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