®rst-order multilayer satellite, 4.98, are shown in Fig. 4. In (a), although there is considerable scattering away from the specular peak, it is still possible to observe a resolution-limited specular peak
Fig. 2. High resolution images from cross-sections of a sample with a Ag buer layer showing well-textured twin-related grains with the [111] axis parallel to the substrate surface. The area with distinct Moire fringes is also marked.
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characteristic of long-range order in the sample surface plane. In (b), the scattering is entirely diuse with no observable specular peak. The diuse scattering is analogous to small-angle scattering and is caused by lateral imperfections within the multilayer structure. Quantitative analysis of the measurements is dicult as the in-plane structure necessitates a three-dimensional structural model of the Co layer in order to simulate the scattering. Such interpretation would be ambiguous without independent structural information. However, from these results initial conclusions are that the samples contain considerable in-plane inhomogeneity consistent with interfacial mixing and compound formation at the interface. These results are in agreement with the HREM imaging and simulation result. Further, in situ X-ray photoelectron diraction studies of the Co±Pt interfaces during their formation suggest that they are not atomically abrupt but are diuse over four monolayers [9]. This interpretation is also consistent with preliminary high resolution z-contrast images [10] of these multilayers that indicate a distribution of 6±8 AÊ for the Co layers in these samples. In any case, one can conclude that the Cointerface layer is diuse with evidence for atomic mixing and/or compound formation but its exact stoichiometry/structure is still unclear given the wide range of miscibility for Co in Pt. There is a 10% lattice mismatch between Cof.c.c. and Pt and in epitaxially grown multilayers this mismatch is accommodated by in-plane lattice strain. Hence, six samples with x=y 3=18, (6/ 18.5), (10.6/18), (13.5/19.1), and n 15, as well as (Co50/Pt50)4 and (Co4.4/Pt4.4)15 were examined. Polar Kerr-rotation measurements of these samples show that the largest perpendicular anisotropy and square hysteresis loop is achieved when x 3 A , but along with increasing Co thickness, the Co and Pt layers lose coherency and the magnetic anisotropy goes from being perpendicular to planar (Fig. 5). The lattice strain was measured by selected area dif-
Fig. 3. Low-angle re¯ectivity for the multilayer for the incident angle y 0:88±5:28. Two satellite re¯ections are seen at 2y 28 and 4.98.
fraction in plan-view samples using the position and displacement of the diraction spots from the Co and Pt layers and calibrated using the standard re¯ections from the GaAs substrate. For x 3 A , y 18 A , there is a 02% compressive strain in the Pt layers while the Co layers are under tension along h220i crystallographic directions. As the Co layers are grown thicker, though the f.c.c. stacking remains the same, relaxation of lattice strain in both the Co and Pt layers occurs. At x y 5 nm, the lattice parameters of both Co and Pt relax to their bulk values (Fig. 6) along with an absence of perpendicular anisotropy. If lattice strain is included, the volume contribution to the anisotropy is modi®ed as Kv Kmc ÿ c ls
4
where Kmc is the bulk magnetocrystalline anisotropy, and the magnetoelastic term is the contribution due to stress (s) and the related magnetostriction (l). Spin-orbit coupling which determines the crystal anisotropy is modi®ed by the sign of the lattice stress and the magnetoelastic interactions in thin ®lms aect their magnetic behavior. In simple terms, the axis of stress is an easy axis if the magnetoelastic contribution to the anisotropy constant (ls) is positive. On the other hand, if ls < 0, the stress axis is a hard axis and the favored direction of magnetization lies in a plane
Fig. 4. Transverse scans across the re¯ectivity rod (y scans): (a) at 2y 2:08; (b) 2y 4:98. In (a) a sharp specular peak is observed whilst in (b) the scattering is entirely diuse in nature.
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perpendicular to the stress axis. The magnetostriction of Cof.c.c. on the close packed (111) planes can be considered to be similar to that on the hexagonal planes of Coh.c.p., i.e. l < 0 [11]. In addition, the Co layers are under tension, i.e. s > 0, in the ®lm plane due to its lattice parameter being smaller than Pt. Therefore, for (111) growth, the product (ls) is negative and a uniaxial anisotropy perpendicular to the in-plane stress axis is favored. In summary, the perpendicular anisotropy observed in metallic multilayers is more complicated than a simple description involving a break in symmetry at the interface. In fact, it is determined by the interface microstructure at the atomic scale including interface mixing, compound formation and strain.
3. HARD MAGNETS
3.1. Stoner±Wohlfarth model and the role of microstructure Modern permanent magnets, generally composed of rare-earth-based compounds, are characterized by high coercivity and energy product. When the ®eld is reversed and increased in magnitude at a certain value (the coercive ®eld, Hc) the magnetization becomes unstable and reverses in the direction of the applied ®eld. In the Stoner±Wohlfarth model [12], the coercivity of these materials assuming a coherent rotation of isolated, magnetically noninteracting, single domain particles is given by Hc
2K : Ms
5
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Here, K is the anisotropy constant and could either arise from shape anisotropy (large aspect ratio precipitates as in the AlNiCo magnets) or the magnetocrystalline anisotropy (as in the modern rareearth permanent magnets). In practice, the coercive ®eld is a function of the grain size and the presence of second-phase particles that could either serve as pinning sites for domains (enhance Hc) or nucleation sites for reverse domains (reduce Hc). These microstructural features are included in a modi®ed [13, 14] formulation of Hc as HN
2K a ÿ Neff Ms Ms
6
where a and Ne are microstructure sensitive parameters. In practice, a range of microstructural features such as grain size and shape, phase distribution, grain boundary type, and the mutual crystallographic orientation between grains are parameters that determine the magnetic behavior of modern permanent magnets. To enhance our understanding of the coercive behavior of permanent magnets, it is best to consider these materials in a hierarchy of three categories: (i) single phase materials where only defects can play a role, (ii) twophase materials with a majority magnetic phase and a minority non-magnetic phase for grain isolation and (iii) two-phase materials where the majority phase (hard) and the minority phase (soft) are both magnetic and are exchange interacting. Case (ii) is simple and straightforward and relates to the practical achievement of the Stoner±Wohlfarth single domain particles [15]. Hence, in the following two sections cases (i) and (iii), highlighting the role of interfaces and intergranular phases, are discussed. 3.2. Single phase materials: epitaxially grown SmCo thin ®lms We begin with the consideration of the magnetic behavior of single phase SmCo thin ®lms prepared
Fig. 5. Polar Kerr±rotation curves with the ®eld normal to the surface for samples (a) [Co3Pt18]15, (b) [Co6Pt18.5]15, (c) [Co10.6Pt18]15, (d) [Co13.5Pt19.1]15, (e) [Co50Pt50]4 showing the change from perpendicular to in-plane magnetization.
Fig. 6. In-plane lattice strain measured by the position/ splitting of the (220) spots for the various components of the multilayer stack. The re¯ections from the GaAs substrate were used to calibrate the diraction patterns and obtain a quantitative measurement of the strain. By careful measurements of plan-view as well as cross-section samples it was determined that the lattice strain was inplane.
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by magnetron sputtering. SmCo ®lms with a nominal composition of Sm2Co7 were deposited onto single-crystal MgO(100) substrates using a 200 AÊ thick Cr buer layer. The average and local chemical composition of the ®lms were measured using energy dispersive X-ray spectroscopy (EDXS) in an analytical TEM (JEOL 200CX), while electron diffraction and high-resolution TEM (HRTEM) imaging were performed using a Topcon 002B microscope operated at 200 keV. The magnetic properties were measured with a Quantum Design d.c. magnetometer equipped with a 9 T magnet and a 7 T SQUID magnetometer equipped with both longitudinal and transverse coils. Details of the growth and characterization are described elsewhere [16, 17]. The crystal structure of Cr is body centered cubic (b.c.c.) whilst SmCo alloys are generally either hexagonal or rhombohedral. When deposited at elevated substrate temperature on MgO, Cr establishes an epitaxial relationship with the substrate providing a template for the subsequent growth of the SmCo ®lm. Figure 7 shows the microstructure of the as-grown SmCo thin ®lms. For MgO(100) substrates, plan-view electron diraction (inset in Fig.7) shows a four-fold symmetry and an epitaxial relationship given by: SmCo 112 00001kCr 100011kMgO 100001. Since
Cr(100) possesses a four-fold symmetry, the [0001] direction of SmCo grains lies along either the Cr[011] or Cr01 1 directions. The SmCo 112 0 ®lm microstructure exhibits small grains (025±60 nm in size), separated by incoherent twin boundaries, with their c-axes normal or parallel to each other, resulting in a bicrystalline morphology. Stacking disorder, normal to the c-axis within the grain structure, can be observed in the micrographs. This stacking disorder can be described as an intergrowth of dierent polytypoids of SmCo alloys. Indeed, close examination using HRTEM (Fig. 8), combined with image simulations and measurements of d0001 spacing, shows that the stacking disorder within a given grain corresponds to the dierence in stacking between SmCo3, Sm2Co7 and SmCo5 phases. The micrograph shows that these SmCo polytypoids have a common c-axis, i.e. their basal planes are parallel to each other. The crystal structures of intermetallic SmCo phases, ranging from SmCo2 to SmCo5, are closely related and are based on a regular stacking along the c-axis of two kinds of layers. One layer is of the SmCo2 Laves phase type and the other is that of SmCo5 type. Since each bilayer is Co-rich, removing one bilayer from Sm2Co7 for instance, results in the formation of a SmCo3 type of stacking.
Fig. 7. Low-magni®cation HRTEM in-plane images showing the microstructure of the SmCo 112 0 thin ®lms. The inset shows the selected area diraction pattern and the c-axis directions in adjacent grains are indicated.
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These SmCo ®lms showed very high coercivity and their initial magnetization curves show a clear pinning type behavior (Fig. 9). The magnetic hardness of SmCo thin ®lms appears to be very sensitive to the crystallography of the phases present as well as the composition and very ®ne-scale structural details within and at the boundaries of the nanometer-size grains. Two kinds of magnetic interactions exist between neighboring SmCo grains with a given crystallographic orientation. The ®rst is magnetostatic that depends mainly on the shape of the grains, whereas the second, exchange interaction, strongly depends on the grain size and intergranular isolation. Micromagnetic modeling has shown that for nanometer-scale grains in a singlephase isotropic permanent magnet, the exchange interaction between grains is dominant in determining its magnetic behavior [18]. In particular, at the remnant state, the spontaneous magnetic polarization was found to deviate from the easy axes of the grains in the vicinity of the grain boundaries. A similar model, involving strong exchange interactions between the grains in the SmCo ®lm would, in principle, explain the observed anisotropies (Fig. 9). Since the epitaxial growth constrains the c-directions of the SmCo grains to essentially lie perpendicular (i.e. only two possibilities, in plane) to each other, strong intergranular exchange interaction would result in the easy direction being at an intermediate orientation, i.e. along MgO[011] or MgO01 1. Moreover, if all the SmCo grains were strongly exchange coupled, individual grain boundaries would not be the likely pinning site to explain the pinning-type coercivity mechanism observed in these ®lms. So the question remains: what is really
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causing the pinning mechanism in these SmCo hard magnet ®lms? Two alternative explanations can be proposed. It has recently been reported that in Co-based alloy thin ®lms with a bicrystalline microstructure [19], a ``cluster'' formed by an ensemble of adjacent grains may lead to an eective anisotropy along an intermediate direction and with a magnitude depending on the strength of the intergranular exchange coupling. One can possibly assume that due to the ferromagnetic exchange coupling between the grains, a similar type of cluster may form in the case of SmCo thin ®lms, such that each cluster is considered as a large grain with an eective anisotropy along MgO[011] or MgO01 1. In such a model, the incoherent twins at the grain boundaries may serve as attractive pinning sites for the magnetic domain walls. The second hypothesis involves the stacking disorder, or the SmCo polytypoids, observed within a given grain with strong variation in local magnetocrystalline anisotropy constants. Although Sm2Co7 has a relatively high anisotropy [20], that of SmCo5 is much higher and hence, it may impede the movement of the domain walls during the magnetization reversal since it has a larger wall energy. This process is only possible if the domain wall motion is parallel to the c-axis. If the magnetization direction is normal to the c-axis, the energy of the wall is independent of the dierence in stacking sequence and should not a priori act as a pinning center. It is clear from this discussion that even in ``single'' phase materials, either the interface between regions with local changes in stacking sequence or the defects at grain boundaries, could serve as pinning sites and enhance the coercivity of SmCo thin ®lms. In addition, for materials such as SmCo with very high magnetocrystalline anisotropy constants, the domain wall widths are on the nanometer scale. These defects which are of similar dimension could eectively pin these domains. However, it is imperative that further work to image these magnetic domains be carried out to resolve the true pinning sites in these ®lms. 3.3. Two-phase materials: exchange-spring magnets
Fig. 8. HRTEM image of an individual grain indicating the stacking disorder along the c-axis or the stacking of dierent SmCo polytypoids with a common c-axis.
There is a principal diculty in achieving both a high energy product (BHmax) and a large coercivity in permanent magnets because, in general, Hc is inversely related to Ms [see equation (5)]. To overcome this limitation, Kneller [21] proposed the concept of the exchange-spring magnet. The key idea is to generate a two-phase microstructure consisting of a minority soft phase in a majority hard magnetic phase such that they are strongly exchangecoupled. In this microstructure, the magnetic reversal is initiated in the soft phase and is followed by the hard phase once the domain walls penetrate and propagate into it. Since the hard phase has a very high value of the magnetocrystalline anisotropy constant, the broad domain walls [see equation (1)]
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civity and an enhancement in remnant magnetization provided one can achieve an ideal microstructure where the soft phase has a critical dimension [21] given by Asp 1=2 : 7 dsp p 2Khp For representative values of Asp and Khp, one gets dsp 05 nm. In practice, this microstructure is approximated by an intergranular soft phase surrounding a hard magnetic phase. A typical example of such a magnet [22], comprising of the hard Nd2Fe14B phase surrounded by soft a-Fe, is shown in Fig. 10. The intergranular phase has the right dimension (5 nm) and the magnet shows a true exchange-spring behavior [23]. Fig. 9. The in-plane magnetization loops measured along dierent axes of the SmCo 11 20 ®lm. Note the nice pinning type behavior (very small slope of the initial magnetization portion) when measured along the MgO[110] direction.
nucleated in the soft phase have to be squeezed substantially for complete reversal of the hard phase. Therefore, one is expected to get both a large coer-
4. MAGNETOTRANSPORT IN OSCILLATORYCOUPLED HETEROSTRUCTURES
The discovery of giant magnetoresistance (GMR) in metallic multilayers (ferromagnetic layers separated by a non-magnetic spacer layer) opened up a new chapter in the ®eld of magnetism and magnetic materials. The origin of this magnetoresistance is
Fig. 10. The microstructure of an exchange-spring magnet with a hard Nd2Fe14B phase surrounded by 5 nm size soft a-Fe.
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Fig. 11. (a) Oscillatory behavior of the magnetoresistance (DR/R) as a function of the Au spacer thickness in permalloy/gold (Py/Au) multilayers. (b) Magnetoresistance vs ®eld for sample AF2 before and after annealing at 2508C/40 min.
believed to be spin-dependent scattering at the interfaces of electrons traversing a thin non-magnetic metal layer/spacer separating adjacent magnetic layers. This scattering and the associated MR is enhanced when the magnetizations of adjacent magnetic layers are in opposite directions (antiferromagnetic or AF coupling) and minimized when the magnetizations are in the same direction (ferromagnetic or FM coupling). In addition, oscillations in MR and the nature of the interlayer coupling (AFM or FM), as a function of the noble-metal
spacer thickness are commonly observed. A typical example of a permalloy (Ni0.8Fe0.2)/gold multilayer system is shown in Fig. 11(a). At each of the four maxima of magnetoresistance, AF coupling through the Au spacers produces an antiparallel alignment of magnetizations in adjacent permalloy layers and leads to a peak in interfacial spin-dependent scattering. When an external ®eld is applied, the magnetic layers are aligned parallel and there is a signi®cant drop in resistance (GMR).
Fig. 12. HREM of as-grown multilayers with one to three monolayer roughness and other defects associated with the (111)f.c.c. epitaxial growth.
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Fig. 13. HREM of annealed sample (AF2). Regions with reduced thickness (a) and (b) fully alloyed Au with twin planes de®ning the original interface.
To facilitate the development of such applications, fundamental understanding of the interlayer coupling, the associated GMR and their dependence on the atomic structure of the interfaces is crucial. Perfect interfaces would produce specular re¯ection and diraction of electron waves without any change in resistivity. However, signi®cant changes in resistivity are expected only from scattering by interface roughness. Moreover, the AF coupling, observed for certain spacer thickness, could be
obscured by structural defects resulting in magnetic bridges (FM coupling) between adjacent magnetic layers. Toward this end, high resolution electron microscopy at 1.7 AÊ resolution, of cross-section samples was used to investigate interface roughness, defect structures of the multilayers and changes in the microstructure on annealing. Multilayers with the Au spacer layer thickness near the second AF peak [AF2 in Fig. 11(a)] were examined before and after annealing at 2508C for 40 min in ultra-high
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vacuum. This annealing led to a decrease of saturation MR by 030%, from 11 to 8% [Fig. 11(b)]. As grown, the multilayer interfaces were 01±3 monolayers in width (Fig. 12). Detailed examination showed that the interfaces were semi-coherent with arrays of irregularly spaced mis®t dislocations (small white arrows) accommodating most, but not all, of the 15% lattice mismatch. Their optical diffractogram showed no splitting of the (111) spots indicating some residual strains in the multilayers. The (111) growth twins with associated twin boundaries parallel to the growth direction, originate from the Pt seed layer (Fig. 12). The latter do not extend through the multilayer stack but are con®ned to the ®rst one to three layers. On annealing, the atomic structure was found to be inhomogeneous. Even though the overall multilayer period remained the same, the interfaces were roughened [Fig. 13(a)] and in some cases the Au spacer had alloyed locally [Fig. 13(b)] with the adjacent permalloy layer. In regions where the Au layer completely disappears, each intermixed multilayer period is separated by a twinning plane [Fig. 13(b)]. Even though bulk Au is almost insoluble in Ni (01 at.%) at 2508C [24], an interface compound in Au/Ni multilayers has been recently observed [25]. The electron diraction pattern obtained from Fig. 13(b), con®rms the intermixed phase to be cubic with a lattice parameter of 03.8 AÊ. Such intermixing results in the roughening of the interface which can be quanti®ed by plotting a normalized histogram of the Au layer thickness along the [112] direction in the growth plane, before and after annealing from such HREM images. This plot (Fig. 14) reveals that the as-grown Au(111) layers were about two monolayers rough before annealing but a bimodal distribution with considerable spread (peaks at 10 and six monolayers) resulted from annealing [26]. The increased roughening and local bridging of permalloy layers in the multilayer both contribute to the reduction of GMR on annealing. Both these eects lead to a decrease in the AF-coupled fraction of permalloy layers in the sample. Direct imaging at atomic resolution and their quantitative interpretation made it possible to discover them for the ®rst time.
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Fig. 14. Histogram showing thickness distribution of Au spacer layers for AF2 before and after annealing. The fractional occurrence of Au(111) spacer thickness (in ML), measured from the HREM images, with the beam along the 11 0 direction is shown.
ing the physical and chemical microstructure at the nanometer scale are suciently advanced with atomic resolutions a practical reality using state of the art TEM instrumentation. This is in contrast with resolving magnetic microstructure (domains, domain walls, etc.) where the techniques are either restricted to surfaces or their resolution is two orders of magnitude larger. In the examples cited in this article, the magnetic behavior has been inferred based on indirect measurements. Development of magnetic imaging techniques and suitable micromagnetic modeling based on experimentally observed microstructural parameters should provide additional insight and aid in the development of new materials with superior properties. AcknowledgementsÐIt is a pleasure to acknowledge the contributions of a number of former students and postdocs involved in this work. In particular, I would like to thank N.-H. Cho, B. Zhang, N. Thangaraj, M. Benaissa, M. A. Brewer and Er. Girt. Other collaborators include R. F. C. Farrow (IBM), P. Panchanathan (Magnequench), E. Fullerton (ANL) and S. Bader (ANL). This work was supported by the Director, Oce of Energy Research, Oce of Basic Energy Sciences, Materials Sciences Division of the U.S. Department of Energy under contract No. DE-AC03-76SF00098.
4. CONCLUSIONS
The role of microstructure, with emphasis on interfaces and intergranular phases, in determining the magnetic properties of novel magnetic materials has been illustrated. In fact, it is quite clear that extrinsic properties control all the salient features of the hysteresis behavior of magnetic materials. In addition, in many such materials mechanical and magnetic properties are often ``coupled'' and this would be a new and exciting area of research [27]. Finally, as has been demonstrated, the techniques for study-
REFERENCES 1. Hadjipanayis, G. C. (ed.), Magnetic Hysteresis in Novel Magnetic Materials. Kluwer, Boston, 1997. 2. Arzt, E., Acta mater., 1998, 46, 5611. 3. Chikazumi, S. and Charap, S., Physics of Magnetism. Krieger, Malabar, FL, 1978. 4. Krishnan, K. M., Appl. Phys. Lett., 1992, 61, 2365. 5. Neel, L., J. Phys. Radium, 1954, 15, 225. 6. Cho, N.-H., et al., J. appl. Phys., 1992, 72, 5799. 7. Zhang, B., et al., Ultramicroscopy, 1993, 51, 298. 8. Cho, N.-H., Krishnan, K. M., Lee, C. H. and Farrow, R. F. C., Appl. Phys. Lett., 1992, 60(9), 237.
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9. Hermsmeier, B. D., Farrow, R. F. C., Lee, C. H., Marinero, E. E., Lin, C. J., Marks, R. F. and Chien, C. J., J. appl. Phys., 1991, 69(8), 5646. 10. Krishnan, K. M., unpublished. 11. Bozorth, R. M., Phys. Rev., 1954, 96(2), 311. 12. Stoner, E. C. and Wohlfarth, E. P., Phil. Trans. R. Soc., 1948, A240, 599. 13. Kronmuller, H., Physica status solidi, 1987, 144, 385. 14. Kronmuller, H. and Schre¯, T., J. Magn. Magn. Mat., 1994, 129, 66. 15. Girt, Er., et al., Proc. Mater. Res. Soc., Spring, 1999. 16. Fullerton, E. E., et al., Appl. Phys. Lett., 1996, 69, 2438. 17. Benaissa, M., et al., I.E.E.E. Trans. Magn., 1998, 34, 1204.
18. Schre¯, T., Fidler, J. and Kronmuller, H., Phys. Rev. B, 1994, 49, 6100. 19. Peng, Q., et al., I.E.E.E. Trans. Magn., 1995, 31, 2821. 20. Buschow, K. H. J., J. less-common Metals, 1973, 33, 311. 21. Kneller, E. F., I.E.E.E. Trans. Magn., 1991, 27, 3588. 22. Benaissa, M., et al., Proc. ICEM, 1998, 14, 533. 23. Benaissa, M., et al., unpublished. 24. Okamoto, H. and Massalski, T. B., in Binary Alloy Phase Diagrams, Vol. 2, ed. T. B. Massalski. ASM International, 1990. 25. Baker, S.P. , Bain, J.A., Clemens, B.M. and Nix, W.D., Proc. Mater. Res. Soc., 1994, p. 343 26. Farrow, R. F. C., et al., Appl. Phys. Lett., 1996, 69, 1963. 27. Special section on ``Coupled property issues in integrated microstructures'', Acta mater., 1998, 46(11).
Acta mater. Vol. 47, Nos 15, pp. 4233±4244, 1999 Published by Elsevier Science Ltd On behalf of Acta Metallurgica Inc. Printed in Great Britain 1359-6454/99 $20.00 + 0.00
MAGNETISM AND MICROSTRUCTURE: THE ROLE OF INTERFACES KANNAN M. KRISHNAN Materials Sciences Division, National Center for Electron Microscopy, Lawrence Berkeley National Laboratory, University of California, Berkeley, CA 94720, U.S.A. AbstractÐThe role of microstructure in determining the magnetic properties of materials is introduced and the role of interfaces, including intergranular phases, is presented in the context of three dierent classes of materials exhibiting novel magnetic behavior. This includes perpendicular interface anisotropy in metallic multilayers, origin of coercivity in hard magnets and the role of interface roughening in giant magnetoresistive materials. It is demonstrated that in these systems the microstructure of the interfaces (structural and compositional roughness, compound formation, strain and defects) and intergranular coupling and/or isolation are the appropriate length scales that determine their magnetic and magnetotransport properties. This approach not only makes it possible to atomically engineer thin ®lms and nanostructures but also oers opportunities to elucidate the physics of magnetism and build new materials with unique properties. Published by Elsevier Science Ltd on behalf of Acta Metallurgica Inc.
1. INTRODUCTION
Tremendous progress has been made in the ®eld of magnetic materials research and technology over the past few years [1]. Superior properties and novel scienti®c questions arise due to our ability to either synthesize arti®cial structures or to tailor microstructures at the appropriate length scales. Microstructure is generally de®ned as the morphological arrangement of crystallites with similar or dierent phase constitutions and of the crystal defects. It is controlled by the processing, which in turn aects the phases present, their topology and their dispersion [2]. There are two key length scales that determine the magnetic behavior of materials. One is the characteristic length scale associated with the dimensional characteristics of the magnetic phenomenon under consideration. The second is the size of the microstructural feature of interest; here, we will speci®cally focus on the atomic scale, i.e. interfaces broadly de®ned to include intergranular phases. It is important to identify the range where these two length scales overlap, for it is there that novel properties and the phenomenon are usually observed. There are three principal magnetic interactions (e.g. Ref. [3])Ðexchange, magnetostatic or dipolar and magnetocrystallineÐand the interplay between them and the physical microstructure determines the magnetic properties of materials. The fundamental interaction giving rise to ferromagnetic behavior is the exchange interaction energy, Eij between neighboring spins (Si, Sj) such that Eij ÿ2Jij Si Sj . For ferromagnetic materials, Jij > 0 and favors parallel alignment of neighboring
spins. Note that Eij depends only on the relative orientations of neighboring spins and not on their relative position. Hence, the interaction is isotropic (amorphous magnets are a reality) and strong coupling across disordered and non-crystalline interfaces is possible. The physical extent of the exchange interaction, called the exchange correlation length, is of the order of the domain wall width (see below). In addition to the exchange interaction, all magnetic materials are in¯uenced by the long-range dipolar interactions. The magnetostatic energy (0kM2s =volume) associated with this dipolar interaction is a function of the shape (0 < k < 4p) and size of the object and is often minimized by the formation of regions of dierent magnetization directions or domains. However, the formation of domains is subject to the additional constraint imposed by an in-built preference in all crystals to be magnetized along certain preferred directions (or easy axes). This magnetocrystalline anisotropy, arising from the spin-orbit±lattice interaction, is phenomenologically de®ned in terms of a series expansions of the direction cosines of the magnetization direction where the constants are material parameters called anisotropy constants (K). For an unperturbed lattice, the competition between the quantum-mechanical exchange interaction (which favors parallel alignment of neighboring spins) and the magnetocrystalline anisotropy (which encourages rapid spin rotation for maximum alignment along the easy axes) determines the domain wall width, d. This wall width is de®ned by the energy minimum between these two competing terms and is a key material parameter given by
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1=2 A dp , K
g 2Kd,
Rc 0
g M2s
1
where A is the exchange integral (a modi®ed form of Jij incorporating the crystal structure). Values for d range from 2 to 3 nm for high anisotropy materials (such as the rare-earth based hard magnets) to 300 nm for magnetically soft nickel. Introduction of such a wall in the unperturbed magnetic lattice is tantamount to the introduction of a twist in the magnetization. The energy per unit area associated with the formation of a wall, g, is balanced with the magnetostatic energy. If the total energy can be minimized, domains are formed; if not each particle remains as a single domain and the critical size for a single domain particle, Rc, is another important materials parameter. The ``hardness'' of a magnet, characterized by the coercive ®eld, Hc required to annul the magnetization completely, is a function of the size of the grains (single domain particles or not). In addition, the presence of second phases and defects/impurities of the size of domain walls that can eectively pin them and impede their movement making domain reversals dicult also aect the coercivity. In summary, it can be argued that the key parameters (coercive ®eld, remanence, hysteresis loss, etc.) de®ning the hysteresis behavior of any magnetic material are essentially extrinsic parameters that can be controlled by the microstructure. In the following sections, three dierent classes of materials that are the focus of much recent research and where interfaces play a controlling role in de®ning the magnetic and magnetotransport properties are discussed.
oriented along the ®lm normal. In such cases, a perpendicular anisotropy in thin ®lms can be achieved by carefully selecting a ferromagnetic material that exhibits uniaxial anisotropy in the bulk, and grow it epitaxially (good lattice matching is important) on appropriate substrates such that the magnetization is along the ®lm normal. Moreover, the phase of interest should be thermodynamically stable in the bulk, and interdiusion as well as interface reactions should be a minimum [4]. Alternatively, for ultrathin ®lms and multilayers (tM < 01 nm), it has been suggested that the surface/interface anisotropy contribution, arising from a break in symmetry at the interface [5] and proportional to tÿ1 M , can overcome the shape anisotropy and result in a spontaneous magnetization perpendicular to the ®lm. In practice, an understanding of the origin of perpendicular anisotropy in such multilayers requires a careful evaluation of the evolution and control of their complex microstructure at the atomic scale [6, 7]. The discussion in this section highlights the role of interfaces in determining the perpendicular anisotropy of [Cox(AÊ)Pty(AÊ)]n, where n is the number of repeats, grown on GaAs (111) substrates with a Ag buer layer. Multilayer stacks (x 3 A , y 15 A , n 15) grown on a 200 AÊ silver buer layer show strong uniaxial magnetic anisotropy perpendicular to the surface whilst direct growth on GaAs resulted in a predominant in-plane component. Magnetic properties (B±H loops) measured from two such samples are shown in Fig. 1. The deposition of a Ag buer layer [Fig. 1(b)] enhances the crystalline quality of the multilayers and leads to better epitaxy.
2. INTERFACE ANISOTROPY IN THIN FILMS AND MULTILAYERS
For a ferromagnetic thin ®lm or multilayer the anisotropy energy, Ean, is written in terms of an eective anisotropy constant, Ke Ean Keff sin2 y
2
where Ke includes contributions from the demagnetizing ®eld or shape anisotropy, surface/interface anisotropy and volume magnetocrystalline anisotropy and is given by Keff ÿ2pM2s 2
Ks Kv tM
3
where Ms is the saturation magnetization, tM is the thickness of the individual magnetic layers and Ks (Kv) is the surface (volume) anisotropy constant. For thick ®lms (tM greater than a few nanometers, for transition metals), the shape anisotropy energy contribution is predominant and the magnetization lies in the plane of the ®lm. However, the volume magnetocrystalline anisotropy can dominate provided the material exhibits strong uniaxial anisotropy and is grown such that the easy axis is
Fig. 1. Magnetic properties (B±H loops) of the [Cox(AÊ)Pty(AÊ)]n multilayers grown (a) without and (b) with a Ag buer layer on GaAs(111) substrate.
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High resolution images from cross-section specimens of the sample with a Ag buer layer (Fig. 2) were recorded with electron beams parallel to the [110] axis of the GaAs substrate. A good epitaxial relationship between the GaAs substrate and the Ag buer layer is observed; the {111} planes of the Ag layer are parallel to the {111} planes of the GaAs substrates. However, twin related grains, 30± 40 nm in diameter, are present in all the components of the multilayer stack. These twins are generated either by the propagation of the twin boundaries in the Ag layer into the multilayers or by nucleation of twin-related Pt grains on the Ag buer surface [8]. Rotational Moire fringes with three times the Pt(111) spacing along the growth direction, due to superposition of these twin related grains are observed in both the Ag buer layer and the Co/Pt multilayer stack. Whilst these Moire fringes explain the observed contrast in the HREM images, neither the contrast in the high resolution
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micrographs, nor the spatial frequencies in the optical diractograms from the multilayer regions in the negatives, indicate the expected 1.83 nm periodicity. However, simulations of the HREM images using a graded composition for the Co interface layer indicate that, in spite of the large dierence in scattering factors for Co and Pt, high resolution electron micrographs will not resolve the interface layer if the probability of Co occupation in the interface layer is less than 40%. Low-angle re¯ectivity measurements in the form of y±2y scans (Fig. 3) clearly show the ®rst- and second-order satellites corresponding to a repeat period of 18.4 AÊ in the multilayer structures. Transverse rocking scans at two values of scattering angle, 2y, (a) at 28, and (b) at the position of the ®rst-order multilayer satellite, 4.98, are shown in Fig. 4. In (a), although there is considerable scattering away from the specular peak, it is still possible to observe a resolution-limited specular peak
Fig. 2. High resolution images from cross-sections of a sample with a Ag buer layer showing well-textured twin-related grains with the [111] axis parallel to the substrate surface. The area with distinct Moire fringes is also marked.
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characteristic of long-range order in the sample surface plane. In (b), the scattering is entirely diuse with no observable specular peak. The diuse scattering is analogous to small-angle scattering and is caused by lateral imperfections within the multilayer structure. Quantitative analysis of the measurements is dicult as the in-plane structure necessitates a three-dimensional structural model of the Co layer in order to simulate the scattering. Such interpretation would be ambiguous without independent structural information. However, from these results initial conclusions are that the samples contain considerable in-plane inhomogeneity consistent with interfacial mixing and compound formation at the interface. These results are in agreement with the HREM imaging and simulation result. Further, in situ X-ray photoelectron diraction studies of the Co±Pt interfaces during their formation suggest that they are not atomically abrupt but are diuse over four monolayers [9]. This interpretation is also consistent with preliminary high resolution z-contrast images [10] of these multilayers that indicate a distribution of 6±8 AÊ for the Co layers in these samples. In any case, one can conclude that the Cointerface layer is diuse with evidence for atomic mixing and/or compound formation but its exact stoichiometry/structure is still unclear given the wide range of miscibility for Co in Pt. There is a 10% lattice mismatch between Cof.c.c. and Pt and in epitaxially grown multilayers this mismatch is accommodated by in-plane lattice strain. Hence, six samples with x=y 3=18, (6/ 18.5), (10.6/18), (13.5/19.1), and n 15, as well as (Co50/Pt50)4 and (Co4.4/Pt4.4)15 were examined. Polar Kerr-rotation measurements of these samples show that the largest perpendicular anisotropy and square hysteresis loop is achieved when x 3 A , but along with increasing Co thickness, the Co and Pt layers lose coherency and the magnetic anisotropy goes from being perpendicular to planar (Fig. 5). The lattice strain was measured by selected area dif-
Fig. 3. Low-angle re¯ectivity for the multilayer for the incident angle y 0:88±5:28. Two satellite re¯ections are seen at 2y 28 and 4.98.
fraction in plan-view samples using the position and displacement of the diraction spots from the Co and Pt layers and calibrated using the standard re¯ections from the GaAs substrate. For x 3 A , y 18 A , there is a 02% compressive strain in the Pt layers while the Co layers are under tension along h220i crystallographic directions. As the Co layers are grown thicker, though the f.c.c. stacking remains the same, relaxation of lattice strain in both the Co and Pt layers occurs. At x y 5 nm, the lattice parameters of both Co and Pt relax to their bulk values (Fig. 6) along with an absence of perpendicular anisotropy. If lattice strain is included, the volume contribution to the anisotropy is modi®ed as Kv Kmc ÿ c ls
4
where Kmc is the bulk magnetocrystalline anisotropy, and the magnetoelastic term is the contribution due to stress (s) and the related magnetostriction (l). Spin-orbit coupling which determines the crystal anisotropy is modi®ed by the sign of the lattice stress and the magnetoelastic interactions in thin ®lms aect their magnetic behavior. In simple terms, the axis of stress is an easy axis if the magnetoelastic contribution to the anisotropy constant (ls) is positive. On the other hand, if ls < 0, the stress axis is a hard axis and the favored direction of magnetization lies in a plane
Fig. 4. Transverse scans across the re¯ectivity rod (y scans): (a) at 2y 2:08; (b) 2y 4:98. In (a) a sharp specular peak is observed whilst in (b) the scattering is entirely diuse in nature.
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perpendicular to the stress axis. The magnetostriction of Cof.c.c. on the close packed (111) planes can be considered to be similar to that on the hexagonal planes of Coh.c.p., i.e. l < 0 [11]. In addition, the Co layers are under tension, i.e. s > 0, in the ®lm plane due to its lattice parameter being smaller than Pt. Therefore, for (111) growth, the product (ls) is negative and a uniaxial anisotropy perpendicular to the in-plane stress axis is favored. In summary, the perpendicular anisotropy observed in metallic multilayers is more complicated than a simple description involving a break in symmetry at the interface. In fact, it is determined by the interface microstructure at the atomic scale including interface mixing, compound formation and strain.
3. HARD MAGNETS
3.1. Stoner±Wohlfarth model and the role of microstructure Modern permanent magnets, generally composed of rare-earth-based compounds, are characterized by high coercivity and energy product. When the ®eld is reversed and increased in magnitude at a certain value (the coercive ®eld, Hc) the magnetization becomes unstable and reverses in the direction of the applied ®eld. In the Stoner±Wohlfarth model [12], the coercivity of these materials assuming a coherent rotation of isolated, magnetically noninteracting, single domain particles is given by Hc
2K : Ms
5
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Here, K is the anisotropy constant and could either arise from shape anisotropy (large aspect ratio precipitates as in the AlNiCo magnets) or the magnetocrystalline anisotropy (as in the modern rareearth permanent magnets). In practice, the coercive ®eld is a function of the grain size and the presence of second-phase particles that could either serve as pinning sites for domains (enhance Hc) or nucleation sites for reverse domains (reduce Hc). These microstructural features are included in a modi®ed [13, 14] formulation of Hc as HN
2K a ÿ Neff Ms Ms
6
where a and Ne are microstructure sensitive parameters. In practice, a range of microstructural features such as grain size and shape, phase distribution, grain boundary type, and the mutual crystallographic orientation between grains are parameters that determine the magnetic behavior of modern permanent magnets. To enhance our understanding of the coercive behavior of permanent magnets, it is best to consider these materials in a hierarchy of three categories: (i) single phase materials where only defects can play a role, (ii) twophase materials with a majority magnetic phase and a minority non-magnetic phase for grain isolation and (iii) two-phase materials where the majority phase (hard) and the minority phase (soft) are both magnetic and are exchange interacting. Case (ii) is simple and straightforward and relates to the practical achievement of the Stoner±Wohlfarth single domain particles [15]. Hence, in the following two sections cases (i) and (iii), highlighting the role of interfaces and intergranular phases, are discussed. 3.2. Single phase materials: epitaxially grown SmCo thin ®lms We begin with the consideration of the magnetic behavior of single phase SmCo thin ®lms prepared
Fig. 5. Polar Kerr±rotation curves with the ®eld normal to the surface for samples (a) [Co3Pt18]15, (b) [Co6Pt18.5]15, (c) [Co10.6Pt18]15, (d) [Co13.5Pt19.1]15, (e) [Co50Pt50]4 showing the change from perpendicular to in-plane magnetization.
Fig. 6. In-plane lattice strain measured by the position/ splitting of the (220) spots for the various components of the multilayer stack. The re¯ections from the GaAs substrate were used to calibrate the diraction patterns and obtain a quantitative measurement of the strain. By careful measurements of plan-view as well as cross-section samples it was determined that the lattice strain was inplane.
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by magnetron sputtering. SmCo ®lms with a nominal composition of Sm2Co7 were deposited onto single-crystal MgO(100) substrates using a 200 AÊ thick Cr buer layer. The average and local chemical composition of the ®lms were measured using energy dispersive X-ray spectroscopy (EDXS) in an analytical TEM (JEOL 200CX), while electron diffraction and high-resolution TEM (HRTEM) imaging were performed using a Topcon 002B microscope operated at 200 keV. The magnetic properties were measured with a Quantum Design d.c. magnetometer equipped with a 9 T magnet and a 7 T SQUID magnetometer equipped with both longitudinal and transverse coils. Details of the growth and characterization are described elsewhere [16, 17]. The crystal structure of Cr is body centered cubic (b.c.c.) whilst SmCo alloys are generally either hexagonal or rhombohedral. When deposited at elevated substrate temperature on MgO, Cr establishes an epitaxial relationship with the substrate providing a template for the subsequent growth of the SmCo ®lm. Figure 7 shows the microstructure of the as-grown SmCo thin ®lms. For MgO(100) substrates, plan-view electron diraction (inset in Fig.7) shows a four-fold symmetry and an epitaxial relationship given by: SmCo 112 00001kCr 100011kMgO 100001. Since
Cr(100) possesses a four-fold symmetry, the [0001] direction of SmCo grains lies along either the Cr[011] or Cr01 1 directions. The SmCo 112 0 ®lm microstructure exhibits small grains (025±60 nm in size), separated by incoherent twin boundaries, with their c-axes normal or parallel to each other, resulting in a bicrystalline morphology. Stacking disorder, normal to the c-axis within the grain structure, can be observed in the micrographs. This stacking disorder can be described as an intergrowth of dierent polytypoids of SmCo alloys. Indeed, close examination using HRTEM (Fig. 8), combined with image simulations and measurements of d0001 spacing, shows that the stacking disorder within a given grain corresponds to the dierence in stacking between SmCo3, Sm2Co7 and SmCo5 phases. The micrograph shows that these SmCo polytypoids have a common c-axis, i.e. their basal planes are parallel to each other. The crystal structures of intermetallic SmCo phases, ranging from SmCo2 to SmCo5, are closely related and are based on a regular stacking along the c-axis of two kinds of layers. One layer is of the SmCo2 Laves phase type and the other is that of SmCo5 type. Since each bilayer is Co-rich, removing one bilayer from Sm2Co7 for instance, results in the formation of a SmCo3 type of stacking.
Fig. 7. Low-magni®cation HRTEM in-plane images showing the microstructure of the SmCo 112 0 thin ®lms. The inset shows the selected area diraction pattern and the c-axis directions in adjacent grains are indicated.
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These SmCo ®lms showed very high coercivity and their initial magnetization curves show a clear pinning type behavior (Fig. 9). The magnetic hardness of SmCo thin ®lms appears to be very sensitive to the crystallography of the phases present as well as the composition and very ®ne-scale structural details within and at the boundaries of the nanometer-size grains. Two kinds of magnetic interactions exist between neighboring SmCo grains with a given crystallographic orientation. The ®rst is magnetostatic that depends mainly on the shape of the grains, whereas the second, exchange interaction, strongly depends on the grain size and intergranular isolation. Micromagnetic modeling has shown that for nanometer-scale grains in a singlephase isotropic permanent magnet, the exchange interaction between grains is dominant in determining its magnetic behavior [18]. In particular, at the remnant state, the spontaneous magnetic polarization was found to deviate from the easy axes of the grains in the vicinity of the grain boundaries. A similar model, involving strong exchange interactions between the grains in the SmCo ®lm would, in principle, explain the observed anisotropies (Fig. 9). Since the epitaxial growth constrains the c-directions of the SmCo grains to essentially lie perpendicular (i.e. only two possibilities, in plane) to each other, strong intergranular exchange interaction would result in the easy direction being at an intermediate orientation, i.e. along MgO[011] or MgO01 1. Moreover, if all the SmCo grains were strongly exchange coupled, individual grain boundaries would not be the likely pinning site to explain the pinning-type coercivity mechanism observed in these ®lms. So the question remains: what is really
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causing the pinning mechanism in these SmCo hard magnet ®lms? Two alternative explanations can be proposed. It has recently been reported that in Co-based alloy thin ®lms with a bicrystalline microstructure [19], a ``cluster'' formed by an ensemble of adjacent grains may lead to an eective anisotropy along an intermediate direction and with a magnitude depending on the strength of the intergranular exchange coupling. One can possibly assume that due to the ferromagnetic exchange coupling between the grains, a similar type of cluster may form in the case of SmCo thin ®lms, such that each cluster is considered as a large grain with an eective anisotropy along MgO[011] or MgO01 1. In such a model, the incoherent twins at the grain boundaries may serve as attractive pinning sites for the magnetic domain walls. The second hypothesis involves the stacking disorder, or the SmCo polytypoids, observed within a given grain with strong variation in local magnetocrystalline anisotropy constants. Although Sm2Co7 has a relatively high anisotropy [20], that of SmCo5 is much higher and hence, it may impede the movement of the domain walls during the magnetization reversal since it has a larger wall energy. This process is only possible if the domain wall motion is parallel to the c-axis. If the magnetization direction is normal to the c-axis, the energy of the wall is independent of the dierence in stacking sequence and should not a priori act as a pinning center. It is clear from this discussion that even in ``single'' phase materials, either the interface between regions with local changes in stacking sequence or the defects at grain boundaries, could serve as pinning sites and enhance the coercivity of SmCo thin ®lms. In addition, for materials such as SmCo with very high magnetocrystalline anisotropy constants, the domain wall widths are on the nanometer scale. These defects which are of similar dimension could eectively pin these domains. However, it is imperative that further work to image these magnetic domains be carried out to resolve the true pinning sites in these ®lms. 3.3. Two-phase materials: exchange-spring magnets
Fig. 8. HRTEM image of an individual grain indicating the stacking disorder along the c-axis or the stacking of dierent SmCo polytypoids with a common c-axis.
There is a principal diculty in achieving both a high energy product (BHmax) and a large coercivity in permanent magnets because, in general, Hc is inversely related to Ms [see equation (5)]. To overcome this limitation, Kneller [21] proposed the concept of the exchange-spring magnet. The key idea is to generate a two-phase microstructure consisting of a minority soft phase in a majority hard magnetic phase such that they are strongly exchangecoupled. In this microstructure, the magnetic reversal is initiated in the soft phase and is followed by the hard phase once the domain walls penetrate and propagate into it. Since the hard phase has a very high value of the magnetocrystalline anisotropy constant, the broad domain walls [see equation (1)]
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civity and an enhancement in remnant magnetization provided one can achieve an ideal microstructure where the soft phase has a critical dimension [21] given by Asp 1=2 : 7 dsp p 2Khp For representative values of Asp and Khp, one gets dsp 05 nm. In practice, this microstructure is approximated by an intergranular soft phase surrounding a hard magnetic phase. A typical example of such a magnet [22], comprising of the hard Nd2Fe14B phase surrounded by soft a-Fe, is shown in Fig. 10. The intergranular phase has the right dimension (5 nm) and the magnet shows a true exchange-spring behavior [23]. Fig. 9. The in-plane magnetization loops measured along dierent axes of the SmCo 11 20 ®lm. Note the nice pinning type behavior (very small slope of the initial magnetization portion) when measured along the MgO[110] direction.
nucleated in the soft phase have to be squeezed substantially for complete reversal of the hard phase. Therefore, one is expected to get both a large coer-
4. MAGNETOTRANSPORT IN OSCILLATORYCOUPLED HETEROSTRUCTURES
The discovery of giant magnetoresistance (GMR) in metallic multilayers (ferromagnetic layers separated by a non-magnetic spacer layer) opened up a new chapter in the ®eld of magnetism and magnetic materials. The origin of this magnetoresistance is
Fig. 10. The microstructure of an exchange-spring magnet with a hard Nd2Fe14B phase surrounded by 5 nm size soft a-Fe.
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Fig. 11. (a) Oscillatory behavior of the magnetoresistance (DR/R) as a function of the Au spacer thickness in permalloy/gold (Py/Au) multilayers. (b) Magnetoresistance vs ®eld for sample AF2 before and after annealing at 2508C/40 min.
believed to be spin-dependent scattering at the interfaces of electrons traversing a thin non-magnetic metal layer/spacer separating adjacent magnetic layers. This scattering and the associated MR is enhanced when the magnetizations of adjacent magnetic layers are in opposite directions (antiferromagnetic or AF coupling) and minimized when the magnetizations are in the same direction (ferromagnetic or FM coupling). In addition, oscillations in MR and the nature of the interlayer coupling (AFM or FM), as a function of the noble-metal
spacer thickness are commonly observed. A typical example of a permalloy (Ni0.8Fe0.2)/gold multilayer system is shown in Fig. 11(a). At each of the four maxima of magnetoresistance, AF coupling through the Au spacers produces an antiparallel alignment of magnetizations in adjacent permalloy layers and leads to a peak in interfacial spin-dependent scattering. When an external ®eld is applied, the magnetic layers are aligned parallel and there is a signi®cant drop in resistance (GMR).
Fig. 12. HREM of as-grown multilayers with one to three monolayer roughness and other defects associated with the (111)f.c.c. epitaxial growth.
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Fig. 13. HREM of annealed sample (AF2). Regions with reduced thickness (a) and (b) fully alloyed Au with twin planes de®ning the original interface.
To facilitate the development of such applications, fundamental understanding of the interlayer coupling, the associated GMR and their dependence on the atomic structure of the interfaces is crucial. Perfect interfaces would produce specular re¯ection and diraction of electron waves without any change in resistivity. However, signi®cant changes in resistivity are expected only from scattering by interface roughness. Moreover, the AF coupling, observed for certain spacer thickness, could be
obscured by structural defects resulting in magnetic bridges (FM coupling) between adjacent magnetic layers. Toward this end, high resolution electron microscopy at 1.7 AÊ resolution, of cross-section samples was used to investigate interface roughness, defect structures of the multilayers and changes in the microstructure on annealing. Multilayers with the Au spacer layer thickness near the second AF peak [AF2 in Fig. 11(a)] were examined before and after annealing at 2508C for 40 min in ultra-high
KRISHNAN: MAGNETISM AND MICROSTRUCTURE
vacuum. This annealing led to a decrease of saturation MR by 030%, from 11 to 8% [Fig. 11(b)]. As grown, the multilayer interfaces were 01±3 monolayers in width (Fig. 12). Detailed examination showed that the interfaces were semi-coherent with arrays of irregularly spaced mis®t dislocations (small white arrows) accommodating most, but not all, of the 15% lattice mismatch. Their optical diffractogram showed no splitting of the (111) spots indicating some residual strains in the multilayers. The (111) growth twins with associated twin boundaries parallel to the growth direction, originate from the Pt seed layer (Fig. 12). The latter do not extend through the multilayer stack but are con®ned to the ®rst one to three layers. On annealing, the atomic structure was found to be inhomogeneous. Even though the overall multilayer period remained the same, the interfaces were roughened [Fig. 13(a)] and in some cases the Au spacer had alloyed locally [Fig. 13(b)] with the adjacent permalloy layer. In regions where the Au layer completely disappears, each intermixed multilayer period is separated by a twinning plane [Fig. 13(b)]. Even though bulk Au is almost insoluble in Ni (01 at.%) at 2508C [24], an interface compound in Au/Ni multilayers has been recently observed [25]. The electron diraction pattern obtained from Fig. 13(b), con®rms the intermixed phase to be cubic with a lattice parameter of 03.8 AÊ. Such intermixing results in the roughening of the interface which can be quanti®ed by plotting a normalized histogram of the Au layer thickness along the [112] direction in the growth plane, before and after annealing from such HREM images. This plot (Fig. 14) reveals that the as-grown Au(111) layers were about two monolayers rough before annealing but a bimodal distribution with considerable spread (peaks at 10 and six monolayers) resulted from annealing [26]. The increased roughening and local bridging of permalloy layers in the multilayer both contribute to the reduction of GMR on annealing. Both these eects lead to a decrease in the AF-coupled fraction of permalloy layers in the sample. Direct imaging at atomic resolution and their quantitative interpretation made it possible to discover them for the ®rst time.
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Fig. 14. Histogram showing thickness distribution of Au spacer layers for AF2 before and after annealing. The fractional occurrence of Au(111) spacer thickness (in ML), measured from the HREM images, with the beam along the 11 0 direction is shown.
ing the physical and chemical microstructure at the nanometer scale are suciently advanced with atomic resolutions a practical reality using state of the art TEM instrumentation. This is in contrast with resolving magnetic microstructure (domains, domain walls, etc.) where the techniques are either restricted to surfaces or their resolution is two orders of magnitude larger. In the examples cited in this article, the magnetic behavior has been inferred based on indirect measurements. Development of magnetic imaging techniques and suitable micromagnetic modeling based on experimentally observed microstructural parameters should provide additional insight and aid in the development of new materials with superior properties. AcknowledgementsÐIt is a pleasure to acknowledge the contributions of a number of former students and postdocs involved in this work. In particular, I would like to thank N.-H. Cho, B. Zhang, N. Thangaraj, M. Benaissa, M. A. Brewer and Er. Girt. Other collaborators include R. F. C. Farrow (IBM), P. Panchanathan (Magnequench), E. Fullerton (ANL) and S. Bader (ANL). This work was supported by the Director, Oce of Energy Research, Oce of Basic Energy Sciences, Materials Sciences Division of the U.S. Department of Energy under contract No. DE-AC03-76SF00098.
4. CONCLUSIONS
The role of microstructure, with emphasis on interfaces and intergranular phases, in determining the magnetic properties of novel magnetic materials has been illustrated. In fact, it is quite clear that extrinsic properties control all the salient features of the hysteresis behavior of magnetic materials. In addition, in many such materials mechanical and magnetic properties are often ``coupled'' and this would be a new and exciting area of research [27]. Finally, as has been demonstrated, the techniques for study-
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