3992 IEEE TRANSACTIONS ON MAGNETICS, VOL. 44, NO. 11, NOVEMBER 2008 Two-Domain Model for Orthogonal Fluxgate Mattia Butta and Pavel Ripka Czech Technical University, Faculty of Electrical Engineering, Prague 166 27, Czech Republic In this paper a new model for orthogonal fluxgate is presented. A first attempt to explain the working principle of the orthogonal fluxgates was done in the 1970’s. We show that this model does not work well on recently developed orthogonal fluxgate sensors with thin-film core on microwire. A new more accurate two-domain model based both on domain wall motion and magnetization rotation is proposed. We show that the new model better explains the observed properties of thin-film orthogonal fluxgate. Index Terms—Magnetic field measurement, model, orthogonal fluxgate, two-domain. I. INTRODUCTION O RTHOGONAL fluxgate was patented in 1951; this prin- ciple was almost forgotten as the mainstream large-size parallel fluxgate has shown lower noise and better stability. Or- thogonal fluxgates based on microwires and planar microstruc- tures reappeared recently; these devices have a good potential for miniaturization as they need no excitation coil—the sensor is excited by the current flowing through the core. This requires high currents to achieve full core saturation. The favorable de- sign is a non-magnetic conductor covered by a magnetically soft film. The conductor is either a circular wire [1], [2] or rectan- gular rod [3]. In such case the magnetic core on the surface of the conductor is better saturated by the excitation current [4]. The orthogonal fluxgate is more sensitive than the “off-diag- onal GMI” (or IWE) mode [5]. The working mechanism of the orthogonal fluxgate has not been fully understood yet. Fluxgates work on second and sometimes higher-order even harmonic frequencies. Paperno has recently shown that in some cases the sensor noise in fundamental mode was lower than the noise of the same sensor in the 2nd harmonic mode [6]. He holds a noise record for transverse fluxgate, which is 20 pT/ Hz at 1 Hz. The poor offset temperature stability of this device was im- proved by periodical bias switching [7]. Temperature coefficient of the open-loop sensitivity can be compensated from 6500 to 100 ppm/K [8]. II. PRIMDAHL’S MODEL In [9] Primdahl proposed a simple model describing the rota- tion of the magnetization M, due to the circumferential magnetic field . That model was based on the assumption of isotropy of the magnetic material; the first hypothesis Primdahl made, was the collinearity of B and H. Fundamental mode transverse fluxgate was later analysed by Sasada [10]; he has shown that this device cannot work without anisotropy. However, in this paper we concentrate on fluxgate which is saturated by excita- tion in both polarities, so that the sensor output is on the second harmonic. Primdahl’s model cannot be applied to the second-harmonic mode orthogonal fluxgates with electrodeposited magnetic wires. Measurement of the circumferential and longitudinal Digital Object Identifier 10.1109/TMAG.2008.2003505 Fig. 1. B(T)-H(A/m) loops in longitudinal (a) and circumferential (b) direction. B-H loops performed as explained in [11] on wire core elec- trodeposited by Atalay [12] revealed significant anisotropy [as seen from Fig. 1(a) and (b)]. We will further show that Primdahl’s isotropic model cannot explain some typical fea- tures of the gating curves. Gating curve is a dependence of the longitudinal flux on circumferential excitation field . Let us assume that the cylindrical core is subjected to longi- tudinal measured field and simultaneously to the circumfer- ential excitation field . According to this model the magneti- zation process has two stages during increasing : in the first stage M and B increase and simultaneously rotate from longitu- dinal towards circumferential direction. In the second phase B and M are saturated and only rotation of the magnetization oc- curs. Since the material is considered isotropic, in the first stage the magnetization in longitudinal direction is constant, as it 0018-9464/$25.00 © 2008 IEEE