Angular dependence of giant magnetoimpedance in an amorphous Co-Fe-Si-B ribbon K. R. Pirota, L. Kraus,* M. Knobel, P. G. Pagliuso, and C. Rettori Instituto de Fı ´sica ‘‘Gleb Wataghin,’’ Universidade Estadual de Campinas (UNICAMP), C.P. 6165, Campinas 13083-970, Sa ˜ o Paulo, Brazil ~Received 8 March 1999! The field response of impedance is studied in a stress-annealed amorphous ribbon as a function of the angle of application of the external magnetic field in order to verify the role of induced anisotropies ~and their distribution! and demagnetizing factors in the giant magnetoimpedance ~GMI! phenomenon which occurs in soft magnetic materials. The experimental results are well explained by a theoretical model, based on the simultaneous solution of Maxwell equations and the Landau-Lifshitz equation of motion. Demagnetizing effects are properly taken into account in the case of ribbons or thin films. The physical parameters necessary to test the theory were obtained through complementary measurements of the ferromagnetic resonance and temperature dependence of magnetization. The results clearly indicate the enormous influence of the distribu- tion of anisotropies on the GMI effect. Also, an experimental procedure for determining the easy-axis distri- bution function is proposed. @S0163-1829~99!15433-X# I. INTRODUCTION Recent research concerning the field and frequency re- sponse of impedance in soft magnetic conductors has un- veiled a new and fascinating phenomenon, known as giant magnetoimpedance ~GMI!. Strong and sensitive field- induced variations of the impedance were first observed in amorphous wires 1 and ribbons, 2 and later in nanocrystalline materials ~wires 3 and ribbons 4 ! and soft magnetic thin films. 5 A major role in GMI is played by the skin depth d, the square of which is directly proportional to the resistivity of the material and inversely proportional to the transversal per- meability and frequency of the probe current. 6 Soft magnetic materials display very large magnetic permeabilities, which are strongly affected by relatively small magnetic fields. These changes are immediately reflected in d and, therefore, in the impedance of the material considered. Although GMI was discovered quite recently, it has been studied inten- sively, mainly owing to the great possibilities for technologi- cal applications. Also, even if the basic aspects of the phe- nomenon can be qualitatively understood in terms of classical electrodynamics, systematic investigation has re- vealed several experimental results which remain to be clari- fied. For example, it is well known that inducing transverse anisotropies contributes to a significant increase of the GMI ratios, which, however, usually occurs with the appearance of new features, such as definite peak structures 5,7 and hys- teretic behavior. 8 Only recently, with the further develop- ment of theoretical models, which now include the dynamics of magnetization rotation through the Landau-Lifshitz equa- tion of motion 9 and take into account the exchange effects, 10,11 has the study of the effect of anisotropies on the GMI behavior become feasible. Hitherto, most studies of GMI effect concentrated on the longitudinal magnetoimpedance ~LMI!, in which the external magnetic field is applied along the direction of the probe current I. LMI in amorphous and nanocrystalline materials with well-defined magnetic anisotropy usually exhibits either a single- or double-peak structure, for the easy axis parallel or perpendicular to the current direction, respectively. 12 Little work on magnetoimpedance with external field applied perpendicular to the current direction has been reported. 5,14–17 In ribbons or thin films two additional geom- etries can be distinguished: transverse magnetoimpedance ~TMI! for the field in the ribbon plane 5,13,16 or perpendicular magnetoimpedance ~PMI! for the field perpendicular to it. 13,14,16 While the behavior of LMI is relatively well under- stood, the TMI and PMI results are rather confusing and not well understood. An observation of TMI was reported by Sommer and Chien in amorphous Fe 73.5 CuNb 3 Si 13.5 B 9 thin films. 5 For the transversely field annealed sample they ob- served a relatively strong GMI effect in both LMI and TMI configurations in similar field ranges. The main difference was the single- and double-peak structure for TMI and LMI, respectively. 5 Similarity in the magnitude, field range, and frequency behavior of LMI and TMI has been also observed in crystalline NiFe and amorphous NiCoFeMnSiB melt ex- tracted fibers. 15 On the contrary, LMI, TMI, and PMI mea- surements in low magnetostrictive amorphous ribbons show similarly large effects, but with different peak structures and in substantially different field ranges depending upon the corresponding demagnetizing factor. 13,14 Recently reported LMI, TMI, and PMI measurements on amorphous FeNiCrSiB films, annealed above the Curie temperature, show similar magnitudes of GMI, but only the single-peak behavior in all the three possible configurations. 16 In this paper we investigate the GMI effect as a function of the angle of application of the external magnetic field in stress-annealed amorphous ribbons in order to verify the role of induced anisotropies ~and their distribution! and demag- netizing factors in the impedance response of soft magnetic samples. In addition to the clues that these experiments fur- nish for the fundamental framework of magnetoimpedance phenomena, they are also important in view of possible ap- plications of GMI elements as nonfixed magnetic sensors, where the field can be applied in any spatial direction. II. EXPERIMENTAL DETAILS Our experiments were performed on an ~Fe 0.053 Co 0.947 ! 70 Si 12 B 18 amorphous ribbon ~width 0.8 mm, PHYSICAL REVIEW B 1 SEPTEMBER 1999-I VOLUME 60, NUMBER 9 PRB 60 0163-1829/99/60~9!/6685~7!/$15.00 6685 ©1999 The American Physical Society