Contents I. INTRODUCTION
The changes in the ac resistance of a ferromagnetic material due to the skin effect when a magnetic field is applied to the material at a higher carrier frequency was investigated in 1935 [Harrison 1935]. This phenomenon induces electricity loss in devices; hence, magnetic devices are designed to minimize the skin effect. In 1994, Mohri and Panina proposed to apply this effect in an amorphous wire to a highly sensitive magnetic field sensor as the magneto-impedance (MI) effect [Panina 1994]. Many investigations on MI including material designs [Vázquez 1997, Kraus 2003], theoretical models for the phenomenon [Machado 1996, Menard 1998, 2000, Kraus 1999, Dong 2002], development of sensor devices [Mohri 2002], and their applications [Hongama 2012] have been conducted [Phan 2008], and MI is still a topic of interest for many researchers [Zhukov 2017, Atalay 2018, Zhukova 2018b, Smolyakov 2019]. Especially, Zhukov's group has conducted much work on microwires in recent year [Corte-León 2019, Zhukova 2018a, Zhukov 2019]. The compass of a mobile phone is an example of a commercialized application of MI [Honkura 2002], while recent research trends are in the development of biomedical applications such as the detection of weak magnetic fields from human hearts [Yabukami 2009, Uchiyama 2012] and biosensors [Buznikov 2018] linked to an immunoassay [Wang 2014]. Denmark [2019] reviewed magnetic nanobiosening techniques and highlighted the advantages and shortcomings of magnetic sensors for biosensing. Its application for nondestructive evaluation (NDE) [Cheng 2016] has also been investigated using small sensors with high sensitivity to enable evaluations at high spatial resolutions as assessments are of localized areas. To realize inspection at a high spatial resolution, it is essential to miniaturize the sensor element size, and the thin-film configuration contributes to the miniaturization of sensor elements. Additionally, thin-films are compatible with integrated driving and detecting circuits. Regarding the sensitivity of MI, the wire and ribbon configuration is superior to the thin-film, and its impedance ratio achieves 800% in elements that are in the range of millimeter to centimeter lengths [Kurlyandskaya 2001]. However, the thin-film type achieves 350% at 25 MHz as a multilayered structure (NiFe/Cu) with a length of 10 mm [García-Arribas 2016]. MI ratios of 100%–200% have been reported for thin-film configurations with elements between 5 and 20 mm in length [Rivero 2003, de Cos 2005, 2008, Volchkov 2011, Kurlyandskaya 2012, 2015, 2016, Chlenova 2016]. Even though multilayer structures are complicated, most research studies have adopted these structures and used the ferromangetic material Permalloy. Miniaturization elements 2 mm in length with MI ratios between 80% and 100% have been reported [Takayama 1999, Nishibe 2003]; however, no studies have reported miniaturized sensor elements that are 1 mm or less in length. Therefore, we previously fabricated thin-film sensor elements with hundreds of micrometers order and showed the behaviors of typical impedance changes against applying a field successfully with overcoming the problem of a demagnetizing field [Kikuchi 2016b]. Shortening the length of an element is an effective way of miniaturization; however, the influence of the demagnetizing field becomes more pronounced, and this letter proposes a solution. For NDE application, detection with high spatial resolution is prior to its sensitivity and does not require high field resolution as does biomedical applications, even though high sensitivity is preferable. In this study, we prepared several thin-film elements composed of simple single layers of lengths less than 1 mm, and their lengths were minimized to 30 µm. We evaluated the frequency properties and field dependence using dc magnetic fields, and assessed their impedance change ratios and sensitivities in a wide frequency range.
