Employing ab initio density functional theory (DFT), we performed a systematic investigation of the electronic structure and the magnetic properties of atomic bilayers composed of a $4d$ transition-metal layer (Rh, Pd, and Ru) and a Co layer on the Re(0001) surface. Our DFT calculations reveal the influence of the bilayer composition and their stacking sequence on the magnetic ground state and magnetic interactions. We obtain the magnetic interactions by mapping the total energies onto an effective spin Hamiltonian which contains the exchange interaction and the Dzyaloshinskii-Moriya interaction (DMI), as well as the magnetocrystalline anisotropy energy (MAE). We observe noticeable changes in bilayer hybridization due to variation in bilayer composition and overlayer symmetry, leading to significant variation in magnetic interactions. In all considered systems, the effective exchange interaction is ferromagnetic, however, the value varies by up to a factor of 5. The effective DMI constant exhibits variation in sign over the films considered, favoring either right- (clockwise) or left-handed (counterclockwise) cycloidal spin spirals. The value of the DMI changes by up to a factor of 27 among the films. For most of the systems, the MAE favors an out-of-plane easy magnetization axis; however, for hcp-Co/Rh and hcp-Co/Ru bilayers on Re(0001), it prefers an in-plane magnetization axis. The magnitude of the MAE varies from a small value of about 0.1 meV/Co atom up to about 2 meV/Co atom for Co/Pd bilayers. The spin spiral energy dispersion curve rises quite quickly close to the ferromagnetic state for films in which the Co layer is adjacent to the vacuum indicating a large effective exchange constant which stabilizes a ferromagnetic ground state in $\mathrm{Co}/4d$ bilayers on Re(0001). The energy dispersion curve becomes flatter for films with a Co layer that is sandwiched between a $4d$ overlayer and the Re(0001) surface. In this case, the exchange constant is much reduced and the ground state is determined by the competition among the exchange interaction, favoring the FM state, the DMI, which favors cycloidal spin spirals, and the MAE, which disfavors spin spirals over the FM state. As a result, hcp-Rh/Co/Re(0001) shows a spin spiral ground state driven by DMI with a period of 13 nm, while the other films exhibit a ferromagnetic ground state. The spin spiral energy dispersion of hcp-Rh/Co/Re(0001) indicates that isolated skyrmions can be stabilized in the ferromagnetic background with an applied magnetic field. Our results further suggest that isolated skyrmions could be realized even in the absence of an external field in fcc-Rh/Co/Re(0001), hcp-Pd/Co/Re(0001), fcc-Pd/Co/Re(0001), and fcc-Ru/Co/Re(0001). A total energy comparison reveals that these five promising films are energetically strongly preferred over films with a Co overlayer. This makes ultrathin films composed of a $4d$ transition-metal overlayer on Co/Re(0001) promising candidates for the search of isolated skyrmions.

• Received 7 December 2023
• Accepted 24 January 2024

DOI:https://doi.org/10.1103/PhysRevB.109.064417