Exploring Molecular Magnetism by Density Functional Theory Calculations
Jens Kortus
[email protected]
HDD storage density doubles every year!
http://www.research.ibm.com/journal/sj/422/morris.pdf Morris and Truskowski, IBM SYSTEMS JOURNAL, 42, 205 (2003)
100 Gb/in2 = 1 b / (80 nm)2
Motivation: Nanomagnets for Data Storage R. F. Service, Science March 2000
• Magnetic Disk Drives: $35 Billion/Year • How small may be a bit in the future? Magnetic Storage Bit 100’s of 15-20 nm grains
?
Single Molecule Magnets •Mn12-Acetate (Friedman - PRL 1996) •Fe8-tacn (Wernsdorfer, PRL April 2000) •V15 (Gatteschi et al. Nature 1991) •Fe13O8 (Wang et al, PRB 1999) •Fe52Pt48 (Heath, Science March 2000)
1-4 nm?
[Fe8O2(OH)12(tacn)6] Br8
Fe3+ s=5/2
total spin S=10
H = DSz2 E(Sx2 Sy2) g µBSB0 D = 0.295 K, E = 0.055 K (Barra et al. Chem. Eur. J. 6, 1608 2000)
Unit cell of Fe8
a=10.5Å, b=14Å, c=15Å
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
Naval Research Laboratory Molecular Orbital Library (NRLMOL) Pederson, Porezag, Kortus and Jackson http://cst-www.nrl.navy.mil/~nrlmol • Electronic structure • Interatomic Forces • Molecular/Cluster Geometries • Reaction Barriers and Stabilities • Vibrational Spectra • Electronic Structure • Magnetic Moments • Hyperfine Parameters
al n io ion t ia rat r Va teg esh In M
• Magnetic Anisotropies
User-friendly computational package for first-principles investigation of molecular and cluster properties.
Calculation of the tunneling barrier with DFT? '
'
'
=∑ ∑ M xy S x S y ' x , y
M
' xy
〈i ∣V x∣ j ' 〉〈 j '∣V y∣i 〉 =∑ i − j ' ij d d d d ∣ j ' 〉 − dy dz dz dy ' S x =〈∣S x∣ ' 〉
〈i ∣V x∣ j ' 〉=〈 i ∣
INCLUDE SPIN-ORBIT COUPLING VIA 2ND ORDER PERTURBATION THEORY Pederson and Khanna PRB 60, 9566 (1999)
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)
Theoretical Determination of D Molecule
S
D(exp.)/K
D(calc.)/K
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
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
4
-0.40
-0.39
Mn4O3Cl4(O2CCH2CH3)3(NC5H5)3 9/2
-0.72
-0.58
Ni4O16C16H40
-0.7 to -0.9
-0.64
J. Kortus and A. V. Postnikov: Molecular Nanomagnets Handbook of Theoretical and Computational Nanotechnology, American Scientific Publishers, Ed. by M. Rieth and W. Schommers, ISBN: 1-58883-049-7, 7 (2006) 503 - 562
States which contribute most to MAE
occupied majority spin
unoccupied minority spin
Phys. Rev. B 66, 092403 (2003) Isosurfaces of the square of wavefunctions 0.005 e/aB3
Contributions of spin channels to MAE occupied
unoccupied
D (K)
DSz2 (K)
majority
majority
-0.039
-6.6
majority
minority
-0.106
-17.9
minority
majority
0.033
5.7
minority
minority
0.055
9.3
all
all
-0.056
-9.5
Exp.: easy-axis system with DSz2 =-8 K
Can large magnetic anisotropy and high spin really coexist?
Why not S=12 and D=-1,39cm-1? synthesis E. K. Brechin et al. 2007
[Mn6O2(sao)6(O2CH)2(MeOH)4]
S=4
D= -1.39 cm-1
[Mn6O2(Etsao)6(O2CPh(Me)2)2(EtOH)6]
S = 12
D= -0.43 cm-1
ChemComm 1 (2008) 52 - 54 The magnitude of the anisotropy barrier is mainly determined by the strength of the spin–orbit coupling and cannot be engineered by independently optimizing D and S.
CoPc on magnetic Co(111) islands grown on Cu(111)
Towards molecular spintronics!
C. Iacovita et al., Phys. Rev. Lett. 101 (2008) 116602-1 - 116602-4 Visualizing the spin of individual CobaltPhthalocyanine molecules
Basic overview of a scanning tunneling microscope (STM)
Source: Michael Schmid, TU Wien http://commons.wikimedia.org/wiki/Image:ScanningTunnelingMicroscope_schematic.png
Scanning Tunneling Microscopy and Spectroscopy of Cobalt Phthalocyanine on Metallic Surfaces
There exist a whole family of phtalocyanine with different metal atoms (Cu, Co, Ni, Fe, Zn ...).
The HOMO for CoPc involves ligand states. The molecule has spin ½. There is still some debate on the occupation of the magnetic orbitals between various DFT calculations and experiment.
Spin-polarized tunneling conductance through CoPc A: Typical spin-polarized dI/dV over two cobalt nanoislands of opposite magnetization
B: Differential conductance over the center of single CoPc molecules adsorbed on cobalt with distinct tips. C: Asymmetries arising from opposite magnetizations: CoPc (dark blue) and Co nanoislands (orange). The asymmetries are an average of all the recorded asymmetries obtained with different tips.
LUMO (spin down)
Simple crystal field does not really work! dx2-y2 dz2
dxy dyz, dzx In tetragonal symmetry the t2g levels split in a two-fold (dyz, dzx) and one-fold (dxy), the eg split into two separate levels. The low spin S=1/2 state is realized by a hole in dz2-orbital.
Hybridization with ligand states is dominating!
Geometry optimization DFT using PWSCF slab model 3 Cu layers + 2Co layers 2.2 nm vacuum to the next periodic repeated layer different geometries: top, bridge and hollow position lowest energy for bridge position Distance between the surface atoms and the cobalt atom of CoPc is about 0.25 nm, close to the Co-Co distance in the surface layers
Small Deformation of Co(111) surface below CoPc
In collaboration with: C. Loose, T. Brumme
TU Bergakademie Freiberg
J. Cirera, E. Ruiz S. Alvarez
University Barcelona, Spain
O. Waldmann
University Freiburg (anisotropy & discussion)
Experiment: J.-P. Bucher M. Drillon
IPCMS - CNRS, Strasbourg France (STM on CoPc)
We would like to thank the ZIH at TU Dresden for providing the computational resources and competent support. Without your help the work could not have been carried out.