Breakdown of the Giant Spin Model in the Magnetic Relaxation of the ${\mathrm{Mn}}_6$ Nanomagnets

We study the spin dynamics in two variants of the high-anisotropy ${\mathrm{Mn}}_6$ nanomagnet by inelastic neutron scattering, magnetic resonance spectroscopy and magnetometry. We show that a giant-spin picture is completely inadequate for these systems and that excited $S$ multiplets play a key role in determining the effective energy barrier for the magnetization reversal. Moreover, we demonstrate the occurrence of tunneling processes involving pair of states having different total spin.

Figure 1

$T$ dependence of the leading relaxation time $\tau$. Circles and squares are experimental data of (i) [8] and (ii) [9], respectively. In the thermally activated regime, $\tau \simeq {\tau }_0\exp (U/k_{B}T)$ with $U\simeq 86.4\mathrm{K}$, ${\tau }_0\simeq 2\times {10}^{-10}\sec$ for (i), and $U\simeq 53.1\mathrm{K}$, ${\tau }_0\simeq 8\times {10}^{-10}\sec$ for (ii). Continuous lines are the present theoretical calculations. The dashed line is the result of the calculation for (ii) when excited multiplets are neglected. Inset: structure of the ${\mathrm{Mn}}_6$ core. $H$ and $C$ ions are omitted for clarity.

Figure 2

INS spectra collected for (i) on IN5 with incident wavelength of 3.4 Å and 6.7 Å (inset) for $T=2\mathrm{K}$ (black) and $T=16\mathrm{K}$ (red). Lines are theoretical calculations.

Figure 3

Energy levels as a function of the $z$-component of the total spin for (i) (a) and (ii) (b). The color maps $S_{\mathrm{eff}}$, where $<S^2>\mathrm{\text{:}}=S_{\mathrm{eff}}(S_{\mathrm{eff}}+1)$. The black dashed lines correspond to the observed value of $U$. Insets: examples of derivative of the hysteresis curves measured in [8, 9] showing the presence of tunneling peaks absent in a giant-spin model. For each value of $B$, there are two points corresponding to increasing or decreasing $B$ in the hysteresis cycle. Arrows indicate the calculated (anti-)crossing positions.

Figure 4

(a) INS spectra collected for (ii) on IN5 with incident wavelength of 3.4 Å for $T=2$ and 16 K. Lines are theoretical calculations. Inset: FDMRS spectra at 5 and 15 K. Arrows indicate the calculated transition energies.