Jens KortusTU Bergakademie Freiberg, Germany
First-principles DFT calculations of the magnetic anisotropy in transition
metal compounds
In collaboration with:
Mark R. Pederson Center for Computational Materials Science NRL, Washington DC, USA
C. S. Hellberg Center for Computational Materials ScienceT. Baruah NRL, Washington DC, USAN. Bernstein
A. Postnikov University Metz, France
C. Massobrio IPCMS - CNRS, Strasbourg FranceM. Drillon
J. Cirera, E. Ruiz University Barcelona, Spain
Experiment:P. Müller University ErlangenO. Waldmann University BernM. Ruben Institute for Nanotechnology, FZ Karlsruhe
Quantum tunneling of the magnetization
J.R. Friedman et al, Phys. Rev. Lett. 76, 3830 (1996)
L. Thomas et al, Nature 383, 245 (1996)
H = DSz2 – E (Sx
2 - Sy2) -gµBSB0
Naval Research Laboratory Molecular Orbital Library (NRLMOL)
Pederson, Porezag, Kortus and Jackson
User-friendly computational package for first-principles investigation of molecular and cluster properties.
• Electronic structure• Interatomic Forces• Molecular/Cluster Geometries• Reaction Barriers and Stabilities• Vibrational Spectra• Electronic Structure• Magnetic Moments• Hyperfine Parameters • Magnetic Anisotropies
Varia
tional
Integration
Mesh
http://cst-www.nrl.navy.mil/~nrlmol
Calculation of the Tunneling Barrier within DFT?
INCLUDE SPIN-ORBIT COUPLING VIA 2ND ORDER PERTURBATION THEORYPederson and Khanna PRB 60, 9566 (1999)
Δ2=∑σσ '∑xyM xy
σσ ' S xσσ ' S y
σ ' σ
Sx
σσ '=< χσ∣S
x∣χ
σ
M xyσσ '
=M yxσσ '
=∑ij
⟨φiσ∣V x∣φ jσ ' ⟩ ⟨φ jσ '∣V y∣φiσ ⟩εiσ−ε
jσ '
⟨φjσ '∣V
x∣φ
iσ⟩=⟨φ
jσ '∣dΦdyddz
−dΦdzddy
∣φiσ⟩
Ferric star
The cluster ground state is ferrimagnetic with S = 5.
The three outer Fe(III) ions (s = 5/2) couple antiferromagnetic to the inner Fe(III) ion.
Fe-Fe(center) distances of 3.2 Å.
Theory D=-0.56 K |E|=0.064 K
Exp. D=-0.57 K |E|=0.056 K
Exp.: S. Schromm, O. Waldmann, P. Müller (Uni Erlangen)
A new Mn9-cluster derived from the Mn12-ac
J. Am. Chem. Soc. 127, 5572 (2005)
Mn9 with a magnetic ground state S=17/2
Mn4+ (s=3/2)
Mn3+ (s=2)
Mn2+ (s=5/2)Moment in sphere 1.2Å1x Mn1 -2.4 → -32x Mn2 -2.4 → -3
1x Mn3 3.6 → 42x Mn4 4.3 → 52x Mn5 3.5 → 41x Mn6 3.3 → 4Total moment:2*5+4*4-3*3=17
Magnetic anisotropy D in cm-1: INS FDMRS DFT-0.249 -0.247 -0.23
INS=Inelastic Neutron scatteringFDMRS=Freq. Domain Magnetic Resonance SpectroscopyJ. Am. Chem. Soc. 127, 5572 (2005)
[Mn10O4(2,2’-biphenoxide)4Br12]4-
Spin-density isosurfaces for 0.03 e/aB3
Exp.: Barra et al. J. Solid State Chem. 145, 484 (1999)
High spin single molecule magnetExp. : S=12Theory: S=13
Negatively charged cluster compensated by unit containing Mn atom[Mn(CH3CN)4(H2O)2]• easy-plane system• MAE 0.1 K• all magnetic properties due to Mn10-cluster
Mn2+ (s=5/2)
Mn2+ (s=5/2)
Mn3+ (s=2)
Isosurfaces of the square of wavefunctions 0.005 e/aB3
occupied majority spin unoccupied minority spin
States which contribute most to MAE
Phys. Rev. B 66, 092403 (2003)
9.30.055minorityminority
-9.5-0.056allall
5.70.033majorityminority
-17.9-0.106minoritymajority
-6.6 -0.039 majoritymajority
DSz2 (K)D (K)unoccupiedoccupied
Contributions of spin channels to MAE
Exp.: easy-axis system with DSz2 =-8 K
Theoretical Determination of D
Kortus et al., Polyhedron 22, 1871 (2003)
Psik-Highlight 61, February 2004, 127-177
Mn12O12(O2CH)16(H2O)4 10 -0.56 -0.56
[Fe8O2(OH)12(C6H15N3)6Br6]2+ 10 -0.30 -0.53
[Mn10O4(2,2’-biphenoxide)4Br12] 13 -0.05 -0.06
Co4(CH2C5H4N)4(CH3OH)4Acl4 6 -0.7 to -0.9 -0.64
Fe4(OCH2)6(C4H9ON)6 5 -0.57 -0.56
Cr[N(Si(CH3)3)2]3 3/2 -2.66 -1.15
Mn9O34C32N3H35 17/2 -0.35 -0.33
Ni4O16C16H40 4 -0.40 -0.39
Mn4O3Cl4(O2CCH2CH3)3(NC5H5)3 9/2 -0.72 -0.58
Molecule S D(exp.)/K D(calc.)/K
Systematic study of monomers
[Fe(H2C(COO)2)3]
[(terpy)Mn(N3)3]
[Mn(acac)3]
[Fe(SC6H5)4]2-
[Fe(acac)3]
[Cl(py)MnTPP]
Results from NRLMol
[Fe(H2C(COO)2)3] Fe3+(d5) +0.12 -0.13
[(terpy)Mn(N3)3] Mn3+(d4) -3.29 -1.65
[Mn(acac)3] Mn3+(d4) -4.52 -2.36
[Fe(SC6H5)4]2- Fe2+(d6) +5.48 +2.18
[Fe(acac)3] Fe3+(d5) +0.16 +0.29
[Fe(dpm)3] Fe3+(d5) -0.18 +0.22
[Cl(py)MnTPP] Mn3+(d4) -3.00 -1.28
[Mn(dbm)3] Mn3+(d4) -4.57 -2.43
Molecule Mn+(dn) D(exp.)/cm-1 D(calc.)/cm-1
Functional for exchange/correlation : PBE
Basis set: Standard basis sets of NRLMol
The trends are well reproduced (there is a factor of 2 missing).
Testing different Basis setsFunctional for exchange/correlation: PBE
3 basis sets: - Standard NRLMol basis sets
- Triple Zeta Valence Bond TZV ( Shafer, Huber and Ahlrichs )
- Standard 6-311g* polarization
[Fe(H2C(COO)2)3] -0.13 -0.13 -0.13 +0.12
[(terpy)Mn(N3)3] -1.65 -1.53 -1.48 -3.29
[Mn(acac)3] -2.36 -2.16 -2.11 -4.52
[Fe(SC6H5)4]2- +2.18 +2.14 +2.04 +5.48
[Fe(acac)3] +0.29 +0.27 +0.26 +0.16
Molecule NRLMol/cm-1 TZV/cm-1 6-311g*/cm-1 D(exp.)/cm-1
Only small variations of the calculated anisotropy parameters.
Testing differents functionalsBasis set: Standard basis set of NRLMol
2 functionals for exchange/correlation: - PBE
- PW91
[Fe(H2C(COO)2)3] -0.13 -0.14 +0.12
[Mn(acac)3] -2.36 -2.40 -4.52
[Fe(SC6H5)4]2- +2.18 +2.15 +5.48
Molecule PBE/cm-1 PW91/cm-1 D(exp.)/cm-1
Only small variations of the calculated anisotropy parameters.
Influence of other excited states on D
5B1g
3B1g
( ) ( )( )' 2 3 51 14 g gD E B E Bλ= − −
'calc DD D= +
B3LYP PBE B3LYP PBE
[MnF6]3- model (Gaussian03)
-1,34 -1,30 -2,97 -3,69
J. Cirera, Uni. Barcelona
2.0
1.5
1.0
0.5
0.0
-0.5
D/c
m-1
1.61.20.80.40.0S(Oh)
[MnCl 6]3-
[FeCl6]4-
1.5
1.0
0.5
0.0
-0.5
-1.0
D/c
m-1
1.61.20.80.40.0S(Oh)
[MnCl 6]3-
[FeCl6]4-
Octahedral environment
z2
z2
xz,yz
xz,yzxy
xy
x2-y2
x2-y2
Jahn Teller distortionElongation Compression
-0.10
-0.05
0.00
0.05D
/cm
-1
3020100S(Td)
[MnCl 4]2-
Interconversion pathways: Spread
Spread ( D2d)
xy, x2-y2
xz,yz,xy
Eg
T2g
z2
xz,yz
xy
x2-y2 B1g
B2g
Eg
A1g
Td environment D4h environment, Square planar
0.6
0.4
0.2
0.0
D/c
m-1
43210S(Tbp)
[MnCl 5]3-
[FeCl5]2-
Berry pseudorotation
( C2v )
x2-y2,xy
xz,yz
z2
xz,yz
z2
xy
x2-y2Trigonal bipyramid Square base pyramid
Interconversion pathways: Berry rotation
Bailar twist ( D3 )
xy, x2-y2
xz,yz,xy
Eg
T2gz2xz,yz
xy,x2-y2
Octahedral, OhTrigonal prism
-0.6
-0.4
-0.2
0.0
0.2
D/c
m-1
151050S(Oh)
[MnCl 6]4-
[FeCl6]3-
Interconversion pathways: Bailer twist
Conclusions and outlookConclusions
NRLMol predicts correctly the sign and the trends of the magnetic anisotropy parameters in transition metal compounds.
We can establish correlations between molecular and electronic structure .
We can follow the modification of D through the rearrangment pathways.
OutlookWe have to extend our calculations to more systems in order to find limitations and problems.
We have to understand the correlations between electronic structure, chemical bonding and D.
Find simple rules for the synthetic chemist to guide the design of SMM.
(TM)4-grid structures
4x [Co(tpy)2]2+ : +8 cation
Different metal ions:Mn2+, Fe2+, Co2+, Ni2+, Zn2+
e.g. M. Rubens et al. Angew. Chem. Int. Ed. 43, 3644 (2004)
Thermodynamically driven synthesis: self assembly, supramolecular chemistry
-0.68 V -1.03 V
-0.55 V -1.0 V
DFT Theory
Experiment
2.5 nm
5 nA
2.5 nm
Addressing the Metal Centers of [2x2] Co4II
Grid-Type Complexes by STM / STS
Angew. Chemie 2005 (December)