RAPID COMMUNICATIONS PHYSICAL REVIEW B VOLUME 57, NUMBER 20 15 MAY 1998-II Magnetic anisotropy of epitaxial Fe films grown on curved W 001... with a graded step density Hyuk J. Choi and Z. Q. Qiu Department of Physics, University of California at Berkeley, Berkeley, California 94720 J. Pearson, J. S. Jiang, Dongqi Li, and S. D. Bader Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439 Received 27 January 1998 Ultrathin Fe films were grown epitaxially onto a stepped W 001 substrate, polished with a curvature to provide a continuously variable step density, with the steps parallel to the 100 crystalline axis. The steps induce an in-plane uniaxial magnetic anisotropy with easy axis perpendicular to the step edges. We found that this step-induced magnetic anisotropy does not enhance the Curie temperature of the Fe film. The strength of the anisotropy varies quadratically with step density, but does not decay with 1/d dependence expected for a surface-type anisotropy. We suggest that strain at the step edges might underlie the result. S0163-1829 98 50620-0 Interest in low-dimensional magnetic systems has intensi- symmetries with different lattice misfit. To that end, we re- fied in the last decade due to the discoveries of antiferromag- port in this paper, results for the Fe/W 001 system, where netic coupling1 and giant magnetoresistance2 in magnetic both Fe and W are bcc and have a lattice misfit of (aW multilayers. Thin-film technology has played an essential aFe) /aFe 10.1% in both directions, which contrasts with role due to the ability to control thickness on the monolayer that of the Fe/Ag case. We find that the step-induced anisot- ML scale. Despite the great progress made with layered ropy depends quadratically on the step density, but is only structures, significantly less effort has been devoted to the weakly thickness dependent, suggesting that its origin is not lateral confinement of magnetic structures. The technical dif- surface based, but might be strain related. Moreover, we find ficulty derives from the short-range character of the magnetic that this step-induced magnetic anisotropy has no effect on interactions, which demands a nanometer-scale lateral con- the Curie temperature of the Fe film. finement in order to manifest the quantum nature of the mag- A W 001 single-crystal disk 2 mm thick and 10 mm in netism. In efforts to achieve this goal, several groups have diameter was mechanically polished down to a 0.25- m fabricated metallic films on stepped surfaces. For example, diamond-paste finish. The 001 orientation was preserved nanometer-scale Cu wires have been decorated onto atomic over half the surface, while the other half was polished to step edges of a Mo 110 surface3 and the steps were shown form a curved shape with a vicinal angle ranging from 0° to to modulate macroscopic magnetic properties.4­7 One of the 9° to provide a continuous variation in the step density. The magnetic properties studied recently is the magnetocrystal- step edges are parallel to the 100 axis of the crystal. The W line anisotropy, which originates from the spin-orbit substrate was ultrasonically cleaned in acetone before being interaction,8 and hence is sensitive to the symmetry of the put into an ultra-high-vacuum chamber of base pressure lattice. Atomic steps can locally break the rotational symme- 7 10 11 Torr. The substrate was mounted on a sample try of the surface of an oriented single crystal and induce a manipulator by a W wire 1-mm diameter by 10-cm length uniaxial anisotropy within the film plane. This kind of step- and heated via electron bombardment. The heater was a induced anisotropy has been observed in several magnetic 0.25-mm diameter W filament located 5 mm behind the overlayer systems grown on stepped substrates, such as sample. By applying 1.5­ 1.7 kV to the substrate and Co/Cu 100 ,4,5 Fe/W 100 ,6 and Fe/Ag 100 .7 To explore the 6 ­ 7 A to the filament, the W crystal could be heated to role of symmetry breaking in the step-induced anisotropy, 2300 °C. The substrate was cleaned by cycles of annealing at Kawakami, Escorcia-Aparicio, and Qiu7 investigated Fe 1500 °C in 10 7 Torr O2 for 5 ­ 15 min and flashing to films on a curved Ag 001 substrate. They found a quadratic 2300 °C in the absence of O2. This is a standard cleaning relation between the step-induced anisotropy and the step method for W surfaces.10­12 The growth of Fe on W 001 density,7 and proposed a simple explanation based on NeŽel's has been extensively studied in the literature.13­15 Fe films pair-bonding model.9 They omit, however, the effect due to were grown onto the W substrate at room temperature using the lattice misfit of 42.5% in the vertical direction and 0.77% a water-cooled evaporator. Fe wedges also were fabricated; in the lateral direction between the bcc Fe and the fcc Ag. this was achieved by moving the substrate behind a knife- Another important consequence of NeŽel's model is a 1/d edge shutter during the deposition. The deposition rate was dependence of the step-induced anisotropy, where d is the 0.5 Ć/min, and the slope of the wedges was 0.5 Ć/mm. film thickness. Weber et al., however, observed an oscilla- The pressure during the growth was 3 ­ 5 10 10 Torr. tory behavior in the strength of the step-induced anisotropy Surface magneto-optical Kerr effect SMOKE measure- upon increasing the film thickness in a Co/Cu 100 system.5 ments were taken at room temperature with a He-Ne laser To understand the origin of the step-induced magnetic an- light source focused at different positions along the curved isotropy, more research is needed to probe different lattice substrate. As the laser beam scans across the sample to mea- 0163-1829/98/57 20 /12713 4 /$15.00 57 R12 713 © 1998 The American Physical Society RAPID COMMUNICATIONS R12 714 CHOI, QIU, PEARSON, JIANG, LI, AND BADER 57 FIG. 1. Hysteresis loops for a 2-ML Fe film grown on a 4.7°- miscut stepped W 001 surface. The square loop is for H perpen- dicular to the step edges and the split loop is for H parallel to the FIG. 2. Easy-axis hysteresis loops at room temperature for Fe step edges. This indicates the presence of a uniaxial magnetic an- films grown on flat and 4.7°-miscut stepped W 001 surfaces. No isotropy with easy axis perpendicular to the step edges. enhancement of the Curie temperature on the stepped surface is observed. sure hysteresis loops, the reflection angle of the beam simul- taneously determines the local vicinal angle. The beam size the Fe film. This raises an interesting question concerning of 0.3 mm would cover 0.7° of vicinal angle, but a nar- the origin of the magnetic long-range order LRO in the row slit was placed on the reflection path to improve the system. It is well known theoretically that an isotropic two- angular resolution to 0.2°. The magnetization is in the film dimensional 2D Heisenberg system does not exhibit LRO plane, thus only longitudinal hysteresis loops are reported at finite temperature;16 but adding uniaxial anisotropy stabi- herein; no polar SMOKE loops were observed. lizes the LRO and makes the magnetic phase transition Figure 1 displays hysteresis loops scaled to a unit satura- Ising-like.17 While experiments on 2D systems with uniaxial tion magnetization for a 2-ML Fe film on a stepped surface anisotropy support this result, there exist other 2D systems of 4.7° vicinal angle. The loops are square and exhibit full usually 100 films with in-plane magnetization whose ex- remanence for the magnetic field H applied perpendicular to perimentally determined magnetization critical exponent the step edges, but are split and lack remanence for H ap- does not belong to any known universality class.18 These plied parallel to the step edges. This behavior clearly estab- latter systems could be described more accurately as 2D XY lishes the existence of a uniaxial in-plane magnetic anisot- systems possessing bulk magnetic anisotropy. Bulk anisot- ropy with easy axis perpendicular to the step edges. There ropy could stabilize the magnetic LRO, but the phase transi- have been reports in the literature that uniaxial anisotropy is tion should not exhibit universal scaling behavior.19 Finite- produced by growing sample at an angle. However, our size effects20 also have been invoked as an alternate samples were grown at normal incidence, therefore a non- explanation of the magnetic LRO and critical exponent of normal deposition angle as a cause for the uniaxial anisot- these systems. Thus Fe on stepped W 001 should serve as a ropy can safely be disregarded. The dips in the split loops are good model system here since it evolves from being domi- due to the polarization effect of the incident beam,6 and will nated by a bulk anisotropy when the surface is flat to a be discussed in detail in a subsequent paper. It is interesting uniaxial anisotropy when it is stepped. The thickness inde- to note that the easy axis of magnetization is different from pendence of TC suggests that the additional uniaxial anisot- that for the Fe/stepped-Ag 001 and Co/stepped-Cu 001 ropy does not alter the magnetic LRO for this 2D XY system systems, for which it is parallel to the step edges. This may with bulk anisotropy. A clearer picture of the nature of the be due to the differences in the film-substrate electronic hy- magnetic phase transition might emerge from an experimen- bridization. To explore the possible consequence of step- tal study of the critical exponents of the Fe films on the flat induced magnetic anisotropy on magnetic properties, we ex- and stepped W 001 surfaces. amined the Curie temperatures TC of the Fe films. First, we To better understand the nature of the step-induced anisot- can estimate the uniaxial anisotropy due to strain at the steps ropy, the relationship between anisotropy and step density and the bulk anisotropy with strain using NeŽel's pair- was investigated. Hysteresis loops normalized to a unit satu- bonding model. We obtain the same order of magnitude ration magnetization for a 2-ML Fe film are shown in Fig. 3 (106 erg/cm3) for both quantities.22 Figure 2 shows easy-axis at different vicinal angles for H parallel to the step edges hysteresis loops normalized by film thickness for several Fe hard axis . The loops are split for 0 and are character- thicknesses at room temperature. Since it is well known that ized by a shift field Hs . The system can be described by a TC sensitively scales with the thickness of the ferromagnetic step-induced uniaxial magnetic anisotropy Ku and a cubic layer 100­200 K/ML , the fact that long-range magnetic bulk anisotropy term K1 . Thus the energy density is E orders of the Fe films on the flat and the stepped surfaces Ku cos2 K1 sin2 cos2 MsH cos , where Ms is the disappear at the same thickness, indicates that the step- saturation magnetization and is the angle between the induced uniaxial magnetic anisotropy does not enhance TC of magnetization M and H. This expression has the same form RAPID COMMUNICATIONS 57 MAGNETIC ANISOTROPY OF EPITAXIAL Fe FILMS . . . R12 715 FIG. 3. Hysteresis loops of a 2-ML Fe film on a curved W 001 substrate with H applied parallel to the step edges hard axis . is FIG. 5. Hs vs thickness along an Fe wedge, which illustrates the the vicinal angle. The shift field H weak thickness dependence as compared to a 1/d dependence s is proportional to the step- induced uniaxial anisotropy. dashed curve expected for a surface-type anisotropy. as that for an antiferromagnetically coupled sandwich, but the 9° angular range studied. Reference 6 reported that the with the antiferromagnetic coupling replaced by the uniaxial step-induced anisotropy vanished beyond 6°. To find the anisotropy.21 That is why the hysteresis loops are similar in relationship between the step-induced anisotropy and , we appearance for the two different types of systems. If the cu- fitted the data to the expression Hs A n, with A and n as bic anisotropy is eliminated (K1 0), then M would increase parameters. The result, A 4.3 0.4 Oe/degreen and linearly with H and saturates at H 2Ku /Ms . A nonzero K1 n 2.05 0.05, is plotted as the curves in Fig. 4. Thus, the opens hysteresis side-loops centered around 2Ku /Ms . fitting yields a quadratic relation, where the slope of the Thus, the shift field Hs in Fig. 3 can be used to characterize straight line in Fig. 4 b gives the power-law exponent n the strength of the step-induced uniaxial anisotropy. Figure 4 2.05. shows Hs vs measured at different positions along the The quadratic relation between the step-induced anisot- curved substrate on linear and log-log scales in a and b , ropy and step density raises a question as to the origin of the respectively. We observe step-induced anisotropy throughout uniaxial anisotropy. There are several possible explanations. Berger, Linke, and Oepen4 imaged the magnetic domain structure of the Co/stepped-Cu 001 system and concluded that the observed uniaxial anisotropy cannot be explained by the cubic bulk anisotropy.4 Dipole-dipole interactions giving rise to shape anisotropy might be another candidate for this uniaxial anisotropy. However, one might expect a shape- anisotropy origin to yield a universal direction for the easy axis of magnetization, but the easy axis we observe, perpen- dicular to the step edges, is opposite to that for the Fe/Ag and Co/Cu systems. Also, NeŽel's pair-bonding model can result in a uniaxial anisotropy at the step edges.22 Recent computer simulations support the idea that step edges can have a strong effect on the coercivity as well.23 Kawakami, Escorcia-Aparicio, and Qiu applied NeŽel's pair-bonding model to a bcc film and found that a coordinate rotation from the crystalline axis to the film axis results in a quadratic dependence of the uniaxial surface-type anisotropy on step density.7 We measured the step-induced anisotropy along an Fe wedge grown on a W 001 substrate with 4.7° vicinal angle, and find only a weak thickness dependence as op- posed to the 1/d dependence expected for a surface-type an- isotropy, as is shown in Fig. 5. We speculate that this could arise from strain induced at the step corners. In NeŽel's pair- bonding model, each nearest-neighbor bond contributes an FIG. 4. a H anisotropy K cos2 , where K is the anisotropy strength and s from Fig. 3 vs vicinal angle . The solid line is the result of a power-law fitting, yielding a quadratic relation be- is the angle between the spin and the bond direction. For an tween Hs and . b Logarithmic plot of Hs vs , where the qua- atom at the step corner, uniaxial magnetic anisotropy can be dratic relation is depicted by the straight line. generated simply by the reduction of nearest neighbors with- RAPID COMMUNICATIONS R12 716 CHOI, QIU, PEARSON, JIANG, LI, AND BADER 57 out the need to change K. This is the effect of lattice sym- In the present work, ultrathin Fe films and wedges were metry breaking. If there is film/substrate lattice misfit, how- grown on a stepped W 001 substrate polished with a curva- ever, the strain induced at the step corners could result in ture to provide a continuous gradation of the step density. different anisotropy strength K for different nearest-neighbor The steps induce a uniaxial magnetic anisotropy whose bondings. Therefore, the effect of strain at the step corners strength depends quadratically on vicinal angle, but the steps should be included in the step-induced magnetic anisotropy do not enhance the Curie temperature. While the origin of in addition to the effect of lattice symmetry breaking. Strain the anisotropy is open to discussion, it does not appear to be due to lattice misfit could persist up to a critical thickness, simply surface-type based, but might be strain induced. leading to a volume-type magnetic anisotropy.24 That is probably why the step-induced anisotropy in the Fe/W sys- tem has a very weak thickness dependence. 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