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Figure 3: Force measurements on a switching complex.(A) Simultaneous frequency shift–distance [Δf(z) (black)] and conductance-distance [G(z) (gray)] measurements at V = −10 mV on a CoH S = 1 complex with hydrogen-functionalized tip. The spin transition, occurring at a relative height z of 50 pm, is evident in both force and conductance channels. (B) Frequency shift was converted to short-range forces (black), and the conductance was deconvoluted to remove averaging over the oscillation amplitude (gray). On either side of the transition region, the deconvoluted conductance (Deconv. cond.) and force increase exponentially and can be described by the expressions G(z′) = G0exp(−2κG(z0 + z′)) and F(z′) = F0exp(−2κF(z0 + z′)), respectively. Inverse decay constants: κG, 13.0 ± 0.5 nm−1 (0 < z′ < 30 pm) and 9.5 ± 0.1 nm−1 (70 < z′ < 200 pm); κF, 10.0 ± 0.5 nm−1 (0 < z′ < 30 pm) and 4.2 ± 0.3 nm−1 (70 < z′ < 200 pm). (C) Interaction potential energy surface during the S = 1 to S = 1/2 transition (black), determined by integrating the experimental F(z′) data. Dashed lines highlight the change in slope and indicate the point where a lower potential energy surface becomes accessible. Vertical dotted lines in (B) and (C) indicate the transition regime. For all curves, zero distance corresponds to the point of closest approach. (D) Simulated diabatic potential energy curves for a CoH/h-BN/Rh(111) complex approached by a hydrogen-functionalized Pt tip (blue dash-dotted curve) and a CoH2 approached with a bare tip (red dash-dotted curve). The approximate adiabatic curve is shown as the gray dotted line. The reaction coordinate dCo-Pt is the distance between the Co and the apex Pt atoms.
To reveal the microscopic forces at work in the spin transition, we track the frequency shift, Δf, of the oscillating tuning fork from its noninteracting resonance frequency, f0 = 29,077 Hz. We measure Δf(z) curves over switching complexes and the bare h-BN. To remove the long-range forces between the extended tip and the sample, we subtract the background from the data, that is, Δf = ΔfCoH − Δfh-BN (see Materials and Methods and fig. S3). The Δf is small and negative before rapidly decreasing upon approach (Fig. 3A, black). This sharp drop in Δf coincides with a change in the G(z) measurement similar to that in Fig. 2B; however, here, this feature is broadened because of averaging over the 100-pm oscillation amplitude (Fig. 3A, gray). Short-range forces, F(z′), were quantified by converting Δf(z) using the method of Sader and Jarvis (24). Before the S = 1 to S = 1/2 transition, the force between the tip and sample is weakly attractive and grows exponentially upon approach. As the hydrogen on the tip apex couples to the CoH complex, the attractive force grows steeply over a transition region of 35 pm before leveling off (Fig. 3B). The instantaneous junction conductance, G(z′), is deconvoluted to remove the influence of an oscillating tip (25), revealing that the force and conductance transition regions coincide.