Strength and directionality of surface Ruderman–Kittel–Kasuya–Yosida interaction mapped on the atomic scale

Abstract

Ruderman-Kittel-Kasuya-Yosida interaction [1][2][3] is an indirect magnetic coupling between localized spins in a non-magnetic host mediated by conduction electrons. In diluted systems it is often the dominating magnetic interaction and has played a key part in the development of giant magnetoresistance devices 4,5 , drives ferromagnetism in heavy rare-earth elements 6 as well as in diluted magnetic semiconductors 7 and gives rise to complex magnetic phases such as spin glasses 8 . For bulk systems, an isotropic and continuous model of Ruderman-Kittel-KasuyaYosida interaction is often sufficient. However, it can be misleading in magnetic nanostructures consisting of separate magnetic atoms adsorbed on the surface of a non-magnetic material. Here, an atomically precise map of the magnetic coupling between individual adatoms in pairs is measured and directly compared with first-principles calculations, proving that Ruderman-Kittel-Kasuya-Yosida interaction is strongly directional. By investigating adatom triplets of different shapes we demonstrate that the map can serve to tailor the magnetism of larger nanostructures.Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction is ubiquitous in solid-state systems containing diluted magnetic moments in a conducting non-magnetic host. It becomes dominant whenever there is a sufficiently strong exchange coupling between the localized moments and the conduction electrons. Then, the spins of the conduction electrons, which are on average unpolarized, are forced into a preferred direction in the vicinity of each moment. This preferential direction oscillates with increasing distance from the moment. A second localized moment will interact with this spin-density oscillation and perceive either a ferromagnetic or an antiferromagnetic coupling to the first, depending on their distance. Therefore, RKKY interaction is also called indirect magnetic exchange. The first indications of indirect magnetic exchange through conduction electrons came with the research on diluted bulk alloys, where a dependence of the interaction strength on the distance between the moments with an oscillation period of half the Fermi wavelength was proposed in an isotropic and continuous model [1][2][3] . Direct experimental evidence for RKKY-like coupling of magnetic layers through transition-metal layers was obtained by spatial-averaging techniques [9][10][11][12] . There have been theoretical [13][14][15] and experimental 16 hints that accurate RKKY models have to take into account the topology of the Fermi surface and the discrete distribution of magnetic moments on the atomic lattice, but a direct experimental proof was hampered by the spatial averaging, which provides only fragmentary information on the distribution. However, as magnetic devices are becoming smaller and approaching the limit of nanostructures built by separate atoms, knowledge of the RKKY interaction on the atomic scale is essential.By using scanning tunnelling spectroscopy, it became possible to investigate magnetic interactions in atom ...

Interplay between the Kondo effect and the Ruderman–Kittel–Kasuya–Yosida interaction

“…Here the distance between the iron atoms is nearly the same, but J ex is stronger for the dimer oriented along the 011 ½ direction. This feature was also observed for magnetic dimers on a metal surface 42,43 and may be explained by an aliasing between the periodicity of the lattice and the wavelength of the RKKY oscillation. As the RKKY interaction is mediated by the conduction electrons also anisotropies in the band structure can cause a directional dependence.…”

Theory of real space imaging of Fermi surface parts

“…Ringlike charge oscillations have been observed around Cs adatoms on Ag(111), 1 and electron waves might even be confined in corrals [2][3][4] and used for quantum holography, 5 These oscillations are important to understand since they mediate, for example, interactions between atoms sitting on surface. 6,7 In contrast to surface impurities, research on subsurface defects has been less intense because of the inherent experimental and theoretical difficulties involved in the investigation. Recently, a strong stream is being created toward the ultimate goal of understanding buried defects and their accompanying electronic waves interferences.…”

Measurement by antilocalization of interactions between InAs surface electrons and magnetic surface species

“…In particular, controllable surface magnetism and its interaction with itinerant electrons in a non-magnetic host has formed the subject of continuous investigations [1][2][3][4] . In a series of comparative experiments, we study the interactions which electrons in the accumulation layer formed on the InAs surface experience from local spin moments due to rare earth (RE) ions located on the surface, upon deposition of an aqueous RE nitrate solution.…”

“…One may expect paramagnetic behavior to be maintained on a substrate, since the 4f shells are partially shielded by the outermost s and p shells and crystal field effects will hence be small. However, the magnetic moments of the RE ions may still be locked to specific orientations by interaction with the substrate atoms, or by Rudermann-Kittel-KasuyaYosida (RKKY) interactions 3,24,25 , leading to spin-glass behavior. Both a paramagnetic system or a spin-glass lead to spin-flip scattering.…”