Fig. 1: Probing Er 4f electron spins through a Ti spin sensor.

a Schematic of the experimental set-up for ESR-STM measurement of an Er-Ti dimer built on MgO/Ag(100). The Ti atom (purple) is positioned close to the Er atom (orange) and located under a spin-polarized (SP) STM tip. The external magnetic field (B) defines the z-direction and is applied at an angle ϑ from the out-of-plane direction. b Projected total angular momentum of Er (J_z) onto the B field direction as a function of ϑ. The strong magnetic anisotropy favors an in-plane alignment of J_Er. c ESR spectra of the Ti atom placed 0.928 nm apart from the Er atom at different ϑ. At ϑ = 8°, a single ESR peak is visible (pink) while, at ϑ = 68° (purple), the two ESR peaks are separated due to the magnetic interactions between the Er and Ti. For the latter, the relative peak intensity indicates a ferromagnetic interaction (set-point: V_dc = 50 mV, I_dc = 20 pA, V_rf = 12 mV, B = 0.3 T). d ESR peak separation, ∆f, as a function of ϑ. The experimental points (black dots) were acquired at different set-points (V_dc = 50 mV, I_dc = 12–30 pA, V_rf = 12–20 mV, B = 0.3 T). We give error bars with 95% confidence interval. The total interaction (solid purple line) calculated by the model Hamiltonian is composed of a dipolar contribution (dashed blue line) and an exchange contribution (dashed pink line). e–g Schematic of the angular momenta of Er and Ti on MgO/Ag(100). The dipolar fields induced by Er are depicted as black curved arrows. When B is applied along the in-plane direction (ϑ = 90°), the J_z is maximum and aligned with the spin of Ti giving the largest ferromagnetic dipolar interaction. When B is rotated, the spin of Ti follows the direction of B while the total angular momentum of Er is aligned preferentially in-plane (f). In the out-of-plane direction (ϑ = 0°), J_z is minimum and aligned with the spin of Ti (g) giving a small antiferromagnetic dipolar interaction.