Single-ion and exchange anisotropy effects in small single-molecule magnets* Richard A. Klemm University of Central Florida, Orlando, FL USA and Dmitri V. Efremov Technische Universität Dresden, Dresden, Germany Quantum Coherent Properties of Spins-III, Dec. 20, 2010 *Phys. Rev. B 74, (2006); Phys. Rev. B 77, (2008).

The giant spin approximation

Eigenstates of giant spin model

Does it work? For large-spin systems such as Mn 12 -ac It seems to work very well What about small-spin systems? Dimers & Tetramers

Dimers (D 2h, C 2v, S 2, C 2 )

D 2h, C 2v, S 2 symmetry

Dipole-dipole exchange is physically different from single-ion interactions

A. Sieber et al., Inorg. Chem. 44, 4315 (2005). D. N. Hendrickson et al., Polyhedron 24, 2280 (2005).

Boskovic et al., JACS 125, (2003).

T d and D 4h

C 4h and C 4v

Lower-symmetry orthorhombic structures

Single-spin quadratic Hamiltonian

Group-symmetric Hamiltonian

is diagonal Quantization:

Two tetramer types Type I: Type II:

Electric polarizations  Katsura, N. Nagaosa, and A. V. Balatsky, PRL  Multiferric behavior for S 4, D 2d

AFM Heisenberg and DM only: Multiferroic behavior s 1 =1/2

Multiferroic behavior

AFM s 1 =1

Phenomenological Hamiltonian

Single-spin matrix elements Schwinger boson method using 6 non- interacting bosons

Strong Exchange Limit

AFM spin ½ level-crossing inductions

Spin 1

Strong exchange limit corrections

Electron paramagnetic resonance For s 1 > 1/2, EPR measurements of the 2 nd excited state manifold (e.g., s = 4s 1 -2 for FM tetramers) can provide an independent determination of the three anisotropy Interactions,

Summary and conclusions Exact single-spin matrix elements allow for analytic expressions for the strong exchange limit energies For FM tetramers, the three first-order anisotropy interactions can be determined from the 2 nd excited state manifold by EPR For AFM tetramers, the level-crossing inductions provide a measure of the various Heisenberg, quartic, and anisotropy interactions