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, 064408 (2006); Phys. Rev. B 77, 184410 (2008).
The giant spin approximation
Eigenstates of giant spin model
Does it work?
For large-spin systems such as Mn12-ac
It seems to work very well
What about small-spin systems?
Dimers & Tetramers
Dimers (D2h, C2v, S2, C2)
D2h, C2v, S2 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).
wareofH.Weihe.
20
nighttreatmentofanethanolicsolutionof
Boskovic et
nX
Cl,Br)leadstoareaction
2 (X
adarkgreenprecipitateandadarkgreen
tatehasbeencrystallographicallyidentified
21
plex[MnX(HL)
2] n. Afterremovalofthe
orationtodryness,theresiduecanbe
NandlayeredwithEt 2O,toyielddarkgreenalsof[Mn
Cl,( 1)orBr( 2)).
4X 4L 4](X
getherwithapale-coloredamorphous
eof
1 andabrownoilinthecaseof
2,
emovedbywashingwithEtOH.An
betweenH 2L andMnCl 2 leadstoadark
ttleprecipitate.Thiscanbeevaporated
vedinCH
2Cl2,andlayeredwithEt
2Oto
talsof[MnCl
4(L )4]( 3).Theseform
coloredamorphousprecipitate,whichcan
ngwithEtOH.Complexes
1 3 areall
lyinreasonableyieldsof10
15%.Itis
rmationofcomplexes
1 3 involves
II toMn III byoxygenfromtheair,asis
5c,22 Thisreactionisrapidin
chemistry.
ntinducedbythepresenceoftheSchiff
ption. LabeledORTEPplotsof 1 2.25MeCN
igure1.ORTEPplotsof
1 and 2 3MeCN
ntstructuralparametersfor
1 2.25MeCN,
al., JACS 125, 14046 (2003).
Figure1. Orteprepresentationsatthe50%probabilitylevelof(a)complex
1 in 1 2.25MeCNnormaltotheMn 4 plane,(b)complex1 in 1 2.25MeCN
intheMn 4 plane,and(c)complex 3.
crystallizesinthetetragonalspacegroup
I4 withoutsolvent,
withtheasymmetricunitconsistingofone-quarterofthe
Td and D4h
C4h and C4v
Lower-symmetry orthorhombic structures
Single-spin quadratic Hamiltonian
Group-symmetric Hamiltonian
Quantization:
is diagonal
Two tetramer types
Type I:
Type II:
Electric polarizations
H. Katsura, N. Nagaosa, and A. V. Balatsky,
PRL 95, 057205 (2005).
Multiferric behavior for S4, D2d
AFM Heisenberg and DM only:
Multiferroic behavior s1=1/2
Multiferroic behavior
AFM s1=1
Phenomenological Hamiltonian
Single-spin matrix elements
Schwinger boson method using 6 noninteracting bosons
Strong Exchange Limit
AFM spin ½ level-crossing inductions
Spin 1
Strong exchange limit corrections
Electron paramagnetic resonance
For s1 > 1/2, EPR measurements of the 2nd
excited state manifold (e.g., s = 4s1-2 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 2nd excited state manifold by EPR
For AFM tetramers, the level-crossing inductions
provide a measure of the various Heisenberg,
quartic, and anisotropy interactions