Magnetic domain transition controlled by distributed normal magnetic field for stepped magneto-impedance sensor

2.1. Experimental procedure

The element was fabricated by a thin film process. An amorphous Co₈₅Nb₁₂Zr₃ film was RF-sputter deposited onto a soda glass substrate and then micro-fabricated into rectangular elements by a lift-off process. The dimensions of the element are 2000 μm long, 20 μm wide, 1.6 μm thick. The element was annealed in a magnetic field to induce uniaxial magnetic anisotropy. The direction of the magnetic anisotropy was controlled by the direction of the magnetic field while annealing. In this study, the magnetic field during annealing, 240 kA/m in 673 K, was oriented in 71 degrees relative to the short-side axis of the element. For the element made by this process, the saturation magnetization was 0.93 T and the anisotropy field was 480 A/m.

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Fig. 2.

Schematic of a M-H diagram and related magnetic domains for the element having a hidden state with indicating both the memorized and the reset state.

Figure 2 shows a schematic of MH diagram of fabricated element which has a uniaxial easy axis in an in-plane inclined direction, 71 degrees relative to the short-side axis of the element. In this case, the element is expected to have a hidden ILLD state. A “Memorized state” is determined here as a state where the in-plane external field is zero (H _x = 0) and the domain is parallel or anti-parallel single domain state. A “Reset state” of the proposed three states memory sensor is defined as the hidden ILLD state. When a sensing field which is larger than a certain threshold value along the in-plane longitudinal direction is applied, the reset state changes to the memorized state and be kept it. The aim of this study is to realize a controlled magnetization transition which changes the single domain state into the “hidden” ILLD state, that is to say reset the memorized state to the reset state

The experiment was carried out by applying a strong magnetic field with constant value along the normal direction of the substrate plane using an apparatus made by a certain structure of NdFeB magnets. It is possible to control the distributed canted angle relative to the normal direction within the applied normal field. An in-plane bias magnetic field could also be controlled by using a Helmholtz coil for measuring a variation in the element domain as a function of in-plane magnetic field. This in-plane field was applied along the length direction, which is the sensing direction, of the rectangular shape element.

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Fig. 3.

Schematic of applied magnetic field with distributed normal field.

Figure 3 shows a schematic of the distributed normal field. An equation of the vector of the normal field, B _normal , is shown as follows; (1)

In this study, the following were assumed; (2) (3)

These assumptions represent a field that has a linearly varied X-directional component within the constant normal field B _z .

In this study, a magnetic flux density B is derived from B = 𝜇₀ H, where 𝜇₀ is the permeability of free space. Therefore the expression B is obtained from the magnetic field in free space.

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Fig. 4.

Schematics of the measurement system.

Figure 4 shows a schematic of the measurement system. The domain structure was observed by a Kerr microscope. The normal magnetic field and the in-plane magnetic field were controlled individually on the observation stage of the Kerr microscope. An applied value of the normal field, B _z , as well as the distributed field, ΔB _x ∕Δx, can be controlled by using the normal field generating ring-shaped magnet. The magnetic field in in-plane sensing direction of the element is controlled by the Helmholtz coil. The distributed field, ΔB _x ∕Δx, on the observation-stage of the Kerr microscope was controlled by the vertical position of the ring-shaped magnet. The variation of the vertical position of this magnet changes slightly the B _z value on the observation-stage. On the other hand, it changes the ΔB _x ∕Δx, therefore it is controllable by changing the Z-position of the ring-shaped magnet.

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Fig. 5.

Example of simulated magnetic field on substrate surface.

An example of the distribution of magnetic field, which is generated by the apparatus of Fig. 4, is shown in Fig. 5. The field is a result of 3-dimensional (3D) FEM simulation. Figure 5a shows a distribution of B _z on the horizontal plane lying at z = −0.5 mm. Here the center of the ring-shaped magnet, shown in Fig. 4, is defined as z = 0, and it is a position where ΔB _x ∕Δx = 0. The variation of B _z was almost 12% within a range of ±2 mm of X–Y plane, here, the central value of B _z was 64.0 mT (640 G). Figure 5b shows a distribution of B _x on the same plane, with the same area of the X–Y plane as in Fig. 5a. The figure shows a canted flat plane of variation. From some simulations in other Z-positions, the inclination of distributed field ΔB _x ∕Δx, was almost a constant value, and it is possible to control the value by changing the vertical position of the measurement plane. In this figure, the z value was chosen as negative value for the reason of visual expression in Fig. 5b. The sign of ΔB _x ∕Δx for z > 0 must be positive, because the apparatus is symmetrical on the X–Y plane.

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Fig. 6.

Relationship between the z position in the ring-magnet and both the B _z and the ΔB _x ∕Δx.

Figure 6 shows a relationship between the z position in the ring-magnet and both the B _z and the ΔB _x ∕Δx. The horizontal axis in this figure represents z value, the vertical right axis represents B _z , and the vertical left axis represents ΔB _x ∕Δx. These relationships are estimated by 3D-FEM magnetic field simulation. The ΔB _x ∕Δx = 0 is obtained for z = 0, and the ΔB _x ∕Δx = 0.4 T/m is obtained for z = 0.8 mm. The value of z in the following experiment was ranging from z = 0 to z = 0.7 mm. In this study, the B _z value in the central area is 64.0 mT, and the variation according to the control of Z -position was lower than 1.2%.

Concerning the variation of magnetic field in the Y-direction, ΔB _y ∕Δy has almost the same value as ΔB _x ∕Δx because the symmetry of the ring magnet shape. However it is negligible owing to the narrow width of this element (20 μm) in this study.

In this subsection, an observed magnetic domain transition of an element which has easy axis at 71° is shown. This is almost the same condition as the previous report which shows an experimental expectation of the existence of hidden ILLD state [7,8]. The observation of the magnetic domain was carried out by observing a central part of the rectangular element.

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Fig. 7.

Typical variation of magnetic domain for the element with easy axis in 71 degrees.

When the normal field B _z = 64 mT and the distributed parameter ΔB _x ∕Δx = 0, that is obtained by the condition z = 0 in Fig. 6, the domain transition of this element was limited between longitudinal parallel and anti-parallel state, when the longitudinal applied field varies. The longitudinal direction is the sensing direction of the sensor. Figure 7 shows a typical variation of magnetic domain. The horizontal axis represents a longitudinal magnetic field which was controlled by the Helmholtz coil of in-plane longitudinal direction. In this figure, some observed domain pictures are shown with each pointed arrow on a point of an expected magnetization curve. The observed magnetic field of negative single domains, the bottom side pictures, were −84.4 A/m (−1.06 × 10⁻⁴ T), −46.2 A/m (−0.58 × 10⁻⁴ T), 16.7 A/m (0.21 × 10⁻⁴ T) and 43.8 A/m (0.55 × 10⁻⁴T) respectively. And the ones for positive single domains, the upper side pictures, it was −44.6 A/m (−0.56 × 10⁻⁴ T), −8.8 A/m (−0.11 × 10⁻⁴ T), 44.6 A/m (0.56 × 10⁻⁴ T) and 67.6 A/m (0.85 × 10⁻⁴ T) respectively. In the case of the increasing magnetic field, the domain transition occurs at about 43.8 A/m (0.55 × 10⁻⁴ T). And in the case of decreases, it occurs at about −45.4 A/m (−0.57 × 10⁻⁴ T).

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Fig. 8.

Initial state of the following trial of multi-domain reconstruction.

Figure 8 shows an initial state of the following trial of multi-domain reconstruction. It is the single domain state in the negative direction, and the external field condition is as follows; the normal field and the distributed field is as the same as Fig. 7, B _z = 64 mT and ΔB _x ∕Δx = 0, and the in-plane field applied to the element’s longitudinal direction was H _x = 0.

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Fig. 9.

Magnetic domain with application of distributed field ΔB _x ∕Δx = 0.24 T/m.

For the purpose of re-constructing the multi-domain state originated from the single domain state of Fig. 8, The distributed field was changed by controlling the Z-position of the ring-shaped magnet. In Fig. 9, the ring-shaped magnet was moved down and the relative position of the observed element was z = 0.6 mm. In this case, the distributed parameter ΔB _x ∕Δx was 0.24 T/m. The magnetization curve in Fig. 9 is an expected one based on the result of refs [8,9]. An appearance of multi-domain state, which was assumed as the ILLD state, was experimentally observed. For the domain picture is not clear, illustration is shown below it.

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Fig. 10.

Magnetic domain after application of ΔB _x ∕Δx = 0.24 T/m and return to ΔB _x ∕Δx = 0.

After the multi-domain reconstruction occur, the distributed field returns to ΔB _x ∕Δx = 0, by changing the Z-position of the ring-shaped magnet to the initial position z = 0 with keeping H _x = 0. The result shows that the multi-domain state had been kept despite the magnet movement procedure. It is shown in Fig. 10. In this figure, the picture of magnetic domain was illustrated below it, for the clear understanding of the observed domain pattern. It was obtained that the multi-domain state had been kept even if the distributed field returned to ΔB _x ∕Δx = 0. It is expected that the domain state changes into hidden stable ILLD state.

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Fig. 11.

Variation of magnetic domain after reconstruction of multi-domain ILLD state.

After the sequential procedure of reconstructing multi-domain state, above mentioned, the in-plane magnetic field was varied and then the variation of magnetic domain was observed. Figure 11 shows the result of this experiment. Here, the normal field B _z = 64 mT and the distributed parameter ΔB _x ∕Δx = 0. Starting from the multi-domain state around H _x ≈ 0, the external field gradually increases, and when the external field exceeds 31.0 A/m (0.39 × 10⁻⁴ T) the domain state suddenly changes to single-domain state. The observed three points in the hidden ILLD state in this figure was around 0, 22.3 A/m (0.28 × 10⁻⁴ T) and 30.2 A/m (0.38 × 10⁻⁴ T) respectively. The domain picture which is just changed from the multi-domain to the single domain was 31.8 A/m (0.40 × 10⁻⁴ T). After the domain transition to the single domain, the external field increased to 42.2 A/m (0.53 × 10⁻⁴ T) and then decreased to ≈ 0. Compared with Fig. 7 which is the original two-state transition phenomena, the value of largest external field in the Fig. 11 was lower than the transition external field 43.8 A/m (0.55 × 10⁻⁴ T) in Fig. 7. In case of Fig. 11, the applied in-plane field was lower than the domain transition field 43.8 A/m. The observed three points in the positive single domain state in this figure was around 0, 31.8 A/m (0.40 × 10⁻⁴ T) and 42.2 A/m (0.53 × 10⁻⁴ T) respectively. The multi-domain state had been changed to the single-domain state, and the single-domain was kept when the external field returned to H _x ≈ 0.