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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.

Science309, 2180 (2005)

A. Imre et al.

Science311, 205 (2006)

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., Nature439, 303 (2006)

Fe8, courtesy ESF.

M.B. Knickelbein

Phys. Rev. B70, 14424 (2004)

|ST,m>

|1,+1>

|5/2,+5/2>

|5/2,+3/2>

|1,0>

|5/2,+1/2>

Energy

Energy

|5/2,-1/2>

|1,-1>

|5/2,-3/2>

|5/2,-5/2>

|0,0>

Magnetic Field

Magnetic Field

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

Science 312, 1021 (2006)

Keep it Simple: Free Mn Atom

4s

- Half filled d-shell
- Weak spin-orbit interactions

3d

Mn: S = 5/2, L = 0, J = 5/2

V

0

Scanning Tunneling Spectroscopy: LDOSEf

eV

tip

sample

Features in the local DOS are reflected in dI/dV.

Magnetic Atoms on Surfaces

Magnetic atom

- Atom’s spin is screened by conduction electrons (Kondo effect)
- A thin insulating layer may isolate the atomic spin

Metal surface

Ef

eV

D

D

eV

X

tip

sample

tip

sample

D

D

|eV| < D

Elastic Channel Open

Inelastic Channel Closed

|eV| > D

Elastic Channel Open

Inelastic Channel Open

Inelastic Electron Tunneling SpectroscopyNon-magnetic tip

Thin insulator

Magnetic atom

dI/dV

kBT < D

σe+σie

σe

Non-magnetic sample

eV

-D

D

0

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

Methods of Electronic-structure Calculation

Cu

Cu

Cu

Cu

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

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

a0=Ö2d0

Cu

d0

Thin Insulator: CuN Islands on Cu(100)d0=2.55Å

a0=3.60Å

1nm

- Atomic resolution on CuN
- Mn atoms bind to Cu and N sites

CuN

Mn

Mn

Mn

Mn

Mn

Mn

Cu(100)

CuN monolayer

Cu(100)

1.80Å

DFT Calculation of Electron Density in CuNN atoms are approximately coplanar with Cu atoms on CuN surface.

N-1

N-1

Cu+0.5

Cu+0.5

Cu+0.5

Cu

Cu

E

|1,+1>

|1,0>

|1,-1>

|0,0>

B

Coupled Spins5

4

…

1

0

- 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

IBM Almaden STM Lab has built chains of up to 10 Mn atoms on Cu binding sites

Cu(100)

2

6

1nm

3

7

10Mn

1Mn

4

8

CuN

1nm

5

9

Mn

Mn

Mn

Chains of Mn AtomsN

Cu

Heisenberg Model of Spin Coupling

J

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)

Heisenberg Dimer Spectrum

- SG=0 and SE=1
- Atomic spin affects numbers of levels but not spacing
- First excited state at J

J

S

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

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

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

Unit Cells Used in Calculating Mn on CuN

Single Mn, larger unit cell

Single Mn, smallest unit cell

Mn dimer, smallest unit cell

N

Cu

Mn

Mn

10.80Å

7.20Å

7.20Å

Electron Density with an Adsorbed Mn Atom

Mn+

N -1.5

N -1.5

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.

A new kind of atomic-scale magnet

- Surface N atoms isolate and bridge Mn atoms.
- This is a “surface” assembled magnet.

Mn

Mn

N

N

N

Cu

Cu

Cu

Cu

Cu

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

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 d2.5 and d3 d1.5
- U=Δεd of the above two

Cu

Calculating Exchange Coupling

H=JS1·S2

|±|S=5/2, Sz=±5/2

DFT total energies

= EE

2S2J=++|H|++ +-|H| +-

(in meV)

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.

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

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