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J. Phys. Chem. B 2005, 109, 10406-10418
Local Atomic Structure of Partially Ordered NiMn in NiMn/NiFe Exchange Coupled Layers: 1. XAFS Measurements and Structural Refinement Francisco J. Espinosa-Faller,†,| Rafael C. Howell,† Angel J. Garcia-Adeva,†,⊥ Steven D. Conradson,*,† Alexander Y. Ignatov,‡ Trevor A. Tyson,‡ Robin F. C. Farrow,§ and Michael F. Toney§,# Materials Science and Technology DiVision, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, Physics Deptartment, New Jersey Institute of Technology, Newark, New Jersey 07102, and IBM Almaden Research Center, 650 Harry Road, San Jose, California 95120-6099 ReceiVed: NoVember 12, 2003; In Final Form: March 1, 2005
The local atomic structure of the Mn in NiMn/NiFe exchange coupled films was investigated using Mn K-edge extended X-ray absorption fine structure (EXAFS) measurements to elucidate the possible correlation between the coercivity that can occur even in samples that display no signs of NiMn L10 ordering in diffraction patterns and such ordering on a length scale below the diffraction limit. Raising the substrate growth temperature from 3 to 200 °C increases the extent of L10 ordering in the NiMn pinning layer and the associated coercivity. A short-range order parameter (SSRO) was derived from EXAFS data for comparison with the long-range order parameter (SLRO) obtained from the X-ray diffraction measurements. Analogous to SLRO, SSRO increases in tandem with the pinning layer coercivity, implying the presence of nanometer-scale ordered clusters at the beginning stages of macroscopic L10 phase formation that apparently foster antiferromagnetism despite their small size. The behavior of the EXAFS, especially the contributions of the more distant shells, also suggests that the overall structure in materials that are not fully L10-ordered is more accurately described as locally ordered, magnetically ordered, incoherent nanodomains of the L10 phase separated by locally disordered, strained, interdomain regions that globally average to the fcc lattice with little or no local fcc structure present. The constraints on the sizes and other characteristics of these domains were explored by examining the diffraction patterns calculated for several two-dimensional analogue structures. These demonstrated that one of the most important structural features in the development of a two-phase diffraction pattern was the presence of dislocations in response to the elastic strain at the interfaces between domains where the accumulated expitaxial mismatch was greater than half of the bond length that rendered the domains incoherent with respect to each other.
Introduction to the Series Understanding and controlling the properties of complex materials, that is, those that exhibit complicated correlated or transformational behaviors when a small number of external parameters change (impurity concentration, temperature, pressure, etc.), are still at the forefront of condensed matter physics and material science. Examples include cuprate superconductors, manganite collosal magnetoresistance (CMR) compounds, martensites, and many alloys and other solid solutions. It is becoming increasingly accepted that the interesting, and oftentimes surprising, properties of these systems are related to scenarios in which phase separation, or at least the formation of two or more distinct structures with domain sizes below the diffraction limit, and resultant nanoscale heterogeneity occur. For example, in cuprate superconductors, holes arrange them* Author to whom correspondence should be addressed. E-mail:
[email protected]. † Los Alamos National Laboratory. ‡ New Jersey Institute of Technology. § IBM Almaden Research Center. | Current affiliation: Centro Marista de Estudios Superiores, Perife ´ rico Norte Tablaje 13941, Me´rida, Yucata´n, Me´xico. ⊥ Current affiliation: Departmento Fisica Aplicada I, Escuela Superior de Ingenieros de Bilbao, Alda. Urquijo s/n, 48013 Bilbao, Spain. # Current affiliation: Stanford Linear Accelerator Center, Stanford University, Stanford, CA 94305.
selves into stripes where they can move without disrupting the long-range magnetic order, effectively giving rise to a separation between regions with magnetic order and regions rich in electrical charges.1 Similarly, in CMR compounds, charge inhomogeneities several unit cells in extent competing with ferromagnetism are believed to be the origin of the CMR effect.2 Moreover, in the case of substitutional impurities in solid solutions, if the impurities attract or repel each other, texture in the form of heterogeneous nanoscale domains may form in response to local composition fluctuations and strain that can result in anomalous lattice changes or complicated phase diagrams below the percolation limit.3 Accepting these ideas poses the challenge of abandoning traditional interpretative frameworks and searching for new experimental probes, theories, and simulation methods. In the present work, we undertake a comprehensive study of the structural and electronic/magnetic properties of NixMn1-x alloy films, a system that falls into the complex materials category. The magnetic and structural properties of NixMn1-x alloy films near the equiatomic composition x ) 0.5 have generated interest both from the applied and basic viewpoints. An essential feature is that such films undergo long-range, crystallographic ordering from a chemically disordered fcc structure into a chemically ordered, L10 tetragonal phase which
10.1021/jp037449+ CCC: $30.25 © 2005 American Chemical Society Published on Web 04/29/2005
Local Atomic Structure of Partially Ordered NiMn comprises alternating atomic planes of Ni and Mn along the c-axis concomitant with a 1.5% contraction perpendicular to these planes.4 In its chemically ordered state, NiMn is a strong antiferromagnet, which makes chemically ordered NiMn a good candidate for use as the exchange coupling material to pin the reference ferromagnetic layer in spin valve magnetic read sensors.5,6 As has been shown, chemically ordered NiMn is capable of providing strong pinning fields, a high blocking temperature, thermal stability, and good corrosion resistance.7-11 However, the scientific issue of understanding the evolution of the remnant coercitivity with the degree of chemical order (amount of L10) prior to full L10 development is not trivial. In fact, for the films analyzed in this work, this quantity is nonzero even for films where diffraction patterns exhibit no sign of the L10 phase. As we will show, this apparent contradiction is reconciled by nonclassical phase separation, perhaps better described as structural hetereogeneity in the sense that the arrangement of atoms and resultant properties are best described with a model consisting of two, coexisting, ordered structures with domain sizes below the diffraction limit that originate in the degree of local chemical ordering of the NiMn. That is, chemical order exists in the form of small nanoscale L10 domains immersed in a chemically disordered matrix (or nanoscale domains of one structure associated with mesoscale ones of the other) with an average, crystallographic fcc structure. These domains do not diffract well because they are too small and are organized in such a way that their only contribution to the diffraction patterns is in the form of smooth and very small contributions to the diffuse scattering component (see ref 12 for examples of distorted lattices where these types of effects occur). In addition, on this length scale, the elastic relaxation length is comparable to the domain size so that there is a continuum of interatomic distances that nevertheless allows all of the atoms to be classed into one of the two end point structures. Within this structural heterogeneity on the nanoscale scenario, the obvious questions are the following: • If standard diffraction experiments are not an adequate tool to experimentally extract structural information about this system, what other probes can we use that give information on the length scale of interest? • How can we conciliate the structural picture extracted with local probes with the one provided by standard diffraction experiments? In other words, what types of distributions of heterogeneous domains can give rise to structures that are compatible with both the long-range average structure reflected in diffraction patterns and local structure? • How does the existence of the chemically ordered L10 phase express itself, if at all, on the electronic and measured magnetic properties of the system? • How can we explain the formation and stability of embedded nanoscale domains from the perspective of energetic/entropic arguments? This is probably one of the hardest issues to understand for the present problem. It is easy to see that analytical models for this problem are necessarily complicated to devise and solve. On the other hand, simulations are also difficult to implement; because of the length scales involved, the number of unit cells/atoms required to obtain representative results is outside current computational capabilities. In this context, however, it is worth mentioning a recent work13 in which a Ginzburg-Landau model for the coupling of strains to charge and magnetization degrees of freedom is simulated. By introducing the apparently innocuous constraint that the local stress produced by charge doping does not generate defects when
J. Phys. Chem. B, Vol. 109, No. 20, 2005 10407 deforming surrounding cells, anisotropic long-range elastic forces appear in the system that lead to the formation of multiscale texture that includes nanoscale phase separation, mesoscale inhomogeneities, and so forth. • What tools can we use to calculate physical properties of such a system? For example, to calculate electronic properties, standard electronic structure methods based on supercell calculations are not applicable, as the disorder cannot be simply described as some isolated defects. In the present work, we address these issues, dividing the results between two papers. In this first one, we will address the first two questions. XAFS measurements on 27-nm NiMn films near the equiatomic composition as a function of deposition temperature will elucidate the formation of the L10 phase and its relation to the remnant coercivity. A heterogeneous model of the structure that includes local L10 ordering on the nanoscale embedded in a chemically disordered fcc (or a variant of this one) is the best calculable interpretation of the XAFS data within the context of the two-phase model derived from crystallography. We also describe simulations of the structure factor and pair distribution functions for lattices composed of two nanophases. These will demonstrate the limits of the typical size and distribution (ordered vs disordered) of the minority phase so that it produces no noticeable signatures in diffraction patterns whereas it is easily identified with local probes. This is an essential component in the reconstruction of the arrangement of atoms because there is no method for extrapolating onedimensional local structure data to longer length scales. It also provides a means for elucidating the effects of elastic strain on the nanoscale. In the second paper, we will present electronic structure calculations for L10 clusters embedded in an fcc matrix, reporting the local density of states and magnetization. These calculations will illustrate how current-day real space methods can deal with heterogeneous systems. Introduction NiMn in its chemically ordered state is a strong antiferromagnet (AF) and thus a good candidate for use as an exchange coupling material. It has been shown that the exchange bias decreases with decreasing AF layer thickness and that a critical thickness is needed to develop the exchange coupling. It has been suggested14 that such thin films (e5-10 nm) are not chemically ordered and hence are not AF, which explains the small exchange coupling in these films. In grazing incidence X-ray diffraction measurements up to Q ∼ 5 Å-1 on NiMn films annealed at 280 °C over this range of thicknesses, no traces of sites in the L10 phase were found.14 In 15-25 nm thick films, the chemically ordered L10 phase grows at the expense of the fcc phase, increasing the exchange bias to 300-400 Oe. We start by exploring in detail the early stages of macroscopic L10 phase formation and the correlation between local order (below the diffraction limit) and the remnant coercivity in materials that exhibit only partial or negligible longer range (crystallographic) L10 ordering. In these samples, the ordering in a 27-nm-thick NiMn pinning layer was varied by the use of different substrate growth temperatures during the fabrication over a range from 3 to 200 °C. XAFS studies provide complementary information not only to diffraction data that gives the long-range average order but also to that obtained from diffuse scattering and pair distribution function analysis, which would be another means for probing the appearance and development of the nucleation sites for the L10 phase.15,16 However, for thin, multilayer, heterogeneous films, the counting
10408 J. Phys. Chem. B, Vol. 109, No. 20, 2005
Espinosa-Faller et al.
TABLE 1: Growth Temperature, Exchange Bias Field, and Long-Range/Short-Range Order Parameters sample
growth temp (°C)
Hex (Oe)
SLRO
SSRO (R ∼ 2.6 Å)
SSRO (R ∼ 4.9 Å); fcc + L10
SSRO (R ∼ 4.9 Å); homogeneous
3C 30C 100C 200C
3 30 100 200
29 39.7 65 119
1 for k g 7 Å-1. Since the split between R1 and R2 is small and Mn-Ni pairs are not distinguishable from Mn-Mn pairs, the total PDF Mn-{Ni, Mn} is anharmonic, implying that the model 2S is one of the possible structural solutions and that there is no unique unfolding into effective L10 (about eight Ni atoms at ∼2.56 Å and about four Mn atoms at ∼2.63 Å) and effective disordered fcc (broad peak of about six Ni and six Mn atoms at ∼2.58 Å). Nevertheless, EXAFS analysis indicates that the structure of Ni1-xMnx (x ∼ 0.52) films grown at applied magnetic fields of 1 kOe and moderate substrate temperatures are more ordered than would be suggested by X-ray diffraction data, albeit on a smaller length scale. This conclusion on the heterogeneity in the NiMn films follows from consideration and reconciliation of both the XAFS and XRD results. It is important to realize that combined refinements of multiple data sets that begin with the crystal structure will not find such heterogeneous structures because there is no path to them in Monte Carlo simulations.
J. Phys. Chem. B, Vol. 109, No. 20, 2005 10417 The heterogeneity of the NiMn films may evidently cause electronic and magnetic properties that are unexpected because they originate in local rather than bulk average characteristics of the lattice. This is precisely the purpose of the second paper of this series, where we will report results of real space electronic structure calculations for clusters containing L10 magnetic clusters embedded in a chemically disordered fcc matrix. This paper will show how the exchange bias field observed by the longitudinal magnetooptic Kerr effect can be attributed to the L10 nanodomains. Data in Table 1 indicate that the exchange bias increases with higher substrate deposition temperatures. Recalling that three types of microscopic domains form the film structure (fcc, L10, and interdomain/interfacial regions), we note that the amount and ordering of the observed L10 phase increases as this temperature is raised. If the interfaces were responsible for the observed behavior, one would expect to observe the exchange bias peaking with equal amounts of fcc and L10 phases, providing the largest interface volume. Therefore, by exclusion, the magnetic behavior is due to the L10 phase, which is consistent with the observed behavior of the bulk materials. Figure 8 shows the dependence of the exchange bias versus fraction of the L10 phase (SSRO from both first-shell and extended analyses) assembled using data from Table 1. The bias increases faster than the volume fraction of the tetragonal phase, suggesting that part of the signal may originate from enhancement of the antiferromagnetic coupling between local L10 domains. This heterogeneous description of the structure must be reconciled with the earlier report that did not find L10 nucleation sites by either diffraction or magnetic measurements.14 These two sets of experiments were performed on different sets of samples; relatively thick films that differed in the substrate deposition temperatures for the EXAFS and thin films of varying thickness that were given a thorough annealing for the diffraction. It could be expected that the former procedure would promote larger numbers of L10 domains as the more mobile atoms find more stable residences in many smaller domains whose size is constrained by the brief interval before they are enveloped by the growing film. The major difference, however, may be equating magnetically ordered L10 nanodomains with nucleation sites that not only will all seed the large L10 domains in the homogeneous polycrystalline films after annealing but also are the limiting factor in this growth. The diminution or absence of the signature of the L10 phase in diffraction patterns and the EXAFS results indicating high but still partial ordering and residual strain in the locally L10 structured regions imply an aperiodic and out-of-registry arrangement of L10 domains with sizes at and below the diffraction limit. The L10 structure will then develop fully as much by the linking and merging of these nanodomains that originally incorporate a large fraction of the material as much as by their growth. Although this contradicts much of the dogma on transformations, the conventional approach to such transitions was based on crystallographic data and concepts, and we have observed extensive local complexity in several systems, for example, PuGa.24 Finally, we have the phase shift result indicating that the shortrange coherent fraction of the material that is the site of the spin ordering undergoes a continuous change in the structure of its more distant component shells rather than being rigidly locked in the end point structure. This has been discussed in the context of the modeling and has been shown to reflect the domain size and possible dislocation-induced stabilization for large domains that destroys the coherence between them. The significance of this in terms of properties is that it is suggests
10418 J. Phys. Chem. B, Vol. 109, No. 20, 2005 that the magnetic properties are initiated prior to full ordering and that the ordering of the spins from the individual atoms on the chemically ordered NiMn lattice is likely to be more important in creating this effect than the structural effect of the tetragonal distortion. The magnetism can therefore occur in the coherent structures, which are characterized by smaller domains. V. Conclusions We have reported on Mn K-edge XAFS measurements of thin films of NiMn. The data were interpreted in combination with XRD results that provide information on long-range order. The results reveal that the films are inhomogeneous or heterogeneous on atomic to nanometer length scales. Though we have not established the uniqueness of the structural solution, the local structure can be understood as a mixture of tetragonal L10 nanodomains with typical size greater than 5-6 Å but smaller than the diffraction limit, in combination with similar large domains that average to the chemically disordered fcc phase and with a significant disordered component that is the interface between these two structures or between incoherent L10 domains. From both the 2S fit and group fits of the extended structure supplemented by a qualitative phase shift analysis of the third to fifth shell contribution, the SSRO parameter increases with increase of the growth temperature. SSRO is substantial even in films grown at only 3 °C, indicating that small domains of the (crystallographic) L10 phase form before the signature of this phase appears in the diffraction patterns. Comparing the amount of L10 domains with exchange coupling values demonstrates that the observed magnetic behavior can be attributed to the presence of nano- and subsequently larger domains of antiferromagnetic, chemically ordered L10 phase. We have also examined the ordering process on the nanoscale and its effect on the structure and signature in diffraction patterns. In coherent structures, diffraction patterns overlook the presence of nanoscale clusters and reveal instead an average higher-symmetry structure. Incoherent structures with dislocations at the interfaces of domains can provide significant stress relief within each domain, and the diffraction patterns show coexisting structures as a result. This suggests that magnetic order is probably more correlated with the L10 chemical ordering than the tetragonal distortions in NiMn. The study of the electronic and magnetic properties of such domains embedded in a chemically disordered fcc matrix is described in the next paper of this series. Acknowledgment. This work was supported by DOE OBES Division of Chemical Sciences under Contract W-7405. XAFS measurements were performed at SSRL (Stanford Linear Accelerator Center) and NSLS (Brookhaven National Laboratory), which are operated by the U.S. Department of Energy, Office of Basic Energy Sciences. This work was partially
Espinosa-Faller et al. performed under the auspices of the U.S. DOE, Division of Materials Science, Office of Basic Energy Sciences, under contract DE-AC02-76CH00016. References and Notes (1) Cho, A. Science 2002, 295, 1992. (2) Moreo, A.; Yunoki, S.; Dagotto, E. Science 1999, 283, 2034. (3) Conradson, S. D.; Espinosa, F. J.; Henderson, A.; Villella, P. M. In Physics in Local Lattice Distortions; AIP Conference Proceedings 554; Oyanagi, H., Bianconi, A., Eds.; American Institute of Physics: Melville, NY, 2001; p 503. (4) Landolt-Bornstein New Series; Hellwege, K. H., Ed.; SpringerVerlag: Berlin, 1971; Vol. 6, p 731. (5) Nogues, J.; Schuller, I. K. J. Magn. Magn. Mater. 1999, 192, 203. (6) Devasahayan, A. J.; Kryder, M. K. IEEE Trans. Magn. 1999, 35, 649. (7) Lin, T.; Mauri, D.; Staud, N.; Huang, C.; Howard, J. K.; Gorman, G. L. Appl. Phys. Lett. 1994, 65, 1183. (8) Mao, S.; Gangopadhyay, S.; Amin, N.; Murdock, E. Appl. Phys. Lett. 1996, 69, 3593. (9) Schonfeld, B. Prog. Mater. Sci. 1999, 44, 435. (10) Anderson, G. W.; Huai, Y.; Pakala, M. J. Appl. Phys. 2000, 87, 5726. (11) Zhang, Y. B.; van der Heijden, P. A. A.; Nozieres, J. P.; Pentek, K.; Chin, T. K.; Tuchscherer, T.; Zeltzer, A. M.; Blank, H. R.; Trotter, S.; Jaren, S.; Speriosu, V. S. IEEE Trans. Magn. 2000, 36, 586. (12) Garcia-Adeva, A. J.; Conradson, D. R.; Villella, P.; Conradson, S. D. J. Phys. Chem. B 2003, 107, 6704. (13) Bishop, A. R.; Lookman, T.; Saxena, A.; Shenoy, S. R. Europhys. Lett. 2003, 63, 289. (14) Toney, M. F.; Samant, M. G.; Lin, T.; Mauri, D. Appl Phys. Lett. 2002, 81, 4565. (15) Warren, B. E. X-Ray Diffraction; Dover: New York, 1969. (16) Lawson, A. C.; Martinez, B.; Von Dreele, R. B.; Roberts, J. A.; Sheldon, R. I.; Brun, T. O.; Richardson, J. W., Jr. Philos. Mag. B 2000, 80, 1869. (17) Teo, B. K. In EXAFS: Basic Principles and Data Analysis; Springer-Verlag: Berlin, 1986. (18) Stern, E. A. Phys. ReV. B 1993, 48, 9825. (19) Zabinsky, S. I.; Rehr, J. J.; Ankudinov, A.; Albers, R. C.; Eller, M. J. Phys. ReV. B 1995, 52, 2995. (20) This principle is known as the phase transferability. However, using the phase shift from the standard sample should be avoided if the primary purpose of XAFS analysis is to reconstruct genuine PDF or to trace driving forces for the local distortions. (21) Cebollada, A.; Weller, D.; Sticht, J.; Harp, G. R.; Farrow, R. F. C.; Marks, R. F.; Savoy, R.; Scott, J. C. Phys. ReV. B 1994, 50, 3419. (22) Dimitrov, D. A.; Ankudinov, A. L.; Bishop, A. R.; Conradson, S. D. Phys. ReV. B 1998, 58, 14227. (23) It is a limitation of the conventional XAFS analysis that it provides the pair distribution function but not a 3D picture of the cluster about the absorption site. (24) Conradson, S. D. Appl. Spectrosc. 1998, 52, A252. (25) Withers, R. L.; Proffen, Th.; Welberry, T. R. Philos. Mag. A 1999, 79, 753. (26) Warren, B. E. X-Ray Diffraction; Dover: New York, 1990. (27) Welberry, T. R.; Butler, B. D. Chem. ReV. 1995, 95, 2369. (28) Welberry, T. R.; Butler, B. D. J. Appl. Crystallogr. 1994, 27, 205. (29) Garcia-Adeva, A. J.; Conradson, D. R.; Villella, P.; Conradson, S. D. J. Phys. Chem. B 2003, 6704. (30) Rose, J. H.; Smith, J. R.; Guinea, F.; Ferrante, J. Phys. ReV. B 1984, 29, 6.
