First-principles DFT calculations of the magnetic anisotropy in transition metal...

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)