Abstract
When the thickness of metal film approaches the nanoscale, itinerant carriers resonate between its boundaries and form quantum well states (QWSs), which are crucial to account for the film’s electrical, transport and magnetic properties. Besides the classic origin of particle-in-a-box, the QWSs are also susceptible to the crystal structures that affect the quantum resonance. Here we investigate the QWSs and the magnetic interlayer exchange coupling (IEC) in the Fe/Ag/Fe (001) trilayer from first-principles calculations. We find that the carriers at the Brillouin-zone center (belly) and edge (neck) separately form electron- and hole-like QWSs that give rise to an oscillatory feature for the IEC as a function of the Ag-layer thickness with long and short periods. Since the QWS formation sensitively depends on boundary conditions, one can switch between these two IEC periods by changing the Fe-layer thickness. These features, which also occur in the magnetic trilayers with other noble-metal spacers, open a new degree of freedom to engineer the IEC in magnetoresistance devices.
Highlights
Results and DiscussionDensity of states, and magnetic coupling. To demonstrate the connection between quantum resonances and the IEC, we take the Fe3/Ag6/Fe3 trilayer as an example (see Methods)
We optimized the supercells of Fe2/AgD/Fe2 and Fe3/AgD/Fe3, with D = 1, 2, 3, 4 by using the Vienna ab initio simulation package (VASP), within the generalized gradient approximation
The lattice structures for D > 4 were constructed based on the structure of D = 4, with D − 4 additional Ag MLs inserted at the spacer center with an equal atomic distance of 2.13 Å
Summary
Density of states, and magnetic coupling. To demonstrate the connection between quantum resonances and the IEC, we take the Fe3/Ag6/Fe3 trilayer as an example (see Methods). When the parabola band points upward (downward), that is the band bottom (top), denoted by a dashed line (a circle), the effective mass of the carriers is positive (negative), forming the electron-like (hole-like) QWS at Γ (the edge of Brillouin zone) These extremes correspond to peaks and steps of the DOSs on the pz-orbital, as shown in the right panels of Fig. 1. As we introduce the quantum confinement, the energy of the top which refers to the hole-like state reduces as Eh ∝ − Nh2/(mh*D2) and can cross the EF to influence the DOSs. An example is shown, the QWS with Nh = 5 evolves from below to above the EF when increasing the Ag spacer from 5 to 6 MLs. the electron-like and hole-like QWSs locate at different regions in the k space, they belong to the same Ag band located at its bottom and top, respectively (see Fig. 2b). They can be fitted by the following formula[26,27],
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
