Extended Debye model for molecular magnets

Abstract

Heat capacity data on Mn12 are fitted within the extended Debye model that takes into account a continuum of optical modes as well as three different speeds of sound.PACS numbers: 75.50. Xx, 65.40.Ba Molecular magnets (MM) such as Mn 12 (Ref. 2) are relatively new materials that have a giant effective molecular spin S (such as S = 10 for Mn 12 ) built from several atomic spins by a strong intramolecular exchange interaction. The magnetic molecules have a uniaxial anisotropy that is responsible for magnetic bistability and long relaxation over the barrier at low temperatures.3 As the magnetic core of these molecules is surrounded by organic ligands, the exchange interaction between different molecules building a crystal lattice is very small. This allows them to relax independently from each other, in contrast to ferromagnets. A fascinating phenomenon discovered in molecular magnets is resonance spin tunneling under the barrier that happens if the energy levels of the spin S in both wells match. 4,5,6Molecular magnets is a new type of condensed magnetic systems whose properties differ from those of ferromagnets and dilute paramagnets. Although in the most temperature range MM are paramagnetic, their relaxation can differ from that of a single spin embedded in an elastic matrix. Since the wave length of emitted and absorbed phonons or photons exceeds the lattice spacing, there can be pronounced coherence effects in relaxation such as superradiance.7 Photon 8 and phonon 9 superradiance in MM can increase relaxation rates by a huge factor. On the other hand, the opposite effect for initial states of spins with random phases should lead to suppression of the rates by a huge factor. Strong inhomogeneous broadening in MM tends to destroy coherence effects, however, so that efforts should be done to understand the relaxation data. Another collective phenomenon in relaxation that is not yet fully understood theoretically is the phonon bottleneck (see Refs. 10,11 for older reference and Refs. 12,13 for recent work).To be able to test more sophisticated collective models of relaxation in MM, one should have reliable theoretical estimations of the single-spin relaxation rates, most notably the one-phonon or direct relaxation rate. The latter can depend, in general, on spin-phonon couplings that are difficult to measure. On the other hand, there is a simple mechanism of spin-lattice coupling through rotations of the magnetic molecules by transverse phonons 14,15 that can serve at least as the low bound on spin-lattice relaxation. As in this mechanism the crystal field acting on the spin is not distorted but only rotated, no unknown coupling constants enter the theory. Also this mechanism is likely to be the dominating relaxation channel since the cores of magnetic molecules should be much less deformable than the ligands. The corresponding results for the relaxation rates Γ due to direct processes, as well as the Raman processes, depend on only one parameter that is currently not precisely known, the speed of transverse s...

Inertia effects in the real-time dynamics of a quantum spin coupled to a Fermi sea

“…= S(S + 1) [39][40][41][42][43]. Indeed, the agreement constantly improves with increasing S, see Fig.…”

Landau-Majorana-Stückelberg-Zener dynamics driven by coupling for two interacting qutrit systems

“…However, the exact solutions of the LMSZ dynamical problem exist and may be given in terms of parabolic cilinder functions 24 . Its popularity is confirmed also by a lot of studies, both theoretical and experimental, which have been developed aiming at generalizing the LMSZ scenario considering N-level systems [25][26][27][28][29] , total crossing of bare energies 30 and the presence of classical and quantum noise stemming from sources of incoherences [31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46] : incoherent (mixed) states, relaxation processes (e.g., spontaneous emission) or interaction with a surrounding environment (e.g., nuclear spin bath). Moreover, recently, the attention has been focused on double interacting spin-qubit systems subjected to LMSZ scenario [47][48][49][50] with the scope of identifying the signatures of the coupling in the two-spin dynamics and their potentiality for possible future applications 51 .…”

Role of dipole–dipole interactions in half-field quantum transitions in magnetic nanoparticles

“…[9], these features can be ascribed to ''forbidden'' transitions Dm¼ 72, 3, 4y with the absorption (emission) of a single photon, which may be allowed due to the mixing of states caused by non-diagonal terms in the spin Hamiltonian. Note that similar mixing of states was considered as an essential factor affecting magnetic relaxation in NPs [10]. A ''giant spin'' approach was also applied to the description of nuclear spin relaxation stimulated by nanoparticles used as contrast agents in MRI treatment [12].…”