We show that the low-temperature physics of molecular nanomagnets, contrary to the prevailing one-molecule picture, must be determined by the long-range magnetic ordering due to many-body dipolar interactions. The calculations here performed, using Ewald's summation, suggest a ferromagnetic ground state with a Curie temperature of about 130 mK. The energy of this state is quite close to those of an antiferromagnetic state and to a glass of frozen spin chains. The latter may be realized at finite temperature due to its high entropy.

We present rigorous solution of problems of tunneling with dissipation and decoherence for a spin of an atom or a molecule in an isotropic solid matrix. Our approach is based upon switching to a rotating coordinate system coupled to the local crystal field. We show that the spin of a molecule can be used in a qubit only if the molecule is strongly coupled with its atomic environment. This condition is a consequence of the conservation of the total angular momentum (spin + matrix), that has been largely ignored in previous studies of spin tunneling. PACS numbers: 75.45.+j, 75.80.+q The problem of tunneling of a large spin [1,2,3,4,5,6,7,8,9] has received considerable attention lately in connection with spin-10 magnetic molecules, [10,11,12,13,14,15,16,17]. High-spin molecules have been proposed as qubits for quantum computers [18]. It is, therefore, important to understand the effect of the atomic environment on spin tunneling and decoherence. In this Letter we present rigorous solution of both problems for a spin of a molecule in an isotropic solid.The Caldeira-Leggett approach [19] to the problem of spin tunneling with dissipation due to phonons was outlined in the second of Refs. [4]. It has been applied in Ref. [20], though a general expression for the effective action has not been obtained. The correct formulation of the problem should account for the conservation of the total angular momentum: spin S plus the angular momentum L of the atomic lattice [21]. In the absence of the external field, tunneling of S between ⇑ and ⇓ should be accompanied by a simultaneous co-flipping of L and is possible only if J = S + L = 0. This can be satisfied by an integer but not by a half-integer S, which is another way to look at the Kramers theorem. The necessity to have L = S in the tunneling state results in the mechanical rotational energy E r = (hS) 2 /2I where I ∼ ρl 5 is the moment of inertia of the atomic lattice; ρ and l being the mass density and the linear dimension of the solid matrix containing S. This energy should be compared with the tunneling splitting ∆. The condition ∆ > E r is needed for the tunneling state with L = S, J = 0 to be the ground state of the system, while in the opposite case of ∆ < E r the ground state should be L = 0, J = S, with S frozen along the anisotropy axis. This translates into a minimal size l (typically of order 1-10 nanometers) of a free particle whose spin can tunnel between equilibrium orientations.The problem of the decoherence is even more subtle. On one hand, the matrix elements of the conventional spin-lattice interaction due to the electrostatic crystal field vanish between (| ⇑> +| ⇓>) and (| ⇑> −| ⇓>) tunneling spin states [22]. On the other hand, the realtime coherent oscillations of S in a solid matrix must be accompanied, through the conservation of the angular momentum, by the oscillating shear deformation of the solid. This should be the source of decoherence. The relevant size of the solid involved in that process is l c = c t /ω c , where c t is the velocity ...

PACS. 75.45.+j -Macroscopic quantum phenomena in magnetic systems. PACS. 75.50.Xx -Molecular magnets.Abstract. -The ground state tunnel splitting for the biaxial spin model in the magnetic field, H = −DS 2x + ES 2 z − gµBSzHz, has been investigated using an instanton approach. We find a new type of spin instanton and a new quantum interference phenomenon associated with it: at a certain field, H2 = 2SE 1/2 (D + E) 1/2 /(gµB), the dependence of the tunneling splitting on the field switches from oscillations to a monotonic growth. The predictions of the theory can be tested in Fe8 molecular nanomagnets.