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`The effect of spatial confinement on magnetism: films, stripes and dots of Fe on Cu(111)
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`2003 J. Phys.: Condens. Matter 15 R1
`
`(http://iopscience.iop.org/0953-8984/15/2/201)
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`Lambeth Magnetic Structures, LLC Exhibit 2006
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`LMBTH-000159
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`INSTITUTE OF PHYSICS PUBLISHING
`
`JOURNAL OF PHYSICS: CONDENSED MATTER
`
`J. Phys.: Condens. Matter 15 (2003) R1–R30
`
`PII: S0953-8984(03)33359-4
`
`TOPICAL REVIEW
`
`The effect of spatial confinement on magnetism: films,
`stripes and dots of Fe on Cu(111)
`
`J Shen1, J P Pierce1,2, E W Plummer1,2 and J Kirschner3
`
`1 Solid State Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
`2 Department of Physics, University of Tennessee, Knoxville, TN 37996, USA
`3 Max-Planck-Institut f. Mikrostrukturphysik, Weinberg 2, D-06120 Halle/Saale, Germany
`
`Received 14 August 2002
`Published 20 December 2002
`Online at stacks.iop.org/JPhysCM/15/R1
`
`Abstract
`In this article, we review recent progress in the exploration of the complex
`magnetic phases of the fcc Fe/Cu(111) system. In particular, we emphasize
`the magnetic properties realized by the synthesis of novel nanostructures of
`Fe on Cu(111). These include monolayer films, one-dimensional stripe arrays
`and nanodot arrays. The effects of spatial confinement, together with strong
`spin–lattice correlations, result in dramatically different magnetic behaviour for
`the various manifestations of the Fe/Cu(111) system. Multi-scale theoretical
`calculations have been used to provide an understanding of the magnetic
`behaviour in each case.
`
`(Some figures in this article are in colour only in the electronic version)
`
`Contents
`
`Introduction
`1.
`2. Thermal MBE growth of Fe on Cu(111): rough and discontinuous films
`2.1. Morphology and structure
`2.2. Magnetism
`3. Laser MBE growth: two-dimensional ultrathin films
`3.1. Laser MBE growth
`3.2. Correlation between structure and magnetism
`4. Step decoration on vicinal surface: quasi-one-dimensional stripe array
`4.1. Formation of one-dimensional nanostructures
`4.2. Quasi-one-dimensional magnetism
`5. Buffer layer assisted growth: Fe dot assemblies on Cu(111)
`5.1. Formation of quasi-zero-dimensional clusters of Fe on Cu(111)
`5.2. Magnetic behaviour of arrayed dots
`6. Effect of spatial confinement on magnetism: direct comparison of films, stripes and
`dots of Fe on Cu(111)
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`0953-8984/03/020001+30$30.00 © 2003 IOP Publishing Ltd
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`Printed in the UK
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`7. Summary and outlook
`Acknowledgments
`References
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`1. Introduction
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`Topical Review
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`In the last decade, basic science has had a remarkable impact on practical devices in the area
`of magnetic recording. In less than ten years, the discovery of giant magnetoresistance, a
`phenomenon that occurs in thin film sandwiches of magnetic and non-magnetic materials,
`developed into a $100 billion per year market for a new generation of hard disk drives.
`This amazingly rapid progress resulted from basic research that gave the community both
`the ability to grow these artificial structures and a basic understanding of their behaviour
`that allowed optimal tuning of their properties. The rich physics associated with these
`magnetic films [1, 2]—which are nanoscale in only one spatial dimension—provides ample
`testament that nanophase magnetic materials are not just smaller but also different! As efforts
`to reduce device size have continued, it has become imperative to investigate the magnetic
`properties of artificial structures on smaller length scales and in reduced dimensionality, as
`in nanowires [3–8], dots [9–12] and pillars [13]. These advances, coupled with emerging
`techniques for synthesizing magnetic nanowires [8, 14, 15], nanoparticles [16] and molecular
`magnets [17, 18], have established the research of spatially confined magnetic materials as a
`new frontier both in basic science and technology.
`New properties that emerge at the nanoscale have at least four origins:
`(1) As the surface-to-volume ratio increases, material properties are increasingly dominated
`by surface and interface effects—a 5 nm cube of bcc Fe contains ∼12 000 atoms, ∼2000
`of which are on the surface.
`(2) Spatial confinement results in new quantum phenomena. The oscillatory exchange
`coupling [19], GMR [20], spin-dependent tunnelling [21] and exchange bias [22–24]
`manifest in magnetic multilayers are linked with one or both of these factors.
`(3) A contribution that can perhaps be called ‘characteristic length effects’. The exotic effects
`seen in GMR spin valves, for example, would not be observed if the individual layers in
`the structure were thicker than the spin-diffusion length, which is the average distance that
`an electron will travel in a material before undergoing a scattering process that changes
`its spin.
`(4) In many spin systems, like colossal magnetoresistance (CMR) materials [25] and magnetic
`semiconductors [26, 27], correlation effects are already important in the bulk spin structure,
`spin fluctuations and spin transport.
`In general, spatial confinement will significantly
`change these correlation effects.
`
`Before the exotic magnetic and electronic properties of various nanostructures like
`ultrathin films, nanowires and nanodots can be explored, important strides must be made in
`controlling their synthesis. While state-of-the-art e-beam lithography may produce structures
`down to the nanometre scale, mass production of such structures by lithography or etching-
`based fabrication has proven to be exceptionally challenging [28, 29]. For this reason, in
`the past decade considerable effort has been devoted to investigating growth methods using
`self-assembly principles. Self-assembled magnetic nanowire and nanodot arrays have been
`achieved on various types of substrates.
`In this paper we will review studies of the spatial confinement effect on magnetism
`in a highly interesting system, Fe on Cu(111). We pick this particular system because it
`provides a classic demonstration of the tremendous impact that novel synthesis techniques
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`Figure 1. Schematics showing the phenomenon of twinning. The spacing between iron atoms on
`the Cu(111) surface is such that iron atoms in a particular island will either occupy ‘A’ sites only
`or ‘B’ sites only, depending on which of these two sites was settled upon by the atom that seeded
`the island. The image shows the fault line that forms when an A-type island tries to merge with a
`B-type island.
`
`can have on the study of nanomagnetism. Ultrathin films, nanowires and nanodots of Fe have
`been successfully grown on the Cu(111) substrate, despite the fact that conventional growth
`techniques like thermal evaporation and sputter deposition do not support the growth of any
`of these nanostructures. The fact that these three types of nanostructures, which are spatially
`confined in different dimensions,can be grown on a common template allows direct observation
`of the effect of spatial confinement on magnetism.
`Another major attraction of the Fe/Cu(111) system is that iron initially grows on this
`surface in the face-centred cubic structure, which is well known for its rich magnetic phases
`and strong spin–lattice coupling [30].
`In general, a small variation of the lattice constant
`or lattice distortion can result in drastic changes of magnetic phases that range from low-
`moment ferromagnetic phase, antiferromagnetic phase, ferrimagnetic phase and high-moment
`ferromagnetic phases. For the very same reason, ultrathin films of fcc Fe on the Cu(100)
`surface have been extensively studied in the last ten years, and many exciting magnetic phase
`transitions [31, 32] and strong spin–lattice correlations [33, 34] have been identified. The fcc
`Fe/Cu(111) system, as we will soon show below, is just as exciting and its degree of complexity
`is just as high. Combining the results for both crystallographic orientations of fcc Fe will also
`lead to a better overall understanding of the material.
`In order to emphasize the critical role of novel synthesis techniques in the study of low-
`dimensional magnetism, we organize this review as follows. In section 2 we will point out that
`conventional molecular beam epitaxy (thermal MBE) fails to yield any of the low-dimensional
`magnetic nanostructures. The structure and magnetism of the thermal MBE grown Fe/Cu(111)
`will be, nevertheless, discussed in that section to provide the readers with a reference point.
`In the following sections we discuss the growth, structure and magnetism of well ordered
`Fe/Cu(111) nanostructures. Ultrathin films, stripe arrays and dot assemblies of Fe on Cu(111)
`are described in sections 3–5, respectively. In section 6, we make a direct comparison of the
`magnetic properties of these manifestations of Fe on Cu(111). The final section provides a
`summary and an outlook on future research.
`
`2. Thermal MBE growth of Fe on Cu(111): rough and discontinuous films
`
`2.1. Morphology and structure
`
`When prepared with a conventional growth technique like thermal evaporation in ultrahigh
`vacuum, Fe has a strong tendency to form multilayer islands on Cu(111) due, in part, to an
`effect called twinning. Twin structures are common features of epitaxial growth on fcc(111)
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`50 nm
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`5th ML
`4th ML
`3rd ML
`2nd ML
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`0
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`30
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`substrate
`40
`50
`nm
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`1.0
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`0.8
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`0.6
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`0.4
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`0.2
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`0.0
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`nm
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`Figure 2. STM image of the rough morphology that results when two atomic layers of Fe are
`deposited via thermal evaporation on the Cu(111) surface at 220 K. The line scan below the image
`shows that this morphology is far from that of an ideal 2.0 ML film. The white arrows indicate the
`locations of ridge-like bcc(110) structures.
`
`surfaces [35]. As shown in figure 1, the rhombic surface unit cell of the fcc(111) surface
`provides two possible sites, A and B, for adatom nucleation. Since the difference between
`the nucleation energies of the two sites is generally very small, an adatom has essentially no
`preference for one site over the other. Those that nucleate at A sites seed the growth of A-type
`islands, and those that nucleate at B sites lead to B-type islands. These two types of islands
`cannot merge to form a smooth film because a fault line, as shown in figure 1, always exists at
`the boundary between them.
`A second feature that leads to roughness is low interlayer mass transport [36]. Because
`there is a high energy barrier for Fe atoms to overcome when moving from one atomic
`layer to the next, the thermal motion of the atoms is unable to ‘heal’ pits and peaks in the
`morphology. The consequences of fcc twinning and low interlayer mass transport can be seen
`in the scanning tunnelling microscope (STM) image of an Fe/Cu(111) film shown in figure 2.
`The film was prepared by MBE at a substrate temperature of 220 K, with the nominal Fe
`dosage of 2 monolayers (ML). The marked line profile shows that the typical island height is
`about 5 ML, and that a considerable fraction of the copper surface (darkest contrast) remains
`uncovered after two atomic layers of Fe are deposited.
`In figure 2, another noticeable feature is the appearance of some ridge-like islands (marked
`by white arrows). These ridge-like structures represent the typical morphology of bcc(110)
`structures, which are elongated due to one-dimensional lattice matching with the fcc Cu(111)
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`Figure 3. Ball model of Kujdimov–Sachs (KS) orientation. There are six Fe bcc(110) domains
`that match the Cu(111) substrate in the three (cid:2)110(cid:3) directions. At the lower left is the low-energy
`electron diffraction (LEED) pattern generated by a 2.7 ML thermal MBE-grown Fe on Cu(111)
`with KS orientation. The schematic at the lower right shows the satellite spots that form due to KS
`orientation.
`
`substrate. A ball model is shown in figure 3 to demonstrate lattice matching between bcc
`Fe(110) and fcc Cu(111). There are, in total, six possible domain configurations (Kurdjumov–
`Sachs or KS orientation) along the three (cid:2)011(cid:3) directions of Cu(111) surface. The six KS
`domains give rise to six satellite spots in the corresponding LEED patterns, as shown in the
`bottom pictures of figure 3 [37]. The morphological and structural evolution, as a function
`of thickness, is shown in the STM images and LEED data in figures 4 and 5, respectively.
`The data in these figures were acquired from Fe films grown on a Cu(111) substrate with a
`. The critical thickness of the fcc → bcc transition in these Fe
`◦
`slight miscut angle of 1.2
`films is between 2.3 and 2.7 ML, as evidenced by the appearance of bcc ridges in figure 4 and
`the change of interlayer distance (as determined by LEED-IV) in figure 5. In the past, there
`has been some inconsistency in values reported for the critical thickness of the fcc → bcc
`transition. A thickness of 5 ML was reported for Fe growth on a flat Cu(111) substrate [37],
`◦
`while 1.5 ML was found for Fe on a vicinal Cu(111) substrate with an 8
`miscut angle [38].
`This inconsistency, however, reflects the fact that the nominal thickness is only an average
`value of the height of an assembly of multilayer islands. STM studies indicate that, when the
`local thickness of a particular island exceeds 6 ML, the morphology of that island becomes bcc-
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`1.8 ML
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`2.3 ML
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`60 nm
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`60 nm
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`2.7 ML
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`5.4 ML
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`60 nm
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`60 nm
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`Figure 4. STM images of thermal MBE-grown Fe on Cu(111) that show the morphological change
`that occurs when the film undergoes an fcc to bcc structural transition between nominal thicknesses
`of 2.3 and 2.7 ML.
`
`like with elongated structures. As we will discuss later, Fe adatoms have a strong preference
`for nucleation at the atomic step edges of a Cu(111) substrate. This implies that the height
`distribution of the mutilayer islands is strongly affected by the density of the substrate steps,
`even if the nominal thickness of Fe is unchanged. With this in mind, most of the varying results
`in the literature are actually consistent with each other.
`The substrate temperature has a profound influence on the growth and especially the
`fcc → bcc transition of Fe on Cu(111). A forward-scattering x-ray photoelectron diffraction
`study showed that the fcc structure of Fe on Cu(111) can only be obtained when the substrate is
`kept warmer than 80 K during growth [39]. At temperatures lower than 80 K, epitaxy of Fe on
`Cu(111) cannot be properly established and the more stable bcc phase dominates the growth.
`At temperatures significantly above room temperature, ∼700 K for example, the bcc Fe phase
`only appears at a thickness greater than 40 ML. However, the seemingly delayed fcc → bcc
`phase transition is a direct consequence of Fe–Cu interdiffusion. In fact, Fe–Cu interdiffusion
`already occurs to some extent at room temperature [40].
`
`2.2. Magnetism
`
`The thermal MBE grown Fe/Cu(111) films have consistently been found to be in a low-
`moment phase, in stark contrast to the high-moment phase observed in thermal MBE grown
`Fe films on the Cu(100) surface [41]. Early experiments on surface-coated Fe/Cu(111) films,
`−8 Torr vacuum, showed that the magnetic moment of the fcc Fe is only about
`prepared in a 10
`0.58 µB [42]. Electron-capture spectroscopy measurements on UHV-grown, uncoated films
`detected short-range ferromagnetic order in films thinner than 2 ML [43], which is consistent
`with the multilayer island morphology and the discontinuity of the films shown in figure 2.
`More recently, the thickness dependence of magnetism of Fe/Cu(111), measured by surface
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`"fcc"
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`"bcc"
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`interlayer distance (nm)
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`0.2
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`0
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`2
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`6
`4
`thickness (ML)
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`8
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`10
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`Figure 5. Plot of the vertical lattice constant of thermal MBE-grown Fe films as a function of
`thickness. A sharp and sudden drop in this lattice constant is observed at a thickness of 2.5 atomic
`layers, which corresponds well to the thickness at which the ridge-like structures appear in the
`STM images in figure 4.
`
`Fe on Cu(111)
`
`fcc
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`bcc
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`saturation magnetization (a.u.)
`
`0
`
`coverage (ML)
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`Figure 6. Thickness dependence of the surface SMOKE signal observed when the magnetization
`of thermal MBE-grown Fe films is saturated in a direction perpendicular to the Cu(111) surface.
`The data show that a low-moment to high-moment magnetic transition occurs at the same thickness
`as the structural changes discussed in figures 4 and 5.
`
`magneto-optical Kerr effect (SMOKE), gave strong evidence that the uncoated fcc Fe has a
`considerably smaller net magnetic moment than that of bulk bcc Fe [44]. Figure 6 shows the
`saturation polar Kerr intensity as a function of Fe/Cu(111) thickness. Apparently, the positive
`slope of Kerr intensity as a function of thickness takes two distinctly different values in the fcc
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`Figure 7. Hysteresis loops obtained with the SMOKE for thermal MBE-grown Fe films of various
`thicknesses. The data indicate that the easy axis of magnetization of these films rotates from the
`perpendicular to the in-plane direction at the thickness at which the previously discussed structural
`transition happens. The vertical scale of the plot of the in-plane loops has been reduced relative
`to that of the plot on the left since the intensity observed in the longitudinal Kerr effect is smaller
`than what is seen in the polar geometry.
`
`and bcc regime, with the bcc slope being nearly four times larger. Assuming that the saturation
`Kerr intensity is roughly proportional to the net magnetic moment of the sample, one would
`conclude that the MBE-grown fcc Fe/Cu(111) has a moment of the order of 0.5 µB. A number
`of photoemission studies show signs of smaller exchange splitting for the films in the fcc
`regime than that of the films in the bcc regime [45–47]. This is consistent with the observation
`of a low-moment phase. Recently, further details regarding the nature of this low-moment
`phase have been revealed by an x-ray magnetic circular dichroism (XMCD) study [48], which
`will be discussed in section 4.
`The fcc → bcc structural transition not only induces the low-moment to high-moment
`magnetic transition, but also drives a spin reorientation transition. Figure 7 shows the side-
`by-side comparison of polar and longitudinal MOKE hysteresis loops of the same Fe/Cu(111)
`sample measured in figures 4 and 5. At thicknesses below 2.3 ML, only polar loops can be
`measured. The polar loops generally have a very low remanence,reflecting the reduced thermal
`stability of the multilayer islands in the system. When the thickness is higher than 2.3 ML,
`in-plane hysteresis loops become detectable, while the saturation field for polar loops increases
`rapidly with increasing thickness. Well-defined square hysteresis loops are measured in the
`in-plane direction when the films are in a bcc structure.
`
`3. Laser MBE growth: two-dimensional ultrathin films
`
`3.1. Laser MBE growth
`
`While Fe/Cu(111) films grown with conventional molecular beam epitaxy show interesting
`features such as a low-moment fcc Fe phase and a perpendicular to in-plane spin reorientation,
`the multilayer island morphology does not have a well-defined dimensionality and is thus not
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`Figure 8. Schematic showing how laser MBE can be incorporated into a surface-analysis system.
`The laser is directed through a window and into the vacuum chamber where it ablates a target
`material onto a substrate that is held nearby.
`
`ideal for studying the effect of spatial confinement on magnetism. In the last decade, a number
`of techniques have been developed for inducing the self-assembly of high quality magnetic
`nanostructures on a given template. In this section we will discuss a very powerful method for
`growing two-dimensional ultrathin films: laser molecular beam epitaxy.
`Laser MBE essentially incorporates most of the growth principles of traditional pulsed
`laser deposition (PLD). In PLD, a powerful, nanosecond-pulsed excimer laser is focused onto
`a target. After a complex laser–solid interaction [49], a plasma plume is generated from the
`target and expands quickly toward the substrate. The plasma plume consists mainly of neutral
`atoms from the target that have a relatively moderate energy (∼1 eV), plus a small fraction of
`ions whose energy can be as high as ∼100 eV. A remarkable feature of PLD is that it yields a
`−1 or higher, which is nearly
`deposition rate (during each laser pulse) of the order of 106 ML min
`6 orders of magnitude higher than that of thermal MBE. This high deposition rate, according
`to growth theory [50, 51], tends to enhance the nucleation density, which in turn favours two-
`dimensional growth. This mechanism is basically similar to the so-called reentrant growth at
`low substrate temperatures, which also leads to high nucleation densities. Attempts to produce
`smooth Fe films using conventional MBE at low substrate temperatures, however, fail since Fe
`forms in the bcc structure from the initial stages of growth [39]. Once the bcc structure forms,
`Fe films will not grow two-dimensionally, or in a layer-by-layer mode, because of the large
`lattice mismatch between bcc Fe (of any surface orientation) and fcc Cu(111). The typical
`rough morphology of the bcc Fe on Cu(111) has already been shown in figure 5.
`The features that distinguish a laser MBE system from a PLD system include the ultrahigh
`vacuum environment and the use of reflection high-energy electron diffraction (RHEED) to
`monitor the growth of individual atomic layers in real time. Figure 8 shows a schematic of
`a typical laser MBE system that has been integrated into a surface analysis chamber at Oak
`Ridge National Laboratory that is equipped with a number of other state-of-the-art tools for
`in situ characterization of film morphology, structure and magnetism. The combination of
`layer-by-layer RHEED intensity oscillations and STM analysis of layer fillings is by far the
`most accurate method for thickness calibration. It was shown recently that such a reliable
`thickness calibration method played a critical role in the determination of the hotly debated
`antiferromagnetic spin structure of the fcc Fe/Cu(100) system [52].
`With the help of the laser MBE growth, nearly ideal layer-by-layer growth of fcc Fe
`films can be achieved, which is in stark contrast to the multilayer island morphology of the
`Fe/Cu(111) produced by thermal MBE. The surface morphology of a single atomic layer of
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`Figure 9. STM images that allow us to compare the morphologies of a single atomic layer of Fe
`as grown on Cu(111) with thermal MBE (left) and laser MBE (right). The laser MBE-grown film
`is a nearly perfect atomic layer. A substrate step runs from top to bottom through the centre of the
`image on the right.
`
`Fe/Cu(111) grown by laser MBE and thermal MBE is compared in figure 9. Both films were
`prepared at an identical substrate temperature of 220 K. The thermal MBE film, as discussed
`earlier, exhibits typical multilayer island morphology that leaves a considerable amount of Cu
`substrate uncovered. The laser MBE Fe film, at nominal thickness of 1 ML, covers about
`95% of the substrate, which can be considered as a nearly perfect monolayer film. This two-
`dimensional layer-by-layer growth persists up to a film thickness of 6 ML, above which an
`fcc → bcc structural transition occurs [53]. As we have discussed earlier, for the thermal
`MBE-grown Fe/Cu(111), the bcc structure starts to form locally in multilayer islands that are
`6 ML high. The consistency of the fcc → bcc critical thickness for the thermally deposited
`and laser MBE-grown Fe/Cu(111) films implies that 6 ML and below is the thickness range in
`which the fcc phase of Fe is stable on a Cu(111) substrate.
`
`3.2. Correlation between structure and magnetism
`
`Laser MBE-grown Fe/Cu(111) films exhibit multiple magnetic phase transitions. Unlike
`thermal MBE-grown Fe/Cu(111), the laser deposited films appear to have a high-moment
`phase when the thickness is less than 3 ML. Above 3 ML, this high-moment phase transforms
`into a low-moment phase, and eventually becomes a high-moment phase again once the films
`complete the fcc → bcc structural transition (>6 ML). Figure 10 shows the magnetic phase
`diagram for laser MBE-grown Fe/Cu(111) films. The change in saturated polar Kerr intensity
`with thickness for films that are thinner than 3 atomic layers is more than 3 times higher than
`that for films thicker than 3 ML. At thicknesses beyond those shown in the plot, when the
`films become bcc (above 6 ML), the slope of the Kerr intensity almost recovers the original
`value (not shown here). Again, assuming the Kerr intensity is proportional to the net moment
`of the films, one would conclude that at low thicknesses (<3 ML), the laser MBE-grown fcc
`Fe/Cu(111) films have a high magnetic moment which more or less equals the bcc Fe moment
`(2.2 µB). This high-moment phase transforms into a low-moment phase of 0.7 µB when the
`film thickness exceeds 3 ML. To date, the nature of the low-moment phase, i.e. whether it
`comes from a low-spin ferromagnetic phase, a ferrimagnetic phase or even a noncolinear spin
`structure [54], is undetermined.
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`4
`3
`2
`thickness (ML)
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`250
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`200
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`150
`
`100
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`50
`
`0
`
`Polar Kerr intensity
`
`Curie temperature (K)
`
`Figure 10. The upper plot shows the magnetization of the laser MBE-grown films as a function
`of thickness. The spin reorientation that occurs at a film thickness of 2 ML does not appear to be
`associated with the high-moment to low-moment transition that is observed at a thickness of 3 ML.
`The lower plot shows the thickness dependence of the Curie temperature of these films.
`IV/LEED
`RHEED
`
`TD
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`PLD
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`bcc Fe
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`fcc Cu
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`2,30
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`2,25
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`2,20
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`interrow distance (Å)
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`0
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`2
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`4
`6
`8
`thickness (ML)
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`10
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`12
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`fcc
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`bcc
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`0
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`2
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`10
`8
`6
`4
`Thickness (ML)
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`12
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`14
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`2.11
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`2.10
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`2.09
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`2.08
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`2.07
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`2.06
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`2.05
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`2.04
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`2.03
`
`Interlayer distance (A)
`
`Figure 11. Structural measurements of laser-deposited Fe films that show a sharp decrease in
`the vertical lattice constant (left) and a sudden increase in the in-plane lattice constant (right) at a
`thickness of 6.0 atomic layers. The decrease of the in-plane lattice constant between 4 and 6 ML
`may be associated with the high-moment to low-moment transition, as discussed in the text.
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`band energy
`dipolar energy
`total energy
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`1
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`4
`3
`2
`thickness (ML)
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`5
`
`6
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`1
`
`0.5
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`0
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`-0.5
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`Magnetic anisotropy energy (meV)
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`-1
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`0
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`Figure 12. Plot of the results of an ab initio calculation of the various contributions to the magnetic
`anisotropy of laser MBE-grown Fe films on Cu(111). The change in sign of the total anisotropy
`energy that is found at 2.5 ML indicates that a perpendicular to in-plane spin flop should occur at
`that thickness. This is in good agreement with experimental observations (courtesy of B Ujfulussy).
`
`Detailed structural analysis indicates that the high-moment to low-moment phase transition
`is associated with a slight change of lattice constant of the Fe films. Figure 11 shows the
`thickness-dependent vertical (a) and lateral (b) lattice constants of the laser MBE-grown
`Fe/Cu(111) films. The vertical lattice constant, or the interlayer distance, was determined
`by LEED-IV measurements. It does not change throughout the entire fcc thickness regime.
`The lateral lattice constant, or the inter-row distance, was determined by RHEED. It initially
`increases with thickness, reaching a maximum between 3 and 4 atomic layers. The distance
`between rows then decreases with increasing thickness, before it adopts a much larger value in
`the bcc regime (>6 ML). Figure 11(b) clearly shows that the thinner Fe films (<4 ML) have
`a larger inter-row distance than that of the thicker Fe films (between 4 and 6 ML). The initial
`increase of the inter-row distance likely reflects the fact that some of the electrons that contribute
`to the diffraction pattern actually diffract from the Cu substrate itself. This effect would make
`the measured value of the Fe lattice constant appear smaller during the initial stages of growth,
`and becomes less important with increasing thickness, since the penetration depth of a RHEED
`beam is typically no more than 2–3 atomic layers. The average inter-row distance peaks at
`3–4 ML, at which the contribution from the substrate is negligible. The subsequent decrease
`of the inter-row distance, however, has to be attributed to the intrinsic structural behaviour of
`the Fe films, since the presence of the substrate no longer affects the measured values. With
`this argument, and the information from both figures 11(a) and (b), one may conclude that, in
`the fcc thickness regime, the atomic volume of Fe films is slightly larger at low thicknesses
`(<3–4 ML) than it is when the films are between 4 and 6 ML thick. Considering the well-
`known fact that a larger lattice constant favours a larger magnetic moment for fcc Fe [30], the
`lattice constant decrease between 4 and 6 ML in figure 11(b) provides a plausible explanation
`of the high-moment to low-moment phase transition for the laser MBE-grown films.
`A perpendicular to in-plane spin reorientation transition was also observed in the laser
`MBE-deposited Fe/Cu(111) films. This occurs at about 2 ML and thus is not associated with
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`LMBTH-000171
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`Topical Review
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`R13
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`either the fcc → bcc structural transition (6 ML) or the high-moment to low-moment magnetic
`transition (3 ML) in this system. This is in stark contrast to the spin flop transition observed
`in thermal MBE-grown Fe/Cu(111), which is originated by an fcc → bcc structural phase
`transition. An ab initio calculation, based on the fully relativistic screened KKR method, was
`recently made by Uljfulussy et al [55], showing that this spin flop transition is governed by the
`balance between perpendicular magnetocrystalline anisotropy and in-plane shape anisotropy.
`As shown in figure 12, the magnetic anisotropy band energy (magnetocrystalline anisotropy)
`has positive values that favour perpendicular magnetization. The weak thickness dependence
`implies that the main contributions to this energy term come from the surface and interface.
`The demagnetizing energy (shape anisotropy), as is the case in all magnetic ultrathin films,
`has negative values and increases linearly with thickness. The total anisotropy energy, i.e. the
`sum of the band energy and demagnetizing energy, changes its sign from positive to negative
`at a thickness of about 2.5 ML, predicting a magnetization reorientation at that thickness. This
`is in good agreement with the experimental findings.
`The unusual thickness dependence of the Curie temperature (TC ) of the Fe ultrathin films,
`which seems to have a maximum at about 2 ML (figure 10), is a puzzle that is still not
`understood. Although some kind of non-monotonic behaviour of TC is expected due to the
`magnetic phase transitions, there are two major surprises regarding its thickness dependence
`in this system. First, TC starts to decrease at 2 ML, a thickness at which the Fe films are
`still uniformly in a high-moment phase. Second, TC monotonically decreases with increasing
`thickness above 2 ML. At that thickness, this behaviour cannot be attributed to the onset
`of the low-moment phase or to the spin reorientation. Interestingly, the first behaviour was
`also observed in the Fe/Cu(100) system, and was understood to be caused by a temperature-
`induced structural transition during the TC measurement [56]. Temperature-induced structural
`transitions have not been carefully examined so far in the Fe/Cu(111) system and cannot be
`used to explain the totally unexpected, monotonic decrease of TC. Further structural and spin-
`polarized electronic information is needed to understand the abnormal behaviour of TC in this
`system.
`
`4. Step decoration on vicinal surface: quasi-one-dimensional stripe array
`
`4.1. Formation of one-dimensional nanostructures
`
`One-dimensional (1D) systems have intrigued scientists for many years. In the years before
`powerful and cheap computing, 1D models, where analytical solutions existed, often appeared
`to be the best theoretical vehicle for studying many phenomena. Physics in one dimension
`is quite different from physics in two or three. For example, in 1D, there can be no phase
`transitions or long-range order [57] nor can there be electrical conduction because all electronic
`states are localized [58]. We live, however, in a space of three dimensions, so