We report the observation of strong coupling of a macroscopic ensemble of ~10^{16} Fe_8 molecular nanomagnets to the resonant mode of a microwave cavity. We use millimeter-wave spectroscopy to measure the splitting of the systems resonant frequency i
nduced by the coupling between the spins and the cavity mode. The magnitude of this splitting is found to scale with Sqrt[N], where N is the number of collectively coupled spins. We control N by changing the systems temperature and, thereby, the populations of the relevant spin energy levels. Strong coupling is observed for two distinct transitions between spin energy states. Our results indicate that at low temperatures nearly all of the spins in the sample couple with the cavitys resonant mode even though there is substantial inhomogeneous broadening of the Fe8 spin resonances.
In a recent Letter [1], Wernsdorfer et al. report an experimental study of a Mn12 molecular wheel which shows essentially identical behavior to the Mn12 wheel studied by Ramsey et al. [2]. In their Letter, Wernsdorfer et al. use the same model of a d
imer of two exchange-coupled spins used in [2] as a basis to extend the study of the influence of the Dzyaloshinskii-Moriya (DM) interaction on the quantum tunneling of the magnetization of this system; in particular, they show that a tilt of the DM vector away from the uniaxial anisotropy axis can account for the asymmetric nature of the quantum interference minima associated with resonances between states of opposite parity, e.g., k = 1(A). We want to stress that the inclusion of DM interactions in a system with inversion symmetry cannot mix states of opposite parity; i.e., the parity operator commutes with the Hamiltonian. Consequently, the use by Wernsdorfer et al. of a single DM vector in a centrosymmetric dimer is strictly forbidden since it implicitly violates parity conservation. The authors correctly point out that the lack of an inversion center between each pair of manganese ions on the wheel justifies the possibility of local DM interactions, even though the complete molecule has an inversion center. However, these local DM interactions must also satisfy the molecular inversion symmetry; i.e., they cannot mix states of opposite parity.We agree that such DM interactions are not always completely innocuous; e.g., they can mix spin states having the same parity. Indeed, in kagome systems [3] (cited in [1]), this can lead to weak ferromagnetism. Nevertheless, the inversion symmetry of the lattice is preserved and parity is still conserved.
