Calculation of GMR-Effect in Confined Current
Path (CCP)-CPP Spin Valves
J. Velev, A. Bandyopadhyay, K. Nagasaka, T. Zhao,
H. Fujiwara, W. H. Butler
MRSEC, IRG-1
Center for Materials for Information Technology
an NSF Materials Science and Engineering Center
Introduction
Areal densities for hard disk drives are doubling annually. However,
it will be difficult to maintain this astounding rate of technological
advance. CIP (current-in-the-plane) spin valves presently being used
are beginning to encounter critical difficulties:
(1) Electrically insulating layers must be inserted between the
spin-valve element and the magnetic layers that form the
read-gap making it difficult to reduce the read-gap length.
(2) The resistance R and the resistance change due to GMR
effect ∆R of the spin-valve element are expressed as;
R = ρeff(w/ht), ∆R = ∆ρ(w/ht)
ρeff: the effective resistivity,
∆ρ:the change of resistivity due to the GMR effect,
w, h and t: the track width, height and thickness of the
element, respectively (See Figure. 1).
It is expected that higher areal densities will be achieved by
decreasing w faster than h, keeping t almost constant, resulting
the decrease of R proportional to w/h. In order to keep the present
output level, we must increase the power applied to the element,
i.e. P=V2/R. This will cause a serious cooling problem, because
the heat flow from the element occurs primarily in the track width
direction through the leads.
(3) The bias field resulting from the sense current becomes higher
proportionally to h/w2.
Advantages of CPP (current-perpendicular to-the-plane) spin
valves:
(1) The magnetic layers forming the read-gap can be made to act
as electrodes, making the head structure much simpler. The
cooling problem is also eased substantially because the heat
flow becomes essentially perpendicular to the element plane.
(2) The disturbance due to the magnetic field induced by the
sense current will also be reduced as the size of the
element decreases.
The major drawback of CPP spin-valves:
The resistance of the element is much smaller than that of
CIP spin-valves.
R = ρeff(t/hw),
∆R = ∆ρ(t/hw), with t << h and w (See Fig.1).
Much higher current is needed to obtain a reasonable
output.
Thus, we plan to investigate a strategy of confining the current path
(CCP) in order to raise the resistance.
Calculation based on two-current model demonstrates that the
resistance of CPP spin valves can be raised with this technique even
with a substantial increase in the magnetoresistance ratio, ∆R/R.
J
CIP sensor
CPP sensor
w
lead h sensor lead
w
h
∆R∝w/(h*t)
J
∆R∝t/(h*w)
bit
track
Schematic of CCP-CPP Spin-Valve
bit
track
Electrode (Cu)
AF-layer (with low ρ to be developed)
pinned-layer (CoFe)
conducting layer (Cu)
free-layer (CoFe)
Electrode (Cu)
Substrate (ATC)
CC-layer:
Insulator with a
hole (or holes)
Fig. 1 It is expected that in advanced magnetic recording systems, the magnetic
bits will become smaller primarily through a reduction in track width in order to
moderate the decline in field at the head which scales exponentially in the ratio of
head-bit separation to bit length. From purely geometric considerations it is
expected that as the track width, w, becomes smaller, the signal, ∆R, from a CIP
spin valve sensor tends to become smaller while that from a CPP sensor becomes
larger.
Two-Current Model
RP = [(1/2R1)+(1/2R2)] –1 <
=2R1/(1+α)
R1<R2
R1
Iup
R2
Idown
R1
R2
RAP = (R1+R2 )/2
= R1(1+α)/2
R1
Iup
R2
Idown
R2
R1
∆R = RAP-RP = (α-1)2R1/(2(α+1))
(1)
∆R/RP=(α-1)2/(4α)
(2)
α ≡ R2/R1 is the scattering asymmetry parameter
Current Confining Effect
Confining factor: β ≡ A/Acond
A: total area of the CC-layer
Acond area of the conducting
part of the CC-layer
Confining factor of the other F-layer:
β’ << β
R1
Iup
R2
R2
Idown
R1
∆R = RAP-RP = (α-1)2ββ’R1/((α+1) (β+β’))
∆R/RP = (α-1)2ββ’/(α (β+β’)2)
For β’= 1(confinement is only for one F-layer)
∆R ~ [(α-1)2R1 (α+1)]β / (β+1): monotonic increase with β
max:2 times
∆R/RP ~ (α-1)2 β /(α (β+1)2): monotonic decrease with β
CPP Spin Valve Model
y z
x
0.5nm
Ry
Rx
I
0.5nm
y
z
40nm
x
Rx
4
m
n
0
Unit cell
Ry
Resister array
No current density change is assumed in z-direction.
The CPP-element area is assumed 40 x 40 nm2. The element is divided
into unit cells of multiple of pillars of 0.5x0.5x40 nm3 and each pillar
is converted into a 4-resistor array each resister being connected at a
Central vertex as shown above.
Calculation Method
We break up the spin-valve into nx times
ny cells and determine the conductance
between every cell and its neighbors. We
are looking to determine the voltages in
every node (middle of every cell).
Vi + nx
gu
gl
gr
Vi −1
Vi
gd
The Kirchhoff’s law for cell i can be
written:
Vi − nx
Vi ( gl + g r + gu + g d ) − Vi −1 gl − Vi +1 g r − Vi + nx gu − Vi − nx g d = 0
Subject of the boundary conditions:
Vi − nx = V0
at the bottom
Vi + nx = V1
at the top
gl = 0
at the left end
gr = 0
at the right end
Vi +1
Every cell conducts only to the cells immediately next to it so the
matrix of coefficients has only a few non-zero diagonals. It can be
efficiently stored and solved to obtain the voltages in the network:
∑g
1
− gl2
0
M
− g 1d+ nx
0
M
0
− g 1r
∑ g2
− gl3
0
L
− g r2
∑ g3
− gu1
0
0 L
− gu2
O
0
− g d2+ nx
0
0
0
0
 V1   V0 g 1d 

  
M

  
nx
   V0 g d 

  
M
M

 =

  

  
n − nx +1

   V1 gu

  
M

  
n 
n


∑ g Vn   V1 gu 
0
0
0
After voltages are known the currents between every 2 nodes are:
I xi =
1
(Vi +1 − Vi ) g ri + (Vi − Vi −1 ) gli )
(
2
I yi =
1
(Vi + nx − Vi ) gui + (Vi − Vi −nx ) g di )
(
2
The total resistance is:
nx
R = (V1 − V0 ) / ∑ I yi
i =1
Parameters Used for Calculation
βCoFe = 0.58, γCoFe/Cu = 0.34
materials
ρup(µΩc
m)
ρdown
(µΩcm)
CoFe
32
120
CoFe/Cu
299
606
Cu
8.4
8.4
Current Distribution
Cu
AF
AFM
80*
80*
AFM/Cu
500*
500*
CoFe
Cu
CoFe
AFM/Co
Fe
500*
500*
Cu
Estimated values through
experiments by Fujitsu
* Assumptions
CC-layers
GMR Ratio and Resistance as Functions of
Two Current Confining (CC)-Layer Locations
AF
Cu
CoFe Cu CoFe
AF
Cu
CoFe Cu CoFe
Cu
Cu
GMR ratio
SV element resistance
(40 nm x 40 nm)
Summary
1. Calculation of GMR effect was performed on CCP-CPP spin
valve structure using a resistor-array model by applying twocurrent model.
2. Potential and current distribution at each node are calculated by
solving a matrix form of Kirchhoff’s law using LAPACK.
3. For a typical example of CCP-CPP structure, we calculated the
dependence of the GMR effect on the location of two CC-layers,
giving parameters determined experimentally when available.
4. The followings have been confirmed:
a. The most effective locations of the two CC-layers are in the
middle of free and pinned layers
b. By this configuration, three times enhancement of the GMR
ratio is attainable for the CC-layers of a 1/80 confinement
factor, with the hole locations matching with each other.
5. The effect of mismatching of the hole location will be examined.