Studying magnetic molecules
one atom at a time
Andreas Heinrich
IBM Research
© 2002 IBM Corporation
© 2008 IBM Corporation
Nanomagnets in science and technology
Top-down
Bottom-up
Address individual structure
Magnetic Manipulations
Atomic-scale control
© 2008 IBM Corporation
2
The giant-spin model of molecular magnets
S = 10
Mn12- ac.
¾ Spin coupling: Quantum Heisenberg
™
8 Mn atoms with S = 2
→ S = 16
™
4 Mn atoms with S = 3/2
→S=6
™
Total S = 10
¾ Magnetic anisotropy: Spin Hamiltonian
© 2008 IBM Corporation
3
Electrical measurements of molecular magnets
“artist’s rendition”
¾ Very difficult to control the junctions
¾ Environmental impact on magnetic and electrical
properties
© 2008 IBM Corporation
4
Studying magnetic molecules one atom at a time
¾Spin excitation spectroscopy:
Spin flips of single atoms
Fe atom
Science 306, 466 (2004)
¾Magnetic anisotropy:
Spin Hamiltonian, Selection rules
S = 1/2
Science 317, 1199 (2007)
Energy
Energy
Magnetic
Magnetic
FieldField
© 2008 IBM Corporation
5
Studying magnetic molecules one atom at a time
¾Spin excitation spectroscopy:
Spin flips of single atoms
Science 306, 466 (2004)
10Mn chain
¾Magnetic anisotropy:
Spin Hamiltonian, Selection rules
Mn atom
Science 317, 1199 (2007)
Energy
|ST,m>
|1,+1>
|1,0>
¾Spin-spin interactions:
Heisenberg exchange coupling
Unpublished and Science 312, 1021 (2006)
|1,-1>
|0,0>
Magnetic Field
© 2008 IBM Corporation
6
Studying magnetic molecules one atom at a time
¾Spin excitation spectroscopy:
Spin flips of single atoms
Science 306, 466 (2004)
¾Magnetic anisotropy:
Spin Hamiltonian, Selection rules
Tip states
-1/2
Science 317, 1199 (2007)
¾Spin-spin interactions:
Heisenberg exchange coupling
E +1/2
Unpublished and Science 312, 1021 (2006)
¾Spin-polarized excitations:
A probe for magnetic bits
D(E)
Unpublished
© 2008 IBM Corporation
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How does an STM image a surface?
Tip
V
z-servo
scan
Trajectory
~1nm
Sample
I,R
¾ Keep I constant
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vertical distance [Å]
Z[Å]
Atomic resolution?
1 .2
1
0 .8
0 .6
0 .4
0 .2
7.5nm 7.5nm
0
0
1
2
3
4
5
lateral distance
[nm]
X [nm ]
6
7
¾ Co atoms on clean Cu (111)
¾ Co atoms appear as 1Å high “bumps” about 10Å wide
© 2008 IBM Corporation
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How to move atoms with STM?
What forces are involved?
Science 2008
FV
FL
¾The adsorbate hops from one site to an adjacent site
© 2008 IBM Corporation
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Elastic spectroscopy with STM
V
Barrier
V
elastic
LDOS
σe
eV
Tip
LDOS
Sample
dI/dV
σe
V
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Pentacene on table salt
¾ J. Repp et al., Phys. Rev. Lett. 94, 026803 (2005).
¾ Pentacene on 1 and 2 layers of NaCl on Cu (100).
¾ About 4eV gap between HOMO and LUMO.
© 2008 IBM Corporation
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Spin excitation spectroscopy
E
B
EZ = gμBB
B
Non-magnetic tip
Magnetic atom
Thin decoupling layer
Non-magnetic sample
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Spin excitation spectroscopy
elastic
+
σe
inelastic
Tip
E
σie
EZ = gμBB
eVZ
B
Sample
dI/dV
5.5 kBT
e|V| = EZ
ρe + ρie
ρe
-VZ
VZ
© 2008 IBM Corporation
V
14
Copper-nitride islands grown on Cu
1nm
Cu(100)
CuN
Cu
N
CuN
Cu(100)
¾
¾
¾
¾
Cu(100) + CuN
Insulator next to metal
Atomic resolution on CuN
N atoms coplanar with Cu
© 2008 IBM Corporation
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Mn on CuN: An almost pure spin
1.0
g-value: 1.90 ± 0.01
0.8
Splitting [meV]
dI/dV [a.u.]
0.9
0.8
0.7
-2
B┴= 0T
3T
7T
T=0.5K
-1
0
Voltage [mV]
1
2
offset: 0.16meV
0.6
Mn
0.4
v v
H = − gμ B BN ⋅ S
mixed
Cu
A 0.15583 0.0094
B 0.1144 0.00225
0.2
0.0
0
1
2
3
4
5
6
7
B [T]
Mn atom on CuN exhibits magnetic behavior:
™ spin-flip excitation
™ small amount of zero-field splitting
© 2008 IBM Corporation
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For comparison: free Mn atom
4s
3d
Mn: S = 5/2, L = 0, J = 5/2
m = -5/2
E
m = -3/2
B
¾
¾
¾
¾
Half filled d-shell
Weak spin-orbit interactions
g-value of the magnetic splitting is g = 2
Why only one step? Selection rule?
© 2008 IBM Corporation
EZ = gμBB
17
Atom-Resolved Spin Excitation Spectroscopy
¾Spin excitation spectroscopy:
Spin flips of single atoms
Science 306, 466 (2004)
¾Magnetic anisotropy:
Spin Hamiltonian, Selection rules
Science 317, 1199 (2007)
¾Spin-spin interactions:
Heisenberg exchange coupling
Unpublished and Science 312, 1021 (2006)
¾Spin-polarized excitations:
A probe for magnetic bits
Unpublished
© 2008 IBM Corporation
18
Anisotropy at a surface
¾ Free atomic spin is rotationally invariant:
all spin orientations are degenerate.
¾ Loss of rotational symmetry breaks
degeneracy of spin orientations.
v v
H = − gμ B B ⋅ S + DS z2
B⊥z
B || z
E
E
B
B
Magnetic field dependence varies with angle of magnetic field.
© 2008 IBM Corporation
19
Fe on Cu-site on CuN
Fe
Cu
N
Conductivity
1.0
0.2mV
0.8
5.7mV
0.6
0.4
3.8mV
B=0
T=0.5K
-10
-8
-6
-4
-2
0
2
4
6
8
10
Voltage [mV]
¾ 3 excitations with large cross section
¾ Same binding site as Mn yet quite different spectrum.
© 2008 IBM Corporation
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Field dependence of Fe spin excitations
easy axis
easy axis
Fe1
Fe
B
Cu
N
Fe
Cu
B
N
¾ Out-of-plane dependence is different yet !
© 2008 IBM Corporation
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Fe
Origin of in-plane easy axis
Easy axis
N-direction
Fe
Cu
N
0.001
0.010
0.100
0.0003
0.003
0.032
0.316
Cu[e- / a03]
¾ DFT to model structure and spin properties.
¾ Strong one-dimensional bonding.
¾ Spin of Fe complex is S = 2.
© 2008 IBM Corporation
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Anisotropy in Fe
Fe
Cu
Fe
N
v v
H = − gμ B B ⋅ S + DS z2 + E S x2 − S y2
(
ε
ε
B||z
)
ε
D<0
D < 0, E ≠ 0
B||z
B||z
© 2008 IBM Corporation
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Mixed eigenstates are great for science
H = DS + E ( S − S ) D = -1.5meV, E = 0.3meV
2
z
2
x
2
y
5.6mV
3.8mV
Eigenvalue
|+2>
0
0.70
0.17
0.71
|+1>
|0>
|-1>
|-2>
0
0.2mV
B=0
T=0.5K
5
-8
-6
-4
-2
0
2
4
6
8
0.70
-0.71
3.77
0.71
-0.71
5.57
0.71
0.71
6.34
-10
-0.17
0.12
0.99
0.12
10
Voltage [mV]
¾ Mixed mz eigenstates have more transitions with Δmz=0, ±1.
¾ Anisotropy allows the observation of several spin excitations.
© 2008 IBM Corporation
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Brief comment: Kondo interactions
Co
Cu
N
ε
S = 3/2
D > 0, E = 0
¾ S = 3/2 spin system with anisotropy
¾ Anisotropy creates pseudo S = ½ system
¾ Two-state system is Kondo screened
© 2008 IBM Corporation
| -3/2 〉
| 3/2 〉
| -1/2 〉
| 1/2 〉
B||z
25
diff. conductance (a.u.)
What transitions do we see at field?
12
| S , mz 〉
10
E
8
| 3/2 , -3/2 〉
6
| 3/2 , 3/2 〉
| 3/2 , -1/2 〉
4
2
0
-10
(D > 0)
-5
0
5
10
| 3/2 , 1/2 〉
B || z
sample bias (mV)
¾
¾
¾
¾
IETS inner step at known energy and known intensity
IETS spectrum WITHOUT Kondo effect
Kondo contribution fitted as two Lorentzians
Nature Physics, November 2008
© 2008 IBM Corporation
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Summary
Fe atom
¾ Spin excitation spectroscopy probes
individual spin systems
¾ STM allows precise assembly
Mn atom
¾ Magnetic anisotropy
¾ Spin coupling: Heisenberg exchange
E
¾ Spin-polarized spectroscopy
SP tip
10Mn chain
Bz
Mn atom
Mn
© 2008 IBM Corporation
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The STM and theory team
Markus
Ternes
Sander
Otte
Cyrus
Sebastian
Hirjibehedin
Loth
Bruce
Melior
Chris
Lutz
Kirsten v.
Bergmann
Harald
Brune
© 2008 IBM Corporation
Gene
Lin
Barbara
Jones
28
Why are some spin transitions strong?
Fe atom
2.0
B || z
7T
dI/dV [A.U.]
1.8
1.6
5T
1.4
3T
1.2
1T
1.0
I30 0T
I20
0.8
0.6
I10
0.4
-10
-8
-6
-4
-2
0
2
4
6
8
10
Voltage [mV]
¾ Empirical selection rule: Δmz=0, ±1
I fi ∝ ψ f S + ψ i
2
+ ψ f S− ψ i
2
2
+ 2 ψ f Sz ψ i
¾ Transition Hamiltonian equals inelastic neutron scattering!
© 2008 IBM Corporation
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How to do that?
l-4He
3He
pump
P ≈ 0.01Torr
UHV
4.2K
B = 7T
STM
0.5K
Exchange
gas
3
l- He
Vacuum
0.35K
© 2008 IBM Corporation
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