Spintronics

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Spintronics
Ideas, technological and experimental
realizations and future for device applications
Kevin Edmonds School of Physics and Astronomy,
University of Nottingham, Nottingham NG7 2RD,
United Kingdom
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Nottingham...
Population 350,000, 20,000 students
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Contents
Today. Introduction to spin and magnetic
materials Magnetoresistance effects and devices
Electrical control of magnetization. Tomorrow.
Semiconductor spintronics magnetic
semiconductors and non-magnetic
semiconductors. Friday. Magnetic domain walls
Nanocontacts and single-electron effects Summing
up.
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Spintronics, or spin-electronics
Lets try a loose definition The utilization of
spin angular momentum for storing, manipulating
and transferring information - relies on
interplay between magnetic and electrical /
optical properties
1 to 1010 spins
5
Spin
dm
B
Classical description of magnetism Magnetic
moment due to circulating current dm I.dA
I
z
Lz h
Lz 0
Quantum mechanics angular momentum is
quantized in units of h Relativistic quantum
mechanics electron has an intrinsic magnetic
moment
x-y
Lz -h
6
Stern-Gerlach experiment
1921 O. Stern proposes an experiment to detect
the magnetic moments of atoms...

• Inhomogeneous magnetic field
• Bz(z) B0 zB1
• Potential of magnetic moment in field
• U -m.B
• Force on particle is

7
Stern-Gerlach experiment
Postcard of experimental results sent by Gerlach
to Bohr, 1922
?Electrons have an intrinsic angular momentum
(spin), the projection of which along any axis
can only take values of ?h/2... ?...and an
intrinsic magnetic moment of eh/2me
mB 9.3x10-24 Am2.
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Spintronics
1959 Richard P. Feynmann, Theres plenty of room
at the bottom ...we can use, not just circuits,
but some system involving quantized energy
levels, or the interaction of quantized spins,
etc.
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Key concepts

• For spintronics we need
• A net spin polarization of the active electrons
• A method of manipulating these spins
• A method of read-out (optical or electrical)

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The importance of being ferromagnetic
Isolated electrons large magnetic field required
to overcome thermal effects Ferromagnetic
material spins on neighbouring atoms aligned by
in-built exchange field
Magnetic moment density
Spontaneous magnetization
Magnetization
M
B
Require only small field to rotate collective spin
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Key point spins conduct in parallel
1936 Mott introduces concept of spin-polarized
current
R?
Two populations of electrons (? and ?) carry
current in parallel
R?
TC
Resistivity
? Different scattering rates for each channel ?
Spin flip scattering time is longer than other
relevant time scales
Magnetization
Temperature
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Spin-polarized density of states

• Exchange interaction J gives splitting of bands
  for spins parallel and antiparallel to
  magnetization
• Imbalance of spin-up and spin-down states at
  Fermi energy EF
• ? spin polarization of current-carrying states

D(EF,?)
D(EF,?)
EF
Spin polarization
J
P D(EF,?) D(EF,?) D(EF,?) D(EF,?)
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Other definitions of spin polarization
For electrical measurements of spin... Diffusive
(ohmic) transport Weight with Fermi velocity
P and scattering time Tunnelling
transport Weight with the matrix elements P
vF?2t?D(EF,?) vF?2t?D(EF,?) vF?2t?D(EF,?)
vF?2t?D(EF,?)
D(EF,?).T?2 D(EF,?).T?2 D(EF,?).T?2
D(EF,?).T?2
Mazin, Phys. Rev. Lett. 83, 1427 (1999) Marrows,
Adv. Phys. 54, 585 (2005)
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Magnetoresistance effects in ferromagnets
Known since 1800s
Anisotropic magnetoresistance Resistance depends
on angle between current and magnetization (typica
lly few effect)
Mz
V
Anomalous Hall effect Hall resistance
proportional to perpendicular magnetization
component Mz
I
H
V
Both effects related to coupling between spin and
orbital angular momentum
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Spin Valves Giant Magnetoresistance

• Multilayered magnetic material with non-magnetic
  (conducting) spacer
• Magnetization of one layer is fixed the other
  is free to rotate

AP
P
R?
R?
R?
R?
R?
I
I
R?
R?
R?
low resistance
high resistance
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Giant Magnetoresistance (GMR)
Fe
nm
Cr
Fe
2007 Nobel prize for Physics
R/R(0)
Large drop in resistance when magnetizations are
aligned
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Magnetic field
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Spin Valve
Dieny et al., Phys. Rev. B 91

• Lower layer is pinned by antiferromagnetic
  underlayer
• Upper layer can rotate in fields lt 1 mT.

Co
Cu
Co
NiO
Change in resistance of a few 10s under
technologically relevant magnetic fields
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Spin valves as read heads
GMR sensors used in read heads for high density
data storage since 1997
Inductive read/write element
Magnetoresistive read element
1990
since 1997
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Tunnelling Magnetoresistance (TMR)

• Insulating spacer between ferromagnetic layers
• tunnel current depends on their relative
  orientation (spin conserved in tunnelling)

P configuration
AP configuration
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Analogy with optical polarization
unpolarized light
Parallel bright Perpendicular dark
polarized light
incoming current (unpolarized)
Parallel high current Antiparallel low current
tunnel current (polarized)
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Magnetic tunnel junction
Depends on barrier properties (Which states are
tunneling?)
D(EF,?).T?2 D(EF,?).T?2 D(EF,?).T?2
D(EF,?).T?2
P
MR gt 400 observed for MgO barriers
Yuasa Nature Materials 04 and APL 06 Parkin
Nat. Mater. 04 Ohno APL 06
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Progress in hard-disk technology
of GMR read heads shipped, 1997-2007 5 x
109
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Progress in hard disk technology, 1970-2008
8GB
gt300GB
1970 256kB
2008
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Magnetic Random Access Memory (MRAM)
New memory device data is stored in a huge array
of magnetic tunnel junctions parallel state
logical ? antiparallel state logical
1 Offers potential for non-volatile, fast,
high density memory
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MRAM Characteristics
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Spin transfer torque
Field-driven switching
Current-driven switching Spin transfer torque
H
re-polarization of current by nanomagnet
I
I

• stray field from current-carrying wire
• need current A
• non-local, difficult to screen

• momentum transfer to / from current-carrying
  electrons
• need current mA
• local control of switching

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Spin transfer torque
Field-driven switching
Current-driven switching Spin transfer torque
H
torque magnetization rotated
I
I

• stray field from current-carrying wire
• need current A
• non-local, difficult to screen

• momentum transfer to / from current-carrying
  electrons
• need current mA
• local control of switching

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Spin transfer torque
Field-driven switching
Current-driven switching Spin transfer torque
H
Reflection of minority spins
I
I

• stray field from current-carrying wire
• need current A
• non-local, difficult to screen

• momentum transfer to / from current-carrying
  electrons
• need current mA
• local control of switching

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Spin transfer torque
Field-driven switching
Current-driven switching Spin transfer torque
H
torque magnetization rotated
I
I

• stray field from current-carrying wire
• need current A
• non-local, difficult to screen

• momentum transfer to / from current-carrying
  electrons
• need current mA
• local control of switching

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Magnetization precession
Magnetization response to external magnetic field
described by Landau-Lifschitz equation dM dM
dt dt
-g M ? Heff a M ?
precession damping
Heff
M
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Magnetization precession
Magnetization response to external magnetic field
described by Landau-Lifschitz equation dM dM
dt dt
-g M ? Heff a M ?
precession damping
Heff
M
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Magnetization precession
Magnetization response to external magnetic field
described by Landau-Lifschitz equation dM dM
dt dt
-g M ? Heff a M ? - P M ? (M ? Mfixed)
precession damping Spin torque term
- damping or anti-damping
Heff
M
Mfixed
Slonczewski (1996)
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Spin transfer torque- first observations
Katine et al., Phys. Rev. Lett. (2000) Cornell
130nm diameter pillar structures Used GMR to
detect switching of free layer Current density
6x1010 A/cm2 ? significant heating effects
2006 Large (technologically relevant) spin
torques in MgO tunnelling structures
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Stable oscillations
Ralph Stiles (2007)
dM dt
-g M ? Heff a M ? - P M ? (M ? Mfixed)
dM dt
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Current-induced microwave emission
Kiselev et al., Nature (2003)
STT
M
damping
Spin transfer torque in high field regime
(applied H opposes spin-torque action) - spin
torque counteracts damping of magnetization
precession - stable precession of magnetization
at GHz frequency - conversion of dc to ac power,
tuneable with field or current
Heff
Current-controlled microwave oscillator with
potential telecom. applications
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Summary so far...

• Spins conduct in parallel transport of
  spin-polarized currents can be very sensitive to
  local magnetic configuration
• Spin-polarized currents exert a torque this can
  be used to control local magnetization

TOMORROW...Spins in semiconductors
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Spintronics
Ideas, technological and experimental
realizations and future for device applications
Part II Spins in Semiconductors
Kevin Edmonds School of Physics and Astronomy,
University of Nottingham, Nottingham NG7 2RD,
United Kingdom
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Semiconductor Physics Group
Bryan Gallagher Tom Foxon Richard Campion Andrew
Rushforth Chris King Vicky Grant Adam
Freeman Mu Wang Oleg Makarovsky Amalia
Patane Laurence Eaves Mo Henini
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Ferromagnetic metal
M
?D?(E) - D?(E)dE

• magnetization
• spin polarization

B
D?(EF) - D?(EF)
Paramagnetic semiconductor
CB
No magnetization, no spin polarization
VB
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Semiconductor spintronics
Microelectronics technology based on highly
engineered semiconductor components
Storage / MRAM based on ferromagnetic (metallic)
components
Semiconductor spintronics combining
semiconductors and magnets offers potential for
integrated storage and logic
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Spin transistor

• Datta Das (1990) transistor structure using
  ferromagnetic electrodes
• Potential for low-voltage operation,
  non-volatility, reprogrammability
• But difficulties due to mismatch between
  semiconductor and ferromagnet

Source
Drain
Field-effect transistor
Gate
Si
Source
Drain
Spin transistor
Gate
InAs
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Diluted magnetic semiconductors (DMS)
Non-magnetic semiconductor crystal
Paramagnetic DMS (random spins)
Ferromagnetic DMS (ordered spins)
Add dopants
Add holes
1978 Paramagnetic (II,Mn)VI semiconductors 1992
Ferromagnetic (In,Mn)As with TC 10K (Ohno et
al.) 1998 Ferromagnetic (Ga,Mn)As with TC 100K
(Ohno et al.)
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Why Mn?
Ga Ar 3d10 4s2 4p1 As Ar 3d10 4s2 4p3 Mn
Ar 3d5 4s2
? Half-filled 3d shell ? S5/2 magnetic
moment ? Missing 4p electron ? acceptor
(p-type conductor)
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Metal-Insulator transition
Density of states
Mn-induced impurity band
Valence band
Insulating (localized holes)
Metallic conduction
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Mean field model

• high concentration of charge carriers (holes) in
  valence band
• interaction between holes and Mn moments
• band splitting due to exchange interaction

EF
EF
3Eexch
Exchange splitting
Predicts TC (Mn density) x (hole density)1/3
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Growth
(Ga,Mn)As is an intrinsically non-equilibrium
system
Molecular beam epitaxy
Ga
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Heated GaAs substrate
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As
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? Require low temperatures and high stability to
prevent clustering
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Mn
Clustering
Mn flux
Mn incorporated
Substrate temperature
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First results
Matsukura Ohno (1998)
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Autocompensation
Increasing EF, decreasing stability
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Compensation mechanism Interstitial Mn
Ga Ar 3d10 4s2 4p1 As Ar 3d10 4s2 4p3 Mn
Ar 3d5 4s2
Mn

• 4s electrons compensate holes
• 3d electrons increase spin disorder

Interstitial
Substitutional
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Low temperature annealing
Increase of Curie temperature, magnetization,
conductivity decrease of lattice constant
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Interstitial Mn
? Mn interstitial defects are highly mobile
d? dt
Before annealing
Mn
? Diffusion to surface and oxidation during
annealing at 150-200C
After annealing
E
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Latest results
Wang et al. (2008)
9 Mn
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An intriguing prediction...
2000 Dietl et al. apply physics of (Ga,Mn)As to
other semiconductors - prediction of room
temperature magnetism in (Ga,Mn)N
RT
Smaller Mn-anion distance
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TC is determined by
Mn impurity level
valence band
GaSb

1. p-d coupling between Mn and anion
2. localization of holes.

GaAs
GaP
GaN
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(Ga,Mn)Sb Metallic with TC 20K
Lim et al. (2004)
(Ga,Mn)P Insulating with TC 60K
Scarpulla et al. (2005)
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(Al,Ga,Mn)As and (Ga,Mn)(As,P)
Rushforth et al. (2008)
Gradual transition from metallic high TC to
insulating low TC with increasing y
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(Ga,Mn)N
Room temperature ferromagnetism??? BUT...

• Small ferromagnetic signal on large background
• No clear correlation between magnetic and
  transport properties
• No obvious dependence of TC on moment
  concentration
• Sloppy magnetization hysteresis curves

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(Ga,Mn)N

• X-ray magnetic circular dichroism (XMCD) -
  directly probes magnetic ordering of transition
  metal dopants
• Magnetic ordering found only at temperatures
  below 10K

Sariggianidou et al. (2006) Freeman et al. (2008)
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(Ga,Mn)As devices
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(Ga,Mn)As transistors
using gate electrode to modify conductivity
Electrical control of magnetic properties
Ohno (2001) Stolichnov (2008)
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Tunnel Magnetoresistance / Spin Torque
80 TMR in (Ga,Mn)As tunnel junctions Tanaka et
al., PRL 01
Spin transfer torque, critical current lt 105
A/cm2 Chiba et al., PRL 04
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Single-layer TMR
Gould et al., Phys. Rev. Lett. (2004) TMR-like
signal with in sample with only one ferromagnetic
layer
64
Origin Tunneling anisotropic magnetoresistance
Rotating the spin orientation modifies allowed
states for tunneling
(Coupling between spin, crystal lattice and band
structure)
I
Fewer available states
High resistance
M
I
More available states
Low resistance
M
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TAMR in room-temperature ferromagnetic metals
Moser et al. PRL 07, Gao et al PRL 07, Park et
al PRL '08
ab intio theory
TAMR is generic to SO-coupled systems including
room-Tc FMs
experiment
66
Spin injection into non-magnetic semiconductors
e.g. for Datta-Das spin transistors
Source
Drain
Gate
InAs
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Spin lifetime in semiconductors
probe
pump

• Spin-polarization generated in semiconductor by
  pumping with circular polarized light
• Long (nanosecond) spin lifetimes demonstrated in
  n-type GaAs
• (much shorter in p-GaAs)
• Can be manipulated with electric fields

Problem lies in transferring spins between
semiconductor and metal...
68
Problems...
Several technical challenges ? interface
reactivity ? local Hall effects ? MR effects in
contacts More fundamental problem if Rsemi
gtgt Rmetal, spin current transferred to
semiconductor is negligible!
Monzon (1999)
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The conductivity mismatch problem
Schmidt et al., PRB (2000) Rashba, PRB (2000)
Fert Jaffres, PRB (2001)

• ? Spin accumulation, splitting of ? and ?
  chemical potentials in interface region
• No. of spin flips DOS, much higher on metal
  side than semiconductor side
• Depolarization of current occurs on metal side,
  before reaching semiconductor

Spin injection coefficient is controlled by the
element having the largest effective resistance
Rashba, PRB (2000)
Fert et al., cond-mat/0612495
70
Spin-injection from DMS
Nature, Dec. 99 spininjection observed using
LED structure
Fiederling et al. ? Paramagnetic DMS (n-type)
90 spin polarization at high magnetic field ?
ferromagnetic DMS (p-type) only a few
polarization
Ohno et al.
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Spin-injection from DMS
Short lifetime of p-type spins in
semiconductors (strong spin-orbit interaction)
p-(Ga,Mn)As Zener diode ? produces
spin-polarized electrons by interband
tunnelling ? extrapolated spin polarization 80
Van Dorpe et al. (2002)
Conversion of spin-polarization from holes to
electrons
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Spin injection using tunnel barriers
Injection from metals via Schottky barriers or
artificial tunnel barriers into spin-LED
I
n-AlGaAs
Low T 300K
CoFe / MgO 52 32
CoFe / AlOx 25 16
Fe / Schottky 30 8
(Zn,Be,Mn)Se 90 0
(Ga,Mn)As 80 0
p-AlGaAs
73
Detection of electrical spin injection
(Minnesota / Los Alamos)
Crooker et al., Science 05 Detection of spin
injection and accumulation in GaAs device from
Kerr rotation
SOURCE
DRAIN
Lou et al., Phys. Rev. Lett. 06 Electrical
detection of spin injection and manipulation in
GaAs device
74
Summary
Doping with magnetic impurities is the best way
to get spin in semiconductors but only at low
temperatures (lt200K), so far. Otherwise, we need
a large interface resistance this only
partially solves the problem.
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Spintronics
Ideas, technological and experimental
realizations and future for device applications
Part III Magnetic domain walls, applications
and devices
Kevin Edmonds School of Physics and Astronomy,
University of Nottingham, Nottingham NG7 2RD,
United Kingdom
77
Spin transistor

• Datta Das (1990) transistor structure using
  ferromagnetic electrodes
• Potential for low-voltage operation,
  non-volatility, reprogrammability
• But difficulties due to mismatch between
  semiconductor and ferromagnet

Source
Drain
Field-effect transistor
Gate
Si
Source
Drain
Spin transistor
Gate
InAs
78
How can the spin be affected by an electric field
in a non-magnetic semiconductor?
Bychkov-Rashba structural inversion asymmetry in
III-V semiconductors with non-uniformity in
growth direction Precession vector ?(k) aBR(k
? n)
k propagation direction n growth direction
n
I
depends on applied electric field
k
Bychkov Rashba, JETP Letters 39, 78 (1984)
Datta Das, Appl. Phys. Lett. 56, 665 (1990)
79
From Fabian et al., Semiconductor Spintronics,
cond-mat/0711.1461
80
Spin Hall effect
Spatial separation of spins in a non-magnetic
conductor in the absence of a magnetic field!
Dyakonov Perel, Possibility of orienting
electron spins with current, JETP Letters 13,
467 (1971)

• Spin-orbit coupling force deflects like-spin
  particles
• Carriers with same charge but opposite spin are
  deflected to opposite sides
• Spin accumulation without charge accumulation

Experimental observation Wunderlich et al.
(2005) Kato et al. (2004)
81
Magnetic domains
Spins in ferromagnet aligned due to exchange
interaction - energy cost due to dipolar
magnetic field
Magnetic energy can be minimized by formation of
magnetic domains.
82
Apply magnetic field
B0
increasing ve B
increasing -ve B

• Parallel domains grow
• Antiparallel domains shrink
• Perpendicular domains rotate

83
Domain walls (DW) separate regions magnetized in
different directions Thickness
where A spin stiffness K anisotropy const.
R?
R?
I
Analogous to antiparallel config. of GMR device ?
electrical resistance?
R?
R?
DW
84

• Intrinsic DW resistance due to spin polarization
  of current traversing wall (spin mis-tracking)
• requires very thin walls
• (rapid change of
• local magnetization)
• Extrinsic DW resistance due to discontinuity of
  conductivity tensor at wall
• ve or ve DR, depending
• on geometry
• not directly related to
• spin polarization of current.

conduction electron
local moments
Partin, J. Appl. Phys. (1974)
85
Current-induced domain wall motion
Spin-polarized current exerts pressure on wall
due to momentum transfer and spin transfer If
pressure greater than pinning force - wall
moves! Direction of motion depends on current
direction
86
Field-driven versus current-driven wall motion
Field-driven
Current-driven
current
current
magnetic field
Parkin (2005) IBM corporation
87
Magnetic racetrack memory
3D Storage / memory device with no moving
parts! Domains driven through reading
/ writing area using current.
Parkin (2005) IBM corporation
88
Current-induced domain wall motion
Yamaguchi et al. (2004) Imaging of DW motion
in NiFe wire
A
I
nucleation point
I

• DW nucleated driven to point A using magnetic
  field
• Imaged using MFM before and after applying
  current pulse
• Determine velocity from displacement during pulse

n.b. Large currents required!
89
Domain walls in a magnetic semiconductor
Yamanouchi et al. (2006) stepped (Ga,Mn)As wire,
T100K ? domain wall can be trapped at step
using magnetic field, and made to propagate
using current pulse
Wall motion at currents 2-3 orders of magnitude
lower than in metals Low moment density favors
small critical currents
j 4.3 x 109 A/m2
Direction of propagation
90
Resonant domain wall motion
Domain walls have mass! Saitoh et al., Nature
(2004)
AC current driven oscillations of DW position in
semicircular NiFe wire, analogous to driven
pendulum. Resonance at frequency
- resonant enhancement of domain wall motion
91
Domain wall resistance
Domain walls pinned at a series of etch pits in
(Ga,Mn)As
Chiba et al. (2006)
Correlation of domain pattern with resistance
measurements gives measurement of resistance per
wall
92
Nanocontact magnetoresistance
Hua Chopra (2003)
gt100,000 magnetoresistance reported - but
atomic-scale contacts are almost impossible to
characterize
93
(Ga,Mn)As double nanocontact structure
Rüster et al., Phys. Rev. Lett. (2003) Wuerzburg
2000 magnetoresistance!
T4K
10nm constriction
Depleted constriction acts as a tunnel
barrier ? tunnelling magnetoresistance
94
(Ga,Mn)As single nanocontact structure
Giddings et al., Phys. Rev. Lett. (2005) and
NJP(2008) Nottingham
4mm
Large MR with single constriction - tunnelling
anisotropic magnetoresistance?
I (nA)
V (mV)
95
(Ga,Mn)As single nanocontact structure
Giddings et al., Phys. Rev. Lett. (2005) and
NJP(2008) Nottingham
Charging effects - device seems to spontaneously
switch between high R and low R states
96
Single-electronics

• tunnelling via island with quantized energy
  levels
• charge on island controlled by gate

Single-electron transistor
Drain
Source
island
QNe
tunnel barrier
S
D
off state Coulomb interaction opposes
addition of charge ? tunnelling gap
Gate
Q(N½)e
S
D
on state Coulomb blockade lifted, current
can flow
Kastner, Rev. Mod. Phys. 64, 858 (1992)
97
(Ga,Mn)As nano-island with adjacent gate

• Huge (1000) magnetoresistance, controlled by
  gate voltage
• Can be positive or negative

Wunderlich et al., Phys. Rev. Lett. (2006)
98
Coulomb blockade in a single-electron transistor
Resistance versus gate voltage at fixed magnetic
field
QNe
S
D
off state Coulomb interaction opposes
addition of charge ? tunnelling gap
Q(N½)e
S
D
on state Coulomb blockade lifted, current
can flow
Sweep magnetic field ? change magnetization
direction ? Phase shift in Coulomb oscillations
99
Present and future device applications
100
Ferromagnetic multilayer devices (GMR, TMR)
Storage applications

• well-established hard disk technology, providing
  gt100Gb / in2, 1Gb/s transfer rates

Memory applications
Potential for faster, more stable non-volatile
memory but currently expensive and
low-density
Niche applications, e.g. Japanese SpriteSat
research satellite
101
Magnetic racetrack
Under development (IBM) ? potential for a
magnetic memory with the capacity of a hard disk
102
Some applications of MR sensors
Linear encoder for biometric testing
Current sensors for wind turbine control
Bit wear monitoring for deep drilling
GMR sensors offer ? High resolution ? Small
dimensions ? Easy assembly ? Robust design
Digital scale for workshop calliper
Motor encoders for Mars Rover
Motor feedback system for BLDC motor
Iris and zoom control for film camera
103
Other applications of GMR/TMR sensors
Microwave sources stable GHz oscillations,
tuneable using current Kisilev et al., 2003
Rippard et al, 2005
Biochips GMR sensor used to detect
functionalized nanoparticles bound to
cell Miller et al., 2003
104
Diluted magnetic semiconductors
Important research applications new insights
into anisotropic magnetoresistance, spin torque,
domain wall resistance, ferromagnetic
single-electron transistors...
BUT...limited technological applications so far
(eg CdMnTe optical isolators) For widespread
applications in spintronics, need reproducible
room temperature ferromagnetism (TC gt 400K at
least)
105
Hybrid 3-terminal devices

• Spin-field-effect transistors
• ? low-voltage reprogrammable logic
• requires highly efficient spin injection and
  detection (difficult / impossible?)
• Hot-electron transistors
• ? huge magnetocurrents possible, but current
  itself is tiny

106
Spintronics without ferromagnets
Optical methods generate and detect spin
populations using circular polarized light
probe
pump

• Electrical methods
• eg Spin Hall effect spatial separation of spins
  in non-magnetic semiconductor, due to spin-orbit
  interaction
• experimentally demonstrated 2004
• Wunderlich et al., Kato et al.

I
107
EuroChip
From European Commission Technology Roadmap for
Nanoelectronics
A camel is a horse designed by a committee,
Anon.
108
Further reading

• Semiconductor Spintronics
• I. Zutic, J. Fabian and S. Das Sarma, Reviews of
  Modern Physics 76, pp323-410 (2004)
• Ferromagnetic semiconductors
• T. Jungwirth, J. Sinova, J. Masek, J. Kucera and
  A.H. MacDonald, Reviews of Modern Physics 78, 809
  (2006)
• Magnetic domain walls
• ? C.H. Marrows, Advances in Physics 54, 585-713
  (2005)

kevin.edmonds_at_nottingham.ac.uk
109
introduce beads (small magnetic spheres 1µ),
decorated with antibody molecules
110
Beads attach to the antigenes via antibodies and
move towards the sensor array following the
magnetic gradient field. There, they attach to
the already present antibodies. Detection via the
magnetoresistance effect.