IBM Research
Atomic-scale Engeered Spins at a Surface
Chiung-Yuan Lin
IBM Almaden Research Center
© 2002 IBM Corporation
© 2006
2005 IBM Corporation
IBM Research
Nanomagnetism and Information Technology
 Magnetism is at the heart
of data storage.
Courtesy of Hitachi
 Many novel computations
schemes are based on
manipulation of magnetic
properties.
J.R. Petta et al.
Science 309, 2180 (2005)
A. Imre et al.
Science 311, 205 (2006)
© 2006 IBM Corporation
IBM Research
Nanomagnets
 Fabricated nanomagnets can
recreate model spin systems
such as spin ice.
R.F. Wang et al., Nature 439, 303 (2006)
 A small number of atomic spins
can be coupled in metal clusters
or molecular magnetic
structures.
Fe8, courtesy ESF.
M.B. Knickelbein
Phys. Rev. B 70, 14424 (2004)
© 2006 IBM Corporation
IBM Research
Assembly and Measurement of Nanomagnets
Top-down
Bottom-up
Atomic-scale control
O
P
Manipulate structures
P
O
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IBM Research
STM Studies of Atomic-Scale Spin-Coupling
 Manipulation on thin
insulators:
build individual nanomagnets
with an STM
10Mn chain
Mn atom
Energy
Energy
|ST,m>
|ST,m>
|5/2,+5/2>
|1,+1>
|5/2,+3/2>
 Spin Excitation Spectroscopy:
collective spin excitations of
individual nanostructures
|1,0>
|5/2,+1/2>
|5/2,-1/2>
|1,-1>
|5/2,-3/2>
|0,0>
|5/2,-5/2>
Magnetic Field
Science 312, 1021
(2006)
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Corporation
IBM Research
Keep it Simple: Free Mn Atom
4s
3d
Mn: S = 5/2, L = 0, J = 5/2
 Half filled d-shell
 Weak spin-orbit interactions
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IBM Research
Scanning Tunneling Spectroscopy: LDOS
Ef
eV
tip
sample
dI/dV
0
V
Features in the local DOS are reflected in dI/dV.
© 2006 IBM Corporation
IBM Research
Magnetic Atoms on Surfaces
Magnetic atom
 Atom’s spin is screened by
conduction electrons (Kondo
effect)
Metal surface
Thin insulating layer
 A thin insulating layer may
isolate the atomic spin
© 2006 IBM Corporation
IBM Research
Inelastic Electron Tunneling Spectroscopy
Ef
D
tip
eV
eV
X
sample
D
Non-magnetic tip
Thin insulator
Magnetic atom
|eV| <
>D
Elastic Channel Open
Inelastic
InelasticChannel
ChannelClosed
Open
dI/dV
Non-magnetic sample
-D
kBT < D
0
© 2006 IBM Corporation
D
σe+σie
σe
eV
IBM Research
Methods of Electronic-structure Calculation
Plane wave
Atomic partial wave
Atomic partial
wave
Atomic spheres
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
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IBM Research

FLAPW basis

Periodic-slab geometry
Cu
vacuum
Cu
vacuum
Cu
vacuum
Methods of Electronic-structure Calculation
Cu
(5-layer Cu + 8-layer vacuum)

Density Functional Theory
Generalized Gradiant Approximation (GGA)
PBE96: Perdew et al., PRL 77, 3865 (1996)

Structure Optimization
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IBM Research
Methods of Electronic-structure Calculation
  2

  Veff i r    i .i r 

 2m

 r
Veff r   V r   
 r    i r 
r  r
dr   XC  r 
2
i

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
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IBM Research
Thin Insulator: CuN Islands on Cu(100)
d0=2.55Å
a0=3.60Å
CuN
a0=2d0
1nm
N
d0
Cu
Mn Mn Mn Mn
Cu(100)
Mn
Mn
CuN monolayer
 Atomic resolution on CuN
 Mn atoms bind to Cu and N sites
Cu(100)
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IBM Research
DFT Calculation of Electron Density in CuN
0.25Å
Cu+0.5
N-1
Cu+0.5
N-1
Cu+0.5
1.80Å
Cu
Cu
N atoms are approximately coplanar
with Cu atoms on CuN surface.
© 2006 IBM Corporation
IBM Research
Manipulation of Mn on Cu(100) / CuN
Pick up Atom
 Move tip in
 Apply 2.0V
 Pull tip back
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IBM Research
Manipulation of Mn on Cu(100) / CuN
 Move tip in
 Apply -0.5V
 Pull tip back
Pick up Atom
Drop off
© 2006 IBM Corporation
IBM Research
Spectroscopy of Mn Dimers
N
Cu
Mn
Mn
 Large step at ~6mV
splits into three distinct
steps at high fields
2.0
dI/dV (a.u.)
B=7T
1.5 B=4T
1.0 B=0T
0.5
0.0
-10
-5
0
5
10
Voltage (mV)
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IBM Research
Coupled Spins
5
4
…
1
0
 S=5/2  S=5/2  ST =
 For ST=0 (singlet) the first excited state is ST=1 (triplet)
E
|ST,m>
|1,+1>

Three excitations around constant
energy shift
|1,0>
|1,-1>
|0,0>
B
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IBM Research
Chains of Mn Atoms
Cu(100)
2
1nm
6
3
7
4
8
5
9
10Mn
1Mn
CuN
1nm
N
Cu
Mn
Mn
Mn
IBM Almaden STM Lab has built
chains of up to 10 Mn atoms on Cu
binding sites
© 2006 IBM Corporation
IBM Research
Spectroscopy of Mn Chains
10Mn
10
1nm
9Mn
9
6
8Mn
8
dI/dV [a.u.]
2
7
7Mn
6
6Mn
5
5Mn
4
4Mn
3
3Mn
2Mn
3
7
4
8
5
9
2
1Mn
1
0
-20
-10
0
10
10
20
Voltage [mV]
Spectra change dramatically with each additional Mn atom.
© 2006 IBM Corporation
IBM Research
Heisenberg Model of Spin Coupling
J
S
 Phenomenological Exchange Coupling


J = Coupling strength
Si = spin of
ith
atom
H   J i, j S i  S j
i, j
 Assumptions

All spins are the same

Nearest-neighbor coupling

All J are the same

J > 0 (antiferromagnetic coupling)
N 1
H  J  S i  S i 1
i 1
© 2006 IBM Corporation
IBM Research
Heisenberg Dimer Spectrum
6
J
20
S
Energy [J]
15
5
5
4
4
4
3
3
3
3
2
2
2
2
2
1
0
1
0
1
0
1
0
1
0
10
5
1
0
0
1/2
1
3/2
2
5/2
 SG=0 and SE=1
 Atomic spin affects
numbers of levels but not
spacing
 First excited state at J
3
Atomic Spin
© 2006 IBM Corporation

IBM Research
Determination of Spin Coupling Strength


2.5
 From the dimer spectrum
J=6.2meV
dI/dV (a.u.)
2Mn
2.0
 Variations in J of ±5% for
different dimers at
various locations
1.5

1.0
-25 -20 -15 -10
-5
0
5
J=6.2meV
10
15
20
25
Voltage (mV)
© 2006 IBM Corporation
IBM Research


Determination of Atomic Spin


4.0
 Using J = 6.2meV, we find
S=5/2
3.5
dI/dV (a.u.)

3.0
3Mn
S=3


2.5
S=5/2
 STM determines both J
and S!
S=2
2Mn
2.0
1.5

1.0
-25 -20 -15 -10
-5
0
5
J=6.2meV
10
15
20
25
Voltage (mV)
© 2006 IBM Corporation
IBM Research
Heisenberg Model for Longer Chains
7
6Mn

6
5
 Use J = 6.2meV and S=5/2

5Mn
 
 Odd chains
dI/dV (a.u.)

4
3
1
0
ground state spin = 5/2

excited state spin = 3/2

3Mn

 Even chains

2

4Mn
2Mn
1Mn
-20

-10
0
10

ground state spin = 0

excited state spin = 1
20
Voltage (mV)
© 2006 IBM Corporation
IBM Research
Unit Cells Used in Calculating Mn on CuN
Single
Mn,
larger unit
Mn
Single
dimer,
Mn,
smallest
smallest
unit
unitcell
cell
cell
N
Cu
Mn
Mn
10.80Å
7.20Å
7.20Å
© 2006 IBM Corporation
IBM Research
Electron Density with an Adsorbed Mn Atom
Mn+
Cu+0.5
N -1.5
N -1.5
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.
© 2006 IBM Corporation
IBM Research
Mn Spin from DFT
majority ()
minority ()
Free Mn atom
3d 5
© 2006 IBM Corporation
S=5/2
IBM Research
A new kind of atomic-scale magnet
Mn
N
N
Cu
Cu
Mn
N
Cu
Cu
Cu
 Surface N atoms isolate and bridge Mn atoms.
 This is a “surface” assembled magnet.
© 2006 IBM Corporation
IBM Research
Control of Spin Coupling Strength
1.0
J=6.2meV
dI/dV (a.u.)
0.5
0.0
J=2.7meV
1.0
0.5
0.0
-8
-6
-4
-2
0
2
4
6
8
Voltage (mV)
STM can switch J by a factor of 2 by selecting the binding site
© 2006 IBM Corporation
IBM Research
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
© 2006 IBM Corporation
IBM Research
Calculating Exchange Coupling
H=J S1·S2
N
Cu
|±|S=5/2, Sz=±5/2
DFT total energies
2S2J= ++|H|++  +- |H| +- = E  E
© 2006 IBM Corporation
IBM Research
Calculating Exchange Coupling
(in meV)
GGA (U=0)
GGA + U(calculated)
GGA + U(calculated+1ev)
STM
Mn on Cu site
Mn on N site
18.5
-1.8 (ferromagnetic!)
6.50 ±0.05
2.5
5.4
5.1
6.2±0.3
2.7
© 2006 IBM Corporation
IBM Research
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.
© 2006 IBM Corporation
IBM Research
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
© 2006 IBM Corporation
IBM Research
Thanks to
Barbara
Jones
Chris
Cyrus
Hirjibehedin Lutz
Andreas
Heinrich
© 2006 IBM Corporation