Since its discovery in 1988, the giant magnetoresistance (GMR) effect has been widely studied from both academic and technological viewpoint^[1–13] because of its advantages such as high sensitivity, large magnetoresistance ratio, and good compatibility with standard integrated circuit processes. The GMR sensor was first industrialized by NVE in 1994 and has been well used in medical and industrial circles, automotive electronics, etc.^[14–19] As a type of magnetic sensing device, the GMR sensor can be used as an angular transducer in the electronic compass, a pedal position detector in vehicles, and an angle encoder in industrial controls^[20–25] to replace the Hall-effect device and anisotropic magnetoresistance (AMR) sensor.^[26,27] The angular dependence of Hall-effect device, AMR sensor and GMR spin-valve sensor have been thoroughly investigated in recent years.^[7,28–32] The angular dependence of the GMR multilayer film has been reported.^[33–38] This dependence was introduced via the angular variation of transmission and reflection coefficient in Fuchs–Sondheimer boundary conditions.^[34,39] The angular dependence of the GMR multilayer film has been systematically and theoretically studied in depth by Vedyayev et al..^[39] They presented an analytical quantum-statistical theory of the angular variation of the GMR in magnetic multilayers, in which both the spin-dependent scattering of conduction electrons and the spin-dependent potential barriers between successive layers are taken into account.^[20] However, the angular dependence of the GMR sensor based on the GMR multilayer film was rarely reported.^[40,41] It is found that the GMR sensor is sensitive to angular variation and can be described with a cosine function.

In this paper, the output characteristics of the sensor are further analyzed, and the angular dependence of the GMR multilayer sensor is studied. First, the magnetic field direction, which is at an angle with respect to the sensitivity axis, is changed. The sensitivity of the GMR multilayer sensor is studied. Second, a series of rotating magnetic fixed fields is applied at different directions from 0° to 360°. Most importantly, a model is proposed to further describe the output characteristics of the GMR multilayer sensor. This model has not been reported in other papers. It differs from that in the work by Zhu,^[43] where only a series of rotating magnetic fixed fields is used, and a simple modified model is proposed to describe the output characteristics of the GMR multilayer sensor.

In this work, the GMR multilayer films were deposited on Si/SiO₂ ( ) substrates by a Nordiko 9606 sputtering system with a base pressure of Torr (1 Torr = 1.33322×10² Pa), and the GMR multilayer film sensor was subsequently fabricated with a series of device processes including resistor patterning, NiFe plating, passivation and pad opening. The GMR multilayer film had a structure of (NiFeCr (4.5 nm)/NiFe (4 nm)/[NiFe (5 nm)/Cu (0.9 nm)/NiFe (3.5 nm)]₃/NiFeCr(5 nm)) with a matrix of 4.5-nm-thick NiFeCr layer and 5-nm-thick NiFeCr layer as the buffer and cap layer. In the NiFe/Cu/NiFe layer structure with NiFeCr layer as a buffer layer, the antiferromagnetic coupling could be well established, so that a good GMR effect was obtained. It also exhibited good thermal stability, making it suitable for practical use in sensor devices.

Figure 1(a) shows the schematic of the GMR sensor with a structure of Wheatstone bridge, which consists of four patterned serpentine GMR multilayer resistors: R₁, R₂, R₃, and R₄, in which R₂ and R₄ were shielded by NiFe thick films, which make the resistors immune to an external field, whereas R₁ and R₃ were placed in the gap of the shielding layers and exposed to a magnetic field. When an external magnetic field was applied, the Wheatstone bridge of the sensor became unbalanced and produced a differential output voltage signal. In this structure, the shielding layers were also used as a flux concentrator, which amplifies the magnetic field in the gap. Although the Wheatstone bridge had a favorable compensation for those effects, the saturation magnetic field and sensitivity of the sensors were still affected by the temperature, which cannot be neglected in practical tests. Thus, the experimental temperature was maintained at 27°C. The topology structure of the processed sensor is shown in Fig. 1(b). Then, the sensor die was packaged as SOP8 before being tested and analyzed.

Fig. 1.

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	Fig. 1. (a) Wheatstone bridge configuration, and (b) topology structure of the sensor.

Two test systems were employed in this work. In the measurement of the low magnetic field range, a Helmholtz coil was used to produce the magnetic fields in a range from −50 Oe to +50 Oe. The Helmholtz coil system consists of a two-dimensional (2D) Helmholtz coil and a device fixture. In the measurement, the sensor under test was fixed on the device fixture, and the sensor transfer curve was obtained by sweeping the magnetic fields by changing the current in the Helmholtz coil. The current source for the Helmholtz coil is controlled by a computer, which adjusts the sweeping range and controls the direction of the magnetic fields. The angle between the direction of the magnetic field and the sensitive axis of the sensor is denoted as θ, as shown in Fig. 2. Figure 2 is combined with Fig. 1(b), where the sensitive axis is along the long side of the GMR sensor. The supply voltage was 3.0 V, and the system could capture the output of the sensor and store it. In the measurement of a high magnetic field range, the high-magnetic-field probe was used to measure the magnetic fields in a range from −2000 Oe to +2000 Oe. The high-magnetic-field probe consisted of a pair of horizontally opposed electromagnets, a device fixture, and a Gaussmeter. The magnetic fields generated by electromagnets were calibrated by the Gaussmeter in advance. The measurement procedure was similar to that for the Helmholtz coil test.

Fig. 2.

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	Fig. 2. Definition of angle θ.

In this work, first, the transfer curves of the GMR sensor were acquired by sweeping the external magnetic field from −50 Oe to +50 Oe in steps of 0.25 Oe along the sensitive axis. Second, the transfer curves of the GMR sensor were recorded by sweeping the external magnetic field from −2000 Oe to +2000 Oe in steps of 50 Oe along the sensitive axis. Third, the transfer curves of the GMR sensor were acquired by sweeping the external magnetic field with different angles with respect to the sensitive axis, from −50 Oe to +50 Oe. Finally, the rotation transfer curves of the GMR multilayer sensor were acquired by a rotating field. The magnitudes of the fields were 6.0 Oe, 10.0 Oe, 14.0 Oe, and 26.0 Oe.

In this paper, the properties of the GMR multilayer sensor are analyzed and the angular dependence of the GMR sensor is characterized. The sensor exhibits excellent performance with a sensitivity of 2.8349 mV/(V/Oe) and a saturation field of 26 Oe along the sensitive axis. The GMR sensor in a high magnetic field is also characterized. The sensitivity decreases from 2.8349 mV/(V/Oe) at 0° to 0.0175 mV/(V/Oe) at 90°. Then, a model is proposed to describe the output characteristics of the GMR sensor. The equation consists of two exactly symmetrical circles in the saturation field of 26 Oe, and the experimental results are consistent with the simulation results. The advantage of this model is that it is simpler and more intuitive, and it can be applied to the research of two-dimensional sensors.