1. Atomic-scale Engeered Spins at a Surface
Chiung-Yuan Lin
IBM Almaden Research Center

2. Nanomagnetism and Information Technology
Magnetism is at the heart of data storage.
Many novel computations schemes are based on manipulation of magnetic properties.
Courtesy of Hitachi
J.R. Petta et al.
Science 309, 2180 (2005)
A. Imre et al.
Science 311, 205 (2006)

3. Nanomagnets
Fabricated nanomagnets can recreate model spin systems such as spin ice.
A small number of atomic spins can be coupled in metal clusters or molecular magnetic structures.
R.F. Wang et al., Nature 439, 303 (2006)
Fe8, courtesy ESF.
M.B. Knickelbein
Phys. Rev. B 70, (2004)

4. Assembly and Measurement of Nanomagnets
Top-down
Bottom-up
Atomic-scale control O P
Manipulate structures

5. STM Studies of Atomic-Scale Spin-Coupling
Manipulation on thin insulators: build individual nanomagnets with an STM
Spin Excitation Spectroscopy: collective spin excitations of individual nanostructures
10Mn chain
Mn atom
Magnetic Field
Energy
|5/2,+5/2>
|ST,m>
|5/2,+3/2>
|5/2,+1/2>
|5/2,-1/2>
|5/2,-3/2>
|5/2,-5/2>
|0,0>
Magnetic Field
Energy
|1,-1>
|1,0>
|1,+1>
|ST,m>
Science 312, 1021 (2006)

6. Keep it Simple: Free Mn Atom3d
Mn: S = 5/2, L = 0, J = 5/2
Half filled d-shell
Weak spin-orbit interactions

7. Scanning Tunneling Spectroscopy: LDOSEf eV
tip
sample
dI/dV V
Features in the local DOS are reflected in dI/dV.

8. Magnetic Atoms on Surfaces
Atom’s spin is screened by conduction electrons (Kondo effect)
A thin insulating layer may isolate the atomic spin
Metal surface
Thin insulating layer

9. Inelastic Electron Tunneling Spectroscopy
|eV| < D
Elastic Channel Open
Inelastic Channel Closed Ef eV
sample
tip X D
|eV| > D
Elastic Channel Open
Inelastic Channel Open Ef eV
sample
tip D
Non-magnetic tip
Thin insulator
Magnetic atom
dI/dV
kBT < D
σe+σie σe
Non-magnetic sample eV -D D

10. Methods of Electronic-structure Calculation
Plane wave
Atomic spheres
Atomic partial wave
Atomic partial
wave
Interstitial region
Full-potential Linearized Augmented Plane Wave basis
Periodic-slab geometry
(5-layer Cu + 8-layer vacuum)
Density Functional Theory
Generalized Gradiant Approximation (GGA)
PBE96: Perdew et al., PRL 77, 3865 (1996)
Structure Optimization

11. Methods of Electronic-structure Calculation
vacuum
vacuum
vacuum
FLAPW basis
Periodic-slab geometry
(5-layer Cu + 8-layer vacuum)
Density Functional Theory
Generalized Gradiant Approximation (GGA)
PBE96: Perdew et al., PRL 77, 3865 (1996)
Structure Optimization

12. Methods of Electronic-structure Calculation
FLAPW basis
Periodic-slab geometry
(5-layer Cu + 8-layer vacuum)
Density Functional Theory
Generalized Gradiant Approximation (GGA)
PBE96: Perdew et al., PRL 77, 3865 (1996)
Structure Optimization

13. Thin Insulator: CuN Islands on Cu(100)
1nm N Cu
a0=Ö2d0 d0
CuN Mn Mn Mn Mn Mn Mn
Cu(100)
CuN monolayer
Atomic resolution on CuN
Mn atoms bind to Cu and N sites
Cu(100)

14. DFT Calculation of Electron Density in CuN
1.80Å
0.25Å
Cu+0.5
Cu+0.5
Cu+0.5 Cu Cu
N atoms are approximately coplanar with Cu atoms on CuN surface.

15. Manipulation of Mn on Cu(100) / CuN
Move tip in
Apply 2.0V
Pull tip back
Pick up Atom

16. Manipulation of Mn on Cu(100) / CuN
Move tip in
Apply -0.5V
Pull tip back
Pick up Atom
Drop off

17. Spectroscopy of Mn DimersCu N Mn
Large step at ~6mV splits into three distinct steps at high fields

18. Coupled Spins 5 4 … 1 S=5/2 Ä S=5/2  ST =
S=5/2 Ä S=5/2  ST =
For ST=0 (singlet) the first excited state is ST=1 (triplet)
Three excitations around constant energy shift
|0,0> B E
|1,-1>
|1,0>
|1,+1>
|ST,m>

19. Chains of Mn Atoms 2 3 4 5 6 7 8 9
1nm
1nm
1Mn
10Mn
CuN
Cu(100) N Cu
IBM Almaden STM Lab has built chains of up to 10 Mn atoms on Cu binding sites Mn Mn Mn

20. Spectroscopy of Mn Chains2 3 4 5 6 7 8 9
1nm 10
Spectra change dramatically with each additional Mn atom.

21. Heisenberg Model of Spin CouplingJ S
Phenomenological Exchange Coupling
J = Coupling strength
Si = spin of ith atom
Assumptions
All spins are the same
Nearest-neighbor coupling
All J are the same
J > 0 (antiferromagnetic coupling)

22. Heisenberg Dimer Spectrum
SG=0 and SE=1
Atomic spin affects numbers of levels but not spacing
First excited state at J J S

23. Determination of Spin Coupling Strength
From the dimer spectrum J=6.2meV
Variations in J of ±5% for different dimers at various locations
J=6.2meV

24. Determination of Atomic Spin
Using J = 6.2meV, we find S=5/2
STM determines both J and S!
S=3
S=5/2
S=2
J=6.2meV

25. Heisenberg Model for Longer Chains
Use J = 6.2meV and S=5/2
Odd chains
ground state spin = 5/2
excited state spin = 3/2
Even chains
ground state spin = 0
excited state spin = 1

26. Unit Cells Used in Calculating Mn on CuN
Single Mn, smallest unit cell
Mn dimer, smallest unit cell
Single Mn, larger unit cell N Cu Mn Mn
10.80Å
7.20Å
7.20Å

27. Electron Density with an Adsorbed Mn Atom
Cu+0.5
Cu+0.5 Cu Cu Cu
N atoms move farther out of surface Cu layer towards Mn atom.
Cu atom being pushed into the surface.
This “isolates” the free spin of Mn atom.

28. Mn Spin from DFT
majority ()
minority ()
Free Mn atom
3d S=5/2

29. A new kind of atomic-scale magnetMn N Mn N N Cu Cu Cu Cu Cu
Surface N atoms isolate and bridge Mn atoms.
This is a “surface” assembled magnet.

30. Control of Spin Coupling Strength
J=6.2meV
J=2.7meV
STM can switch J by a factor of 2 by selecting the binding site

31. GGA+U GGA+U (strong Coulomb repulsion on Mn 3d)
Calculating U by constraint GGA
Calculating U
Lock d-orbital into the atomic sphere
Do GGA for Mn d3 d2.5 and d3 d1.5
U =Δεd of the above two

32. Calculating Exchange Coupling
H=J S1·S2 Cu N
|±|S=5/2, Sz=±5/2
DFT total energies
2S2J= ++|H|++  +- |H| +-
= E  E

33. Calculating Exchange Coupling
(in meV)
Mn on Cu site
Mn on N site
GGA (U=0)
18.5
-1.8 (ferromagnetic!)
GGA + U(calculated)
6.50 ±0.05
2.5
GGA + U(calculated+1ev)
5.4
5.1
STM
6.2±0.3
2.7

34. Summary of theoretical work
The nontrivial structure of the engineered spins requires DFT to determine.
Calculated structure shows a new kind of molecular magnets.
GGA+U produces correct S and very accurate J; very helpful for searching a system of desired S and J.

35. What’s Next Can we understand IETS processes?
matrix elements, selection rules, transition strengths
What is the origin of the exchange coupling?
superexchange, delocalized electrons
Are other interactions possible?
vary distances, shapes, types of atoms
Can we control anisotropy effects?
Find a way to store and transfer spin information: bits and circuits based on atomic spins

36. Thanks to
Barbara
Jones
Cyrus Hirjibehedin
Chris
Lutz
Andreas
Heinrich