Quantum Interference Oscillations of the Superparamagnetic Blocking in anFe8Molecular Nanomagnet

Abstract

We show that the dynamic magnetic susceptibility and the superparamagnetic blocking temperature of an Fe8 single molecule magnet oscillate as a function of the magnetic field Hx applied along its hard magnetic axis. These oscillations are associated with quantum interferences, tuned by Hx, between different spin tunneling paths linking two excited magnetic states. The oscillation period is determined by the quantum mixing between the ground S = 10 and excited multiplets. These experiments enable us to quantify such mixing. We find that the weight of excited multiplets in the magnetic ground state of Fe8 amounts to approximately 11.6 %. PACS numbers:High-spin molecular clusters [1, 2] display superparamagnetic behavior, very much as magnetic nanoparticles typically do. Below a time-(or frequency-)dependent blocking temperature T b , the linear magnetic response "freezes" [3,4] and magnetization shows hysteresis [5]. The slow magnetic relaxation of these single-molecule magnets (SMMs) arises from anisotropy energy barriers separating spin-up and spin-down states. Because of their small size, the magnetic response shows also evidences for quantum phenomena, such as resonant spin tunneling [3,[6][7][8]. In the case of molecules that, like Fe 8 (cf Fig. 1A and [4]), have a biaxial magnetic anisotropy, tunneling between any pair of quasi-degenerate spin states ±m can proceed via two equivalent trajectories, which, as illustrated in Fig. 1B, cross the hard anisotropy plane close to the medium anisotropy axis. A magnetic field along the hard axis changes the phases of these tunneling paths, leading to either constructive or destructive interferences. This phenomenon is known as Berry phase interference [9,10].Experimental evidences for the ensuing oscillation of the quantum tunnel splitting ∆ m , shown in Fig. 1C, were first observed in Fe 8 [11,12] and then in some other SMMs [13][14][15][16][17][18][19] by means of Landau-Zener magnetization relaxation experiments. Interference patterns measured on Fe 8 at very low temperatures, which correspond to tunneling via the ground state doublet m = ±10, are reproduced by the following spin Hamiltonian C/k B = −2.9 × 10 −5 K are magnetic anisotropy parameters, and g = 2. The sizeable fourth-order parameter C reflects not only the intrinsic anisotropy but, mainly, it parameterizes quantum mixing of the S = 10 with excited multiplets (S-mixing) and how it influences quantum tunneling via the ground state [20].In the present paper, we study the influence of Berry phase interference on the ac magnetic susceptibility χ and T b of Fe 8 , that is, on those quantities that characterize the standard SMM (or superparamagnetic) behavior. Close to T b , magnetic relaxation is dominated by tunneling near the top of the anisotropy energy barrier, thus also near excited multiplets with S = 10. In this way, we

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