IEEE TRANSACTIONS ON MAGNETICS, VOL. 36, NO. 4,JULY 2000 2057 Nonlinear AC Response and Noise of a Giant Magnetoresistive Sensor J. R. Petta, Thaddeus Ladd, and M. B. Weissman Abstract—We compare bridge voltage response measurements to ac magnetic fields from a giant magnetoresistive sensor with noise measurements on the same sensor. The small-signal response (for applied ac magnetic fields between 0.1 mOe rms and 30 mOe) is much less than is the slope of a dc voltage versus field curve, because of hysteretic effects. Noise statistics are used to estimate the size and number of the sites at which domain realignments occur near the response peak. Similar estimates are made by using fine-structure on the ac response curve. For ac fields of about 0.3 mOe rms, sharp spikes appear in the field-dependent response, giving rise to large harmonic distortion, varying in an irregular way with the ac amplitude. Domain sizes are estimated for the re- gions, giving these nonlinear response spikes, and for the domains, giving the magnetic noise, and a comparison based on a fluctua- tion–dissipation relation of the noise, and the response shows the importance of hysteresis. I. INTRODUCTION T HE POSSIBILITY of using giant magnetoresistive (GMR) materials in device applications [1]–[3] is often limited by the transport noise of the GMR materials, which typically originates in the fluctuations of magnetic domains [4]–[9]. Thermal fluctuations in the magnetic domain struc- ture give rise to noise in the resistance , which is largest at fields for which the magnitude of is large [4]–[9]. When the applied magnetic field changes over time, Barkhausen noise from the uneven growth of domains aligned with the field often becomes the dominant noise mechanism [4]. Practical application of GMR devices as low-field sensors requires maximizing their linear response to small fields, while minimizing their noise. Both the quasi-equilibrium thermal noise and the Barkhausen noise provide information about the size of the magnetic do- mains and the processes by which they align [4]–[7]. In this paper, we combine measurements of fine structure in the ac re- sponse of a particular GMR sensor with measurements of noise spectra and non-Gaussian statistics to obtain such information on a particular sensor. Our purpose is less to elucidate the prop- erties of that particular sensor than to show the utility of some new characterization techniques, which can be used without de- structive testing or microscopic examination. We measured the normalized response of the device voltage to small ac magnetic fields at dc field . We define to be the rms voltage response of the device (at a fixed Manuscript received January 7, 1999; revised November 28, 1999. This work was supported by the Jet Propulsion Laboratory and the National Science Foun- dation, under Grant DMR 96-23478. The authors are with the Department of Physics, University of Illinois at Ur- bana-Champaign, Urbana, IL 61801-3080 USA (e-mail: mbw@uiuc.edu). Publisher Item Identifier S 0018-9464(00)05847-7. current bias) divided by the rms ac field applied, with giving the in-phase response and the out-of-phase. The first question to be addressed is whether the response comes from a fairly homogeneous magnetization rotation (as is often assumed in simplified theories) or whether the response is the sum of responses from many domain walls, each responding over a narrow range of . We shall present a fairly unsurprising result—that the response is an inhomogeneous sum of many dis- tinct responses, each limited to a narrow field range. The ques- tions then become how narrow is the range over which these individual responses occur, how many domains or domain wall segments are active in any range of , and to what extent are the individual responses linear in small applied ac fields. If the response function developed from either a single smoothly rotating domain or a very large number of independent domains or domain wall segments, it would be expected to be a smooth function of . (We henceforth use “domain” to refer to a region in the material whose magnetization responds coherently to the applied ac field, although this region may only include a small area around the border between two big domains.) If developed from a small number of sites at any particular , it would be expected to be a rough function of , because of the statistical variation in the number of sites contributing at each . The variance in then can be used to estimate the number of domains responding to a given ac field, which combined with the net response, allows an estimate of the size of the individual domain realignments [10], [11]. In some cases, spikes in are big enough to measure individually, allowing direct determination of the size of those domain realignments. The width of the spikes in also directly depends on the range of dc fields over which those do- mains are active. In general, the response at any given ac field will consist of two parts: a genuinely linear response, which therefore obeys a fluctuation–dissipation relation and a microhysteretic response, which will give Barkhausen noise but which will not be ac- companied by any quasi-equilibrium noise in the absence of a time-varying field. It has been shown that for GMR devices with sufficiently homogeneous sensitivity of to the magnetization, the noise can be predicted from the out-of-phase response of to [4]. For the true linear response, the deviation of the noise statistics from the Gaussian statistics expected for the sum of a large number of independently fluctuating units also allows an estimate of the number of fluctuating domains and, hence, of the size of each such domain fluctuation [10], [11]. Further information on the fraction of the sample contributing to the nonhysteretic response can be obtained from a compar- ison of the magnitude of the in-phase response to small ac mag- 0018–9464/00$10.00 © 2000 IEEE