Transcript Slide 1

Magnetic properties of Surface
Mn ML film on W(110)
Atomicresolution
!
S. Heinze, et al,
Science 2000
June 9; 288:
1805-1808.
spin-polarized scanning tunneling microscopy
Magnetic materials
•
•
•
•
ferromagnetic materials:
Elements: Fe, Ni, Co, and their alloys
Oxides: Ferrite, Ni-Zn Ferrite
some ionic crystals: CrBr3, EuI
(anti-ferromagnetic materials, etc…, what are the definitions?)
magnetism is based on quantum mechanical
exchange interaction!
Hysteresis curve
Quantities:
Ms = saturation
magnetization
Hc = coercive field
µ = (initial) permeability
- hard magnetic materials
Hc > 300 Oe
- soft magnetic materials
Hc < 0.05 Oe
Magnetic Energies
• Exchange energy
alignement of spins, cost of energy to change direction of
magnetization
compensated by thermal energy phase transition at Tc
•
magnetostatic energy
discontinuity of normal component across interface
demagnetizing factor f(shape of sample)
•
magnetocrystalline anisotropy
preference of magnetization along crystallographic directions
•
magnetoelastic energy
Change of magnetization due to strain (magnetostriction)
•
Zeeman energy
potential energy of magnetic moment in a field
Magnetostatic Energy
Domain Wall Energy
Energetic considerations:
domain wall costs wall energy, but reduces magnetostatic energy
More Domains =
smaller spacing d
Magnetostatic energy density
Domain wall energy density 
Competition  minimization of
energy
Types of domain Walls
a) Bloch
b) Neel
c) cross-tie
(c)
Influence of reduced dimension
(surface and interface)
• Real dimensionality effect.
transition?
• Influence from surface and interface
(symmetry breaks)
There is transition and effects are gradual:
reduced neigbors  reduced overlap  smaller dispersion of electron bands 
higher electron density  different electrons number for spin up and spin down 
different magnetic moment.
Density of states (DOS) from free
electron theory
• 3 dimensional case:
K space
The density of states as function of k:
dS(k )  4k 2 dk
k  2m E / 
m
dk  2 dE
k
sphere
N(E)  dS/dE  E1/2
N(E)
Density of the states:
E
2 dimensional case:
K space
The density of states as function of k:
dS(k )  2kdk 
dk
N(E)
N ( E )  E 0  constant
E
dk
1 dimensional case:
dS(k )  dk 
N (E)  E
N(E)
The density of states as function of k:
1/ 2
E
Stoner Model for Band
Ferromagnetism
Spin-dependent exchange
coupling > different electron
density of states (N+ and N-)
Majority
Minority
For different spin electron, potential


1
V  V0  JM
2
1
g ( E )  g 0 ( E  JM )
2
EF
1
1
M   [ g 0 ( E  JM )  g 0 ( E  JM )]dE

2
2

EF
M  N  N   [ g  ( E )  g  ( E )]dE

Stoner Model for Band
Ferromagnetism
The three solutions for
EF
M   [ g0 (E 

To be magnetic, require
df
( M  0)  1
dM
High exchange coupling
1
1
JM )  g 0 ( E  JM )]dE  f ( M )
2
2
J  g0 ( EF )  1
High DOS at EF
In the bulk Fe, Co, and Ni satisfies the requirement. While on the
surface, the band width is different and so the density of states at fermi
surface is also changed, it causes the magnetic moment different from
the bulk, while Cr and Mn can be magnetic at the surface.
Molecular theory (Weiss, 1907)
Hˆ   H si   J i , j si s j
i
with approximation,
where,
Heff  H   J i , j  S
 Si  e
i
j
 si  s j  si S
Average field (molecular field)
j
i
 Si  S 
i
j
i, j
Hˆ   si  Heff
s s
e
Si  H eff / kT
(For Ising model,
Si  H eff / kT
si  1)
j i, j
e eff  e eff
H
S  Heff / kT Heff / kT  tanh(H eff / kT )  arctanh(S )  
kT
kT
e
e
i
H
/ kT
H
J S
/ kT
T
H
 arctan h( S )  c  S 
T
kT
with
J
j
k
i, j
 Tc
For third order approximation,
S 3 Tc H
1
S  
 S    S 3  H / kT
3 T kT
3
When H=0 and 
 0(T  Tc ), two solutions:
S 0
S   3  M  1 
Tc
T
With
  1
Tc
T
H
  0(T  Tc )
1/ 2
H  0  H  f (S )
  0(T  Tc )
S
1-d Ising model
1
2
3
N-1
N
Chain of N spin, spins only
+1 or -1 Only interact with
the next neighbor
Study two spin correltion <SkSl>
 Sk Sl  Sk Sk 1Sk 1Sk 2 Sk 2 Sk 3    Sl 1Sl 1Sl  replace SkSk+1 with Sk,K+1

(  S k ,k 1e
J S k ,k 1 / kT l  k
)
sk ,k 1
( e
J S k ,k 1 / kT l  k
)
e J / kT  e  J / kT l  k
J l k
 ( J / kT
)  (tanh )
 J / kT
e
e
kT
sk ,k 1
For large system and l-k is large number,
No long range order at finite T!
1
 S k Sl  {
0
T 0
T 0
2d-Ising and 3d-Ising and more
Landau 2d-Ising 3d-Ising
½
1/8
~0.325
3d-XY
3d-Heisenberg
~0.3454 ~0.3646
 
1
7/4
~1.316
~1.3866
H  M
3
15
~4.81
~4.803
M 

~1.24
~4.816
Theory on 3-d models are all numeric. It was proven that no ferromagnetism at finite T in less
than 3 dimensions in a spin system with a certain isotropy. Magnetism in reduced dimensions
stabilized by anisotropy.
0.8MLFe/W(110)
β ~ 0.124
γ ~ 1.75
Ni/W(110)
Thickness of Tc on film thickness
Assume ferromagnetism only
if d<t, it understandable there
will be thickness dependence
of Tc on film thickness.
Tc()  Tc(t )
 t 1/
Tc()
Co/Cu(001)
ν~0.71
Ni/W(110)
Islands contributions
Volume vs. interface anisotropy
Spin-reorientation transition (SRT)
Phenomenological separation of anisotropy into “volume” and “interface”
Generally, Volume (including shape)
contribution tends to make spin in-plane.
G eff
2 K1s
(
 2M 2 ) cos2 
d
When K1s<0, there will be SRT from outof-plane to in-plane SRT.
Ni/Cu(001)
Unusual SRT due to the contribution
from magnetoelastic anisotropy.
Exchange coupling
RKKY Model for 3d free
electrons gives:
H dd
sin 2k F R
cos 2k F R

5
2
(2k F R)
( 2k F R ) 3
Period is

kF
Scanning Electron Microscopy
with Polarization Analysis
(SEMPA) from Fe/Cr/Fe
More sophisticated theory and exp.
K1
K2
Period determined by Fermi surface:
“spanning vectors” in direction of the
film normal gives oscillation period:
For Cu(001):
1 4.7 Ǻ
 2  10.6 Ǻ
For Au(100)
1  4.1 Ǻ
Fe/Au/Fe
Overlap
of two
periods
2  14 Ǻ
Magnetic Quantum Well States
the origin of exchange coupling
When ferromagnetic layer contacts diamagnetic
layer, for majority spin electrons at EF in FM are
s electrons like in the diamagnetic layer, while
minority electrons at EF are mainly d electrons,
which have different from in the diamagnetic
layer (s). s electrons with minority character in
diamagnetic layer are confines and cause
quantum well states with spin dependence.
Only Minority has strong effect
In diamagnetic layer
between two FM layers,
DOS changes while the
thickness of diamagnetic
layer changes, to lower the
total energy
Different alignment of the two FM layers at different
diamagnetic layer thickness
Exchange coupling !
Giant magnetoresistance (GMR)
Simple model
In ferromagnetic material:
    R  R 
RAF
R  R


2
RF  2
R R
R  R
2
R RAF  RF ( R  R )


R
RF
4 R R
Spin Valves
One layer free
One pinned
Notice the bias
hard magnetic underlayer “pins“
soft magnetic top layer
resisitivity changes abrupt for
flip of magnetization
Toward Spintronics
Spin-valve transistor
PLD to make spintronics
Science 291: 840-841(2001)
VSM (Vibrating Sample Magnetometer)
According to Faradays laws of
magnetic induction, an ac voltage
is induced in the electrical which
is proportional to the rate of
change of magnetic flux linking
the circuit, and therefore to the
size of the moment within the
sample due to the applied
magnetic field. As the sample is
vibrated in the vertical direction
near the detection coil, an ac
signal is generated at a
frequency determined by the
sample oscillation.
Most common technique that is employed for
Various materials. Bulk.
hysteresis loop measurements.
MOKE (Mangeitc optical Kerr effect)
Polar
Longitudinal
Transverse
roatation of polarization plane of polarized light due to sample magnetization
depends on direction of magnetization.
Very sensitive and stable, but lack the surface sensitivity, can be used as
magnetic microscopy signal source and hysteresis loop measurements
SEMPA
(Scanning Electron Microscopy with Polarization Analysis)
SEMPA images the magnetization by measuring the spin polarization of secondary
electrons emitted in a scanning electron microscope. The secondary electron spin
polarization is directly related to the magnetization of the sample. SEMPA therefore
produces a direct image of the magnitude and the direction of the magnetization in the
region probed by the incident electron beam.
First layer
measure
magnitude
and
direction
of
the
magnetization.
high spatial resolution (about 10 nm), long working
distance, large depth of field characteristic of SEM.
independent from topography but with topography.
surface sensitive technique(~1 nm)
Second layer (remove first)
Antiparallel Magnetic Order in Weakly
Coupled Co/Cu Multilayers (J. A. Borchers,et
al., PHYSICAL REVIEW LETTERS, 48 (1999)
2796
SQUID (superconducting quantum
interference devices)
SQUID is loop of superconductor that contains one or more Josephson Junctions.
(interface between two superconducting materials separated by a non-superconducting
barrier. A current may flow freely within the superconductors, but the barrier prevents the
current from flowing freely between them. However, the supercurrent may tunnel through
the barrier, depending on the quantum phase of the superconductors. The amount of
supercurrent that may tunnel through the barrier is restricted by the size and substance of
the barrier. The maximum value the supercurrent may attain is called the critical current of
the Josephson junction, and is an important phenomenological parameter of a junction).
Parallel Josephson
junctions made by
photolithography. When
bias current (Ib) is applied
to the SQUID, voltage
through the SQUID is zero
if the current is less than
critical current. When bias
current exceeds critical
current (Ic), the SQUID
turns to the normal state
and voltage is produced.
Magnetic
field
measure
SQUID
A SQUID sensor
with 0.5 mm
wide step-edge
Josephson
junctions.
When a flux is introduced into the SQUID loop, the critical current decreases. When
the bias current is fixed at a slightly higher value than the critical current and an
external magnetic field is applied, the voltage will change in a periodic wave in
accordance with the flux quantization. We can measure the magnetic field by
monitoring the change in voltage.
AC-Susceptibility measurement
With IDc to change the magnetic
field and Ac current to modulate
it, the pick up coil will detect the
ac susceptibility.
ac 
integrate
M
H
XMCD
(synchrotron related)
From the selection rules, the
IL3 and IL2 are proportional to
d holes, while the spin and
orbital moment can be
calculated from the difference
A and B (dichroism).(Sum rule)
Element-specific, quantitative.
Can be used as signal for
electron microscopy. With
good design, magnetic loop
can also be measured.
It is also elementresolved!
XMLD (synchrotron related)
Only sensitive to spin along which axis
XMLD can study the AFM ordering, by combining XMCD more magnetic
information can be obtained.
Spin-polarized photoemission
Spin-resolved photoemission is
powerful tool to study spinresolved electronic structure (for
example band mapping for
valence band), which can
compare directly with theory.
PRB. 51, (1995) 12627
Spin detectors
Spin detector is the essential part for spin-resolved experiments.
Mott detector: The Micro-Mott polarimeter utilises Mott scattering of
electrons from a target foil (big Z, normally Au) that is maintained at a
potential of 20kV. The scattered electrons are then decelerated to close to
ground potential for detection by channel plates. There are four detectors,
each placed at angle of 120° to the incident electron beam, and
equispaced in azimuth, so as to detect back-scattered electrons. These
are used to measure the two transverse components of the beam
polarisation.
SPLEED detector: based on spin-polarized low energy electron
diffraction (SPLEED) from big Z target (W(110)). It uses low voltages
(scattering energy is 104 eV) and features a very high asymmetry
function of > 0.2. Four integrated channeltrons allow simultaneous
measurement of transversal spin vector components. Its total scattering
intensity is concentrated into a few well-defined diffraction spots.
Spin detectors
Mott detector
SPLEED
Scattering is generally low efficient, which means tedious and time consuming:
sometime alternative photoemission dichroism can offer similar information.
Magnetic dichroism in angularresolved photoemission (MDAD)
No sum rule yet!
2p
levels as
example
By reversing magnetization or helicity of the light, there will be different
photoemission spectrum (dichroism) when M have a component along the direction
of the light. (MCDAD)
With linear or un-polarized light, M reversing along normal of the plane consisting of
q and k, there will be also MLDAD.
Symmetry break….
MDAD
Notice the reversed sign for the two 2p
Levels.
Hall effect
If an electric current flows through a conductor in a
magnetic field, the magnetic field exerts a
transverse force on the moving charge carriers
which tends to push them to one side of the
conductor. This is most evident in a thin flat
conductor as illustrated. A buildup of charge at the
sides of the conductors will balance this magnetic
influence, producing a measurable voltage
between the two sides of the conductor.
n density of mobile charge density, e elctron charge.
The Hall effect can be used to
measure magnetic fields with a
Hall probe.
Can be used for scanning
microscope, with resoltuion of
mm. (SQUID probe….)
Spin-resolved STM
Basically use magnetic or anti-ferromagnetic tip to have spin dependent tunneling:
One kind separate the spin-dependent part of
the tunnel current by rapidly changing the
magnetization of the tip in combination with a
lock-in detection of the variations in the tunnel
current.
S. Heinze, et al, Science 2000 June 9; 288: 1805-1808.
Even Atomic scale Hysteresis (Science
2001, June 15:292:2053-2056)
STM images of the topography (a) the magnetic
domain structure of the same area (b) of Co(0001).
Sample bias: 0.2 V; tunneling current: 0.5 nA; (a)
height variations 4 nm; (b) spin contrast: 3.6%.
Appl. Phys. Lett. 75, 1944, (1999)