2002 London NIRT: Fe 8 EPR linewidth data M S dependence of Gaussian widths is due to D-strainM S dependence of Gaussian widths is due to D-strain Energies  M S 2, therefore energy differences  M SEnergies  M S 2, therefore energy differences  M S  D = 0.6%  D = 0.6% D-strain  disorder; multiple environmentsD-strain  disorder; multiple environments S. Hill, S. Maccagnano, K. Park, R. M. Achey, J. M. North and N. S. Dalal, Phys. Rev. B 65, (2002).S. Hill, S. Maccagnano, K. Park, R. M. Achey, J. M. North and N. S. Dalal, Phys. Rev. B 65, (2002). Temperature dependence of Gaussian widths is due to intermolecular spin-spin interactions (dipolar and exchange)Temperature dependence of Gaussian widths is due to intermolecular spin-spin interactions (dipolar and exchange) 117 GHz 89 GHz

field//z z, S 4 -axis BzBz Magnetic dipole transitions (  m s = ±1 ) - note frequency scale! High-frequency EPR data S = 10

2002 London NIRT: Fe 8 EPR linewidth data M S dependence of Gaussian widths is due to D-strainM S dependence of Gaussian widths is due to D-strain Energies  M S 2, therefore energy differences  M SEnergies  M S 2, therefore energy differences  M S  D = 0.6%  D = 0.6% D-strain  disorder; multiple environmentsD-strain  disorder; multiple environments S. Hill, S. Maccagnano, K. Park, R. M. Achey, J. M. North and N. S. Dalal, Phys. Rev. B 65, (2002).S. Hill, S. Maccagnano, K. Park, R. M. Achey, J. M. North and N. S. Dalal, Phys. Rev. B 65, (2002). Temperature dependence of Gaussian widths is due to intermolecular spin-spin interactions (dipolar and exchange)Temperature dependence of Gaussian widths is due to intermolecular spin-spin interactions (dipolar and exchange) 117 GHz 89 GHz

Attempts to model this behavior (spin-spin interactions)

Kyungwha Park, M.A. Novotny, N.S. Dalal, S. Hill, P.A. Rikvold, Phys. Rev. B 65, (2002).Kyungwha Park, M.A. Novotny, N.S. Dalal, S. Hill, P.A. Rikvold, Phys. Rev. B 65, (2002). Kyungwha Park, M.A. Novotny, N.S. Dalal, S. Hill, P.A. Rikvold, Phys. Rev. B (In press, October 2002); cond-mat/ Kyungwha Park, M.A. Novotny, N.S. Dalal, S. Hill, P.A. Rikvold, Phys. Rev. B (In press, October 2002); cond-mat/ Fe 8 Br  easy axis line position data Temperature dependent shifts are due to competing short range ferromagnetic exchange (J =  7 gauss) interactions and longer range antiferromagnetic dipolar coupling (  20 gauss)Temperature dependent shifts are due to competing short range ferromagnetic exchange (J =  7 gauss) interactions and longer range antiferromagnetic dipolar coupling (  20 gauss) Quantitative agreement with simulations taking both interactions into accountQuantitative agreement with simulations taking both interactions into account First evidence for exchange in this widely studied SMMFirst evidence for exchange in this widely studied SMM

field//z z, S 4 -axis BzBz Magnetic dipole transitions (  m s = ±1 ) - note frequency scale! Obtain the axial terms in the z.f.s. Hamiltonian: High-frequency EPR data

Fe 8 Br (S = 10)  easy axis linewidth data 117 GHz 89 GHz -10 Hill et al., Phys. Rev. B 65, (2002)

Body-centered tetragonal magnetic lattice  [Cu 2+ ] 2 dimer J J'J' J'J' JfJf Each Cu 2+ provides a spin-½ Intra-dimer separation: 2.74 Å NN inter-dimer distance: 7 Å NNN inter-dimer distance: ~10 Å All J s are antiferromagnetic Intra-dimer J = 4.45 meV (36 cm  1 ) J' = 0.51 meV (4 cm  1 ) J f < J' is frustrating interaction a b c To lowest order, treat as independent spin-½ dimersTo lowest order, treat as independent spin-½ dimers [Cu 2+ ] 2 Hamiltonian has perfect cylindrical [U(1)] symmetry[Cu 2+ ] 2 Hamiltonian has perfect cylindrical [U(1)] symmetry

Properties of the isolated dimer Triplet (T ) Singlet (S ) TTTT TTTT S TTTT Magnetic field JHeisenberg: EnergyZeeman:

Temperature dependence – Low T S. Sebastian et al., cond-mat/

Angle dependence – origin of anisotropy Dipolar interaction

F. Mila, Euro Phys. J. B. 6, 201 (1998). T. Giamarchi & A. M. Tsvelik, PRB 59, (1999). Insight from the two leg ladder J J'J' i = K.E.P.E.C.P. Mobile quasiparticles  dispersion (bandstructure)

Temperature dependence – Low T S. Sebastian et al., cond-mat/

8 sin exact diagonalization Spin-1 chain with easy-plane anisotropy

Antiferromagnetic exchange in a dimer of Mn 4 SMMs m1m1m1m1 m2m2m2m2 [Mn 4 O 3 Cl 4 (O 2 CEt) 3 (py) 3 ] Monomer Zeeman diagram D =  0.75(1) K B 0 4 = 5 × K J  0.12(1) K Wolfgang Wernsdorfer, George Christou, et al., Nature, 2002,

Antiferromagnetic exchange in a dimer of Mn 4 SMMs m1m1m1m1 m2m2m2m2 To zeroth order, the exchange generates a bias field B J = Jm'/g   which each spin experiences due to the other spin within the dimer Wolfgang Wernsdorfer, George Christou, et al., Nature, 2002, [Mn 4 O 3 Cl 4 (O 2 CEt) 3 (py) 3 ] Dimer Zeeman diagram     EPR Bias should shift the single spin (monomer) EPR transitions.Bias should shift the single spin (monomer) EPR transitions. D =  0.75(1) K B 0 4 = 5 × K J  0.12(1) K

S 1 = S 2 = 9 / 2 ; multiplicity of levels = (2S 1 + 1) (2S 2 + 1) = 100 Look for additional splitting (multiplicity) and symmetry effects (selection rules) in EPR.

S 1 = S 2 = 9 / 2 ; multiplicity of levels = (2S 1 + 1) (2S 2 + 1) = 100 Look for additional splitting (multiplicity) and symmetry effects (selection rules) in EPR.

Clear evidence for coherent transitions involving both molecules J z = J xy = 0.12(1) K Experiment Simulation S. Hill et al., Science 302, 1015 (2003) f = 145 GHz D =  0.75(1) K B 0 4 =  5 × K J  0.12(1) K

Although most aspects of earlier EPR line width studies on Mn12Ac and Fe8 have been understood in terms of competing exchange and dipolar interactions,20–22 an explanation for the behavior of the ground-state resonance (mS ) -4 to -3 in the present study) has remained elusive for kBT < Δ0. We speculate that this behavior is related to the development of short-range intermolecular magnetic correlations/coherences (either ferro- or antiferromagnetic) which are exchange averaged at higher temperatures. Ni 4 SMMs Inorg. Chem. 47, (2008).

Exchange biased S = 4 Ni 4 SMM A. Ferguson et al., Dalton Trans., 2008, , DOI: /b807447j

Exchange biased S = 4 Ni 4 SMM A. Ferguson et al., Dalton Trans., 2008, , DOI: /b807447j

S = 4 Mn 6 SMMs