Introduction to spin polarized tunneling
Karthik V. Raman
TIFR Centre for Interdisciplinary sciences (TCIS)
TIFR Hyderabad
Quantum Nature of Electrons
Courtesy: J.M.D. Coey
Magnetic moments associated with the electron
Magnetic moments associated with the electron
An electron orbiting a nucleus constitutes a current lo
m
An electron orbiting a nucleus constitutes a current loop with a
me
magnetic moment given by
m
A
= current, A = loop area
×
e
= -ev/2p r gives
l = m er × v
and
l
g
=
gyromagnetic
ratio
m = g ll =-(e/2me)l
µl ħ
µB=eħ/2me=Bohr magneton
ħ
µ
Orbital g-factor =1
l is quantized; lz = mlħ
mz = -glµBml
The intrinsic spin angular momentum likewise gives rise to an intrinsic magnetic moment:
ms = g ss = -(e/me)s
ħ
µ
msz= -gsµBms,
Spin g-factor = 2.0023
s is quantized; sz = msħ
g s = 2g therefore spin angular momentum is twice as effective as orbital angular momentum
in creating a magnetic moment.
fi
–
The interaction energy of a moment m with a magnetic field B is – m.B
Thus the general Zeeman interaction Hamiltonian for an electron is
µ ħ
Hz = (µB/ħ)(l + 2s).B
Courtesy: J.M.D. Coey
Spin-orbit interactions
Interaction energy
1. Important for heavier atoms and inner shells
2. Lanthinide and Actenide series possess high SO coupling strength
Ferromagnetism in metals
s
•
Creation of crystal lattice leads to overlap
and broadening of valence electrons
•
Band formation leads to larger bandwidth
for s-electrons
•
d-bands are relatively localized compared to
s-bands
•
Magnetism arises due to exchange splitting
of the d-bands ~ 1eV
d
ΔEex
Stoner criterion for itinerant ferromagnetism
Magnetic Periodic Table
1H
2 He
4.00
1.00
66Dy
Atomic Number
3 Li
4 Be
6.94
1 + 2s 0
9.01
2 + 2s0
11Na
Atomic symbol
Atomic weight
162.5
3 + 4f9
179 85
Typical ionic change
Antiferromagnetic TN (K)
5B
6C
7N
14.01
8O
16.00
9F
10Ne
10.81
12.01
19.00
20.18
12Mg
13Al
14Si
22.99
1 + 3s0
24.21
2 + 3s0
26.98
3 + 2p6
28.09
30.97
32.07
17Cl
18Ar
35.45
39.95
19K
20Ca
21Sc
22Ti
23V
24Cr
25Mn
26Fe
27Co
28Ni
29Cu
30Zn
31Ga
32Ge
33As
34Se
35Br
36Kr
38.21
1 + 4s 0
40.08
2 + 4s0
44.96
3 + 3d0
47.88
4 + 3d0
50.94
3 + 3d2
52.00
3 + 3d3
312
55.85
2 + 3d5
96
55.85
3 + 3d5
1043
58.93
2 + 3d7
1390
58.69
2 + 3d8
629
63.55
2 + 3d9
65.39
2 + 3d10
69.72
3 + 3d10
72.61
74.92
78.96
79.90
83.80
37Rb
38Sr
39Y
40 Zr
41Nb
42 Mo 43 Tc
44 Ru
45 Rh
46 Pd
47 Ag
48 Cd
49 In
50 Sn
85.47
1 + 5s 0
87.62
2 + 5s0
88.91
2 + 4d0
91.22
4 + 4d0
92.91
5 + 4d0
95.94
5 + 4d1
101.1
3 + 4d5
102.4
3 + 4d6
106.4
2 + 4d 8
107.9
1 + 4d10
112.4
2 + 4d10
114.8
3 + 4d10
118.7
4 + 4d10
51 Sb
52 Te
121.8
127.6
126.9
83.80
55Cs
56Ba
57La
72Hf
73Ta
74W
75Re
76Os
77Ir
78Pt
79Au
80Hg
81Tl
82Pb
83Bi
84Po
85At
86Rn
13.29
1 + 6s0
137.3
2 + 6s0
138.9
3 + 4f0
178.5
4 + 5d0
180.9
5 + 5d 0
183.8
6 + 5d0
186.2
4 + 5d3
190.2
3 + 5d5
192.2
4 + 5d5
195.1
2 + 5d8
197.0
1 + 5d10
200.6
2 + 5d10
204.4
3 + 5d10
207.2
4 + 5d10
209.0
209
210
222
87Fr
88Ra
89Ac
223
226.0
2 + 7s0
227.0
3 + 5f0
61Pm 62Sm 63
Eu
64Gd
65Tb
66Dy
67Ho
68Er
69Tm 70Yb
71Lu
157.3
3 + 4f 7
292
158.9
162.5
3 + 4f 8
3 + 4f9
229 221 179 85
164.9
3 + 4f 10
132 20
167.3
3 + 4f 11
85 20
168.9
3 + 4f12
56
175.0
3 + 4f 14
Ferromagnetic TC (K)
35
58Ce
59Pr
140.1
4 + 4f 0
13
140.9
3 + 4f2
90Th
91Pa
232.0
4 + 5f 0
231.0
5 + 5f0
97.9
60Nd
144.2
3 + 4f3
19
92U
238.0
4 + 5f2
145
150.4
3 + 4f5
105
93Np
94Pu
238.0
5 + 5f 2
244
152.0
2 + 4f7
90
95Am 96Cm 97Bk
243
247
247
98Cf
251
15P
16S
53 I
173.0
3 + 4f13
99Es 100Fm 101Md 102No 103Lr
252
257
259
258
Nonmetal
Diamagnet
Ferromagnet TC > 290K
Metal
Paramagnet
Antiferromagnet with TN > 290K
Magnetic atom
Antiferromagnet/Ferromagnet with TN/TC < 290 K
Radioactive
BOLD
54Xe
260
Courtesy: J.M.D. Coey
Courtesy: J.M.D. Coey
Fermi Surfaces (k-space)
• In Free electron model, the electronic states i.e. k points are
uniformly distributed along kx,ky and kz direction.
• Fermi surface is a sphere
• Introduction of lattice potential breaks this symmetry & Fermi
surfaces are anisotropic in k-space and also spin-dependent
http://www.phys.ufl.edu/fermisurface/
Fermi surfaces in Ferromagnets
bcc- Fe (majority)
bcc- Fe (minority)
hcp- Co (majority)
fcc-Ni (majority)
hcp- Co (minority)
fcc-Ni (minority)
Band structures of Ni, Co and Fe showing the position of
Fermi level
Ni
1422 emu/cc
484 emu/cc
Large d band DOS at EF for Ni
1714 emu/cc
Tat-Sang Choy et al., JAP 86 562 (1999)
M. Zeise and M. J. Thorton (Eds.), Spin electronics,
(2001)
Mott’s two current model
Spin-disorder scattering
Current
J=J +J
Js= J - J
Assumptions
E
• Spin-flip transitions are
neglected
• Conduction is almost by
means of s-electrons, they
have low effective mass
than d-electrons
EF
Density of states N(E)
Sub-band contributions to spin polarization
density of states
n
n
d
s
conductance
High negative
polarization
i
n  n 
Pn  n  n
i
Low positive spin
polarization
i i 
Pnv2  i i
i j,FMa nj vF,2t j j
Separate currents j=s,p,d
effective mass me and Fermi velocity play an
important role
s-band: large bandwidth
(M. B. Stearns, JMMM 5,167 (1977)
what states decay fastest
s-like, d-like, etc
d-band: localised compared to s-band
s - d hybridization: Itinerant electrons in ferromagnetism of 3d metals
s-like conduction electrons : positively polarized
Butler et al, (2001); Tsymbol et al (1997); Oleinik et al (2000); Mathon and Umerski (2001)
Courtesy: J.M.D. Coey
Evolution of spintronics
P. M. Tedrow, R. Meservey, PRL 26, 192 (1971).
He3 cryostat, upto 5T field
Robert Meservey
Paul Tedrow
• Studying superconductivity in thin films
of Pb (bulk Tc 7.2K) and Al (bulk Tc 1.2 K)
• Performing conductance studies in
metal/insulator/ superconductors and
SC/insulator/SC junction devices
Base temperature, 300 mK
Tunneling…..
E
x
VB
VB-Ex
Ex
simple potential barrier
d
How to realize tunneling?
metal-insulator-metal tri-layers
Thin film growth
e- from filled to empty states
need a bias voltage …
metal insulator metal
Determining tunneling current
Fermi-Dirac function
f (E)
E
eV
Occupied states in Left
electrode
1- f (E + eV)
Tunneling probability at
Energy E
I tunneling (V) = I l®r (V)- I r®l (V)
Unoccupied states in Right
electrode
Tunneling is exponential
VB
VB-Ex
Ex
d
• tunneling current, free electrons
– exp. in barrier thickness, height
– exp. in voltage
I ~ GV + gV3
dI/dV ~ V2
–can extract barrier parameters
• typical Al2O3-based junction
• how do we use this sensitivity?
– STM !
Superconductivity (BCS theory)
Below TC
Normal metal
C
Fermi surface
per pairs
SC state
Cooper pair energy per electron = Δ
SC electrons
BCS density of states in H = 0
T = 0K
T > 0K
Relative to Fermi level
Fermi surface
In a magnetic field applied in-plane
Zeeman split states in SC
E
Al/Al2O3/Ag
Increasing field
Quasi Particle DOS
BCS density of states in H:
For Spin 
For Spin 
Tunnel Conductance
k = quasi particle energy,  = half SC energy gap,
 = 1/kT
SC as a spin-detector ?
Meservey – Tedrow Technique of SPT spectroscopy
SC / Insulator / ferromagnet
tunneling
Tunneling e spin polarized
P = ( n - n  ) / ( n + n  )
Spin Polarization (P)
(Nv2) - (Nv2)
P (Nv2) + (Nv2)


Physics Today, J. S. Moodera et. al. (April 2010)
First demonstration of Spin Polarized Tunneling !!!
…….in Ni/Al2O3/Al junctions
PRL 26, 192 (1971)
PNi ~ 5 – 6%
Measured spin polarization (with Al2O3 barrier)
Earlier results Current values
Fe
40%
44%
Co
35%
42%
Ni
5-11% (later 23%) 46%
Permalloy 32%
48%
Co0.5Fe0.5
-55%
Why Al as the spin detector?
o Smooth, ultra thin films easily and reproducibly prepared
o Clean, surface oxide, great as a tunnel barrier
o Comfortable Tc and High HcII (~5 tesla)
o Low S-O scattering and long spin life time
What about other materials? V, a-Ga, Be, VN, V-Ti alloy
Using Vanadium
Probing Absolute Spin Polarization at the Nanoscale, Nano Lett. 14, 7171 (2014)
Highly interface sensitive measurements !
Tunnel into ultrathin FM onset of FM?
FM
1976
Backed by Al - full P in ~2ML
Polarization for ultrathin barriers
Total polarization
Analysis with the two current model
P
Al/Al2O3/Fe junction
0.6
id Pd  isp Psp
id  isp
-1.00
-0.75
-0.25
0.4
Pd
-0.50
0.00
0.8
0.9
P
id,0
1.0
i j  i j ,0 e
0.2
4
8
 j t
12
tAl O (Å)
2
Fe
16
id,0 , kd, Pd
Al3+
3
Tunneling measurements
indicate sp - and d - spin current
O2-
isp,0 , ksp, Psp
O chemisorbed
Al
Spin Polarized Tunneling
-What we learn• Superconductors :
2, phonon spectrum. spin-orbit,
orbital depairing, Fermi liquid effects….
Poster
• Ferromagnets :
DOS itinerant electrons - Interfacial density of states
Surfaces, Interfaces and Proximity effects
Band structure ?
• Excellent spatial (Å), energy (eV) resolution
• Probes at low T and high H;
• Extremely surface sensitive, E  0
Spin-polarized electron tunneling • R. Meservey and P. M. Tedrow
Physics Reports, Vol. 238, Issue 4, (1994), Pages 173-243 (A Review)
Concept of
Tunneling
Magnetoresistance
Magnetoresistance effect
Parallel State
Spacer Layer
M1
M2
Non-magnetic metal,
semiconductor,
or insulator
FM2
FM1
Low Resistance
Magnetoresistance effect
Anti-Parallel State
Spacer Layer
M
M
Non-magnetic metal,
semiconductor,
or insulator
FM2
FM1
High Resistance
Switching M by external magnetic field
FM1
Spacer Layer
MR curve
Anti-parallel
Resistance (R)
H
Parallel
0
Magnetic field (H)
FM2
Magnetic Tunnel Junction showing
magnetoresistance response
1995
Co/Al2O3/NiFe (8A Al Oxidized)
R(k)
4.5
77 K - 34 %
295 K - 25 %
4.0
NiFe
Al2O3
Co
3.5
Substrate
3.0
2.5
-60
MTJ
-40
-20
0
20
40
60
Field (Oe)
J. S. Moodera
T. Miyazake
JMR agrees with Julliere䇻s model: JMR = 2P1P2/1+P1P2
( PCo = 35% and PPY = 45% )
Even best junctions, show T and V dependence
effects, defects….
Extremely interface sensitive.
– magnons, phonons, band
…Why did it take so long ?
•
In-situ deposition
•
Controlled oxidation of thin film
of Al
Tunneling from the Fermi surface – k space approach to tunneling
Tunneling probability depends on convolution of the Fermi surface cross sections
between left and right FM electrodes
Antiparallel
alignment
Parallel
alignment
Magnetism & Magnetic materials (Cambridge), J.M.D. Coey
Improvement of TMR effect
2004
2007 reaching > 500% at RT !!
Giant Magnetoresistance (GMR) / Pseudo spin valve effect
2007
Peter Grünberg & Albert Fert
1988
Fe/Cr stack
Polarized neutron Reflectometry
Fe/Cr/Fe wedge trilayer structures
Phys. Rev. B 39, 4828(R)-1989
Explained by RKKY
Interactions
Observation of oscillatory
exchange coupling
Physical Review Letters 64 (19), 2304 (1990)
Exchange Bias Effect in GMR devices
F1
F1
F2
F2
Spacer Layer
FM1
Tunnel barrier
FM1
FM2
P1
FM2
Semiconductor
or Metal
P2
Spin Valve
MTJ
Jullière’s Model
TMR 
2 P1P2
1  P1P2
Modified Jullière’s
Model
2 P1 P2e  ( d d o ) / s
GMR 
1  P1 P2e ( d d o ) / s
Half metallic ferromagnets
Theoretical prediction of 100% spin polarization
Si - band gap
Band gap for one spin direction !
Half metallic ferromagnet CrO2
Other examples: NiMnSb, SrFeMoO,
Co2MnSi
Fe - no band gap
Spin filtering….
Creating spin polarization by spin selection!
Mag. semicond. EuS, EuO and EuSe
T < TC
2EX
(0.36 eV)


|T| 2 >> |T| 2
M
Tunnel Current:
J()  exp (-()½ d)
P=
J - J
J + J
M
EuS or EuO
barrier
EuO as Spin-Filter, higher Tc and exch. splitting 0.6eV
Spin Filter MTJs
Parallel  Low R
Anti-Parallel  High R
EuS
TMR =
EuS
RAP – RP
RP
2 PSF PFM
=
1 - PSFPFM
FM is a spin detector
Spintronics : Contribution to technology
Pioneering works in GMR & TMR effect
1956
IBM 350
Storage capacity 3.75MB
In-plane recording medium
Hard Disk Drive Structure & Components
Head Gimbal Assy (HGA)
Cover
Slider
Read & Write Heads
Suspension
Spindle
Motor
Electronics
Card
*TMR = Tunnel Magneto-Resistive
R/W
head
Slider
฀~1mm )
Disk
Assembly
Voice-Coil
Motor
฀VCM฀
< 1990
Suspension
BaseCasting
Actuator
(VCM & HeadSuspension Assembly
AMR sensor
Gimbal
Disk
Shields
Return Pole
*TMR
Read
Element
CIP GMR sensor
1990 - 2000
TMR sensor
2001 - 2007
CPP GMR
& TMR sensor
2007 - present
Coil
Main
Pole
Recording
Medium
SUL
Lube
Overcoat (carbon)
Recording layer
Growth Control
Soft Underlayer
Substrate
(glass or AlMg)
Recording Medium
Perpendicular magnetic recording
Storage medium: Stability of a 䇺bit䇻
Magnetic anisotropy energy (MAE) of the bit
1. Magneto-crystalline anisotropy – induced by SO coupling
High Z materials will have large anisotropy energy (Co/Pt multilayer/alloy)
2. Shape-anisotropy – By shape of the bit
3. Magneto-static energy – Magnetic field created by the bit that can
demagnetize the bit
Magnetic Field lines
B
For technology
MAEbit > 10 kBT
Confidential
1
0
Spin transfer Torque
Conservation of
electron angular
momentum
Univ. of Hamburg
•
STT-MRAMs using new class of ferromagnet/insulator materials