Electronic states in magnetic nanostructures

IBM Journal of Research and Development, Jan 1998 by Himpsel, Franz J, Jung, Thomas A, Seidler, Paul F

This paper provides a survey of electronic states in magnetic nanostructures, how they differ from bulk states, and how these changes are related to interesting magnetic phenomena such as oscillatory coupling and giant magnetoresistance (GMR). After explaining the role of quantum well states and spindependent electron reflectivity in magnetic multilayers, we turn our attention to lowerdimensional structures such as stripes and dots. Fabrication methods are described that use a stepped surface as template. For monitoring the growth mode, it is critical to distinguish and identify different metals at a surface by scanning tunneling microscopy (STM). This is achieved via resonant tunneling through metal-specific surface and image states.

Why nanostructures?

The popularity of the affix nano begs the question why the physics and technology of nanostructures should be special. Are there phenomena occurring at the nanometer scale that are not encountered in the more familiar microworld? A rather global answer concentrates on two related phenomena: 1) Nanometer dimensions are comparable to the electron wavelength in a solid. 2) When electrons are confined to dimensions comparable to their wavelength, the continuum of bulk energy bands becomes quantized into discrete quantum well states.

The energy spacings of the states increase as the structures become smaller, eventually becoming greater than the thermal energy kT. If that happens for states at the Fermi level E^sub F^, only a single quantum level is accessible thermally. Consequently, the dimensionality of electrons is reduced in a nanostructure because they cannot propagate along the directions of the confinement. These effects can be illustrated by analyzing the electronic states in thin metal overlayers by photoemission and its time-reversed counterpart, inverse photoemission. The two techniques are particularly useful for probing electronic states, since they make it possible to determine the complete set of quantum numbers that characterize an electron in a crystal, i.e., energy E, momentum p (or wave vector k = p/h), angular symmetry, and spin. Photoemission measures occupied states, inverse photoemission unoccupied states. We focus on electronic states near the Fermi level which are essential in transport properties, such as magnetoresistance, and drive magnetic transitions. For a recent review of magnetic nanostructures, see [1].

The density of unoccupied states at E^sub F^ with parallel momentum k^sup ||^ = 0 is displayed in Figure 1 for Cu films grown epitaxially on an fcc Fe film which, in turn, was grown epitaxially on a Cu(100) single crystal [2]. As the thickness of the Cu overlayer is increased, the density of states oscillates with a period of about six atomic layers (about 1 nm), which brings us into the nanometer regime. The amplitude of the oscillations is significant-there is no zero offset in Figure 1. In fact, the amplitude appears to be limited by the smoothness of the interfaces that is achievable by current growth techniques. The smoother the films, the larger the amplitude [3]. This explains why such oscillations have been difficult to observe in thin films so far.

The density-of-states oscillations can be understood by a simple interferometer model [4] (Figure 1, top). Reflection of electrons at the interfaces builds up standing waves whenever the round-trip phase is a multiple of 27r. The resulting interference fringes appear with a period of lambda/2, where lambda is the wavelength of the electrons. Thus, we are measuring the wavelength of electrons directly in real space, using the world's smallest interferometers. In the case of Cu(100) at E = E^sub F^ and k^sup ||^ = 0, we obtain a wavelength of 2 nm. It might be puzzling why this value is so much larger than the Fermi wavelength, which is comparable to a lattice constant. What is measured here is the wavelength of an envelope function that modulates the normal Bloch function in order to satisfy the boundary conditions at the interfaces [2].

To see the connection between density of states and quantum well states [2], we have to look at the whole spectrum of electronic states (Figure 2). For a bulk Cu(100) crystal (top spectrum), a continuous spectrum is observed which corresponds to the s, p band with delta symmetry that straddles the Fermi level and has an upper cutoff at 1.8 eV above EF, which corresponds to the p^sub 2^-like X'^sub 4^ point of the Cu band structure. In the thin-film spectra, which were obtained from overlayers differing in Cu thickness by two layers from one curve to the next, the continuous spectrum breaks up into discrete quantum well states. These states change their energy with decreasing Cu thickness and cross the Fermi level at regular thickness intervals. These Fermi-level crossings give rise to the density-of-states maxima in Figure 1. The fact that quantum well states change their energy with thickness is easy to understand by electron counting. In a finite slab of N atomic layers, one has N states at each k^sup ||^ point. Therefore, the energy interval between adjacent states shrinks as l/N with increasing film thickness and approaches zero for the bulk. For the very thin films in Figure 2, the spacings are still large compared to kT = 0.026 eV (at room temperature): e.g., five unoccupied states within 2 eV for a 20-monolayer film, giving an average spacing of 0.4 eV. We would have to make the films 15 times thicker (about 50 nm) to reach the point at which the energy spacing becomes comparable to kT. Again, these dimensions place the region of interest in the nanometer regime.