© 2002 IBM Corporation
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Atomic-scale Engeered Spins at a Surface
Chiung-Yuan LinIBM Almaden Research Center
IBM Research
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Nanomagnetism and Information Technology
A. Imre et al.Science 311, 205 (2006)
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)
IBM Research
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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. KnickelbeinPhys. Rev. B 70, 14424 (2004)
IBM Research
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Assembly and Measurement of Nanomagnets
Top-down Bottom-up
Atomic-scale control Manipulate structures
IBM Research
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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
Ene
rgy
|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
Ene
rgy
|1,-1>
|1,0>
|1,+1>
|ST,m>
Science 312, 1021 (2006)
IBM Research
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Keep it Simple: Free Mn Atom
3d
4s
Mn: S = 5/2, L = 0, J = 5/2
Half filled d-shell
Weak spin-orbit interactions
IBM Research
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Scanning Tunneling Spectroscopy: LDOS
Ef eV
sampletip
Features in the local DOS are reflected in dI/dV.
dI/dV
V0
IBM Research
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Magnetic Atoms on Surfaces
Metal surface
Magnetic atom Atom’s spin is screened by
conduction electrons (Kondo effect)
A thin insulating layer may isolate the atomic spin
Thin insulating layer
IBM Research
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dI/dV
eV0
σe
Inelastic Electron Tunneling Spectroscopy
-
σe+σie
kBT <
|eV| < Elastic Channel Open
Inelastic Channel Closed
Ef eV
sampletipX
|eV| > Elastic Channel Open
Inelastic Channel Open
Ef eV
sampletip
Thin insulator Magnetic atom
Non-magnetic tip
Non-magnetic sample
IBM Research
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Methods of Electronic-structure Calculation
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
Interstitial regionAtomic partial wave
Plane wave
Atomic spheresAtomic partial wave
IBM Research
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Cu Cu Cu Cu
vacu
um
vacu
um
vacu
um
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
Methods of Electronic-structure Calculation
IBM Research
© 2006 IBM Corporation
rrVm iiieff .
22
rrrr
rrr
XCeff dVV
i
i
2rr
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
Methods of Electronic-structure Calculation
IBM Research
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Thin Insulator: CuN Islands on Cu(100)
Cu
N
d0
a0=2
d 0
d0=2.55Åa0=3.60Å
Atomic resolution on CuN
Mn atoms bind to Cu and N sites
Cu(100)
CuN
1nm
Cu(100)
CuN monolayerMn Mn
Mn MnMn Mn
IBM Research
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DFT Calculation of Electron Density in CuN
N atoms are approximately coplanar with Cu atoms on CuN surface.
Cu+0.5 Cu+0.5N-1 N-1
Cu Cu
Cu+0.5
1.80Å
0.25Å
IBM Research
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Pick up Atom
Move tip in Apply 2.0V Pull tip back
Manipulation of Mn on Cu(100) / CuN
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Pick up Atom
Drop off
Move tip in Apply -0.5V Pull tip back
Manipulation of Mn on Cu(100) / CuN
IBM Research
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Spectroscopy of Mn Dimers
Large step at ~6mV splits into three distinct steps at high fields
-10 -5 0 5 100.0
0.5
1.0
1.5
2.0B=7T
B=4T
dI/d
V (
a.u.
)
Voltage (mV)
B=0T
Cu
N
Mn Mn
IBM Research
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S=5/2 S=5/2 ST =
For ST=0 (singlet) the first excited state is ST=1 (triplet)
Three excitations around constant energy shift
Coupled Spins
|0,0>
B
E
|1,-1>
|1,0>
|1,+1>
|ST,m>
54…10
IBM Research
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IBM Almaden STM Lab has built chains of up to 10 Mn atoms on Cu binding sites
Chains of Mn Atoms
2
3
4
5
6
7
8
9
1nm
1nm
1Mn10Mn
CuN
Cu(100)Cu(100)
Cu
N
MnMn Mn
IBM Research
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Spectroscopy of Mn Chains
Spectra change dramatically with each additional Mn atom.
2
3
4
5
6
7
8
9
1nm
10
IBM Research
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Heisenberg Model of Spin Coupling
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)
ji
jiji SSJH,
,
SJ
1
1
1
N
i
ii SSJH
IBM Research
© 2006 IBM Corporation
0111
0111
22222
0111
22222
3333333
0111
22222
3333333
444444444
0111
22222
3333333
444444444
55555555555
0111
22222
3333333
444444444
55555555555
6666666666666
0
5
10
15
20
35/223/21
Ene
rgy
[J]
Atomic Spin1/2
Heisenberg Dimer Spectrum
SG=0 and SE=1
Atomic spin affects numbers of levels but not spacing
First excited state at J
SJ
IBM Research
© 2006 IBM Corporation
-25 -20 -15 -10 -5 0 5 10 15 20 251.0
1.5
2.0
2.5
2Mn
dI/d
V (
a.u
.)
Voltage (mV)
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
IBM Research
© 2006 IBM Corporation
Determination of Atomic Spin
Using J = 6.2meV, we find S=5/2
STM determines both J and S!
-25 -20 -15 -10 -5 0 5 10 15 20 251.0
1.5
2.0
2.5
3.0
3.5
4.0
3Mn
2Mn
dI/d
V (
a.u
.)
Voltage (mV)
S=2
S=3
S=5/2
J=6.2meV
IBM Research
© 2006 IBM Corporation
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
-20 -10 0 10 200
1
2
3
4
5
6
7
6Mn
1Mn
2Mn
3Mn
4Mn
5Mn
dI/d
V (
a.u
.)
Voltage (mV)
IBM Research
© 2006 IBM Corporation
N
Cu
Mn
Unit Cells Used in Calculating Mn on CuN
Single Mn, smallest unit cellSingle Mn, larger unit cellMn dimer, smallest unit cell
Mn
7.20Å
10.80Å
7.20Å
IBM Research
© 2006 IBM Corporation
Electron Density with an Adsorbed Mn Atom
• 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.
Cu+0.5
Cu
Cu+0.5 N -1.5 N -1.5
Mn+
Cu Cu
IBM Research
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Mn Spin from DFT
majority ()minority ()
Free Mn atom
3d 5 S=5/2
IBM Research
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A new kind of atomic-scale magnet
Surface N atoms isolate and bridge Mn atoms. This is a “surface” assembled magnet.
Cu
CuCu
N
CuCu
Mn MnNN
IBM Research
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Control of Spin Coupling Strength
J=2.7meV
J=6.2meV
STM can switch J by a factor of 2 by selecting the binding site
IBM Research
© 2006 IBM Corporation
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 d3 d
2.5 and d3 d
1.5
• U =Δεd of the above two
IBM Research
© 2006 IBM Corporation
H=J S1·S2
2S2J= ++|H|++ +- |H| +- = E E
DFT total energies
Cu
N
Calculating Exchange Coupling
|±|S=5/2, Sz=±5/2
IBM Research
© 2006 IBM Corporation
Calculating Exchange Coupling
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
(in meV)
IBM Research
© 2006 IBM Corporation
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.
IBM Research
© 2006 IBM Corporation
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
IBM Research
© 2006 IBM Corporation
Thanks to
ChrisLutz
AndreasHeinrich
BarbaraJones
CyrusHirjibehedin