3469 IEEE TRANSACTIONS ON MAGNEI'ICS. VOL. 29, NO. 6, NOVEMBER zyxwvu 1993 zyxwvu Initial Susceptibility vs. Applied Stress in Amorphous Alloys with Positive and Negative Magnetostriction zyxw Carlo Appino, Fausto Fiorillo, and Antonella Maraner lstituto Elettrotecnico Nazionale Galileo Ferraris and GNSM-INFM C.so M. d'Azeglio 42, 101 25 Torino, Italy zyxwv Abstract - The dependence of initial susceptibility x on applied tensilelcompressive stress Q has been determined for Fe and Co based amorphous alloys, characterized by positive and negative magnetostriction, respectively. The contribu- tions to x originating from coherent spin rotationlr,) and domain wall motion Ir,) are separated by means of suitably devised experiments and found to correlate with the evolu- tion of the domain structure vs. Q, as directly verified by means of magneto-optical Kerr effect observations. High tensile stresses produce entirely longitudinal (transverse) domain structure in Fe (Col based ribbons. The longitudinal (transverse) pattern evolves into a transversal (longitudinal) one by progressively changing tension into compression. x, and xw correspondingly pass through a maximum at interme- diate stress values. The evolution of the domain pattern and of susceptibility vs. tensilelcompressive applied stress in amorphous ribbons is described in this paper by modelling the spatial distribution of the magnetization upon a postulat- ed distribution of the quenched-in local anisotropies and their combination with the stress-induced macroscopic anisotropy. The stress dependence of x,, quantitatively predicted in this way, is in good agreement with the experiments. I. INTRODUCTION Amorphous alloys, lacking any magnetocrystalline anisotropy, exhibit a magnetic behavior strongly dependent on induced anisotropies. Frozen-in stresses are the source of local anisotropies in as-obtained samples. Shape effects and applied stress can addi- tionally provide relevant macroscopic anisotropy terms. Further contributions arise after annealing, with or without an applied field. Optimization of the alloy properties under the conditions met in applications requires understandingof the role of such anisotropies on the magnetization process. In this framework special emphasis should be attached to the quantita- tive analysis of the effect of stress. This should help, for instance, in the design of sensors or in a rational approach to stress relief by means of annealing. Stress building strongly affects the domain structure zyxwvuts [I 1, with profound consequences on permeability, coercivity and losses [21-[41. This effect is often treated by assuming that the magnetic domains can lie either longitudinally or transversally with respect to the ribbon axis [51, [61. An applied stress is expected to induce, through magnetoelastic coupling, a change in the domain population along these two orthogonal directions, Manuscript received February 15, 1993. resulting in modifications of the macroscopic magnetic properties. This simplified approach is somewhat in contrast with the actually observed domain structure and with experiments on the stress dependence of hysteresis losses [41. In the present paper an improved model for the space distribution of the magnetization /, in amorphous ribbons is therefore worked out. It is based on a postulated uniform angular distribution of the local unidirectional anisotropies originating from quenched-in stresses. Additional macroscopic anisotr- opy terms, deriving from possible ordering effects [71 and/or magnetostatic contributions [81 are also taken into account. The role of applied stress, whether tensile or compressive, is accounted for by means of a uniform anisotropy term, with easy axis longitudinal- ly or transversally directed, according to the sign of both stress and magnetostriction constant A,. The model is used to predict the rotational contribution zy x, to the initial susceptibility and its behavior vs. the applied stress. x, is experimentally determined exploit- ing in a suitable way the time decay of the total susceptibility x (aftereffect), which is assumed to affect the domain wall contribution xw only. Kerr effect observations of the domain structure are employed to confirm the validity of the model. Agreement between the theoretically predicted behavior of x, and experi- ments performed in a wide range of applied stresses (- 300 MPa zyxwv s u I 500 MPa) is found. II. THEORY As-quenched amorphous ribbons are characterized by a typical meandered domain structure in the demagne- tized state, which points to the presence of local anisotropies, basically due tQ frozen-in long range stresses [I 1. An applied stresi cr, introducing a macro- scopic anisotropy term, causes a modification of such structure, which may pass, according to sign and amplitude of the magnetostriction constant A, and of u, from entirely longitudinal to entirely transverse. This evolution will be here considered, by assuming that the role of the random frozen-in stresses can be described by means of the correspondinganisotropies. The local direction of the magnetization vector I, coincides, in the absence of any macroscopic anisotropy, with the direction of the local stress-induced easy axes. Ac- cording to domain structure observations, these axes are assumed to lie in the ribbon plane, but for a 0018-9464/93$03.00 Q 1993 IEEE Authorized licensed use limited to: Istituto Nazionale di Ricerca Metrologica - INRIM. Downloaded on September 16, 2009 at 09:30 from IEEE Xplore. Restrictions apply.