Dipolar ordering in a molecular nanomagnet detected using muon spin relaxation

Implanted muons have been used as a local probe to detect the magnetic ordering in the molecular magnetic nanodisk system Fe${}_{19}$. Two distinct groups of muon sites are identified from the relaxation data, reflecting sites near the magnetic core and sites distributed over the rest of the molecule. Dipole field calculations and Monte Carlo simulations confirm that the observed transition in Fe${}_{19}$ is consistent with magnetic ordering driven by interactions between molecules that are predominantly dipolar in nature. The triclinic crystal structure of this system gives the dipolar field a significant component transverse to the easy spin axis and the parallel component provides a dipolar bias closely tuned to the first level crossing of the system. These factors enhance the quantum tunneling between levels, thus enabling the system to avoid spin freezing at low temperatures and efficiently reach the dipolar ordered state.

Figure 1

The ferrimagnetic spin arrangement of $S=5/2$ Fe atoms within the Fe${}_{19}$ molecule leading to the $S=35/2$ ground state (the easy axis is within the plane of the disk pointing in the direction shown by the central spin [8]).

Figure 2

Comparison of zero field $\mu$SR above and below the 1.2 K transition. The inset plots the difference between the signals in the two temperature regions, showing that on cooling below $T_{\mathrm{c}}$ the fast component becomes faster and the slow component becomes slower.

Figure 3

Temperature dependence of the fast and slow relaxation rates. The changes below $T_{\mathrm{c}}$ can be represented by mean-field $T$ dependence of Eq. (3) (solid lines).

Figure 4

The ordering pattern driven by dipolar interaction for Fe${}_{19}$(m), looking down the $a$ axis with the $b$ axis running left to right and the $c$ axis running from the top left molecule to the bottom right molecule.

Figure 5

MC calculation of the ratio of the ordering temperature to the ground-state energy for a simple rhombohedral lattice with different orientations of the easy spin axis. For dipolar interactions, the ordering ratio is highly dependent on the easy axis direction and generally significantly lower than for Ising interactions. The dipolar ordering mode is AF, except for the marked cases with $\langle$111$\rangle$ spin orientation.

Figure 6

The solid line shows the estimated probability distribution of the axis-projected local field $\Delta /{\gamma }_{\mu }$ for random muon stopping sites in the (0, 0, 1/2) dipolar ordered state of Fe${}_{19}$(m). The dashed line illustrates the bimodal distribution inferred from the two observed relaxation components and their relaxation rates. This consists of a broad component (${\Delta }_{\mathrm{s}}$) with low coupling frequency and a narrow component (${\Delta }_{\mathrm{f}}$) with high coupling frequency.

Figure 7

Comparison between the level structures and relaxation paths of Fe${}_{19}$(m), Fe${}_8$, and Fe${}_{17}$. The characteristic dipolar field bias produced by neighboring molecules when the system is close to order is indicated by the dashed line in each case; the lower panel includes a typical broadening seen in EPR [8], reflecting unresolved hyperfine structure from the large number of nuclear spins in the cell. Tunneling fields (marked with circles) are accessible without external field in the case of Fe${}_{19}$ and Fe${}_{17}$, thus providing efficient paths towards the ordered ground state (arrows). In contrast, internal fields for Fe${}_8$ are insufficient to reach a tunneling condition and the application of an external field is needed to reach an ordered state [5].