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Two-Dimensional Field-Sensing Map and Magnetic Anisotropy Dispersion

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Two-Dimensional Field-Sensing Map and Magnetic Anisotropy Dispersion PHYSICAL REVIEW B 83, 144416 (2011) Two-dimensional field-sensing map and magnetic anisotropy dispersion in magnetic tunnel junction arrays Wenzhe Zhang* and Gang Xiao† Department of Physics, Brown University, Providence, Rhode Island 02912, USA Matthew J. Carter Micro Magnetics, Inc., 617 Airport Road, Fall River, Massachusetts 02720, USA (Received 22 July 2010; revised manuscript received 24 January 2011; published 22 April 2011) Due to the inherent disorder in local structures, anisotropy dispersion exists in almost all systems that consist of multiple magnetic tunnel junctions (MTJs). Aided by micromagnetic simulations based on the Stoner-Wohlfarth (S-W) model, we used a two-dimensional field-sensing map to study the effect of anisotropy dispersion in MTJ arrays. First, we recorded the field sensitivity value of an MTJ array as a function of the easy- and hard-axis bias fields, and then extracted the anisotropy dispersion in the array by comparing the experimental sensitivity map to the simulated map. Through a mean-square-error-based image processing technique, we found the best match for our experimental data, and assigned a pair of dispersion numbers (anisotropy angle and anisotropy constant) to the array. By varying each of the parameters one at a time, we were able to discover the dependence of field sensitivity on magnetoresistance ratio, coercivity, and magnetic anisotropy dispersion. The effects from possible edge domains are also discussed to account for a correction term in our analysis of anisotropy angle distribution using the S-W model. We believe this model is a useful tool for monitoring the formation and evolution of anisotropy dispersion in MTJ systems, and can facilitate better design of MTJ-based devices. DOI: 10.1103/PhysRevB.83.144416 PACS number(s): 75.30.Gw, 73.50.Jt, 75.47.De, 85.75.−d I. INTRODUCTION the magnetic parameters that govern the behavior of MTJ devices. By recording an MTJ device resistance as a function Magnetic tunnel junctions (MTJs) with crystalline tunnel of the applied field angle, information about the free layer’s barriers have been extensively studied over the last few anisotropy orientation can be provided. Although Safron years. A tunneling magnetoresistance ratio (TMR) in excess suggested that analysis of an MTJ’s remnant resistance curve of 200% in such devices has made them excellent candi- may yield the dispersion of the free layer anisotropy, they did dates for applications in spin-based electronics.1,2 One of not give a quantitative approach. the applications, a magnetoresistive field sensor, is usually In Safron’s work, the Stoner and Wohlfarth (S-W)9,10 configured such that the magnetization of the free layer is model was employed to yield theoretical estimations for perpendicular to that of the pinned layer (pinning axis), either the anisotropy angle and the anisotropy constant for an due to biasing magnetic fields3 or high shape anisotropy.4 When subjected to a magnetic field along the pinning axis, the MTJ’s free layer. The model describes the rotation of the magnetization of the free layer undergoes a coherent rotation, magnetic moment of a single-domain magnetic particle with yielding an almost linear response on the magnetoresistance. an anisotropy easy axis. The S-W model generates both the In hoping to increase this linearity and to boost the sensor reversible and irreversible changes in magnetization under sensitivity to the picotesla scale, several research groups have a multidimensional magnetic field, taking into account the proposed a variety of techniques: Using a single field applied arbitrary strength of magnetic anisotropy. A single MTJ at an angle between the hard and easy axes, P. Pong et al.5 element with a well-defined free layer having a uniaxial anisotropy follows the S-W model relatively well. On the other obtained a linear nonhysteretic response in Al2O3-based MTJs with a magnetic field sensitivity as high as 13.8%/Oe. The hand, for an MTJ magnetic sensor array made up of multiple introduction of a second antiferromagnetic thin film adjacent elements, each sensing element has its own anisotropy due to to the detection layer, as reported by Negulescu et al.,6 allowed inherent disorder in local structures or the patterning process. tuning both the sensitivity and the linear range of the MTJ The anisotropy parameters of the sensing elements, such as sensor. anisotropy axis and anisotropy constant, are not uniform, yet As demonstrated by the rapidly growing amount of litera- they satisfy certain statistical distribution. A series of tests have tures on the subject, the magnetic properties of MTJ devices indicated that the dispersion in this type of distribution often can be characterized by using the acquired magnetotransport acts against achieving good sensitivity. Since the modeling properties, thus revealing the micromagnetics of the free layer, of the magnetic behavior of such a spintronic device is more which is often in micron to submicron scales. For instance, complicated than what the simple S-W model can predict, Mazumdar et al.7 mapped the magnetic field sensitivity and developing a more complete model is needed to understand low-frequency 1/f voltage noise of an MTJ in orthogonal the magnetic properties of such systems, and that is the aim of magnetic fields. The so-called noise map uncovered the this study. possible origin of intrinsic magnetic noise of MTJ devices. This paper is arranged in the following manner. First we will Safron et al.8 used a circle transfer curve method to determine determine the magnetic sensitivity by using a two-dimensional 1098-0121/2011/83(14)/144416(7)144416-1 ©2011 American Physical Society WENZHE ZHANG, GANG XIAO, AND MATTHEW J. CARTER PHYSICAL REVIEW B 83, 144416 (2011) field-sensing map as described in Ref. 7, and then we will III. COMPUTATIONAL METHODS present a model to account for the anisotropy dispersion. To understand the sensitivity map, we attempted to model Finally, we will talk about conclusions derived from this a system consisting of a collection of S-W single-domain model, and its comparison to the experimental work. magnetic particles, with each particle corresponding to one free layer element in our MTJ array. Each element or particle II. EXPERIMENTAL METHODS is specified by its magnetic moment (ms ), anisotropy constant We deposited MTJ multilayer films on thermally (Ku), and easy-axis direction (α). Because of the inherent oxidized silicon wafers using a custom multitarget disorder in local structures or due to the patterning process, high-vacuum magnetron sputtering system (base pressure of these parameters are not uniform. However, they satisfy certain 2 × 10−8 Torr). The MTJ stack has the following structure statistical distributions. In this study, we ignored any magneto- (thicknesses in angstroms): 50Ta/300Ru/50Ta/20CoFe/ static interactions between the neighboring magnetic particles 150IrMn / 20CoFe / 8Ru / 30CoFeB / 19MgO /30CoFeB/50Ta/ (which can be justified in Sec. IV). We only considered the 100Ru. All layers except the MgO barrier were deposited magnetic energies of these particles in a two-dimensional by dc sputtering at a constant Ar pressure of 2.05 mTorr. external magnetic field (H), applied in the plane of these The MgO barrier was deposited by radio frequency (rf) magnetic particles (thin films). The magnetic moments can magnetron sputtering at an Ar pressure of 1.1 mTorr. During only rotate within the plane (i.e., only the in-plane anisotropy the sputtering process, the substrates were rotated at a is considered). constant speed to maximize uniformity throughout each The total energy of a single S-W particle as shown in Fig. 1 = 2 − − wafer. Micron-sized elliptical junctions were patterned using is given by E Ku sin θ1 Hms cos(θ2 θ1), where θ1 is standard photolithography and ion-beam milling process. the angle between the magnetization vector (ms ) and the easy A 150-nm thick gold layer was deposited over the defined axis of the particle, and θ2 is the angle between the applied field junction area and patterned into low resistance top contact vector (H) and the easy axis. In the S-W model, the equilibrium leads. The free layers of the junctions studied had lateral direction of ms of a single particle is obtained by minimizing = dimensions of 50 × 90 μm2, and the MTJ arrays consisted of the total energy of the particle using the criteria ∂E/∂θ1 0 2 2 = 38 free layer elements connected in a series with the whole and ∂ E/∂ θ1 0. The solutions of these two equations 11 resistance about 2 K. can be obtained by using the Newton-Raphson method. 12–14 After deposition and patterning, high-temperature magnetic A geometric construction, known as the Asteroid Rule annealing was used to define the intrinsic magnetic axis (see Fig. 1), is employed to visualize the determination of the and to achieve a high magnetoresistance ratio. Typically, equilibrium direction of ms . According to the Asteroid Rule, the MTJs were annealed at 310◦C for 4 hours at 8 × the equilibrium direction is parallel to one of the lines tangent 10−8 Torr in an applied magnetic field of 4.5 KOe. The field to the asteroid and passing through the tip of magnetic field was applied along the shorter axis of the free layer oval. After annealing, the magnetic pinning direction of the pinned layer is always parallel to the shorter axis of the free layer. The magnetic anisotropy of the free layer is predominantly due to the magnetocrystalline anisotropy induced by the magnetic annealing. Because of this, the easy axis of the free layer is, in fact, the shorter axis. We performed magnetic sensitivity measurements in or- thogonal magnetic fields applied along the easy (HE) and hard (HB ) axis of the MTJ elements.
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