First-principles DFT calculations of the magnetic anisotropy in transition metal compounds. Jens Kortus TU Bergakademie Freiberg, Germany

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1 First-principles DFT calculations of the magnetic anisotropy in transition metal compounds Jens Kortus TU Bergakademie Freiberg, Germany

2 In collaboration with: Mark R. Pederson Center for Computational Materials Science NRL, Washington DC, USA C. S. Hellberg T. Baruah N. Bernstein Center for Computational Materials Science NRL, Washington DC, USA A. Postnikov University Metz, France C. Massobrio M. Drillon IPCMS - CNRS, Strasbourg France J. Cirera, E. Ruiz University Barcelona, Spain Experiment: P. Müller O. Waldmann M. Ruben University Erlangen University Bern Institute for Nanotechnology, FZ Karlsruhe

3 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 (Sx2 - Sy2) -gµbs B0

4 Naval Research Laboratory Molecular Orbital Library (NRLMOL) Pederson, Porezag, Kortus and Jackson Electronic structure Interatomic Forces Molecular/Cluster Geometries Reaction Barriers and Stabilities Vibrational Spectra Electronic Structure Magnetic Moments Hyperfine Parameters Magnetic Anisotropies al n io ion t ia rat r g h Va te es In M User-friendly computational package for first-principles investigation of molecular and cluster properties.

5 Calculation of the Tunneling Barrier within DFT? INCLUDE SPIN-ORBIT COUPLING VIA 2ND ORDER PERTURBATION THEORY Pederson and Khanna PRB 60, 9566 (1999) ' σσ ' σ ' σ Δ2 = M σσ S Sy xy x σσ ' xy S x =< χ σ S x χ σ φ iσ V x φ jσ ' φ jσ ' V y φ iσ σσ ' σσ ' M xy = M yx = ε iσ ε jσ ' ij dφ d dφ d φ jσ ' V x φ iσ = φ jσ ' φ iσ dy dz dz dy σσ '

6 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)

7 A new Mn9-cluster derived from the Mn12-ac J. Am. Chem. Soc. 127, 5572 (2005)

8 Mn9 with a magnetic ground state S=17/2 Mn4+ (s=3/2) Mn2+ (s=5/2) Moment in sphere 1.2Å 1x Mn x Mn x Mn x Mn x Mn x Mn Total moment: 2*5+4*4-3*3=17 Magnetic anisotropy D in cm-1: Mn3+ (s=2) J. Am. Chem. Soc. 127, 5572 (2005) INS FDMRS DFT INS=Inelastic Neutron scattering FDMRS=Freq. Domain Magnetic Resonance Spectroscopy

9 [Mn10O4(2,2 -biphenoxide)4br12]4mn2+ (s=5/2) Mn3+ (s=2) Mn2+ (s=5/2) High spin single molecule magnet Exp. : S=12 Theory: 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 Exp.: Barra et al. J. Solid State Chem. 145, 484 (1999) Spin-density isosurfaces for 0.03 e/ab3

10 States which contribute most to MAE occupied majority spin unoccupied minority spin Phys. Rev. B 66, (2003) Isosurfaces of the square of wavefunctions e/ab3

11 Contributions of spin channels to MAE occupied unoccupied D (K) DSz2 (K) majority majority majority minority minority majority minority minority all all Exp.: easy-axis system with DSz2 =-8 K

12 Theoretical Determination of D Molecule S D(exp.)/K D(calc.)/K Mn12O12(O2CH)16(H2O) [Fe8O2(OH)12(C6H15N3)6Br6] [Mn10O4(2,2 -biphenoxide)4br12] Co4(CH2C5H4N)4(CH3OH)4Acl4 6 Fe4(OCH2)6(C4H9ON) Cr[N(Si(CH3)3)2]3 3/ Mn9O34C32N3H35 17/ Mn4O3Cl4(O2CCH2CH3)3(NC5H5)3 9/ Ni4O16C16H to Kortus et al., Polyhedron 22, 1871 (2003) Psik-Highlight 61, February 2004,

13 Systematic study of monomers [Fe(H2C(COO)2)3] [Mn(acac)3] [(terpy)mn(n3)3] [Fe(SC6H5)4]2- [Fe(acac)3] [Cl(py)MnTPP]

14 Results from NRLMol Functional for exchange/correlation : PBE Basis set: Standard basis sets of NRLMol D(exp.)/cm-1 Molecule Mn+(dn) [Fe(H2C(COO)2)3] Fe3+(d5) [(terpy)mn(n3)3] Mn3+(d4) [Mn(acac)3] Mn3+(d4) [Fe(SC6H5)4]2- Fe2+(d6) D(calc.)/cm [Fe(acac)3] Fe3+(d5) [Fe(dpm)3] Fe3+(d5) [Cl(py)MnTPP] Mn3+(d4) [Mn(dbm)3] Mn3+(d4) The trends are well reproduced (there is a factor of 2 missing).

15 Testing different Basis sets Functional for exchange/correlation: PBE 3 basis sets: - Standard NRLMol basis sets - Triple Zeta Valence Bond TZV ( Shafer, Huber and Ahlrichs ) - Standard 6-311g* polarization Molecule NRLMol/cm-1 TZV/cm g*/cm-1 D(exp.)/cm-1 [Fe(H2C(COO)2)3] [(terpy)mn(n3)3] [Mn(acac)3] [Fe(SC6H5)4] [Fe(acac)3] Only small variations of the calculated anisotropy parameters.

16 Testing differents functionals Basis set: Standard basis set of NRLMol 2 functionals for exchange/correlation: - PBE - PW91 Molecule PBE/cm-1 PW91/cm-1 [Fe(H2C(COO)2)3] [Mn(acac)3] [Fe(SC6H5)4] D(exp.)/cm-1 Only small variations of the calculated anisotropy parameters.

17 Influence of other excited states on D B1g 3 B1g 5 ( D ' = 4λ 2 E ( 3 B1g ) E ( 5 B1g ) [MnF6]3- model (Gaussian03) B3LYP Dcalc = D + D ' -1,34 PBE B3LYP PBE -1,30-2,97-3,69 J. Cirera, Uni. Barcelona )

18 Jahn Teller distortion 2.0 Elongation [MnCl 6 ] 0.5 [FeCl 6 ] D/cm D/cm [MnCl 6 ] 0.5 [FeCl 6 ] Compression x2-y2 0.8 S(Oh) S(Oh) z2 xy xz,yz z2 0.0 xz,yz x2-y2 Octahedral environment xy

19 Interconversion pathways: Spread 0.05 [MnCl 4 ] 2- D/cm Spread ( D2d) S(T d) Td environment T2g xz,yz,xy Eg xy, x2-y2 D4h environment, Square planar x2-y2 B1g xy B2g xz,yz z2 Eg A1g

20 Interconversion pathways: Berry rotation 0.6 [MnCl 5 ] [FeCl 5 ] 3-2- D/cm Berry pseudorotation ( C2v ) Trigonal bipyramid 2 S(Tbp) z2 xz,yz x2-y2,xy 3 4 Square base pyramid x2-y2 z2 xy xz,yz

21 Interconversion pathways: Bailer twist 0.2 [MnCl 6 ] [FeCl 6 ] 4-3- D/cm Bailar twist ( D3 ) S(Oh) Octahedral, Oh Eg xy, x -y T2g xz,yz,xy Trigonal prism xy,x2-y2 xz,yz z2

22 Conclusions and outlook Conclusions 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. Outlook We 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.

23 (TM)4-grid structures Thermodynamically driven synthesis: self assembly, supramolecular chemistry 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)

24 Addressing the Metal Centers of [2x2] Co4II Grid-Type Complexes by STM / STS DFT Theory 2.5 nm V -1.0 V Experiment 5 na 2.5 nm V Angew. Chemie 2005 (December) V