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Structural Effects on the Magnetic Anisotropy in Cyanide Bridged Single
Molecular Magnets
Final Meeting Priority Program „MolecularMagnetism“, Bad Dürkheim, February 8th-10th, 2009
Mihail Atanasov and Peter Comba(Sofia,Heidelberg) (Heidelberg)
CN-Based SMM
<FeC1N1=176.9o
<MnN1C1=141.8o
MnN1
1
C1Fe
K[(5-Brsalen)2(H2O)2-Mn2FeIII(CN)6].2H2OJ.Long et al, Inorg.Chem.43,2004,1606P.L.Tregenna-Piggott, et al, Inorg.Chem.48,2009,128.
J.Long et al, Inorg.Chem.43,2004,1606P.L.Tregenna-Piggott, et al, Inorg.Chem.48,2009,128.
Effects on the magnetic anisotropy due to the orbitaldegeneracy (Jahn-Teller Effect) or near degeneracy(strain: geometrical (subtle distortions) or chemical(heteroligand complexes)
Inorg.Chem.47,2449(2008)
2T2g
2B2g
2Eg
2A1g
2Eg
2B2g
2B3g
2A1g
Rtteq=1.907
Rttax=2.032
Θ=56.10Rtr=1.904
Reqrh=1.902
Raxrh=1.908
α= 87o
Vibrations contribution to the [Tg⊗(εg+τ2g) Jahn-Teller coupling problem (Tg=2T2g, 3T1g)].
IH1 ])QQ(QK21)Q(QK
21[
QVQVQV
QV)Q23Q
21.(VQV
QVQV)Q23Q
21.(V
2ζ
2η
2ξτ
2ε
2θε
θεξτητ
ξτεθεζτ
ητζτεθε
+++++
⎥⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢⎢
⎣
⎡
−−−
−+−
−−−
=
Jahn-Teller Effect in 3d- Transition MetalHexacyano Complexes with Orbitally Degenerate Ground States
J.Phys.Chem.A111,9145(2007)
Effect of Spin-Orbit Coupling
2Eg
-2VτQτ
VτQτ
-ζ
ζ/22T2g
2A1g Γ7
Γ8
[Fe(CN)63-]
(t2g5)
(ζ=347 cm-1)
(-1/3) (2+4k)
(1/3) (2-2k)
405 cm-1 520 cm-1
Vτ=1052 cm-1/ÅQτ=0.128 Å
Combined effect of spin-orbit coupling andtrigonal distortions
Effect of trigonal distortions of [Fe(CN)63-] on theanisotropy of the g-tensor
Angles along the pseudo C3axis: <CFeC=α=91.28,90.89,90.92o
δθ=0.73o; gz=0.91; gxy=2.33
Glaser et al, Inorg.Chem.,2009
2sin( ) sin( / 2)3
θ α=
Static strain along τ2g (Ci-type) distortions: singlecrystal g-tensor values and magnetic susceptibilitiesof Fe(CN)63-
gi:
Anisotropic Exchange in [CNMIIN4-NC-FeIII(CN)5]2-
Pairs (MII=Cu,Ni)
Inorg.Chem.47,2449(2008)
BgsBgssAssDssDsssJH BBsph 221'1212
'1222212
'12
'1 ˆˆˆˆˆˆˆˆˆˆ μμ +++++−=
⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢
⎣
⎡
−−
+−
=⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
−−=
DDD
DEDD
DDED
DDDDDDDDDD
yzxz
yzxy
xzxy
yyxxyzxz
yzyyxy
xzxyxx
34
232
232
12D
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
−−
−=
00
0
xy
xz
yz
AAAAAA
12A
The J and D are deduced from explicit calculations using: FeJTFeFeFeM HslOssH ++−= ς
Acting on SM=s2=1/2,ms=±1/2 (Cu2+) or s2=1,ms=0,±1 (Ni2+) spinsand the (ml=ξ,η,ζ)⊗(ms=±1/2) spin-orbital basis of Fe3+:
Jξξ=(M-Fe,dyz); Jηη=(M-Fe,dxz); Jζζ=(M-Fe,dxy) exchange couplingparameters
ζζηηξξεεθθ
ζζηζξζ
ηζηηξη
ξζξηξξ
222222ˆˆˆˆˆˆˆ
11 tttttteeeeaa JJJJJJJJJJJJJJJ
TTTTTTO +++++=⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡=
21ˆˆ ˆ2
= =a1T 1 L 2 1ˆˆ ˆ ˆ ˆ( ) ( )3 3
= − = −2 2 2eθ z zT L 1 L L
11 ( )3aJ J J Jξξ ηη ζζ= + + 1 ( )
2еJ J J Jθ ξξ ηη ζζ= + −
Fe 2E 2E 2B2
J(2E) J(2E) J(2B2)Cu(dz2) 19.4 19.4 1.6Ni(dz2,dx2-y2) 12.9 12.9 0.0
94.5)(31)(
31
49.4)(91)(
92
)(121)(
61)(
)(41)(
61)(
)(121)(
61)(
222
222
222
222
2
222
1
=−=
−=−−=
−=
+−=
−−=
BJEJD
BJEJJ
BJEJEE
BJEJBE
BJEJBE
cm-1
cm-1
The Cu-NC-Fe Pair
72.134
32
111 −=−−=== kggg zyx00.2;18.2 222 === zyx ggg
⎥⎥⎦
⎤
⎢⎢⎣
⎡
+−
+−= )(
31)(
)(0),(ˆ
22
21
21
21 BJBgg
BggBBH
zzB
zzB
μ
μ 28.0)( 12 =+= zzz ggEg0)( =Egxy
The dependence of the parameters J and D of the spin Hamiltonian (1) on the angle of trigonal distortion Δθ. Vibronic coupling parameters Vτand Xτ of the [Fe(CN)6
3-] complex are 1052 cm-1/Å and 449 cm-1/Å2, respectively.
Anisotropic susceptibility and average reduced magnetizations for theCuII-FeIII pair without angular distortions(orthoaxial geometry, no orthorhombicity,Jxx=Jyy=19.4 cm-1, Jzz=1.6; ζFe=345 cm-1, k=0.79,gxx(Cu)=gyy(Cu)=2.18,gzz(Cu)=2.00
Anisotropic susceptibility and average reduced magnetizations for theCuII-FeIII pair with trigonal compression of [Fe(CN)6
3-] of only 1.4o,corresponding to the trigonal minimum of the ground state potentialenergy surface of the [Fe(CN)6
3-] complex.
Complexδα
(C-Fe-C)δβ
(Fe-C-N)δγ
(C-N-MII)
Cu3Fe2Fe4-Cu1,2,3
Fe5-Cu1,2,3
-3.1,-0.8,-1.8,-3.6,-3.4,0.9
-2.4,-3.1,-3.6,-3.2,-1.9,-2.8
-10.4,-7.3,-8.8-6.0,-8.3,-8.5
Ni3Fe2Fe4-Ni1,2,3
Fe5-Ni1,2,3
-1.90.5
-0.8-0.9
-4.2-10.8
Effect of Tetragonal Strains within the Fe-CN Unit
4
44
4
0 02
0 02
0 0
D h
s D hD h
D h
H
Δ⎡ ⎤−⎢ ⎥⎢ ⎥
Δ⎢ ⎥= −⎢ ⎥⎢ ⎥Δ⎢ ⎥⎢ ⎥⎣ ⎦
e.g. in a (hypothetical) trans-[FeIII(N-amine)2(CNCuIIL4)4]
e.g. in the trans-[Fe(porph)(CN)CuN4]
Acknowledgements:Financial Support:
DFG: SPP Molecular MagnetismUniversity of Heidelberg