We studied low-frequency noise in NiFe-Al 2 O 3 -NiFe based magnetic tunnel junctions ͑MTJ's͒ with and without a hard-axis bias field. The 1/f noise is observed to be magnetic-field dependent and reduced with the application of hard-axis bias fields, attributed to thermally activated magnetization fluctuations in the magnetic electrodes. A linear dependence of noise on derivative of magnetoresistance has been observed, and the magnetic-field noise for MTJ sensing elements is defined and evaluated to be as low as 60 nT m/Hz 1/2 .The study of noise of magnetoresistive materials is important for understanding the performance of spin-dependent electronic devices as well as the physical processes that govern their magnetic properties. There are many processes that can contribute to the noise of a magnetoresistive based device. Based on its physical origin, the noise is categorized into three types. Thermal resistance noise, also known as Johnson or Nyquist noise, results from a thermal smearing of the density of states near the Fermi level. Shot noise is due to the stochastic nature of electron transport with an applied current. The third kind of noise, 1/f noise, also called flicker noise or excess noise, arises from the coupling of electronic processes with magnetization fluctuations. 1,2 The first two noise sources are frequency independent, while 1/f noise scales inversely with frequency, as suggested by its name.Usually 1/f noise is an indirect noise and manifests itself as resistance fluctuations in different physical systems in lowfrequency range. As examples, resistance fluctuations in twodimensional electron system in semiconductor heterostructures 3 and high-T C superconductor 4 have different physical origin. Due to its nature, there is not a universal explanation to physical origin of 1/f noise.In this paper we are interested in magnetoresistance ͑MR͒ fluctuations at low fields in Py-Al 2 O 3 -Py ͑PyϭPermalloy, Ni 79 Fe 21 ) based magnetic tunnel junctions ͑MTJ's͒. This spin-dependent system shows great potential for high sensitivity, low-noise magnetic-field sensing applications, due to its low saturation field and high MR ratio ͑defined as ⌬R/R, where ⌬R and R are the maximum resistance change and the minimum resistance, respectively͒. In addition, the exponential dependence of junction resistivity on the barrier thickness allows for a large degree of control over device resistance. A typical tunnel junction consists of two ferromagnetic ͑FM͒ metal layers separated by an ultrathin insulating barrier. Changes in the relative magnetization orientations between these two FM layers in applied magnetic field͑s͒ determine the final resistance, i.e., MR. Although many fundamental aspects of this system, including magnetization reversal processes, 5 scattering mechanisms, 6 and electron transport behavior have been studied in detail, the lowfrequency noise characteristics have not been fully explored.In a recent work, Ingvarsson et al. have studied magnetic noise produced by magnetization fluctuations in MTJ's ͑...