Philips Magnetoresistive Sensor User Manual
Page 15
2000 Sep 06
15
Philips Semiconductors
Magnetoresistive sensors for
magnetic field measurement
General
APPENDIX 1: THE MAGNETORESISTIVE EFFECT
Magnetoresistive sensors make use of the fact that the
electrical resistance
ρ
of certain ferromagnetic alloys is
influenced by external fields. This solid-state
magnetoresistive effect, or anisotropic magnetoresistance,
can be easily realized using thin film technology, so lends
itself to sensor applications.
Resistance
- field relation
The specific resistance
ρ
of anisotropic ferromagnetic
metals depends on the angle
Θ
between the internal
magnetization M and the current I, according to:
ρ(Θ) = ρ
⊥
+ (ρ
⊥
− ρ
||
)
cos
2
Θ
(1)
where
ρ
⊥
and
ρ
||
are the resistivities perpendicular and
parallel to M. The quotient
(ρ
⊥
− ρ
||
)/ρ
⊥
= ∆ρ/ρ
is called the magnetoresistive effect and may amount to
several percent.
Sensors are always made from ferromagnetic thin films as
this has two major advantages over bulk material: the
resistance is high and the anisotropy can be made
uniaxial. The ferromagnetic layer behaves like a single
domain and has one distinguished direction of
magnetization in its plane called the easy axis (e.a.),
which is the direction of magnetization without external
field influence.
Figure 17 shows the geometry of a simple sensor where
the thickness (t) is much smaller than the width (w) which
is in turn, less than the length (l) (i.e. t « w ‹ l). With the
current (I) flowing in the x-direction (i.e. q = 0 or Q = f) then
the following equation can be obtained from equation 1:
R = R
0
+ DR cos
2
f(2)
and with a constant current
Ι
, the voltage drop in the
x-direction U
x
becomes:
U
x
=
ρ
⊥
Ι
(3)
Besides this voltage, which is directly allied to the
resistance variation, there is a voltage in the y-direction,
U
y
, given by:
U
y
= ρ
⊥
Ι
(4)
This is called the planar or pseudo Hall effect; it
resembles the normal or transverse Hall effect but has a
physically different origin.
All sensor signals are determined by the angle
φ
between
the magnetization M and the ‘length’ axis and, as M
rotates under the influence of external fields, these
external fields thus directly determine sensor signals. We
can assume that the sensor is manufactured such that the
e.a. is in the x-direction so that without the influence of
external fields, M only has an x-component
(
φ
= 0˚ or 180˚).
Two energies have to be introduced when M is rotated by
external magnetic fields: the anisotropy energy and the
demagnetizing energy. The anisotropy energy E
k
, is given
by the crystal anisotropy field H
k
, which depends on the
material and processes used in manufacture. The
demagnetizing energy E
d
or form anisotropy depends on
the geometry and this is generally a rather complex
relationship, apart from ellipsoids where a uniform
demagnetizing field H
d
may be introduced. In this case, for
the sensor set-up in Fig.17.
(5)
where the demagnetizing factor N
−
t/w, the saturation
magnetization M
s
≈
1 T and the induction constant
µ
0 = 4
π
-7
Vs/Am.
The field H
0
−
H
k
+ t/w(M
0
/m
0
) determines the measuring
range of a magnetoresistive sensor, as f is given by:
Fig.17 Geometry of a simple sensor.
handbook, halfpage
y
x
L
M
Ι
MBH616
ϕ
W
ϑ
L
wt
------
1
∆ρ
ρ
-------
cos
2
φ
+
1
t
---
∆ρ
ρ
-------
sin
φ
cos
φ
H
d
t
w
----
M
s
µ
0
-------
≈