Optimizing the sensitivity of a GMR sensor for superparamagnetic nanoparticles detection: Micromagnetic simulation

Journal of Magnetism and Magnetic Materials 446 (2018) 37–43

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Research articles

Optimizing the sensitivity of a GMR sensor for superparamagnetic nanoparticles detection: Micromagnetic simulation R.D. Crespo ⇑, L. Elbaile, J. Carrizo, J.A. García Dpto. de Física de la Universidad de Oviedo, c/ Calvo Sotelo s/n, 33007 Oviedo, Spain

a r t i c l e

i n f o

Article history: Received 16 May 2017 Received in revised form 27 July 2017 Accepted 21 August 2017 Available online 24 August 2017 Keywords: Micromagnetic simulation OOMMF GMR sensor Magnetization process

a b s t r a c t The magnetoresistance (MR) of different sensor setups of bilayer arrays by micromagnetic simulations has been studied in order to detect 20 nm diameter Fe3O4 superparamagnetic nanoparticles. The MR signal of sensors with different sizes and/or different aspect ratios has been compared. We have proved that for a sensor with a given shape and size, the sensor sensitivity can be increased by raising the aspect ratio of its bilayers. The sensors can detect from hundreds down to a few tens of superparamagnetic nanoparticles randomly distributed on the sensor surface. Ó 2017 Published by Elsevier B.V.

1. Introduction Magnetoresistive sensors are linear magnetic field transducers based either on the intrinsic magnetoresistance of the ferromagnetic material, or on ferromagnetic/non-magnetic heterostructures (giant magnetoresistance multilayers, spin valve and tunneling magnetoresistance devices) [1]. The ability of the mentioned sensors to detect very weak magnetic field signals, combined with their low cost, small size, and an electronic signal suitable for an automated analysis, allows them to be a powerful tool in a growing number of applications. Thus, the use of magnetic labels to be detected by a magnetoresistance sensor is a powerful tool for the detection of microbial pathogens in medical diagnostics, environmental control and food safety [1–11]. On the other hand, the iron oxide magnetic nanoparticles with a diameter less than 30 nm have attracted special attention in biomedical applications such as contrast agent for magnetic resonance imaging (MRI). This type of nanoparticles are also used in medical drug targeting for tumor therapy and biomarker detection, due to their response to magnetic field, their non-toxicity, high biocompatibility, low background signals due to the absence of magnetic material in biological samples and their superparamagnetic behavior that avoids the agglomeration of the particles [12–15]. It is well known that the sensor sensitivity is highly dependent on the relationship between the sensor surface size and the particle size [16–19], while the number of labels detected by the sensor, ⇑ Corresponding author. E-mail address: [email protected] (R.D. Crespo). http://dx.doi.org/10.1016/j.jmmm.2017.08.066 0304-8853/Ó 2017 Published by Elsevier B.V.

and therefore the resulting signal, increases when increasing the sensor surface. On the other hand, in order to improve the signal-to-noise ratio of the sensor, it is necessary to pay attention to the sensor surface shape, because the signal-to-noise ratio of the sensor is strongly dependent on the aspect ratio of the sensing area [20]. So, we are going to carry out a systematic study of the sensor signal dependence on both sensor size and shape, as well as the sensor response to different number of particles. In this paper, we propose a setup for a magnetoresistance sensor replacing a multilayer structure with bilayer arrays, where each bilayer is composed of two magnetic layers of Permalloy separated by Cu as nonmagnetic spacer (Fig. 1). The response of different sensor setups has been studied by micromagnetic simulations in order to find the optimal sensor that provides the best response in detecting superparamagnetic nanoparticles (MNPs). In order to work with particles of the size used in biomedical applications due to their superparamagnetic behavior, 20 nm diameter particles have been chosen [15]. The MR signals of sensors with different sizes and/or different aspect ratio have been compared. The sensors analysed can detect from hundreds down to a few tens of superparamagnetic nanoparticles with a random arrangement on the sensor surface.

2. Micromagnetic simulation The micromagnetic theory is based on the approximation of using a continuous magnetization vector instead of discrete magnetic moments located on the sites of the crystal lattice, and the

38

R.D. Crespo et al. / Journal of Magnetism and Magnetic Materials 446 (2018) 37–43 !

Hk ¼

2K u

 ! ! ! Mp  k k ; 2

l0 Ms

!

with K u denoting a uniaxial anisotropy constant, Mp the particle !

magnetization, and k the unit vector in the easy axis direction [24].The magnetization of each nanoparticle as a function of the applied external field, the demagnetization field and, the anisotropy field, was calculated by means of an iterative method, assuming a random orientation of the anisotropy axis. From the nanoparticles magnetization, the dipolar field induced by a set of MNPs was calculated using NumPy code considering a random arrangement over the sensor surface and a random orientation of their axes of aniso!

tropy, being the external field the sum of the applied field Hac (par!

Fig. 1. Sensor diagram of bilayers array.

!

allel to the x-axis) and the bias field Hb (parallel to the y-axis). !

notion of the effective field Heff acting on the magnetizationM [21]. This effective field is obtained from the superposition of four different interactions between the spins of magnetic material that include exchange energy, anisotropic energy, Zeeman energy and demagnetization energy. The sum of their energies is the total energy E of the system, which becomes minimal in stable spin configurations, so the effective field is given by: !

Heff ¼ 

dE

!

l0 d M

The starting point in the study of dynamic micromagnetics is the Landau-Lifshitz-Gilbert (LLG) equation; this equation describes !

the change of the magnetization vector M over time as a function !

of the effective magnetic field Heff and some parameters inherent in a magnetic system, i.e. the saturation magnetization Ms , the gyromagnetic constant c and the phenomenological damping constant a:

0 1 ! ! ! ! dM a @ ! d MA M ¼ jcj M Heff  dt Ms dt

Within this framework, we have solved the LLG equation for a sen!

sor under the action of an ac magnetic field Hac (±600 Oe), the dc !

bias applied field Hb of 300 Oe, the magnetic field generated by a !

set of MNPs and the antiferromagnetic field Haf . In order to obtain the magnetization evolution of the free layer during one period of the ac field, a series of simulations are performed in a quasistatic way and the magnetization output of each simulation step is inputted as the initial state for the next step. The magnetic field !

2.2. Sensor model As mentioned above, the micromagnetic sensor simulations were carried out solving LLG using software OOMMF. Simulations were done with the standard Permalloy (Py) parameters: 8.6  105 A/m as the saturation magnetization, 1.3  1011 J/m as the exchange constant and 1.49  106 J/m2 and 4.1  107 J/ m2 for the bilinear and biquadratic exchange constants respectively. The cell size was 10  10  2 nm3. To calculate the electrical resistance R of the sensor, we have taken into account that the resistance depends on the angles between the magnetization directions of the adjacent ferromagnetic layers [25]. Therefore, a good approximation of the angular variation of the resistance due to the GMR effect is given by:

  DR RðhÞ ¼ R0 1 þ ð1  cos hÞ 2R0 ,where h is the angle between the magnetization directions of the two successive magnetic layers, R0 is the resistance at saturation (at h = 0°) and DR ¼ RAP  RP is the sensor resistance change between the antiparallel RAP and parallel RP magnetic configurations respectively.In order to calculate the total resistance of our sensor, the relative resistances of all pairs of opposing cells are computed from the angles between their respective magnetization vectors provided by the main output of the OOMMF simulation program. In this way, for cell number i, j, k in the three-dimensional array of each layer 1 and 2, that correspond to the top and bottom layers !

!

Hac is applied in the longitudinal direction x and the bias field Hb , that provides a magnetization to the nanoparticles, is applied in the transverse direction y. The simulations are performed in three steps. First, the dipolar field induced by the set of MNPs is calculated using a Numpy code [22], in order to include this field in the sensor simulation. Secondly, the LLG equation is solved for the sensor using the object-oriented micromagnetic framework OOMMF [23]. Finally, the resistance of the sensor is computed using Numpy code.

!

respectively, the angle between the M1ijk and M2ijk magnetization vectors is given by: !

hijk ¼

!

M 1ijk  M 2ijk !

j M j2

The total fractional resistance for a particular magnetization configuration of a sensor model is obtained by:

0 0 !1 111 Ny Nz Nx X X X   R N N D R y z @ AA ¼@ Nx þ 1  cos hij R0 2R0 i¼1 Nx k¼1 j¼1

2.1. Nanoparticles model The nanoparticles model was simulated taking into account the uniaxial magnetocrystalline anisotropy from the effective anisotropy vector field defined as:

where Nx, Ny and Nz are the nodes in the x, y and z directions. The fractional change in the resistance has been obtained for a different number of nanoparticles and for the different configurations of the arrays.

R.D. Crespo et al. / Journal of Magnetism and Magnetic Materials 446 (2018) 37–43

3. Results 3.1. Bilayer The first step in our study is to analyse the fractional change in the resistance of a sensor formed by one magnetic bilayer of Py (Ni80Fe20). The Py layers are 4 nm thick and are separated by 2 nm thick layer of Cu as nonmagnetic spacer (z direction) corresponding to the second maximum antiferromagnetic coupling factor [26]. Given that the sensor sensitivity is highly dependent on the relationship between the sensor surface size and the particle size, the response of a bilayer depending on its size and shape has been analyzed. Four types of bilayers with different lengths in the x and y directions have been considered: S-type (200  100 nm2), Mtype (400  200 nm2), L-type (800  400 nm2) and N-type (1600  200 nm2). In order to compare the sensitivity of the different bilayers, Fig. 2 shows the dependence of the maximum fractional change in the resistance, DRm = (Rmp  Rms)/Rms, with the number of particles. Rmp and Rms represent the maximum fractional change in the bilayer resistance with and without particles, respectively. As expected, the smaller bilayer is the most sensitive but, due of its small size, it can detect only a very small number of particles. On the other hand, the results obtained for the two largest bilayers L and N type indicate that the best way to improve the sensitivity of the sensor in order to detect a greater number of particles is to increase the x:y aspect ratio of the sensor surface. Based on the previous results and with the idea of finding the optimal bilayer sensor shape that provided a greater sensitivity, the response of a bilayer with a 16:1 aspect ratio with a size of

Fig. 2. Maximum fractional change in the bilayer resistance, DRm, in percent versus the number of magnetic particles.

Sensor Surface (nm2) Size ratio (nmxnm)

1600  100 nm2 was studied. The simulations for this shape showed no variation of the bilayer magnetoresistance with the applied field Hac. In this case, the magnetization vectors of output OOMMF indicate that the sensor layers are not antiferromagnetically coupled for any value of applied field in the range of ±600 Oe. The same behavior was observed in a bilayer of 3200  200 nm2. With the idea of modeling a larger sensor with optimal sensitivity to detect a wide range of particle number, different sensors consisting of arrays of bilayers are taken into account (Fig. 1). From now on we will refer to this type of sensors as Bilayer Array Sensor (BA sensor). 3.2. Bilayer array sensors BA sensor configurations with different aspect ratios, 2:1, 4:1, 8:1 and 16:1, have been studied. In Fig. 3 a scheme for the different setups is shown. Each setup was simulated with Py bilayers, being 10 nm the distance between the adjacent bilayers in the x and y directions. The number of bilayers considered in each sensor was determined by their size and shape and the aspect ratio of the BA sensor in order to compare setups with the same sensing surface. Table 1, shows DRm results for the BA sensors studied for several particle numbers, where 400 and 800 particles depict approximately 50% of the sensor surface covering for the two sizes studied sensors, respectively. In all cases, for the same particle number, the results were obtained with the same random orientation anisotropy axis and the same spatial distribution of the particles on the sensor surface. The simulations show that the BA sensor made by N-type bilayers is the most sensitive and, in cases where the shape of the sensor does not allow this configuration, the M-type BA sensor is the most sensitive. Fig. 4 shows DRm values depending on the number of particles for M-type and N-type BA sensors of Table 1. These values were obtained by repeating the calculations with different magnetic particle positions on the sensor surface and different random orientation of their anisotropy axis. The results show that the sensor sensitivity depends on both the particles number as well as on the size and shape of the sensing surface. Contrary to what one might expect, not always the smallest sensors are the most sensitive. Thus, depending on the number of particles to detect, the shape and not the size is what determines the optimal sensor sensitivity. Comparing the results obtained for 8:1 and 16:1 sensors, depending on the number of particles to detect, the larger size with greater aspect ratio presents a greater sensitivity. In fact, for a particle number lower than about 300, the greatest 16:1 sensor is the

32x104 2:1 (800x400)

8:1 (1600x200)

64x104 4:1 (1600x400)

S (200x100) Array

39

M (400x200) L (800x400) N (1600x200) Bilayer Fig. 3. Scheme of BA sensor configurations studied.

16:1 (3200x200)

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R.D. Crespo et al. / Journal of Magnetism and Magnetic Materials 446 (2018) 37–43

Table 1 Change of maximum magnetoresistance, DRm, in percent, for the different structures analyzed. S, M, L and N denote the different configuration of the BA sensors. Sensor surface(nm2)

32  104

64  104

Size ratio (nm  nm)

2:1 (800  400) 8:1 (1600  200) 4:1 (1600  400) 16:1 (3200  200)

Number of Particles

DRm (%) Array

100 400 100 400 100 800 100 800

Fig. 4. Variation of maximum magnetoresistance DRm versus the number of magnetic particles. Rates 2:1 and 8:1 refer 32  104 nm2 size M-type BA sensor and rates 4:1 and 16:1 refer 64  104 nm2 size N-type BA sensor.

Fig. 5. DRm versus sensor area covered with nanoparticles. Rates 2:1 and 8:1 refer 32  104 nm2 size M-type BA sensor and rates 4:1 and 16:1 refer 64  104 nm2 size N-type BA sensor.

most sensitive. A similar behavior is observed comparing the 2:1 and 4:1 sensors. Furthermore, the simulations performed by a small number of particles, results in a DRm independent of the number of particles. This DRm depends on the shape and size of each sensor. Thus, for the bilayer sensor N-type for a particles number between 1 and 10, the signal fluctuates between 3.3% and 3.4%; For the N-type BA 16:1 array with a number of particles smaller than 50 particles, the signal fluctuates between 6.3 and 6.6%. Below this minimum, the results provide a value of DRm that can be considered as a noise level of the detection. As a result, each sensor has a minimum number of detectable nanoparticles depending on its size and shape that ranges from 10 to 50 particles. For a greater particle number than 10 for the N-type bilayer sensor and 50 for the Ntype BA 16:1 array, the behavior of DRm with the number of particles is linear.

Bilayer

S

M

L

N

0.7 2.7 1.4 9.4 0.2 2.4 1.6 5.2

1.5 6.5 5.0 10.6 0.9 6.0 4.0 10.4

– – – – 0.7 2.8 – –

– – – – 1.8 6.5 6.9 13.5

0.9 4.5 7.4 12.8 0.9 4.8 – –

In order to compare the sensor response according to its shape and regardless of its size, Fig. 5 shows the values DRm as a function of the particle-covered sensor surface. The results show again that the sensitivity of the sensor increases with its aspect ratio. To explain the previous results we have analyzed the magnetization simulations of two sensors of the same size with M-type and N-type bilayers respectively. If we compare the two BA sensors Fig. 6a) and b) with the same sensing surface, the same aspect ratio and, different bilayer numbers, we can observe that the shape anisotropy of each bilayer determines the applied magnetic field for which the magnetization inversion process takes place. So, for a higher aspect ratio, it is necessary to apply a higher magnetic field to reverse the magnetization. Additionally, as we can see S and leaf domain states are formed. Fig. 6c) shows the magnetoresistance curves corresponding to the N and M-type sensors. It is well known that domain structures in the strips depend on the balance between exchange and shape anisotropy [27,28]. In the case of soft magnetic materials (Py) that present in-plane magnetization in the longitudinal direction, transverse and asymmetrical transverse walls may appear. Fig. 7a) shows as an example, the equilibrium magnetization for the N-type BA sensor at 1 mT, where we can observe a tail-to-tail domain wall at the top layer and a head-to-head at the bottom layer [29,30]. Fig. 7b) shows the equilibrium magnetization for the M-type BA sensor at +1 mT that corresponds to the magnetoresistance maximum. The dipolar field created by the particles on both sensors causes an increase of the exchange energy of 7,1% and 7% with respect to the sensors without particles for the N-type and M-type BA respectively. The presence of different S, C and leaf states can be observed during the magnetization process for the M-type BA sensor. Furthermore, in both sensors, the presence of nanoparticles substantially decreases the magnetic field required for the magnetization inversion. This fact makes the switching magnetization process more gradual, producing an increase in both width and height of the MR curve and an increase in the sensor sensitivity as shown in Fig. 8 In Video 1, we can observe the magnetization process of the Ntype BA sensor over a range of applied magnetic fields ranging from 7 mT to +7 mT. Each sensor is formed by two bilayers. Being a soft magnetic material, 4 nm thick and with a bilayer aspect ratio of 16:1, the sensor presents an in-plane magnetization along the longitudinal direction. As can be seen in this video, at an applied magnetic field of 2 mT emerging asymmetrical transverse walls appear on the right end of the bottom layer and on the left of the top layer. These walls propagate in opposite directions. It is well known that in the flat strips the dipolar field is highly nonhomogenous, being very intense close to the edges. Due to the stray field, the strip cannot be uniformly magnetized at least in the absence of an external field. We can appreciate that in the long strips two transverse walls are formed, one a head-to head domain to the right end of the bottom layer and the other a tail-to-tail

R.D. Crespo et al. / Journal of Magnetism and Magnetic Materials 446 (2018) 37–43

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Video 1. N-type BA sensor video.

Fig. 6. Magnetization structures in a) N-type BA sensor and b) M-type BA sensor related to the state of magnetoresistance maximum without particles at 6 mT and 5 mT applied field Hac respectively. The black point indicates the top layer in both configurations, and c) magnetoresistance curves corresponding to the two setups.

domain on left end of the top layer respectively, which propagate in opposite directions. In Video 2, the magnetization process of the M-type BA sensor over a range of applied magnetic fields ranging from 8 mT to +8 mT can be observed. This sensor is formed by eight bilayers. Comparing the magnetization process of the previous sensor with the M-type BA sensor, we can note that in the latter, transverse walls are formed on both the outermost bilayer of both top and bottom layer at an applied magnetic field of 5 mT, and later each one of the bilayers reverses individually. At a magnetic applied

field of 2 mT the outermost bilayer on the bottom right reverses its magnetization. At an applied magnetic field of 1 mT the outermost bilayer on the top left is the one that reverses its magnetization. From 0 mT to 6 mT there is very little change in the magnetization and several domain structures are formed. In the M-type BA sensor, the dipolar field created by the particles on the sensor causes an increase of the exchange energy with respect to the sensor without particles and allows the presence of different S, C and leaf states that can be observed during the magnetization process. Although there are only slight differences in the dipolar

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Video 2. M-type BA sensor video.

Fig. 7. Magnetization configurations in a) N-type BA sensor and b) M-type BA sensor related to the state of magnetoresistance maximum with particles at 1 mT and 1 mT applied field Hac respectively.

Fig. 9. Change of maximum sensor magnetoresistance, DRm, in percent versus distance between the nanoparticles and the sensing surface for M-Type BA sensor of 8:1 size ratio.

Fig. 8. Magnetoresistance curves corresponding to a) the N-type BA sensor and b) the M-type BA sensor.

and exchange energies between the two sensors, these are relevant because they determine the patterns of magnetization and the inversion processes of the magnetization. With the idea of knowing the resolution for nanoparticle detection, Fig. 9 shows the behavior of DRm% versus the distance d between the particles and the sensor surface. In the figure we can appreciate a linear behavior until about 45 nm. Fig. 10a) shows the magnetoresistance sensor response for different nanoparticle random positions and, in Fig. 10b) we can see the magnetoresistance curves corresponding to different

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References

Fig. 10. Magnetoresistive curves a) for different random arrangements of nanoparticles on the sensor surface and, b) for different anisotropy axes orientations of the particles.

anisotropy axis orientations of the nanoparticles. This results corresponding to the M-Type BA sensor with aspect ratio 8:1 and with 50% covered surface. As can be seen, the particle positions do not affect the magnetoresistance curve and the results obtained for the different random assignments of their anisotropy axes show slight variations in the magnetoresistance curves that do not affect the sensitivity of the sensor. 4. Conclusions Different Bilayer Array Sensor configurations for the detection of 20 nm superparamagnetic nanoparticles (Fe3O4) have been studied by micromagnetic simulations. The magnetoresistance properties of bilayer arrays were investigated as a function of the size and shape of the bilayers. It has been confirmed that the size and shape of the bilayers together with the shape ratio of the array determine the sensitivity of the sensor. We have verified that, for a given sensor surface, the sensitivity of the sensor can be heightened by increasing aspect ratio of both the sensor and its bilayers. For this reason, the most sensitive sensor of those studied is the type N BA sensor with 3200  200 nm2 dimensions. A linear relationship between nanoparticle quantity (from a few tens to hundreds) and sensor signal has been found. The micromagnetic simulations have shown that a high aspect ratio increases the magnetic field necessary for the magnetization inversion due to the strong anisotropy and produces a greater sensitivity to the presence of particles. Acknowledgements This work was supported in part by the Principality of Asturias Governments under GRUPIN 14-037.

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