E. Liviotti

S-mixing contributions to the high-order anisotropy terms in the effective spin Hamiltonian for magnetic clusters

The magnetic clusters are usually described by an effective Hamiltonian acting in a fixed S space. This single-spin description neglects the mixing between states with different total spin S produced by anisotropic interactions, such as the local crystal field and the magnetic dipole-dipole coupling. We have developed a general and simple procedure, based on a perturbational approach, where the S-mixing effects are included in some new terms to be added to the original effective Hamiltonian. These terms contain some new operators, which depend on the anisotropic interactions and on the difference ΔS between the spin of the states involved in the mixing. Interestingly, these operators are very similar (in some specific cases equal) to the well known Stevens operator equivalents. A list of them for ΔS=1 and ΔS=2 and for second-order anisotropic interactions is presented. The method has been applied to study the S-mixing in two iron nanomagnets, Fe4 and Fe8.

Spin dynamics of heterometallic Cr7M wheels (M=Mn, Zn, Ni) probed by inelastic neutron scattering

Inelastic neutron scattering has been applied to the study of the spin dynamics of Cr-based antiferromagnetic octanuclear rings where a finite total spin of the ground state is obtained by substituting one Cr(III) ion (s = 3/2) with Zn (s = 0), Mn (s = 5/2) or Ni (s = 1) di-cations. Energy and intensity measurements for several intra-multiplet and inter-multiplet magnetic excitations allow us to determine the spin wavefunctions of the investigated clusters. Effects due to the mixing of different spin multiplets have been considered. Such effects proved to be important to correctly reproduce the energy and intensity of magnetic excitations in the neutron spectra. On the contrary to what is observed for the parent homonuclear Cr8 ring, the symmetry of the first excited spin states is such that anticrossing conditions with the ground state can be realized in the presence of an external magnetic field. Heterometallic Cr7M wheels are therefore good candidates for macroscopic observations of quantum effects.

S mixing and quantum tunneling of the magnetization in molecular nanomagnets.

The role of S mixing in the quantum tunneling of the magnetization in nanomagnets has been investigated. We show that the effect on the tunneling frequency is huge and that the discrepancy (more than 3 orders of magnitude in the tunneling frequency) between spectroscopic and relaxation measurements in Fe(8) can be resolved if S mixing is taken into account.

NMR as a Probe of the Relaxation of the Magnetization in Magnetic Molecules

We investigate the time autocorrelation of the molecular magnetization M(t) for three classes of magnetic molecules (antiferromagnetic rings, grids, and nanomagnets), in contact with the phonon heat bath. For all three classes, we find that the exponential decay of the fluctuations of M(t) is characterized by a single characteristic time tau(T,B) for not too high temperature T and field B. This is reflected in a nearly single-Lorentzian shape of the spectral density of the fluctuations. We show that such fluctuations are effectively probed by NMR, and that our theory explains the recent phenomenological observation by Baek et al. [Phys. Rev. B 70, 134434 (2004)] that the Larmor-frequency dependence of 1/T(1) data in a large number of AFM rings fits to a single-Lorentzian form.

Macroscopic evidence of quantum coherent oscillations of the total spin in the Mn-[

Abstract.Molecular nanomagnets, besides promising to open new frontiers in technology, have attracted huge interest in the scientific community because they can exhibit the phenomenon known as quantum tunnelling of the magnetization, i.e. coherent fluctuations of the direction of the total spin vector. In this paper we study a different quantum phenomenon involving fluctuations of the magnitude of the total spin vector. These fluctuations are related to the mixing between states with different spin quantum number, and imply new macroscopic effects, which we theoretically investigated in the Mn-[

\mathsf{3\times3}

\mathsf{3\times3}

] molecular nanomagnet

grid.

Effective spin Hamiltonian for magnetic clusters in presence of S mixing

A quite general and straightforward procedure to study the contributions to the high-order anisotropy terms due to the mixing between states with different spin S in magnetic clusters has been presented. This procedure is based on a perturbational approach and consists of adding to the effective spin Hamiltonian some terms depending on the anisotropic interactions causing the mixing. These terms are written as functions of some new operators which depends on the total spin S. The present approach has been applied to study the behavior of the cluster Cr8.

Quantum fluctuations of the total spin in molecular nanomagnets: Evidence from torque and specific heat

Macroscopic quantum phenomena arising from S-mixing in molecular nanomagnets are studied. While in the lack of an external magnetic field such effects are usually negligible, when a field of suitable intensity and direction is applied total-spin fluctuations can be amplified to the point that they dominate the macroscopic behavior at low temperature. In particular, the behavior of torque and heat capacity as a function of the field strength is dominated by S-mixing, and the former is characterized by peculiar peak-like structures. Our calculations show that the Mn-[3×3] grid is particularly suited to observe these effects.

Relaxation of the magnetization in magnetic molecules

Several mechanisms characterize the relaxation dynamics in magnetic molecules. We investigate two of them, spin-lattice coupling and incoherent quantum tunneling. The effect of the phonon heat bath is studied by analyzing the exponential time decay of the autocorrelation of the magnetization. We show that in ferromagnetic (Cu6) and antiferromagnetic (Fe6) molecular rings this decay is characterized by a single characteristic time. At very low temperature, relaxation through incoherent quantum tunneling may occur in nanomagnets such as Fe8 or Ni4. The mixing between levels with different values of the total spin (S mixing) greatly influences this mechanism. In particular, we demonstrate that a fourth-order anisotropy term O44, required to interpret experimental electron paramagnetic resonance and relaxation data in Ni4, naturally arises when S mixing is considered in calculations.