Specific heat and magnetic relaxation of the quantum nanomagnet Mn 12 Ac

Self Cite

The magnetic properties of the molecular cluster Mn 12 Ac are due to the four Mn 3+ ions which have spins S=3/2 and the eight Mn 4+ ions with spins S=2. These spins are coupled by an exchange mechanism. We determine the four exchange couplings assuming a Heisenberg-type interaction between the ions. We use exact diagonalization of the spin Hamiltonian by a Lánczos algorithm and we adjust the couplings to reproduce the magnetization curve of Mn 12 Ac. We also impose the constraint of reproducing a gap of 35 K between a S=10 ground state and a first excited state with S=9. We predict that there is an excited level with S=8 at 37 K above the ground state, only slightly above the S=9 excited state which lies at 35 K and the next excited state is a S=9 multiplet at 67 K above the S=10 ground state.

Section: The Spin Hamiltonianmentioning

confidence: 99%

Exchange coupling in the magnetic molecular clusterMn12Ac

Regnault¹,

Jolicœur²,

Sessoli

et al. 2002

Self Cite

“…6 There exist two macroscopic experimental approaches to the study of spin tunneling in Mn 12 (see, e.g., Refs. 6,7,8,25,26,27,28,29,10,9,30,11,12,31,32 and references therein). Both clearly demonstrate the effect of resonant spin tunneling.…”

Section: Introductionmentioning

confidence: 99%

Dislocation-induced spin tunneling inMn12acetate

Garanin

Chudnovsky

2002

Comprehensive theory of quantum spin relaxation in Mn12 acetate crystals is developed, that takes into account imperfections of the crystal structure and is based upon the generalization of the LandauZener effect for incoherent tunneling from excited energy levels. It is shown that linear dislocations at plausible concentrations provide the transverse anisotropy which is the main source of tunneling in Mn12. Local rotations of the easy axis due to dislocations result in a transverse magnetic field generated by the field applied along the c-axis of the crystal, which explains the presence of odd tunneling resonances. Long-range deformations due to dislocations produce a broad distribution of tunnel splittings. The theory predicts that at subkelvin temperatures the relaxation curves for different tunneling resonances can be scaled onto a single master curve. The magnetic relaxation in the thermally activated regime follows the stretched-exponential law with the exponent depending on the field, temperature, and concentration of defects.

“…16, whereas the coefficient in the T -linear term is 0.022. Subtracting this small constant and fitting the rest, one obtains (16) as well as…”

mentioning

confidence: 99%

Extended Debye model for molecular magnets

Garanin

2008

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...