3. MAGNETIC MARKERS
3.2. Structure and common applications of magnetic microspheres
3.2.1. Principles of magnetic microsphere detection
Since all magnetic microspheres display superparamagnetic behavior, an external magnetic field has to be applied in order to magnetize the particles and to obtain measurable magnetic stray fields in biosensor applications. In principle, two distinctly different setups are thinkable: the magnetizing field could be applied perpendicular or parallel to the film plane of the magnetoresistive sensor.
However, it is important that the magnetizing field does not affect the sensitivity of the magnetoresistive sensor elements. Both our GMR- and TMR-type sensors consist of ferromagnetic layers with thicknesses between 3 and 8 nm, which, compared to the lateral dimensions of 1-50 µm, can be approximated as being infinitely thin. Thus, the demagnetizing field Hd in the direction perpendicular to the plane of the ferromagnetic layers can be expressed as Hd=Nd·M≅M, since the demagnetizing factor Nd reduces to ≅ 1 in the case of infinite layer thinness (Ref. 142). The sense layer of our magnetoresistive devices consists of permalloy (Py), which is a common material in sensor applications due to its high permeability, low coercivity and vanishing magnetostriction (Ref. 143). With the room temperature saturation magnetization of Py being 860 kA/m (Ref. 143), a demagnetizing field of about the same magnitude hinders the magnetization of the sense layer to align perpendicular to its plane.
Therefore, it is possible to apply a rather large magnetic field in the out-of-plane orientation of the magnetoresistive sensor, thus magnetizing the magnetic microspheres without affecting the magnetization configuration of the sense layer.
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Since all of our fabricated magnetoresistive devices are highly sensitive at or near zero in-plane magnetic bias, most of the measurements presented in chapter 1,1 and 1 are obtained by applying a perpendicular magnetizing field. Such a setup was initially introduced by scientists from the Naval Research Laboratory (Ref. 15) and got adopted later by most other research groups active in the field of magnetic biosensors.
Applying the magnetizing field in the plane of the sensor is not completely out of the question, but it either requires magnetoresistive devices with sensitive regions at rather large in-plane fields or ferromagnetic markers. Otherwise, the magnetic moment of the microspheres is insufficient to produce measurable stray fields.
Additionally, the presence of the microspheres would affect all the measurements, since they would always display the same magnetic moment in the crucial sensitive field range of the magnetoresistive sensor. Contrary, the microsphere’s magnetic moment can be ‘turned on and off’ by varying the magnitude of the magnetizing field in the out-of-plane setup without affecting the magnetoresistive sensor itself. Thus, the same sensor element can also act as a reference, which efficiently eliminates inconsistencies due to variations in the magnetic or electrical transport properties from one sensor element to another.
Next, a brief calculation of the stray fields within the sense layer generated by a magnetized microsphere is presented. A uniformly magnetized sphere with volume V and magnetization M can be approximated as an ideal magnetic dipole placed in the sphere’s center with a total magnetic moment of m=VM (Ref. 144). Even though magnetic microspheres are composed of homogeneously dispersed small superparamagnetic particles embedded in a polymer matrix, they can be treated the same way, with an effective saturation magnetization MS=Mmag·Vmag / Vms due to symmetry. Vmag is the total volume of all individual magnetite particles in the microsphere, Vms the total microsphere’s volume and Mmag the saturation magnetization of the magnetic material. The stray field generated by a single magnetized microsphere with moment mG
centered at the origin at a position xG has dipole-character and is given by (Ref. 144):
0
3
3n(n m) m x
B(x) with n
4 x x
µ ⋅ −
= =
π
G G G G G
K K G
G G Equation 1
The resulting stray field components within the sense layer are illustrated in Figure 18, both for the microsphere’s magnetic moment lying parallel and perpendicular to the sense layer. Here, d is the vertical distance between the center of the microsphere and the sense layer. Though stronger in the perpendicular moment orientation, the out-of-plane stray field components do not play an important role due to the large demagnetizing field in this direction. Thus, the local magnetization configuration of the sense layer is mostly affected by the in-plane stray field components.
In the case of parallel moment orientation, the in-plane stray field in the vicinity of the marker is rather homogeneous in direction and points opposite to the microsphere’s moment, with a maximum value directly underneath the microsphere. For perpendicular directions, the in-plane stray field is radially symmetric around the microsphere’s center and reaches a maximum at a horizontal distance from the center of d/2. This can be seen from the stray field components along the x-axis, which are also displayed in Figure 18. Analytically, they are given by:
Chapter 3: Magnetic markers
x 0
z 0
m out-of-plane: in-plane strayfield component: B ( ) B ( ) out-of-plane strayfield component: B ( ) B ( ) m in-plane: in-plane strayfield component:
ξ = ⋅Γ ξ ξ = ⋅ ∆ ξ G
G
x 0
z 0
0 0 3
2 2
5/ 2 5/ 2 5/ 2
2 2
B ( ) B ( ) out-of-plane strayfield component: B ( ) B ( )
m x
with B ,
4 d d
3 2 2
and ( ) , ( ) , ( )
1 1 1 2
1 ξ = ⋅Ω ξ ξ = ⋅Γ ξ
=µ ξ =
π
ξ − ξ ξ
Γ ξ = ∆ ξ = Ω ξ =
+ ξ + ξ + ξ
−
Equation 2
Even though the geometry and relative magnitude of the induced in-plane magnetic stray field is favorable for the parallel compared to the perpendicular moment orientation, it is not possible to achieve high moments without saturating the sensor by the magnetizing field in the in-plane setup for our magnetoresistive devices.
Therefore, we are using the out-of-plane setup for our measurements.
-5 -4 -3 -2 -1 0 1 2 3 4 5
-1,0 -0,8 -0,6 -0,4 -0,2 0,0 0,2 0,4 0,6 0,8 1,0
moment in-plane:
in-plane out-of-plane stray field component
ξ=x/d
Ω
-5 -4 -3 -2 -1 0 1 2 3 4 5
-2,0 -1,8 -1,6 -1,4 -1,2 -1,0 -0,8 -0,6 -0,4 -0,2 0,0 0,2 0,4 0,6 0,8 1,0
Γ
moment out-of-plane:
in-plane out-of-plane stray field component
ξ=x/d
z magnetization
parallel to plane magnetization
perp. to plane
y x
d
sense layer
y
z x
Γ
∆
Figure 18: Magnetic stray field of a magnetized particle
top: configuration middle: stray field pattern in the sense layer bottom: stray field component amplitudes along the x-axis for y=0
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