I. INTRODUCTION
A few decades have passed since the magneto-impedance (MI) effect was found and the MI element was applied to a magnetic field sensor having a higher sensitivity in 1994 [Panina 1994]. Many contributions to optimal material designs [Vázquez 1997, Kraus 2003], development of theoretical models for the phenomena [Machado 1996, Ménard 1998, 2000, Kraus 1999, Dong 2002], and applications in the industrial field [Honkura 2002], have been made [Phan 2008]. The research started with amorphous wires [Panina 1994, Beach 1994, Vázquez 2001], and then grew to include ribbons [Kim 1998, Guo 1998] and thin films [Sommer 1995, Panina 1995], and interest continues to grow in enhancing their performance [García-Arribas 2013, Fernández 2015, Zhukov 2016]. Its application as a compass in mobile phones was commercialized [Cai 2005], and recent focus is on applications to medical [Yabukami 2009, Uchiyama 2012] and bioresearch fields [Chiriac 2005 , Kurlyandskaya 2009, Wang 2014 ] and nondestructive evaluation techniques [Kim 2002, Ozawa 2013]. The main research focuses on improving its sensitivity to achieve a magnetic field sensor of pico tesla order at room temperature [Yabukami 2009, Uchiyama 2012]. MI-type sensors typically have a length in millimeters, which is larger than those of the magnetoresistance types (GMR, TMR) and Hall sensor type. Demands for a measurement with a higher spatial resolution are increasing, along with requests for miniaturization of the sensing element and availability of the edge piece of the sensing element to detect near field. As to the miniaturization, advances in the fabrication of nanowires [Nakayama 2014, Talaat 2016] and thin film techniques contribute to the miniaturization as well as compatibility of integrated electronic devices.