Study on Detection of a Small Magnetic Particle Using Thin Film Magneto-Impedance Sensor with Subjecting to Strong Normal Field

This paper deals with the detection of small magnetization using a thin film magneto-impedance sensor with subjecting to strong normal field. The sensor was made by soft magnetic amorphous thin-film with uniaxial magnetic anisotropy in the width direction of the element. It was reported that the sensor has very high sensitivity, such as pico-tesla order, when it is driven by hundreds of MHz. In this paper, a sensitive measurement method aiming for detection of a small particle or a cluster of nano-particles, having low-remanence, is proposed. The point is the application of strong normal field in the measurement area including sensor element and particle. The normal strong field is applied in the normal direction of the sensor plane in the value almost hundreds of mT. Instead of such strong normal field, the sensor keeps high sensitivity, because of the demagnetizing force in the thickness direction. A theoretical estimation for clarifying an efficiency of the method, experimental results of sensor property and sensitivity with subjecting to the normal field, and also a confirmation of detection of a small particle using the proposed method is reported. As a special mention, detection fundamentals when a applied surface normal field has a distribution and also a particle would run through in the vicinity of sensor is discussed.


Introduction
Detection of small magnetic particle is important for avoiding a contamination of industrial and chemical products. It is also important for detecting magnetic nano-particles included in cells and biomolecules for medical and healthcare technology [1].
For industrial cases, inspection of all items in manufacturing processes is desirable for the recent advanced manufacturing systems, aiming at a reduction of product's defects, a detection of damaged machine tools, and a tuning of the processing conditions. For example, the detection of small conductive particle is important for avoiding a contamination of high-capacity battery, such as Li-ion secondary batteries. The inclusion of conductive particle in the insulation layer, which is called "separator" of Li-ion battery, causes an extraordinary heating while operation. Our pre-liminary study for the magnetic property of small particle, which was actually sampled from raw material of Li-ion battery, shows that it contains a certain amount of low-remanence magnetic particle. The particle would be assumed to come from a naturally included in graphite minerals and also tool steel chips of grinding machines. This type of battery is getting used in the field of air-plane power-supply or life support robots. The extraordinary heating or unexpected shutdown of the system has a possibility to make a disaster. Even if a very rare inclusion of such small particle, it would be recognized as a serious problem. Therefore, full inspection of small particle, such as under one hundred micro-meters diameter, while fabrication process is needed for Li-ion separator. The detection must be applicable for a kind of roll-to-roll method with the width of the separator sheet more than 1 m and the running speed more point of this study is the application of strong static normal field in the measurement area including both sensor element and small particle. This paper composed of a theoretical estimation for clarifying efficiency of the proposed detection method, an experimental measurement of sensor property and sensitivity of the sensing system, while exposed in the surface normal field, and a confirmation of detection of small particle using this method, especially in the vicinity of sensor element. This paper shows a comprehensive fundamentals of magnetic particle detection using thin film MI sensor operated in a strong surface normal magnetic field.
This paper is constructed based on a Japanese paper of technical meeting [21], which was copyrighted 2016 IEEJ, and Japanese patent [22] applied in 2013, to be rewritten as an English article with some important additional data and discussion.

Case of Far Distance batween Sensor and Magnetized Particle
Firstly, in order to make clear the efficiency of the proposed method, a theoretical analysis is carried out. Figure 1 shows a schematic illustration of the proposed measurement system. The strong magnetic field in surface normal direction, which is relative to the sensor substrate surface, magnetizes the magnetic particle, consequently its magnetization makes a field in the X direction at the sensor position, which is a measurement direction of the sensor and which is along the sensor plane. Based on the formula of magnetic dipole (1), an estimation of the field is carried out.
where m is the magnetic moment, r is the vector of particle position.
In this study, a method of detection of small magnetic particle, which has low nence property, using a thin film magneto-impedance sensor is investigated. The this study is the application of strong static normal field in the measurement area ing both sensor element and small particle. This paper composed of a theoretical tion for clarifying efficiency of the proposed detection method, an experimental m ment of sensor property and sensitivity of the sensing system, while exposed in face normal field, and a confirmation of detection of small particle using this met pecially in the vicinity of sensor element. This paper shows a comprehensive fun tals of magnetic particle detection using thin film MI sensor operated in a strong normal magnetic field.
This paper is constructed based on a Japanese paper of technical meeting [21 was copyrighted 2016 IEEJ, and Japanese patent [22] applied in 2013, to be rewritt English article with some important additional data and discussion.

Case of Far Distance batween Sensor and Magnetized Particle
Firstly, in order to make clear the efficiency of the proposed method, a the analysis is carried out. Figure 1 shows a schematic illustration of the proposed m ment system. The strong magnetic field in surface normal direction, which is rel the sensor substrate surface, magnetizes the magnetic particle, consequently its m zation makes a field in the X direction at the sensor position, which is a measu direction of the sensor and which is along the sensor plane. Based on the formula netic dipole (1), an estimation of the field is carried out.

= − ∇ •
where m is the magnetic moment, r is the vector of particle position. For simplify the equation, it is restricted in X-Z plane. Figure 2 shows the sc of the analysis coordinates. The magnetic dipole moment, approximated as a nonpoint, is placed on the origin of coordinate. A magnetic field in the X direction on of z = const. is shown in Equation (2). For simplify the equation, it is restricted in X-Z plane. Figure 2 shows the schematic of the analysis coordinates. The magnetic dipole moment, approximated as a non-volume point, is placed on the origin of coordinate. A magnetic field in the X direction on the line of z = const. is shown in Equation (2). Then, where I is the magnetization, V is the volume of particle.

Figure 2.
Schematic of the analysis coordinates [21]. Figure 3 shows a variation of magnetic flux density this case z = 1 mm, particle diameter is 65 μm, and magne one maximum and one minimum point and each point from dBx/dx = 0.  It is supposed that the magnetization in the volume of particle is a constant value. Then, where I is the magnetization, V is the volume of particle. Figure 3 shows a variation of magnetic flux density B x as a function of X position. In this case z = 1 mm, particle diameter is 65 µm, and magnetization I = 0.2 T. The profile has one maximum and one minimum point and each point is on x = ±z/2, which is obtained from dB x /dx = 0.
It is supposed that the magnetization in the volume of particle is a Then, where I is the magnetization, V is the volume of particle.

Figure 2.
Schematic of the analysis coordinates [21]. Figure 3 shows a variation of magnetic flux density Bx as a function this case z = 1 mm, particle diameter is 65 μm, and magnetization I = 0.2 T one maximum and one minimum point and each point is on x = ±z/2, w from dBx/dx = 0.  Figure 4 shows a variation of Bx as a function of z, in case of particle The magnetization of the particle is 0.1 T, 0.4 T, and 1.0 T respectively. the sensor of 10 −9 T sensitivity can detect the particle with 50 μm of diam magnetization within the distance of z = 7.5 mm. From Equation (2) the B to magnetization I.  Figure 4 shows a variation of B x as a function of z, in case of particle diameter 50 µm. The magnetization of the particle is 0.1 T, 0.4 T, and 1.0 T respectively. From this result, the sensor of 10 −9 T sensitivity can detect the particle with 50 µm of diameter and 0.1 T of magnetization within the distance of z = 7.5 mm. From Equation (2) the B x is proportional to magnetization I.   Figure 5 shows a variation of Bx as a function of z, in case 1.0 T. The diameter of the particle is 20 μm, 65 μm, and 200 μ result, the sensor of 10 −9 T sensitivity can detect the particle w 1.0 T of magnetization, within the distance of z = 6.5 mm. From Bx is proportional to the cube of the particle diameter.  . Simulated variation of flux density, B x , as a function of particle height, z, in case of particle diameter 50 µm [21]. Figure 5 shows a variation of B x as a function of z, in case of particle magnetization 1.0 T. The diameter of the particle is 20 µm, 65 µm, and 200 µm respectively. From this result, the sensor of 10 −9 T sensitivity can detect the particle with 20 µm of diameter and 1.0 T of magnetization, within the distance of z = 6.5 mm. From Equations (2) and (3) the B x is proportional to the cube of the particle diameter.  Figure 5 shows a variation of Bx as a function of z, in case 1.0 T. The diameter of the particle is 20 μm, 65 μm, and 200 μ result, the sensor of 10 −9 T sensitivity can detect the particle wi 1.0 T of magnetization, within the distance of z = 6.5 mm. From Bx is proportional to the cube of the particle diameter. These results show, in order to detect a tens of microme sensitive sensor, the particle must be magnetized almost satura These results show, in order to detect a tens of micrometer magnetic particle by a sensitive sensor, the particle must be magnetized almost saturation, that is why application of strong normal field is needed, and placed it in the vicinity of the sensor.

Case of a Magnetized Particle Running in the Vicinity of Sensor Element
The previous subsection described a case in which the magnetic field at the sensor position was uniform and independent of sensor element position. This situation arises when the distance between the sensor and the magnetized particle is large enough.
In this subsection, a discussion is made for the case when a magnetized particle is running in the vicinity of sensor element. Figure 6 explains an interaction between the magnetized particle and thin film sensor in a vertical magnetic field. The magnetic particle is magnetized in the vertical direction just above the sensor element, and the generated field affected the sensor output caused by a positional changing magnetic field. An effect of a distributed magnetic field on a sensor impedance is formulated as follows; omachines 2022, 13, 1199 Figure 6. Explanation of interaction between the magnetized particle and thin tical magnetic field [21].
The high-frequency impedance of the magneto-impedance sensor it is caused by the skin-effect in the sensor element. The skin-depth changes as a function of high-frequency permeability of the soft magne In case of a frequency range which is larger than roughly MHz, the pe based on a magnetization vibration, instead of the magnetic domain w Figure 7 indicates a schematic explanation of magnetization vibra magneto-impedance sensor, when a surface normal field is applied. Th show a variation of magnetic moment, in which the orientation and t each cases of different external magnetic field along the sensor length d right schematic explains a moment vibration as a perturbation around right sectional schematic explains the effect of demagnetizing force a direction. In this figure, the magnetic anisotropy field is shown as H easy axis of the magnetic anisotropy lies in width direction in this Fig  study, the domain variation depends on the easy-axis direction. In ca directing along the in-plane inclined direction, a domain wall moveme area ratio of the contiguous domain changes as a function of applied field is in the direction of element's longitudinal axis. The left schemat Figure 6. Explanation of interaction between the magnetized particle and thin film sensor in a vertical magnetic field [21].
The high-frequency impedance of the magneto-impedance sensor is well-known that it is caused by the skin-effect in the sensor element. The skin-depth of the current flow changes as a function of high-frequency permeability of the soft magnetic sensor element. In case of a frequency range which is larger than roughly MHz, the permeability appears based on a magnetization vibration, instead of the magnetic domain wall movement. Figure 7 indicates a schematic explanation of magnetization vibration in the thin film magneto-impedance sensor, when a surface normal field is applied. The left three figures show a variation of magnetic moment, in which the orientation and the vibration are in each cases of different external magnetic field along the sensor length direction. The upper right schematic explains a moment vibration as a perturbation around a stable state. The right sectional schematic explains the effect of demagnetizing force along the thickness direction. In this figure, the magnetic anisotropy field is shown as H k . The direction of easy axis of the magnetic anisotropy lies in width direction in this Figure. Based on our study, the domain variation depends on the easy-axis direction. In case of the easy-axis directing along the in-plane inclined direction, a domain wall movement appears and the area ratio of the contiguous domain changes as a function of applied field. The applied field is in the direction of element's longitudinal axis. The left schematic of Figure 7 is the case which has the easy-axis in an ideal width direction. The domain width in our Co 85 Nb 12 Zr 3 element is roughly 20 µm to 50 µm which is narrow enough compared with the whole element length, 1000 µm to 2000 µm, then a positional variation of magnetic field, which is applied in the sensing direction, has a possibility to effect on the partial element impedance proportionally changing to the external field within a continuous strip element.
Co85Nb12Zr3 element is roughly 20 μm to 50 μm which is narrow enough c the whole element length, 1000 μm to 2000 μm, then a positional variatio field, which is applied in the sensing direction, has a possibility to effect element impedance proportionally changing to the external field within a co element.  . Schematic explanation of magnetization vibration in the thin film magneto-impedance sensor as a function of sensing field in X-direction, when a surface normal field is applied [21].
Based on the assumption mentioned above, the whole impedance of the sensor element is assumed to estimate as an integral of partial impedance of the element as shown in Figure 8. In case of a L mm length sensor, which is placed from x = 0 to x = L, the total impedance is expressed as Equation (4) cromachines 2022, 13,1199 Based on the assumption mentioned above, the whole impedan ment is assumed to estimate as an integral of partial impedance of th in Figure 8. In case of a L mm length sensor, which is placed from x = impedance is expressed as Equation (4) Here, is a sensing magnetic field at the position x. The following experimental results and discussions in this pa based on this equation.

Experiment and Discussion
This section reported an effect of magnetic field variation on a when a strip of thin film magneto-impedance sensor is placed in a s netic field and detects a vertically magnetized magnetic small partic Here, H x is a sensing magnetic field at the position x. The following experimental results and discussions in this paper are constructed based on this equation.

Experiment and Discussion
This section reported an effect of magnetic field variation on a sensor impedance, when a strip of thin film magneto-impedance sensor is placed in a surface normal magnetic field and detects a vertically magnetized magnetic small particle in the vicinity of the sensor. This section discusses about two viewpoints. The former explains an effect of distribution of the normal magnetic field for the sensitivity, and the latter reports and discusses a result of actual particle detection running in the vicinity of the sensor element.

Variation of MI-Curve as a Function of Normal Field
Variation of the MI-curve and the sensitivity of the sensor are experimentally measured as a parameter of the normal field. The MI-curve means the variation of sensor impedance as a function of external magnetic field applied along the in-plane sensing direction, which is the X direction in Figure 1.
The sensor element was fabricated by a thin film process. An amorphous Co 85 Nb 12 Zr 3 film was RF-sputter deposited onto soda glass substrate and then micro-fabricated into rectangular elements by lift-off process. The dimensions of the element are ranging from 1000 µm to 2000 µm of length, 20 µm to 50 µm of width, and 1.35 µm to 2.15 µm of thickness. The element was annealed in magnetic field in order to induce uniaxial magnetic anisotropy. The direction of the magnetic anisotropy was controlled by the direction of the magnetic field. In this study, the magnetic field during annealing, 240 kA/m, 673 K, was oriented in short-side axis, therefore width direction, of the element. Figure 9 is a photograph of sensor element. A coplanar structure was used for fitting a G-S-G type high-frequency wafer probe used for the impedance measurement.   Figure 10 shows a schematic illustration of measurement apparatus. Th was generated by two NeFeB magnets, which is fixed on heads of Si stee with the opposite poles facing each other, in this study the north pole is upper side. The sensor element is placed in the middle position between th nets. A Helmholtz coil is placed for the purpose of applying magnetic fie direction; X. This apparatus can control the strength of the vertical field by size and the distance of magnets. The sensor impedance was measured by lyzer using S11 measurement. The frequency of current induced in the se MHz and 800 MHz, and input power was −14 dBm. In this frequency rang non which is caused by resonance appears with variation of applied magn reason why this frequency was chosen is because an effect of the vertical fie tion of magnetic momentum, caused by high-frequency current, can be cle by the experiment.  Figure 10 shows a schematic illustration of measurement apparatus. The normal field was generated by two NeFeB magnets, which is fixed on heads of Si steel c-shape core with the opposite poles facing each other, in this study the north pole is placed in the upper side. The sensor element is placed in the middle position between these two magnets. A Helmholtz coil is placed for the purpose of applying magnetic field in sensing direction; X. This apparatus can control the strength of the vertical field by changing the size and the distance of magnets. The sensor impedance was measured by network analyzer using S11 measurement. The frequency of current induced in the sensor was 500 MHz and 800 MHz, and input power was −14 dBm. In this frequency range, a phenomenon which is caused by resonance appears with variation of applied magnetic field. The reason why this frequency was chosen is because an effect of the vertical field for a vibration of magnetic momentum, caused by high-frequency current, can be clearly observed by the experiment.
MHz and 800 MHz, and input power was −14 dBm. In this frequency non which is caused by resonance appears with variation of applied reason why this frequency was chosen is because an effect of the verti tion of magnetic momentum, caused by high-frequency current, can by the experiment.  Figure 11 is a photograph of actual measurement system. A wood for feeding a small magnetic particle, with a particle fixing at the tip. applied vertical magnetic field was controlled by both the thickness distance of magnets.  Figure 11 is a photograph of actual measurement system. A wooden needle was used for feeding a small magnetic particle, with a particle fixing at the tip. The strength of the applied vertical magnetic field was controlled by both the thickness of magnets and the distance of magnets.    Figure 12 represents an impedance variation for 1000 μm lengt MHz of induced current. Figure 13 represents an impedance variatio 500 MHz. And Figure 14 represents an impedance variation for 2000 MHz. In these figures the caption "a" represents a variation of |Z|, the sents a variation of real part of impedance, Re(Z), and the caption "c" tion of imaginary part of impedance, Im(Z). The results for 1000 μm le that the impedance around zero X-direction fields has slight change ev   Figure 12 represents an impedance variation for 1000 µm length element with 800 MHz of induced current. Figure 13 represents an impedance variation for 1000 (micro-)m with 500 MHz. And Figure 14 represents an impedance variation for 2000 µm length with 500 MHz. In these figures the caption "a" represents a variation of |Z|, the caption "b" represents a variation of real part of impedance, Re(Z), and the caption "c" represents a variation of imaginary part of impedance, Im(Z). The results for 1000 µm length element show that the impedance around zero X-direction fields has slight change even when the surface normal field is changed. Here both the Re(Z) and the Im(Z) has slight change. On the other hand, the peak value of impedance decreases as the normal field increases. The peak value of impedance decreases for the both case of Re(Z) and Im(Z). For the range where the impedance changes rapidly, where the |H| is ranging from 5 to 15 Oe (almost 400 A/m to 1200 A/m), the Im(Z) has negative and minimum value for the case of Figure 12, that means an existence of resonance. As increasing the normal field, the absolute value of the minimum Im(Z), i.e. |min Im(Z)|, decreases. On the other hand, the Figure 14 represents different properties. For the case of this 2000 µm element, the peak value decreases as same as previous one, but the impedance value around zero increases and finally has a peak value as the normal field increases. The magnetic domain of element was Landau-Lifshitz-domain when both the Xdirection field and normal field is zero. The magnetization process of the element which has uniaxial easy axis in width direction is magnetization rotation. Figure 7 shows a schematic explanation of arrangement of magnetic momentum in the sensor element as a function of external field. When the X-direction field is zero, the momentum orients in width direction, therefore Y-direction, forming contiguous opposite domain areas. As increasing the Xdirection field, the momentum rotates in the X direction according to the strength of applied field with keeping the wall position. In this case, the high-frequency permeability, which has influence on sensor impedance, initially increases, then has a maximum at the applied field nearly equals the anisotropy field, Hk, and after that decreases as the X-direction field increases. This high-frequency permeability arises from the vibration of momentum which is explained by perturbation theory. From the result of unchanged impedance around zero fields, in spite of the surface normal field application, it is supposed that the normal field, within the value of our experiment, has no effect of enhancement or decline of permeability, therefore it has slight effect for changing the direction of momentum or changing the perturbation potential distribution. On the other hand, the decrement of maximum value means that the normal field has an effect of decline permeability. With consideration of decrement of |min Im(Z)|, the normal field is supposed to have an effect of decline permeability both real and imaginary within the range where the impedance change rapidly until the area around it has maximum. The details of this consideration would be a future subject of this study.  There is another explanation for the change of MI-curve caused by applying normal field. Our measurement apparatus has un-uniformity of X-direction field within the length of the sensor, more than several Oe. This un-uniformity also has the effect of making the impedance profile flat. It is based on Figure 8 and Equation (4). An impedance of whole element of a sensor is assumed to be estimated by an integral of impedance of small section ∆x.
Whereas if a normal field with distributed vector in X-direction is applied, the applied field on the sensor element has a distributed profile in X direction ( Figure 15). This distributed X-directional field makes a change of MI-profile on individual ∆x pieces as shown in Figure 16. As a result, the un-uniformity of X-field makes the MI-curve of whole element to be flat. In this case, the sensor impedance is explained as following equation. where applied normal field on the sensor film H normal is shown as follows; The magnetic domain of element was Landau-Lifshitz-domain when both the X-direction field and normal field is zero. The magnetization process of the element which has uniaxial easy axis in width direction is magnetization rotation. Figure 7 shows a schematic explanation of arrangement of magnetic momentum in the sensor element as a function of external field. When the X-direction field is zero, the momentum orients in width direction, therefore Y-direction, forming contiguous opposite domain areas. As increasing the X-direction field, the momentum rotates in the X direction according to the strength of applied field with keeping the wall position. In this case, the high-frequency permeability, which has influence on sensor impedance, initially increases, then has a maximum at the applied field nearly equals the anisotropy field, Hk, and after that decreases as the X-direction field increases. This high-frequency permeability arises from the vibration of momentum which is explained by perturbation theory. From the result of unchanged impedance around zero fields, in spite of the surface normal field application, it is supposed that the normal field, within the value of our experiment, has no effect of enhancement or decline of permeability, therefore it has slight effect for changing the direction of momentum or changing the perturbation potential distribution. On the other hand, the decrement of maximum value means that the normal field has an effect of decline permeability. With consideration of decrement of |min Im(Z)|, the normal field is supposed to have an effect of decline permeability both real and imaginary within the range where the impedance change rapidly until the area around it has maximum. The details of this consideration would be a future subject of this study.
There is another explanation for the change of MI-curve caused by applying normal cromachines 2022, 13,1199 Whereas if a normal field with distributed vector in X-direction plied field on the sensor element has a distributed profile in X direct distributed X-directional field makes a change of MI-profile on ind shown in Figure 16. As a result, the un-uniformity of X-field makes th element to be flat. In this case, the sensor impedance is explained as f where applied normal field on the sensor film Hnormal is shown as follo = + ℎ ( ), = .    The result in Figure 14 shows a measurement for 2000 µm length element. The difference of variation of MI-curve with changing the normal field, compared with the result of Figure 13 of 1000 µm element, would be affected by the distribution of X-direction field.
Based on these discussions, a generating apparatus of the surface normal magnetic field which can make more uniform in X-direction and stronger in Z-direction and can control them individually is effective for clarify the mechanism of the sensor surface normal field.

Sensitivity Evaluation Using Carrier-Suppressing Circuit
The sensor system in this study is a combination of thin film MI sensor and highfrequency measurement circuit. A well-known combination is with the carrier-suppressing circuit [6]. Figure 17 shows the block diagram of the circuit. The device list is shown in Table 1. A high-frequency alternating signal f 0 , which is called "carrier-signal", is divided into two. One is inputted to the sensor, and the reflection signal from the sensor is introduced to the right side divider. Another signal is set in the same amplitude and opposite phase as the sensor reflection signal. Consequently, the combined signal come out from right divider is a carrier eliminated signal. When the ac magnetic field f ac is applied to the sensor, the output signal has spectrum of f 0 ± f ac , which is known as side-band spectrum. The merit of this circuit is the very low noise level in the side-band frequency, because of the effect of carrier-suppressing. In this study, the sensitivity of the sensor with subjecting to the surface normal field is evaluated by using this circuit. The sensor element is the same one as measured in Figures 12 and 13. The high-frequency carrier signal come out from signal-generator (S.G.) was −8 dBm, 410 MHz. The applied ac magnetic field to the sensor was 310 Hz.
is the same one as measured in Figures 12 and 13. The high-frequency carrier signal come out from signal-generator (S.G.) was −8 dBm, 410 MHz. The applied ac magnetic field to the sensor was 310 Hz. Figure 18 shows a photograph of whole measurement system, and Figure 19 shows an enlarged view of the carrier-suppressing circuit connected with the sensor. The circuit was covered by Aluminum foil while measurement, for the purpose of reducing measurement noise.
. Figure 17. Block diagram of the carrier-suppressing circuit using reflection signal [21].    Figure 18 shows a photograph of whole measurement system, and Figure 19 shows an enlarged view of the carrier-suppressing circuit connected with the sensor. The circuit was covered by Aluminum foil while measurement, for the purpose of reducing measurement noise.  Our original proposal in the circuit was an application of high-frequency circulator. Our original proposal in the circuit was an application of high-frequency circulator. It has a merit of reducing number of connected cables, which is to make as 1-cable, then a reduction of connected electrode-pads and a space reduction of connected cable with the thin film small sensor. It also has a demerit of decreasing sensitivity, due to a signal loss of the circulator itself and an existence of leakage carrier-signal, f 0 , from port-1 to port-3 and from port-2 to port-1. The leakage signal reduces the sensitivity especially when the sensing AC field, f ac , has a low frequency. It induces the deviation of frequency between the f 0 and f ac to be reduced, then it makes difficult to detect the signal separately. The performance of the driving circuit for low frequency signal would be improved using a logarithmic amplifier IC-chip, which was tried in this paper in Section 3.2.2, and connected to a development of driving circuit which can detect low frequency signal including DCsignal [23].  Our original proposal in the circuit was an application of high-frequency circulator. It has a merit of reducing number of connected cables, which is to make as 1-cable, then a reduction of connected electrode-pads and a space reduction of connected cable with the thin film small sensor. It also has a demerit of decreasing sensitivity, due to a signal loss of the circulator itself and an existence of leakage carrier-signal, f0, from port-1 to port-3 and from port-2 to port-1. The leakage signal reduces the sensitivity especially when the sensing AC field, fac, has a low frequency. It induces the deviation of frequency between the f0 and fac to be reduced, then it makes difficult to detect the signal separately. The performance of the driving circuit for low frequency signal would be improved using a logarithmic amplifier IC-chip, which was tried in this paper in Section 3.2.2, and connected to a development of driving circuit which can detect low frequency signal including DC-signal [23].
The high-frequency devices shown in Figure 17 are listed in Table 1. This trial was carried out almost 10 years ago, then a connection of discrete units was adopted in this experiment. A recent sophisticated IC-tips can reduce the whole circuit volume and increase signal stability using the concept of our proposed circuit. It is shown in our following study [9][10][11]. Figure 20a shows the result of evaluating sensitivity when the normal field is zero. Sensor sensitivity is evaluated by the extrapolation method. The sensitivity was 1.4 nT/Hz 1/2 in this case. Figure 20b shows the sensitivity with subjecting to normal field of 83.2 kA/m, in this case it was 1.7 nT/Hz 1/2 . These results show that the 83.2 kA/m normal field has slight effect of degradation for the sensor sensitivity. The high-frequency devices shown in Figure 17 are listed in Table 1. This trial was carried out almost 10 years ago, then a connection of discrete units was adopted in this experiment. A recent sophisticated IC-tips can reduce the whole circuit volume and increase signal stability using the concept of our proposed circuit. It is shown in our following study [9][10][11]. Figure 20a shows the result of evaluating sensitivity when the normal field is zero. Sensor sensitivity is evaluated by the extrapolation method. The sensitivity was 1.4 nT/Hz 1/2 in this case. Figure 20b shows the sensitivity with subjecting to normal field of 83.2 kA/m, in this case it was 1.7 nT/Hz 1/2 . These results show that the 83.2 kA/m normal field has slight effect of degradation for the sensor sensitivity.  Figure 21 shows a MI-curve and its tangential line at a bias-point of the high-sensitivity measurement. Figure 21a is the one when the normal field is zero, and Figure 21b is when the normal field is 83.2 kA/m. A value of dZ/dH at the bias point represents the sensor sensitivity. A comparison of ratios of sensitivity which is shown in Figure 20a vs.  Figure 21 shows a MI-curve and its tangential line at a bias-point of the high-sensitivity measurement. Figure 21a is the one when the normal field is zero, and Figure 21b is when the normal field is 83.2 kA/m. A value of dZ/dH at the bias point represents the sensor sensitivity. A comparison of ratios of sensitivity which is shown in Figure 20a vs. Figure 20b, (1/1.4)/(1/1.7) = 1.21, with the ratios of dZ/dH in Figure 21a vs. Figure 21b, (21 mΩ/(A/m))/(17 mΩ/(A/m)) = 1.24, shows that these ratios are in good agreement. Based on this result, a higher sensitivity is realized when a sensor is designed to have larger value of dZ/dH, which is the same design rule as ordinary magneto-impedance sensor. This work was a basis of the following developments of both the sensor driving circuit using a chip-sized high frequency devices [23] and also the uniform magnetic field generator of surface normal field [10,11], which is applied to a thin film MI sensor used inside a strong magnetic field. A sensitivity confirmation and magnetic domain variation during the sensor operation in stronger field had been carried out and reported in Ref. [9].

Measurement in Case of Single Strip Sensor
In this experiment, detection of magnetic small particle using a single sensor strip was carried out. The particle, which has 65 μm diameter and 1 T saturation magnetization, was detected by the sensor with subjecting to 83.2 kA/m normal field. M-H loop of the particle is shown in Figure 22. This particle has remanence of 0.05 T, and corecivity of 11 kA/m. Figure 23 shows a schematic illustration of the measurement system of magnetic small particle. A soft magnetic sphere-shaped particle was mechanically scanned above the sensor element. The whole measurement area which contains both the sensor and the particle was within 83.2 kA/m of the surface normal field. Variation of the field Hz is less than 5% within 2.5 mm from the center of the area. The sensor element is the same one This work was a basis of the following developments of both the sensor driving circuit using a chip-sized high frequency devices [23] and also the uniform magnetic field generator of surface normal field [10,11], which is applied to a thin film MI sensor used inside a strong magnetic field. A sensitivity confirmation and magnetic domain variation during the sensor operation in stronger field had been carried out and reported in Ref. [9].

Measurement in Case of Single Strip Sensor
In this experiment, detection of magnetic small particle using a single sensor strip was carried out. The particle, which has 65 µm diameter and 1 T saturation magnetization, was detected by the sensor with subjecting to 83.2 kA/m normal field. M-H loop of the particle is shown in Figure 22. This particle has remanence of 0.05 T, and corecivity of 11 kA/m. Figure 23 shows a schematic illustration of the measurement system of magnetic small particle. A soft magnetic sphere-shaped particle was mechanically scanned above the sensor element. The whole measurement area which contains both the sensor and the particle was within 83.2 kA/m of the surface normal field. Variation of the field H z is less than 5% within 2.5 mm from the center of the area. The sensor element is the same one above mentioned, the length is 1 mm. machines 2022, 13, 1199 Figure 22. Measured M-H loop of φ200 μm diameter soft magnetic particle [21].  Figure 24 shows the result. The measurement circuit was based on t pressing method. A modification of final stage was an addition of log-amp combination of an offset compensation and a ×100 amplifier. The particle the sensor plane was 0.5 mm. The particle was scanned along Y = 0. The made an output variation between ±6 V with the profile having one maxi minimum point at around the longitudinal edges of element.   Figure 24 shows the result. The measurement circuit was based on pressing method. A modification of final stage was an addition of log-am combination of an offset compensation and a ×100 amplifier. The partic the sensor plane was 0.5 mm. The particle was scanned along Y = 0. Th made an output variation between ±6 V with the profile having one ma minimum point at around the longitudinal edges of element. Figure 23. Schematic illustration of the measurement system of magnetic small particle [21]. Figure 24 shows the result. The measurement circuit was based on the carriersuppressing method. A modification of final stage was an addition of log-amp detection with combination of an offset compensation and a ×100 amplifier. The particle altitude from the sensor plane was 0.5 mm. The particle was scanned along Y = 0. The 65 µm particle made an output variation between ±6 V with the profile having one maximum and one minimum point at around the longitudinal edges of element. pressing method. A modification of final stage was an addition of log-amp dete combination of an offset compensation and a ×100 amplifier. The particle alti the sensor plane was 0.5 mm. The particle was scanned along Y = 0. The 65 μ made an output variation between ±6 V with the profile having one maximum minimum point at around the longitudinal edges of element. Figure 24. Result of measurement of scanned magnetic small particle along sensor long rection [21]. The consideration of the measurement result on Figure 24 is as following. The output profile with one maximum and one minimum at both edges is the common characteristic for measurement of X-directional field produced by vertically magnetized particle. Figure 25 shows a variation of magnetic field in X-direction as a function of X-position. The 65 µm diameter magnetic particle, which is magnetized in I = 0.2 T, is placed on x = 0, y = 0, and z = 0.5 mm. The detection of magnetic field was carried out on X-axis. This profile is calculated by Equation (2). Based on this X-field distribution, a consideration is made for an estimation of impedance of whole element of the 1 mm length sensor. The magnetic field induced by the magnetized particle is localized and the effect is changed as a function of particle position, which was shown in Figure 6. A distributed magnetic field is made on the sensor element, which is generated in the vicinity of magnetic dipole, and the distributed profile is changed as a function of particle position, which is running through just above the sensor. An estimation of element impedance as a function of particle position is tried as follows; omachines 2022, 13,1199 The consideration of the measurement result on Figure 24 is as following. profile with one maximum and one minimum at both edges is the common ch for measurement of X-directional field produced by vertically magnetized part 25 shows a variation of magnetic field in X-direction as a function of X-posit μm diameter magnetic particle, which is magnetized in I = 0.2 T, is placed on and z = 0.5 mm. The detection of magnetic field was carried out on X-axis. Th calculated by Equation (2). Based on this X-field distribution, a consideration an estimation of impedance of whole element of the 1 mm length sensor. Th field induced by the magnetized particle is localized and the effect is changed as of particle position, which was shown in Figure 6. A distributed magnetic fie on the sensor element, which is generated in the vicinity of magnetic dipole, a tributed profile is changed as a function of particle position, which is running th above the sensor. An estimation of element impedance as a function of particle tried as follows; Figure 25. Calculated X-directional field on X-axis made by 0.2 T magnetized φ65 placed on z = 0.5 mm [21]. Impedance variation of the sensor is shown in collinear approximation in of bias point. The field on sensor made by 65 μm particle is so small that this a in reasonable. Based on the measured sensor property with applying normal fi Figure 25. Calculated X-directional field on X-axis made by 0.2 T magnetized ϕ65 µm particle, placed on z = 0.5 mm [21]. Impedance variation of the sensor is shown in collinear approximation in the vicinity of bias point. The field on sensor made by 65 µm particle is so small that this assumption in reasonable. Based on the measured sensor property with applying normal field, Figure 21b, it is assumed as follows; The element impedance is estimated by the following equation. The estimation is based on the same assumption as Equation (4). The element position and dimensions are the same as shown in Figure 23. Then Here H x is analytically obtained based on the equation of magnetic dipole, Equation (2), when a particle is placed in x'. Then A result of numerical estimation is shown in Figure 26. The vertical-axis is an impedance of the element. The output level of measurement system is proportional to the sensor impedance, so Figure 26 shows the reason of the profile having one maximum and one minimum point at around the longitudinal edges of element, shown in Figure 24. The difference between Figures 24 and 26 is assumed that the numerical estimation does not take into consideration of a positional variation of demagnetizing field, which is especially affected in the vicinity of longitudinal edge of the sensor element. It is also assumed that the difference come from an existence of electrode-pads at the sensor edge. There is a certain dimensions of electrode pad, as shown in Figure 9, then an uncertainty of sensor edge appears. romachines 2022, 13,1199 A result of numerical estimation is shown in Figure 26. The vertical-axis ance of the element. The output level of measurement system is proportional t impedance, so Figure 26 shows the reason of the profile having one maxim minimum point at around the longitudinal edges of element, shown in Fig  difference between Figures 24 and 26 is assumed that the numerical estimat take into consideration of a positional variation of demagnetizing field, which affected in the vicinity of longitudinal edge of the sensor element. It is also a the difference come from an existence of electrode-pads at the sensor edge. T tain dimensions of electrode pad, as shown in Figure 9, then an uncertainty of appears. Figure 26. Result of numerical estimation of sensor impedance as a function of particl [21]. Figure 27 shows a measured variation of impedance as a function of part y in case of x = 0, i.e., the position of impedance peak for Figure 24. The parti the same as Figure 24, z = 0.5 mm. The application of the surfase normal fiel Figure 26. Result of numerical estimation of sensor impedance as a function of particle position [21]. Figure 27 shows a measured variation of impedance as a function of particle position y in case of x = 0, i.e., the position of impedance peak for Figure 24. The particle height is the same as Figure 24, z = 0.5 mm. The application of the surfase normal field makes the measured whole particle magnetize in the same direction Z. This makes the estimation of interaction between the sensor and the particle easy. Figure 26. Result of numerical estimation of sensor impedance as a function of particle position [21]. Figure 27 shows a measured variation of impedance as a function of particle posit y in case of x = 0, i.e., the position of impedance peak for Figure 24. The particle heigh the same as Figure 24, z = 0.5 mm. The application of the surfase normal field makes measured whole particle magnetize in the same direction Z. This makes the estimation interaction between the sensor and the particle easy.

Measurement in Case of Meander Shaped Differential Sensor
In this study, a detection of adjacent particle from the sensor element was inve gated using differential sensor. The sensor we used was a pair of meander shaped t film MI sensors, adjacently located on a glass substrate, which is shown in Figure 28.

Measurement in Case of Meander Shaped Differential Sensor
In this study, a detection of adjacent particle from the sensor element was investigated using differential sensor. The sensor we used was a pair of meander shaped thin film MI sensors, adjacently located on a glass substrate, which is shown in Figure 28. The differential sensor was composed by two meander sensors, each of them consisted of 10 strips of 50 µm width MI sensors. Each strips were connected by Cu connecting strip to form a meander sensor. The typical length of the strips was 1.25 mm, the sensor width was 0.95 mm as a solo one, and the whole width of the differential sensor was 2 mm.
Micromachines 2022, 13, 1199 differential sensor was composed by two meander sensors, each of them con strips of 50 μm width MI sensors. Each strips were connected by Cu connec form a meander sensor. The typical length of the strips was 1.25 mm, the se was 0.95 mm as a solo one, and the whole width of the differential sensor was Figure 28. Photograph of the meander shaped differential sensor. Figure 29 shows a driving circuit of our differential sensor. It consisted of tion of the previous circuit of this paper, Figure 7, to formed a differential layo detection of this circuit was carried out by a logarithmic amplifier with differe In this circuit, both the amplitude and the phase of inputted signals were set Figure 28. Photograph of the meander shaped differential sensor. Figure 29 shows a driving circuit of our differential sensor. It consisted of a combination of the previous circuit of this paper, Figure 7, to formed a differential layout. The final detection of this circuit was carried out by a logarithmic amplifier with differential inputs. In this circuit, both the amplitude and the phase of inputted signals were set as the same value using the attenuators and the phase shifters. The logarithmic amplifier can detect 410 MHz signal to a static voltage output which is logarithmically proportional to the differential of two inputs. The output was set as minimum value when a vertical magnetic field was applied and also there was nothing to detect. In this circuit, the maximum output of the final amplifier was 4.3 V, then a saturation appears when the output would be a large value. Figure 28. Photograph of the meander shaped differential sensor. Figure 29 shows a driving circuit of our differential sensor. It consisted of a c tion of the previous circuit of this paper, Figure 7, to formed a differential layout. T detection of this circuit was carried out by a logarithmic amplifier with differentia In this circuit, both the amplitude and the phase of inputted signals were set as t value using the attenuators and the phase shifters. The logarithmic amplifier ca 410 MHz signal to a static voltage output which is logarithmically proportional to ferential of two inputs. The output was set as minimum value when a vertical m field was applied and also there was nothing to detect. In this circuit, the maximum of the final amplifier was 4.3 V, then a saturation appears when the output wo large value. Figure 29. Block diagram of the driving circuit of differential sensor. Figure 30 is a photograph of measurement system of the differential detectio iment. A G-S-S-G non-magnetic wafer probe was use for contacting the sensor, an magnetic small particle was 2D scanned using XYZ-manipulator. The measurem sults are indicated as follows; Figure 29. Block diagram of the driving circuit of differential sensor. Figure 30 is a photograph of measurement system of the differential detection experiment. A G-S-S-G non-magnetic wafer probe was use for contacting the sensor, and a soft magnetic small particle was 2D scanned using XYZ-manipulator. The measurement results are indicated as follows; Micromachines 2022, 13,1199 Figure 30. Photograph of measurement system of the differential detection experiment. Figure 31 is a 2D-mapping of a measured signal, when a particle having a of 200 μm was scanned on the sensor substrate with the height of 1 mm. There treme value just above the right edge of the sensor element, and the polarity was on the differential pair sensor. The measurement was restricted in the left half reg to the existence of contact needles of wafer probe, but the result is easily estima left end.  Figure 31 is a 2D-mapping of a measured signal, when a particle having a diameter of 200 µm was scanned on the sensor substrate with the height of 1 mm. There is an extreme value just above the right edge of the sensor element, and the polarity was opposite on the differential pair sensor. The measurement was restricted in the left half region, due to the existence of contact needles of wafer probe, but the result is easily estimate on the left end. Figure 31 is a 2D-mapping of a measured signal, when a particle having a d of 200 μm was scanned on the sensor substrate with the height of 1 mm. There treme value just above the right edge of the sensor element, and the polarity was o on the differential pair sensor. The measurement was restricted in the left half reg to the existence of contact needles of wafer probe, but the result is easily estimat left end. For the purpose of confirming the edge effect precisely, measurements of scan along the X-axis on different Y-position as a parameter was carried out. Figure 32 is output profiles as a function of X-position. The Y-position was a eter. The y = 1 and y = −1 are the position of outer end strip of the meander senso = 0.5 and y = −0.5 are at the middle of each meander sensor. The particle height mm in this case. This result also shows that the extreme value of sensor output ap the edge of the sensor element, x = 0. It is confirmed the validity of the proposed es procedure of sensor impedance in case of the magnetic particle is placed in the vi the thin film MI sensor element.
This measurement was carried out using the apparatus shown in Figure 30 apparatus, the particle, which was fixed at the tip of wooden needle, was scanned manually controlled XYZ-manipulator. The turning of nob was carried out cautiou a certain positional uncertainty of the apparatus unit appears, then an asymmetr curred on measurement. The output base line of the sensor driving circuit had drifting tendency in this paper, where the experiment was carried out in 2016. I Figure 31. 2D-mapping of a measured signal, when a particle having a diameter of 200 µm was scanned on the sensor element with the height of 1 mm.
For the purpose of confirming the edge effect precisely, measurements of linearly scan along the X-axis on different Y-position as a parameter was carried out. Figure 32 is output profiles as a function of X-position. The Y-position was a parameter. The y = 1 and y = −1 are the position of outer end strip of the meander sensor. The y = 0.5 and y = −0.5 are at the middle of each meander sensor. The particle height was 1.5 mm in this case. This result also shows that the extreme value of sensor output appears at the edge of the sensor element, x = 0. It is confirmed the validity of the proposed estimation procedure of sensor impedance in case of the magnetic particle is placed in the vicinity of the thin film MI sensor element.
cromachines 2022, 13, 1199 22 be improved in later article, such as Ref. [10], based on this paper's investigation. asymmetricity of this data, in Figure 32, came from both of these reasons.

Conclusions
This paper discussed detection fundamentals of magnetic small particle using film magneto-impedance sensor. In this study, the particle is magnetized in vertical d tion relative to the flat substrate plane of the sensor. There is an application of strong tical magnetic field in the measurement area including sensor element for the purpos detecting a low-remanence magnetic particle simultaneously with magnetization. variation of sensor impedance, which is determined by a magnetic field coming from This measurement was carried out using the apparatus shown in Figure 30. In this apparatus, the particle, which was fixed at the tip of wooden needle, was scanned using a manually controlled XYZ-manipulator. The turning of nob was carried out cautiously, but a certain positional uncertainty of the apparatus unit appears, then an asymmetricity occurred on measurement. The output base line of the sensor driving circuit had a slight drifting tendency in this paper, where the experiment was carried out in 2016. It would be improved in later article, such as Ref. [10], based on this paper's investigation. The asymmetricity of this data, in Figure 32, came from both of these reasons.

Conclusions
This paper discussed detection fundamentals of magnetic small particle using thin film magneto-impedance sensor. In this study, the particle is magnetized in vertical direction relative to the flat substrate plane of the sensor. There is an application of strong vertical magnetic field in the measurement area including sensor element for the purpose of detecting a low-remanence magnetic particle simultaneously with magnetization. The variation of sensor impedance, which is determined by a magnetic field coming from the particle, was estimated and formulated both the case of far distance and also the case of in the vicinity of sensor element. In case of far distance, the field is estimated using the equation of magnetic dipole. Whereas in the case of adjacent distance, the effect of magnetic field distribution on a sensor strip must be take into consideration using an assumption of impedance integral of partial strips of sensor element. This assumption was experimentally confirmed in two cases. One is the effect of distributed field for the sensor sensitivity. A distribution must be minimized for preventing sensitivity decrement. The other is that it is predicted that the extreme value of sensor impedance would be obtained when a particle is placed just above the sensor longitudinal edge. This phenomenon was confirmed in the both case of single sensor and also differential meander shaped sensor.
This paper is constructed based on a Japanese paper of technical meeting [14] and Japanese patent [15] to be an article of International Journal.