Patent Publication Number: US-8975891-B2

Title: Apparatus and method for determining in-plane magnetic field components of a magnetic field using a single magnetoresistive sensor

Description:
BACKGROUND 
     It is desirable to be able to sense two components of a planar field using batch fabricated devices on the same substrate without the need of sawing and packaging. Currently available technology solves this problem by annealing-in orthogonal Pinned Layer/Reference Layer (PL/RL) magnetization directions on neighboring tunnel junctions. 
     Magnetic tunnel junctions have high magnetoresistance ratio (i.e., (R max −R min )/R min =ΔR/R) on the order of 100&#39;s of % and are currently used to measure moderate to high levels of magnetic fields. Magnetic tunnel junctions also have a high 1/f noise. The high noise density at low frequencies prevents the use of magnetic tunnel junctions for measuring small levels of magnetic field at frequencies less than of the order of a kHz. 
     SUMMARY 
     The present application relates to a method to measure an applied magnetic field in a plane. The method includes applying a first alternating drive current to a first strap. At least a portion of the first strap overlays a magnetoresistive sensor. The first strap has a dimension extending in a first direction. The method also includes simultaneously applying a second alternating drive current to a second strap. At least a portion of the second strap overlays the at least a portion of the first strap. The second strap has a dimension extending in a second direction. The second direction is non-parallel to the first direction and the second alternating drive current is out of phase with respect to the first alternating drive current so the magnetoresistive sensor is subjected to a periodically rotating magnetic drive field rotating in the plane in the magnetoresistive sensor. When the applied magnetic field to be measured is superimposed on the periodically rotating magnetic drive field rotating in the plane, the method further includes extracting a second harmonic component of an output voltage output from the magnetoresistive sensor. The magnitude of the magnetic field to be measured in the plane is proportional to an amplitude of the extracted second harmonic component of the output voltage. The orientation of the magnetic field to be measured in the plane is related to a phase angle of the extracted second harmonic component of the output voltage. 
     The details of various embodiments of the claimed invention are set forth in the accompanying drawings and the description below. Other features and advantages will become apparent from the description, the drawings, and the claims. 
    
    
     
       DRAWINGS 
         FIG. 1A  is a block diagram of one embodiment of a multilayered magnetoresistive sensor, a first drive strap, and a second drive strap in accordance with the present invention; 
         FIG. 1B  shows the magnetic drive field periodically rotating at an angular frequency in the X-Y plane of the magnetoresistive sensor of  FIG. 1A ; 
         FIG. 2A  is a block diagram of one embodiment of a magnetic tunnel junction, electrical contacts, a first drive strap, and a second drive strap in accordance with the present invention; 
         FIG. 2B  is a block diagram of one embodiment of a giant magnetoresistor, electrical contacts, a first drive strap, and a second drive strap in accordance with the present invention; 
         FIG. 3A  is a block diagram of one embodiment of a circuit to measure output voltage of the magnetic tunnel junction of  FIG. 2A  in accordance with the present invention; 
         FIG. 3B  is a block diagram of one embodiment of a circuit to measure output voltage of the giant magnetoresistor of  FIG. 2B  in accordance with the present invention; 
         FIGS. 4A and 4B  are block diagrams of embodiments of magnetoresistive sensor systems including the magnetoresistive sensor of  FIG. 1A  in accordance with the present invention; 
         FIGS. 5A and 5B  show simulated output for different applied magnetic fields applied to an exemplary magnetoresistive sensor in accordance with the present invention; 
         FIG. 6  is block diagram of an embodiment of a magnetoresistive sensor system including a magnetoresistive sensor in accordance with the present invention; 
         FIG. 7  shows embodiments of tailored shapes of drive currents; and 
         FIG. 8  is a flow diagram of one embodiment of a method to measure an applied magnetic field in a plane in accordance with the present invention. 
     
    
    
     Like reference numbers and designations in the various drawings indicate like elements. 
     DETAILED DESCRIPTION 
     MagnetoResistive (MR) sensors are used for magnetic compassing, magnetic anomaly detection, gear-tooth sensing, etc., i.e., in any application where small values of magnetic field, or small changes in Earth&#39;s magnetic field must be sensed. Fluxgates and Superconducting Quantum Interference Devices (SQUIDs) are bulk level magnetic sensors capable of measuring small values of magnetic field or small changes in magnetic fields. 
     Chip scale magnetoresistive sensors can be made at low cost and are thus advantageous over bulk level magnetic sensors. Anisotropic MagnetoResistance (AMR) sensors, Giant MagnetoResistance (GMR) sensors and Magnetic Tunnel Junction (MTJ) sensors are manufactured on a chip scale. GMR and MTJ stacks include a ferromagnetic free layer of which the magnetization orientation can be changed, a ferromagnetic reference layer having a fixed magnetization orientation, and a barrier layer therebetween. Anisotropic magnetoresistors have magnetoresistive ratios ΔR/R of about 2-3%. Giant magnetoresistors advantageously provide higher magnetoresistive ratios ΔR/R on the order of 10&#39;s of %. Magnetic tunnel junctions provide even higher magnetoresistive (MR) ratios on the order of 100&#39;s of %. 
     Another advantage of chip scale GMR or MTJ sensors is their small size. For example, multilayered magnetoresistive sensors (GMR or MTJ) can have dimensions of the order of a few 10&#39;s to 100&#39;s of nanometers. A 200 nm wide metal line overlaying a 100-150 nm wide MTJ has a “field conversion factor” of 32 μAmp/Oe, and a micron wide line has a field conversion factor of 159 μAmp/Oe. Thus, fields required to switch, rotate, or saturate the free layer of an appropriately built multilayered magnetoresistive sensor can be produced by applying modest currents to such a sensor using simpler Application-Specific Integrated Circuits (ASICs) consuming modest power consumption. 
     However, noise power spectral density (including the 1/f and Barkhausen noise components) of multilayered magnetoresistive (GMR or MTJ) sensors is higher than that of AMR sensors. For magnetic changes occurring at low frequencies, the 1/f noise dominates, thus the higher magnetoresistance ratios of multilayered magnetoresistive sensors do not translate into correspondingly higher signal-to-noise ratios. In order to translate the high magnetoresistance ratios of multilayered magnetoresistive sensors into a low minimum detectable field (mdf) or noise equivalent field resolution, it is necessary to improve the signal-to-noise (SN) ratio. At frequencies above the knee of a 1/f noise versus frequency plot, the signal-to-noise (SN) ratio increases. 
     Embodiments of systems and methods to improve the signal-to-noise ratio of multilayered magnetoresistive sensors and to measure in-plane magnetic field components of a magnetic field using a single multilayered magnetoresistive sensor are described. As defined herein, the “magnetic field components of a magnetic field in a plane” are the projection of the magnetic field onto the basis vectors spanning the plane (axes of the plane). For example, the magnetic field components of a magnetic field in an X-Y plane are the projections of the magnetic field onto the X axis and the Y axis. As defined herein, the “applied magnetic field in an X-Y plane” is the applied magnetic field projected onto the X-Y plane. The terms “X-Y plane”, “planar field”, and “selected plane” are used interchangeably herein. The in-plane magnetic field components of a magnetic field provide an orientation and magnitude of the magnetic field in the selected plane. Specifically, an X-component and a Y-projection of the magnetic field provide information indicative of the orientation and magnitude of the magnetic field in the selected plane. The sensor systems described herein take advantage of unique properties of magnetic tunnel junctions and/or giant magnetoresistors that enable low cost, and low power consumption with high resolution. The term multilayered magnetoresistive (MR) sensor as used herein applies to both magnetic tunnel junction sensors and giant magnetoresistor sensors that have magnetoresistance ratios greater than AMR sensors. 
     The magnetoresistive sensor systems described herein differ from prior art in that the orientation and magnitude of an in-plane applied magnetic field are measured using a single tunnel junction, which can be fabricated on wafer using the same annealing-in of the orthogonal PL/RL magnetization directions for all the tunnel junctions on the wafer. Thus, the tunnel junctions described herein do not need to create orthogonal directions of pinned layer/reference layer magnetizations as is done in the prior art. As defined herein, the “applied magnetic field” is a magnetic field that is incident on (applied to) the magnetoresistive sensor from a source external to the magnetoresistive sensor system. In the magnetoresistive sensor systems described herein, a periodically rotating magnetic drive field is generated in the free layer of the magnetoresistive sensor. The periodically rotating magnetic drive field is large enough to saturate the free layer but small enough that the synthetic antiferromagnet of the magnetoresistive sensor is generally unaffected. Thus, the free layer rotates with the period of the rotating magnetic drive field. 
     In the presence of additional external DC (or low frequency) field, the sensor output of the magnetoresistive sensor develops a second harmonic component that is detected using phase-sensitive detection techniques. The amplitude and phase angle of the second harmonic component are functions of the magnitude and orientation of the external field, respectively, thus allowing for determination of both components of the in-plane field. The detection circuitry can be either external to the sensor chip, or can be integrated on Silicon with the MTJ using complementary metal oxide semiconductor (CMOS) process. 
       FIG. 1A  is a block diagram of one embodiment of a multilayered MagnetoResistive (MR) sensor  10 , a first drive strap  71 , and a second drive strap  72  in accordance with the present invention. At least a portion  65  of the first drive strap  71  (also referred to herein as first strap  71 ) overlays the magnetoresistive sensor (MS)  10  to carry a first alternating drive current. The first drive strap  71  has a dimension extending in a first direction. As shown in  FIG. 1A , the first direction is parallel to the X axis. At least a portion  66  of the second drive strap  72  (also referred to herein as second strap  72 ) overlays the magnetoresistive sensor  10  and the portion  65  of the first drive strap  71  to carry a second alternating drive current. The second drive strap  72  has a dimension extending in a second direction, the second direction being perpendicular to the first direction. As shown in  FIG. 1A , the second direction is parallel to the Y axis. Thus, the second strap  72  overlays and is perpendicular to the first strap  71 . The second alternating drive current is ninety degrees out of phase with respect to the first alternating drive current so the magnetoresistive sensor  10  is subjected to a periodically rotating drive field rotating in the X-Y plane of the magnetoresistive sensor  10 . In one implementation of this embodiment, the first direction and the second direction are not orthogonal (are non-parallel) and, in this case, the second alternating drive current is out of phase with respect to the first alternating drive current by an amount that will generate a periodically rotating drive field in a selected plane. However, this non-orthogonal system requires additional computation and adds complexity to the system. 
     The multilayered MR sensor  10  includes an antiferromagnet (AFM)  20 , a synthetic antiferromagnet (SAF)  11 , a barrier layer  55 , and a free layer  60  stacked from bottom to top. The synthetic antiferromagnet  11  includes a ferromagnetic pinned layer  30 , a Ru layer  40 , and a reference layer  50  stacked from bottom to top. The “barrier layer  55 ” is also referred to herein as “barrier  55 ”. The barrier  55  is an oxide insulator barrier if the sensor  10  is a magnetic tunnel junction sensor. The barrier  55  is a conductive non-magnetic metal layer if the sensor  10  is a GMR sensor. 
     The reference layer magnetization  400  of the reference layer  50  in a properly designed AFM/SAF structure is “fixed”, i.e., an applied magnetic field (up to a high level, typically ˜kOe) does not significantly change the reference layer magnetization  400 . Thus, the reference layer  50  is a referred to as a hard layer. In the exemplary magnetoresistive sensor  10  shown in  FIG. 1A , the reference layer magnetization  400  of the reference layer  50  is parallel to the Y axis. 
     The reference layer  50  lies directly under the barrier  55 , which separates the reference layer  50  from a free layer  60 . The free layer is very soft so its magnetization can be driven into saturation with the application of modest drive fields. The periodically rotating drive field H rotating  and any applied magnetic field H applied    450  easily change the magnetization of the free layer  60 . Thus, the free layer  60  is referred to as a soft layer. 
     The magnetic susceptibility of the free layer  60  is a result of the net sum of all the magnetic interactions at the free layer  60 . This includes free layer&#39;s material and shape anisotropy as well as fields from the other layers comprising the Tunnel Junction. A free layer with a circular profile advantageously eliminates in-plane shape anisotropy, although ideas incorporated in this patent will work well with other geometries, e.g., square or rectangular. It is assumed here that with a combination of materials, processing, and geometric choices a very soft free layer is obtained. Such materials, processing and geometric choices are generally familiar to one skilled in the arts. 
     As shown in  FIG. 1A , the first alternating drive current i drive1 (f) generates a first magnetic drive field H drive1 (f) while the second alternating drive current i drive2 (f+Δφ) generates a second magnetic drive field H drive2 (f+Δφ), where Δφ is π/2 radians. The first alternating drive current i drive1 (f) can be written as I x (f)=I 1  sin(ωt) while the second alternating drive current i drive2 (f+Δφ) is written as I y (f)=I 2  cos(ωt). The effects of the first magnetic drive field H drive1 (f) and the second magnetic drive field H drive2 (f+Δφ) and the externally applied magnetic field H applied    450  on the free layer magnetization are described below with reference to  FIGS. 4 and 5 . The externally applied magnetic field H applied    450  is the field to be measured by the magnetic sensor  10 . The terms “applied magnetic field” and “magnetic field to be measured” are used interchangeably herein. The applied magnetic field H applied    450  can be a weak DC magnetic field or a weak magnetic field changing at low frequency that is much less than the drive frequency f. 
     The AFM  20  is typically made of an alloy such as NiMn, PtMn, IrMn or FeMn. Exchange bias is created on the pinned layer  30  by annealing SAF/AFM  11 / 20  in a field of the order of kOe at temperatures in the range of approximately 200° C.-350° C. for a few hours. This sets the direction of uncompensated spins in AFM  20  at the interface between AFM  20  and pinned layer  30  thus providing a bias field to the pinned layer  30 . The strong antiferromagnetic coupling between the pinned layer  30  and reference layer  50  sets the direction of reference layer magnetization  400  opposite to that of pinned layer magnetization  405 . The net magnetization of SAF  11  is tailored to be nearly zero. Thus, high applied fields of the order of several kOe are required to change the magnetization of pinned layer/reference layer pair  30 / 50 . 
     The resistance R of the magnetoresistive sensor  10  is a function of the angle between the reference layer magnetization  400  and the free layer magnetization according to the formula R(θ)=R 0 +ΔR(1−cos θ)/2, θ being the angle between the reference layer magnetization  400  and free layer magnetization. R 0  is the resistance of the magnetoresistive sensor  10  when the magnetizations of the two layers are parallel. Thus, when only the rotating magnetic drive field H rotating    440  (also referred to herein as magnetic drive field H D    440 ) large enough to saturate the free layer is applied to sensor  10 , the rotation of the free layer magnetization under the influence of this applied rotating drive field H rotating    440  produces a periodic magnetoresistance. 
       FIG. 1B  shows the magnetic drive field H D    440  periodically rotating at an angular frequency ω in the X-Y plane of the magnetoresistive sensor  10  of  FIG. 1A . As defined herein, a “periodically rotating drive field” is a magnetic drive field periodically rotating at an angular frequency ω indicated as H rotating =H D =H 0 e iωt , where H 0  is the magnitude of the magnetic drive field H D    440 . The tip of the vector H 0  traces a circle in the X-Y plane with each rotation. All angles are measured with respect to the X axis of the X-Y coordinate system of the plane. The reference layer magnetization  400  is at an angle φ R  with respect to the X axis. As shown in  FIG. 1B , the externally applied magnetic field H applied  to be measured is in the X-Y plane at an angle φ with respect to the X axis. 
       FIG. 2A  is a block diagram of one embodiment of a magnetic tunnel junction  14 , electrical contacts  27  and  28 , a first drive strap  71 , and a second drive strap  72  in accordance with the present invention. The magnetic tunnel junction (MTJ)  14  is a magnetoresistive sensor  10  as shown in  FIG. 1A . The barrier layer  55  shown in  FIG. 1A  is an oxide barrier layer  56  in the magnetic tunnel junction  14 . A non-magnetic cap layer  61  overlays the free layer (FL)  60  of the magnetic tunnel junction  14 . The electrical contact (bottom lead)  27  overlays an insulator  26  on a silicon (Si) substrate  25 . A non-magnetic seed layer  22  overlaying the electrical contact  27  is used to facilitate growth of the AFM layer  20 . The electrical contact (top lead)  28  overlays the cap layer  61 . An insulator layer  73  isolates the electrical contact  28  from the first drive strap  71 , which is covered by an insulator layer  70 . At least a portion of the second drive strap  72  overlays the insulator layer  70  and at least a portion of the first drive strap  71 . The electrical contacts  27  and  28  are configured to connect the magnetic tunnel junction  14  to a circuit to measure the magnetoresistance R(θ) of the magnetic tunnel junction  14 . As shown in  FIG. 2A , the current is directed from the bottom lead (electrical contact  27 ) to the top lead (electrical contact  28 ).  FIG. 3A  is a block diagram of one embodiment of a circuit  90  to measure output voltage V out  of the magnetic tunnel junction  14  of  FIG. 2A  in accordance with the present invention. 
       FIG. 2B  is a block diagram of one embodiment of a giant magnetoresistor  13 , electrical contacts  128  and  129 , a first drive strap  71 , and a second drive strap  72  in accordance with the present invention. The GMR  13  is a multilayered magnetoresistive sensor  10  as shown in  FIG. 1A . The barrier layer  55  shown in  FIG. 1A  is a non-magnetic conductive layer  57  (such as, a copper (Cu) layer  57 ) in the giant magnetoresistor  13 . The giant magnetoresistor  13  is operable in the current-in-plane (CIP) mode. A seed layer  22  overlaying insulator  26  is used to facilitate growth of the AFM layer  20 . A non-magnetic cap layer  61  overlays the free layer  60  of the giant magnetoresistor  13 . Two electrical contacts (lead  1  and  2 )  128  and  129  overlay opposing edge portions of the cap layer  60 . The electrical contacts  128  and  129  are separated from each other by the insulator layer  73 . The insulator layer  73  also isolates the electrical contacts  128  and  129  from the first drive strap  71 , which is covered by an insulator layer  70 . The second drive strap  72  overlays the insulator layer  70 . 
     The electrical contacts  128  and  129  are configured to connect the magnetoresistive sensor  10  to a circuit to measure the magnetoresistance of the giant magnetoresistor  13 . As shown in  FIG. 2B , the current is directed from lead  1  (electrical contact  128 ) to lead  2  (electrical contact  129 ).  FIG. 3B  is a block diagram of one embodiment of a circuit  91  to measure output voltage V out  of the giant magnetoresistor  13  of  FIG. 2B  in accordance with the present invention. In one implementation of this embodiment, the giant magnetoresistor  13  is configured to operate in current-perpendicular to plane (CPP) mode as is known to one skilled in the art. 
       FIGS. 4A and 4B  are block diagrams of embodiments of magnetoresistive sensor systems including the magnetoresistive sensor of  FIG. 1A  in accordance with the present invention. The magnetoresistive sensor system  4  shown in  FIG. 4A  includes the magnetoresistive sensor  10 , an amplifier  221 , the first drive strap  71 , the second drive strap  72 , a detection circuit  150 , a frequency generator  200 , a frequency divider  210 , and a generator  213  to generate two sinusoidal drive currents that are mutually π/2 radians out of phase. The magnetoresistive sensor  10  is shown as dashed box underlaying the first drive strap  71  and the second drive strap  72 . The magnetoresistive sensor  10  is either a magnetic tunnel junction or a giant magnetoresistor. 
     The detection circuit  150  includes a bandpass filter  220 , a phase sensitive detector  230 , a first low pass filter (LPF)  222 , and a second low pass filter (LPF)  223 . The periodic output voltage V out  is output from the magnetoresistive sensor  10  via amplifier  221  to the detection circuit  150 . The bandpass filter  220  outputs a sense voltage to the phase sensitive detector  230 . The phase sensitive detector  230  outputs information indicative of the amplitude and phase of the second harmonic component, or equivalently, X and Y-components of the second harmonic. Thus, the phase sensitive detector  230  has two outputs: an X-output (V x ) proportional to the X-component of the second harmonic; and a Y-output (V y ) proportional to the Y-component of the second harmonic. The X-output is passed through low pass filter (LPF)  222  to produce a DC signal proportional to the X-component of applied field H applied . The Y-output is passed through low pass filter (LPF)  223  to produce a DC signal proportional to the Y-component of applied field H applied . 
     As shown in  FIG. 1A , the magnetoresistive sensor  10  includes a ferromagnetic free layer  60  having a rotatable magnetization orientation, a ferromagnetic reference layer  50  having a pinned magnetization orientation (reference layer magnetization  400 ), and a barrier layer  55  there between. The first drive strap  71  overlaying the magnetoresistive sensor  10  is operably configured to carry an alternating drive current i drive1 (f), which alternates with a frequency f. The second drive strap  72  overlaying the magnetoresistive sensor  10  and orthogonally overlaying the first drive strap  71  is operably configured to carry an alternating drive current i drive2 (f+Δφ), which alternates with a frequency f. 
     As shown in  FIG. 4A , the frequency generator  200  generates a reference signal alternating at frequency  2   f  and outputs the signal to the frequency divider  210 . The frequency generator  200  also outputs the signal alternating at frequency  2   f  to the phase sensitive detector  230 . The frequency divider  210  divides the signal alternating at frequency  2   f  in half. 
     The generator  213  at the output of the frequency divider  210  provides the two drive currents to respective drive straps  71  and  72  that are π/2 radians out of phase with respect to each other. Specifically, generator  213  outputs the first alternating drive current i drive1 (f) at the frequency f to the first drive strap  71  and a second drive current i drive2 (f) to the second drive strap  72  that is π/2 radians out of phase with respect to i drive1 (f). There are other techniques that can be used to apply mutually orthogonal alternating drive currents at the frequency f to the first drive strap  71  and the second drive strap  72 , as is understandable to one skilled in the art. In one implementation of this embodiment, non-orthogonal and non-parallel first and second straps overlay the magnetoresistive sensor. In this case, the first alternating drive current and the second alternating drive current applied to the respective first and second straps are driven with appropriately phase separated periodic drive signals as is understandable to one skilled in the art upon reading and understanding this document. 
     In one implementation of this embodiment, the generator  213  simultaneously supplies the signal i x (f)=i 1  sin(ωt) as the first alternating drive current to the first drive strap  71  and the signal i y (f)=i 2  cos(ωt) as the second alternating drive current to the second drive strap  72 . In some embodiments, i 1 =i 2 . The leads to connect the magnetoresistive sensor  10  to a circuit (such as circuit  90  or  91  as shown in  FIGS. 3A and 3B , respectively) are not shown in  FIG. 4A  for ease of viewing the fields in the magnetoresistive sensor  10 . 
     The first drive current i drive1 (f), which is shown in  FIG. 1A  as the double arrow labeled  431  in the first drive strap  71 , generates a first magnetic drive field H drive1 (f), which is shown in  FIG. 1A  as the circular-double arrow labeled  433 . The second drive current i drive2 (f+Δφ), which is shown in  FIG. 1A  as the double arrow labeled  432  in the second drive strap  72 , generates a second magnetic drive field H drive2 (f+Δφ), which is shown in  FIG. 1A  as the circular-double arrow labeled  434 . The first magnetic drive field H drive1 (f)  433  and the second magnetic drive field H drive2 (f+Δφ)  434  both extend into the free layer  60  and are superimposed on each other to form a periodically rotating drive field H rotating , which is rotating in the X-Y plane as shown by the circular arrow labeled  440  in  FIGS. 1A and 4A . The “periodically rotating drive field  440 ” is also referred to herein as a “periodically rotating magnetic drive field  440 ”. 
     As shown in  FIGS. 1A ,  4 A, and  4 B, the periodically rotating drive field H rotating    440  rotates counter-clockwise (CCW) as viewed in the negative Z direction, the free layer magnetization is periodically rotated to be parallel to the rotating magnetic field in the free layer  60 . In one implementation of this embodiment, the phase delay Δφ is added to the current applied to the first drive strap  71  instead of the second drive strap  72 . In this case, the periodically rotating drive field H rotating    440  rotates clockwise (CW) as viewed in the negative Z direction. 
     The periodically rotating drive field H rotating    440  shifts the operating point of the magnetoresistive sensor  10  beyond the knee of the 1/f noise power spectral density curve to take advantage of the high ΔR/R of the MTJ or GMR. Thus, the periodically rotating drive field H rotating    440  advantageously permits the magnetoresistive sensor system  4  to achieve high signal-to-noise ratio, or conversely, to lower the minimum detectable field (mdf). As defined herein, the operating point of the magnetoresistive sensor is that point on the noise versus frequency function of the magnetoresistive sensor  10  at which the magnetoresistive sensor  10  is driven to operate by the periodically rotating drive field H rotating    440 . 
     The magnetoresistive sensor  10  (a magnetic tunnel junction  14  or a giant magnetoresistor  13 ) provides a transfer function between free layer&#39;s magnetic induction and resistance, so that voltage measurements can be made in the detection circuit  150 . 
     Specifically, within a range of the first drive current i drive1 (f)  431  and the second drive current i drive2 (f+Δφ)  432  (with amplitude that is sufficiently high to saturate the free layer  60 , but low enough that the reference layer  50  is substantially unaffected) the free layer magnetization  421  periodically rotates through 360 degrees (2π radians) to create a periodic resistance change in the magnetoresistive sensor  10 . As shown in the top view of the magnetic sensor  10  in  FIG. 4A , the free layer magnetization  421 ′ at a first time t 1  is at the angle θ 1  from the reference layer magnetization  400  and at a time t 2 , the free layer magnetization  421 ″ is at the angle θ 2  from the reference layer magnetization  400 . When only a periodic drive current is applied to the magnetoresistive sensor  10 , and no DC (or low frequency) magnetic field H applied    450  is present, the ideal output of the magnetoresistive sensor  10  includes only odd harmonic multiples of frequency f. 
     In general, the dynamics of magnetization of the free layer  60  (the free layer magnetization  421 ) depends on the size, aspect ratio, and other material properties (grain size, defect density, 4πM s ) of the free layer  60  and the magnetoresistive sensor  10 . For larger magnetoresistive sensors  10  (dimensions&gt;˜1 μm) the dynamics of magnetization during switching from one state of saturation to the opposite state of saturation involves domain wall dynamics. Domain wall mediated switching generally involves Barkhausen jumps that are the source of Barkhausen noise. For magnetoresistive sensors  10  that have dimensions smaller than ˜1 μm, the free layer  60  generally switches from one state of saturation to the opposite state of saturation by nucleation and the propagation of magnetic vortices. The size dependence described above is not exact and the transition from domain wall mediated dynamics to vortex mediated dynamics is also a function of other material parameters of the ferromagnetic material comprising the sensor. These dynamics also apply to any large changes in the state of magnetization and are not limited to switching from one state of saturation to another state of saturation. 
     When the magnetization of free layer  60  is coherently rotated by the periodically rotating magnetic drive field H rotating    440 , Barkhausen noise is reduced. Thus, coherent rotation of the free layer magnetization  421  is ensured by maintaining the periodically rotating magnetic drive field H rotating    440 . The magnitude of the periodically rotating magnetic drive field H rotating    440  is determined empirically by examining the quality of the output waveform of the magnetoresistive sensor  10 . Since the magnetoresistive sensors  10  have small dimensions, the first drive strap  71  and the second drive strap  72  are operable to produce the periodically rotating magnetic drive field H rotating    440  at modest values of current and power. 
     When an external magnetic field to be measured H applied    450  is applied to the magnetoresistive sensor  10 , the magnetic field to be measured H applied    450  is superimposed on the periodically rotating magnetic drive field H rotating    440  in the X-Y plane of the magnetoresistive sensor  10 . In this case, the magnetic field in the free layer  60  equals the superposition of the periodically rotating drive field H rotating    440  and the externally applied magnetic field  450 . The output of magnetoresistive sensor  10  resultant from this superposition includes even harmonic components. The lowest order even harmonic is the second harmonic component at frequency  2   f.    
     The detection circuit  150  extracts the second harmonic component of the output voltage V out  of the magnetoresistive sensor  10 . The magnitude of the magnetic field to be measured H applied    450  in the X-Y plane (|H applied | in the exemplary case shown in  FIG. 1B ) is proportional to an amplitude of the extracted second harmonic component of the output voltage V out . The orientation (angle φ in the exemplary case shown in  FIG. 1B ) of the magnetic field to be measured H applied    450  in the X-Y plane is simply related to a phase angle of the extracted second harmonic component of the output voltage V out . 
     This mathematical relationship between the applied field H applied    450  and the amplitude and the phase angle of the second harmonic is now derived. Initially assume that the external field h is zero (e.g., h=H applied =0). A rotating drive field H D  (e.g., H D =H rotating ) is applied at a frequency f in the plane of the sensor. The amplitude of the drive field is such that it does not affect the reference layer. It is also assumed that that anisotropy of the free layer  60  is sufficiently small and the drive field H D  sufficiently large that the drive field H D  saturates the free layer magnetization (shown as  421 ′ and  421 ″ in  FIGS. 4A and 4B ), i.e., the free layer magnetization always points in the instantaneous direction of the rotating drive field H D . 
     The drive field is given by H D =H 0  exp(iωt), where ω=2πf. With the assumption of saturation described above, the magnetoresistance (MR) is also sinusoidal at the frequency f. Next, in the presence of a sinusoidal drive field and an external field h, the free layer magnetization now points in the direction of the total field vector H D (ω)+h. A unit vector in the direction of free layer magnetization, using the complex number notation, is given by 
     
       
         
           
             
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                         cos 
                         ⁡ 
                         
                           ( 
                           
                             
                               ω 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               t 
                             
                             - 
                             ϕ 
                           
                           ) 
                         
                       
                     
                   
                 
               
             
           
         
       
     
     The unit vector k R  parallel to reference layer magnetization is given by
 
 k   R   =e   iφ     R   .
 
     The unit vector parallel to the free layer magnetization is k M . The angle between the free layer magnetization (i.e., instantaneous free layer magnetization  421 ′ or  421 ″) and reference layer magnetization (i.e., reference layer magnetization  400 ) is given by
 
cos θ= Re ( k   M   ·k   R *),
 
     where k R * is the complex conjugate of k R . The time dependence of magnetoresistance is given by the time dependence of cos θ. 
     
       
         
           
             
               MR 
               = 
               
                 
                   - 
                   
                     1 
                     2 
                   
                 
                 ⁢ 
                 
                   ( 
                   
                     
                       Δ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       R 
                     
                     R 
                   
                   ) 
                 
                 ⁢ 
                 
                   ( 
                   
                     
                       
                         cos 
                         ⁡ 
                         
                           ( 
                           
                             
                               ω 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               t 
                             
                             - 
                             
                               ϕ 
                               R 
                             
                           
                           ) 
                         
                       
                       + 
                       
                         u 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           cos 
                           ⁡ 
                           
                             ( 
                             
                               ϕ 
                               - 
                               
                                 ϕ 
                                 R 
                               
                             
                             ) 
                           
                         
                       
                     
                     
                       
                         1 
                         + 
                         
                           2 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           u 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             cos 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   ω 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   t 
                                 
                                 - 
                                 ϕ 
                               
                               ) 
                             
                           
                         
                         + 
                         
                           u 
                           2 
                         
                       
                     
                   
                   ) 
                 
               
             
             , 
           
         
       
     
     where u=h/H 0 . Expanding the above expression in linear power of u, one obtains, 
     
       
         
           
             MR 
             = 
             
               
                 - 
                 
                   1 
                   2 
                 
               
               ⁢ 
               
                 ( 
                 
                   
                     Δ 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     R 
                   
                   R 
                 
                 ) 
               
               ⁢ 
               
                 
                   ( 
                   
                     
                       cos 
                       ⁡ 
                       
                         ( 
                         
                           
                             ω 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             t 
                           
                           - 
                           
                             ϕ 
                             R 
                           
                         
                         ) 
                       
                     
                     - 
                     
                       
                         u 
                         2 
                       
                       ⁢ 
                       
                         cos 
                         ⁡ 
                         
                           ( 
                           
                             
                               2 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               ω 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               t 
                             
                             - 
                             
                               ( 
                               
                                 ϕ 
                                 + 
                                 
                                   ϕ 
                                   R 
                                 
                               
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                   ) 
                 
                 . 
               
             
           
         
       
     
     Within the linear approximation in powers of (h/H 0 ), the amplitude of the second harmonic is proportional to the applied field h, and the phase of the second harmonic equals (φ+φ R ). Since the reference layer phase angle φR is known, one can deduce the phase angle of the applied field. Thus, in the proposed mode of operation, the second harmonic component provides both the amplitude and direction of the applied field. 
     This analysis ignored the effects of free layer anisotropy H k . With a nonzero anisotropy of the free layer, the magnetization direction will not point parallel to the instantaneous direction of the field. However, for sufficiently large amplitude of the drive field (H 0 &gt;&gt;H k ), it is expected that the anisotropy adds a correction term to the formula derived above. The overall scheme described herein still works. 
     This amplitude and phase can be converted into orthogonal components (e.g., X-component and Y-component) as is known to one skilled in the art. For a range of values of H applied , such that H applied &lt;H 0 , where H 0  is the amplitude of the periodic drive field, the amplitude of the output voltage V out  is proportional to H applied . 
     When a periodically rotating drive field H rotating    440  rotating at an angular frequency ω is applied in the plane of the sensor (e.g., the X-Y plane), the free layer magnetization points in the instantaneous direction of the periodically rotating drive field H rotating    440 . The instantaneous direction of the periodically rotating drive field H rotating    440  does not affect the reference layer  50 . Since the anisotropy of the free layer  60  is sufficiently small and the drive field sufficiently large (i.e., H 0 &gt;&gt;H k ), the drive field saturates the free layer magnetization. 
     By driving the magnetoresistive sensor  10  at a frequency f that is past the knee of the 1/f noise curve, the signal-to-noise ratio of the magnetoresistive sensor  10  is higher than the signal-to-noise ratio of the magnetoresistive sensor in operation near zero frequency. The periodically rotating drive field H rotating    440  at an angular frequency ω=2πf is set so that f=ω/2π is greater than the knee of the 1/f noise curve. 
     The frequency generator  200  outputs a spectrally pure driving waveform without any second harmonic components. If there are even harmonic components present in the first drive current i drive1 (f) and/or the second the drive current i drive2 (f+Δφ)  432 , the output V out  will have even harmonic components even in the absence of an applied field (i.e., a null offset). If a spectrally pure driving waveform is not produced by the frequency generator  200 , the null offset at the output of the detection circuitry can be calibrated out by the user. 
     The magnetoresistive sensor system  5  shown in  FIG. 4B  includes the components of the magnetoresistive sensor system  4  of  FIG. 4A  as well as a feedback circuit  160 . In this magnetoresistive sensor system  5 , the first drive strap  71  and the second drive strap  721  are used to operate the magnetoresistive sensor  10  in a closed loop mode. 
     The feedback circuit  160  includes an X-component amplifier  233 , an X-component integrator  237 , a Y-component amplifier  234 , and a Y-component integrator  238 . The X-output (V x ) proportional to the X-component of the amplitude of the second harmonic that is output as signal  330  from the low pass filter  222 . The signal  330  is input to the X-component amplifier  233 . The output from the X-component amplifier  233  is input to the integrator  237 . Simultaneously, the Y-output (V y ) proportional to the Y-component of the second harmonic is output as signal  331  from the low pass filter  223 . The signal  331  is input to the Y-component amplifier  234 . The output from the Y-component amplifier  234  is input to the integrator  238 . Signal  330  is proportional to the X-component of H applied    450  and signal  331  is proportional to Y-component of H applied    450 . 
     The feedback circuit  160  takes input signals  330  and  331  from the detection circuit  150  and outputs the first nulling current I nulling1    415  to the first drive strap  71  and outputs the second nulling current I nulling2    416  to the second drive strap  72 . The first drive strap  71  and second drive strap  72  are both overlaying the magnetoresistive sensor  10  in order to generate a first nulling magnetic field H null1    425  and a second nulling magnetic field H null2    426  opposing the Y and X-components, respectively, of the magnetic field being detected (H applied )  450 . 
     The first nulling current I nulling    415  can be measured by measuring the voltage drop V 1  across a first stable series resistor R 1 . The first nulling current  415  or the corresponding voltage drop V 1  across the series resistor R 1  is proportional to the Y-component of the applied magnetic field H applied    450 . The resistor R 1  is a fixed, temperature stable resistor. 
     The second nulling current I nulling2    416  can be measured by measuring the voltage drop V 2  across a second stable series resistor R 2 . The second nulling current I nulling2    416  or the corresponding voltage drop V 2  across the series resistor R 2  is proportional to the X-component of the applied magnetic field H applied    450 . The resistor R 2  is a fixed, temperature stable resistor. 
     Thus, the X and Y-components of the second harmonic signal  330  and  331 , respectively, are amplified, integrated, and used as feedback current (i.e., second nulling current I nulling2    416  and first nulling current I nulling    415 ) to buck the X and Y-components of the external applied magnetic field H applied    450 . It is assumed that the time scales of the applied magnetic field H applied    450  and that of periodically rotating drive field H rotating    440  are well separated, i.e., applied magnetic field H applied    450  is of low frequency or near DC. 
     In this manner, the only excursions of magnetization of the free layer  60  are those caused by periodically rotating magnetic drive field H drive (f)  440 . There is no DC shift in the magnetization states of the free layer  60  as the magnetoresistive sensor  10  senses a range of applied fields, since any applied magnetic field H applied    450  in the X-Y plane is nulled by the superposition of the first nulling magnetic field H null1    425  and the second nulling magnetic field H null2    426 . This feedback reduces Barkhausen noise so that the signal-to-noise ratio of the magnetoresistive sensor  10  is further improved, and also increases the field dynamic range of the magnetoresistive sensor  10 . 
     As shown in  FIGS. 4A and 4B , the magnetoresistive sensor  10  has a rectangular profile in the X-Y plane. In another implementation of this embodiment, the magnetoresistive sensor has a circular profile in the X-Y plane. 
       FIGS. 5A and 5B  show simulated output for different applied magnetic fields applied to an exemplary magnetoresistive sensor in accordance with the present invention. A rotating drive field H 0 =10 Oe at a period of 32 time units in the plots of  FIGS. 5A and 5B  is implicit and is not shown. 
       FIG. 5A  shows the simulated output for H applied  equal to 2 Oe. The waveform  495  is a plot of V out  when H applied =0 Oe. The waveform  494  is a plot of V out  when H applied =2 Oe with a phase angle φ=45 degrees ( FIG. 1B ). The waveform  493  is a plot of V out  when H applied =2 Oe with a phase angle φ=120 degrees ( FIG. 1B ). The difference waveform  490  plots the difference between waveform  494  and waveform  495 . The difference waveform  491  plots the difference between waveform  493  and waveform  495 . The difference waveforms  490  and  491  contain only even harmonics, the leading Fourier component being the second harmonic. 
       FIG. 5B  shows the simulated output for H applied  equal to 4 Oe. The waveform  465  is a plot of V out  when H applied =0 Oe. The waveform  464  is a plot of V out  when H applied =4 Oe with a phase angle φ=45 degrees ( FIG. 1B ). The waveform  463  is a plot of V out  when H applied =4 Oe with a phase angle φ=120 degrees ( FIG. 1B ). The difference waveform  460  plots the difference between waveform  464  and waveform  465 . The difference waveform  461  plots the difference between waveform  463  and waveform  465 . The difference waveforms  460  and  461  contain only even harmonics, the leading Fourier component being the second harmonic. Thus,  FIGS. 5A and 5B  clearly show how the output difference waveform changes based on the amplitude and phase angle of H applied . 
       FIG. 6  is block diagram of an embodiment of a magnetoresistive sensor system  6  including a magnetoresistive sensor  11  in accordance with the present invention. As shown in  FIG. 6 , the magnetoresistive sensor  11  has a circular profile in the X-Y plane. In another implementation of this embodiment, the magnetoresistive sensor is rectangular in shape. The function of the magnetoresistive sensor system  6  is the same as the function of the magnetoresistive sensor systems  4  and  5  described above with reference to  FIGS. 4A and 4B . The magnetoresistive sensor system  6  includes a magnetoresistive sensor  11 , a first drive strap  71 , second drive strap  72 , which overlays the first drive strap  71  and the magnetoresistive sensor  11 . The magnetoresistive sensor system  6  also includes a frequency generator  200 , and a detection circuit  151 . The structure of the magnetoresistive sensor system  6  differs from the magnetoresistive sensor systems  4  and  5  of  FIGS. 4A and 4B  in that the detection circuit  151  includes a digital processor  250  rather than the band pass filter  220 , the phase sensitive detector  230  and the low pass filter  222  of the detection circuit  150 . 
     The digital processor  250  receives an output voltage V out  from the magnetoresistive sensor  11 , extracts a second harmonic component of the output voltage V out  and outputs two signals: an X-output (V x ) proportional to the X-component of the amplitude of the second harmonic; and a Y-output (V y ) proportional to the Y-component of the second harmonic. Thus, the function of the digital processor  250  is the same as the function of the detection circuit  150  ( FIGS. 4A and 4B ). 
       FIG. 7  shows embodiments of tailored shapes of drive currents. By tailoring the shapes of the first and second alternating drive currents applied to the first and second drive straps  71  and  72 , respectively, the amplitude of the extracted second harmonic component is increased as is known to one skilled in the art. 
     Two exemplary sets  651  and  652  of first and second alternating drive currents are shown in  FIG. 7 . For ease of viewing, the first set  651  of alternating drive currents  701  and  702  is offset from the second set  652  of alternating drive currents  751  and  752 . 
     The first set  651  of first and second alternating drive currents includes a first alternating drive current  701 , which has a first saw-tooth shape over time and a second alternating drive current  702 , which has a second saw-tooth shape over time. The first alternating drive current  701  is shown superimposed on the second alternating drive current  702 . The π/2 (90 degree) phase shift is indicated between the peak of first alternating drive current  701  and the peak of the second alternating drive current  702 . The exemplary first alternating drive current  701  is applied to the first strap  71 . The exemplary second alternating drive current  702  is applied to the second strap  71 . 
     The second set  652  of first and second alternating drive currents includes a first alternating drive current  751 , which has a first saw-tooth shape over time and a second alternating drive current  752 , which has a sinusoidal shape over time. The first alternating drive current  751  is shown superimposed on the second alternating drive current  752 . The π/2 (90 degree) phase shift is indicated between the peak of first alternating drive current  751  and the peak of the second alternating drive current  752 . The exemplary first alternating drive current  751  is applied to the first strap  71 . The exemplary second alternating drive current  752  is applied to the second strap  71 . As is understood, these are exemplary shapes and other shapes of the current versus time can be used. 
       FIG. 8  is a flow diagram of one embodiment of a method  800  to measure an applied magnetic field H applied  in a plane in accordance with the present invention. The method  800  is applicable to the embodiments of magnetoresistive sensor systems  4 ,  5 , and  6  described above with reference to  FIGS. 4A ,  4 B, and  6 , respectively. 
     At block  802 , a first alternating drive current i drive1 (f)  431  is applied to a first strap  71  overlaying a magnetoresistive sensor (MS)  10 . A first alternating magnetic drive field H drive1 (f)  433  is generated in the magnetoresistive sensor  10  by the alternating drive current i drive1 (f). As shown in  FIG. 4A , the first alternating magnetic drive field H drive1 (f)  433  oscillates parallel to the Y axis, which lies in the X-Y plane of the magnetoresistive sensor (MS). 
     The first alternating drive current i drive1 (f)  431  shifts the operating point of the magnetoresistive sensor  10  to a low noise region. The low noise region is above the knee in the 1/f noise spectrum. In one implementation of this embodiment, the first alternating drive current i drive1 (f)  431  is applied to a first drive strap  71  overlaying a magnetic tunnel junction  14  ( FIG. 2A ) to shift the operating point of the magnetic tunnel junction  14  to the low noise region. In another implementation of this embodiment, the first alternating drive current i drive1 (f)  431  is applied to the first drive strap  71  overlaying a giant magnetoresistor  13  ( FIG. 2B ) to shift the operating point of the giant magnetoresistor  13  to the low noise region. 
     In one implementation of this embodiment, the alternating drive current i drive1 (f)  431  is applied to a first drive strap  71  as follows: a signal at an initial frequency  2   f  is output from a frequency generator  200  to a frequency divider  210 ; the signal at the initial frequency  2   f  is frequency divided in half to generate the signal at a drive frequency f; and the signal at the drive frequency f is, in turn, used to generate an input to the first drive strap  71  at a generator  213 . The first alternating drive current i drive1 (f)  431  is alternating at the drive frequency f. The drive frequency f is half of the initial frequency  2   f.    
     At block  804 , a second alternating drive current i drive2 (f+Δφ)  432  is applied to a second drive strap  72  overlaying a magnetoresistive sensor (MS)  10  simultaneously with the first alternating drive current i drive1 (f) being applied to a first drive strap  71 . The second drive strap  72  is orientated at an angle (i.e., non-parallel) with the first drive strap  71 . In one implementation of this embodiment, the second drive strap  72  is orientated perpendicular to the first drive strap  71 . Specifically, the first drive strap  71  has a dimension extending in a first direction and the second drive strap  72  has a dimension extending in a second direction, the second direction being perpendicular to the first direction. The first alternating drive current i drive1 (f)  431  is applied to flow in the first direction, while the second alternating drive current i drive2 (f+Δφ)  432  is simultaneously applied to flow in the second direction. 
     A second alternating magnetic drive field H drive2 (f+Δφ) is generated in the magnetoresistive sensor  10  by the alternating drive current i drive2 (f+Δφ)  432 . 
     If the second drive strap  72  is orientated at some angle other than 0 degrees and 90 degrees to the first drive strap  71 , then Δφ is set as appropriate to generate to a periodically rotating magnetic drive field rotating in the plane in the magnetoresistive sensor  10  or  11 . If the second drive strap  72  is orientated perpendicular to the first drive strap  71 , Δφ is set equal to π/2 radians. As shown in  FIG. 4A , the second alternating magnetic drive field H drive2 (f) oscillates parallel to the X axis, which lies in the X-Y plane of the magnetoresistive sensor (MS). 
     The second alternating drive current i drive2 (f+Δφ)  432  shifts the operating point of the magnetoresistive sensor  10  to a low noise region. In one implementation of this embodiment, the second alternating drive current i drive2 (f+Δφ)  432  is applied to the second drive strap  72  overlaying a magnetic tunnel junction  14  ( FIG. 2A ) to shift the operating point of the magnetic tunnel junction  14  to the low noise region. In another implementation of this embodiment, the second alternating drive current i drive2 (f+Δφ)  432  is applied to the second drive strap  72  overlaying a giant magnetoresistor  13  ( FIG. 2B ) to shift the operating point of the giant magnetoresistor  13  to the low noise region. 
     The second alternating drive current i drive2 (f+Δφ)  432  is applied to a second drive strap  72  as follows: the signal at an initial frequency  2   f  is output from a frequency generator  200  to a frequency divider  210 ; the signal at the initial frequency  2   f  is frequency divided in half to generate the signal at a drive frequency f; and the signal at the drive frequency f is, in turn, used to generate an input to the first drive strap  71  at a generator  213 . Specifically, the second signal applied to the second drive strap  72  at the drive frequency f is phase delayed (or advanced) by Δφ from the current applied to the first strap  71  at the generator  213 . The second alternating drive current i drive2 (f+Δφ)  432  is alternating at the drive frequency f. 
     As is shown in  FIG. 1B , the periodically rotating drive field H D =H 0 e iwt , numerically labeled as  440 , which rotates in the X-Y plane of the magnetoresistive sensor  10 , is generated by the superposition of the first alternating magnetic drive field H drive1 (f)  433  ( FIGS. 1A and 4A ) with the second alternating magnetic drive field H drive2 (f+Δφ)  434  ( FIGS. 1A and 4A ). Specifically, the first alternating magnetic drive field H drive1 (f)  433  oscillating along the Y axis and the second alternating magnetic drive field H drive2 (f+Δφ)  434  simultaneously oscillating along the X axis generates the periodically rotating drive field H rotating    440 , which is shown as rotating in counter-clockwise direction around the Z axis. 
     At block  806 , a second harmonic component of an output of the magnetoresistive sensor  10  is extracted from the magnetoresistive (MR) sensor  10 . The second harmonic component is only generated when a magnetic field to be measured H applied    450  is superimposed on the periodically rotating magnetic drive field H rotating    440  that is rotating in the X-Y plane of the free layer  60  of the magnetoresistive sensor  10 . 
     In one implementation of this embodiment, the second harmonic component of the output of the magnetoresistive sensor  11  ( FIG. 6 ) is extracted as follows: an output voltage V out  is output from the magnetoresistive sensor  11  to a digital processor  250 ; the output voltage is Fourier decomposed at the digital processor  250 ; a reference signal  460  at the initial frequency is input to the digital processor  250  from the frequency generator  200 ; and the second harmonic component of the Fourier decomposed output voltage at the initial frequency ( 2   f ) is extracted. The magnetoresistive sensor system  6  shown in  FIG. 6  is configured to extract the second harmonic component of the output of the magnetoresistive sensor  11  in this manner 
     In another implementation of this embodiment, the second harmonic component of the output of the magnetoresistive sensor  10  is extracted as follows: an output voltage from the magnetoresistive sensor is filtered at a band pass filter  220 ; an output (sense voltage) of the band pass filter  220  is input to a phase sensitive detector  230 ; a reference signal at the initial frequency  2   f  is input to the phase sensitive detector  230  from the frequency generator  200 ; and the second harmonic component of the filtered output voltage is extracted at the phase sensitive detector  230 . The magnetoresistive sensor systems  4  and  5  shown in  FIGS. 4A and 4B  are configured to extract the second harmonic component of the output of the magnetoresistive sensor  10  in this manner. 
     At block  808 , a signal indicative of the X-projection of the extracted second harmonic component of the output voltage V out  is output from the detection circuit. The X-component of the magnetic field to be measured H applied    450  in the X-Y plane of the free layer  60  is proportional to the X-projection of the extracted second harmonic component of the output voltage V out . 
     In one implementation of this embodiment, X-projection of the extracted second harmonic component of the output voltage V out  is output from the phase sensitive detector  230  as shown in  FIGS. 4A and 4B . In another implementation of this embodiment, the X-projection of the extracted second harmonic component of the output voltage V out  is output from the digital processor  250  as shown in  FIG. 6 . 
     At block  810 , a signal indicative of Y-projection of the extracted second harmonic component of the output voltage V out  is output from the detection circuit. The Y-component of the magnetic field to be measured H applied    450  in the X-Y plane of the free layer  60  is proportional to the Y-projection of the extracted second harmonic component of the output voltage V out . 
     In one implementation of this embodiment, a Y-projection of the extracted second harmonic component of the output voltage V out  is output from the phase sensitive detector  230  as shown in  FIGS. 4A and 4B . In one implementation of this embodiment, the signal indicative of the Y-projection of the extracted second harmonic component of the output voltage V out  is output from the digital processor  250  as shown in  FIG. 6 . 
     It is to be understood that the signal output from the detection circuit  150  during blocks  808  and  810  can be: a first signal that includes the information indicative of the projection of the extracted second harmonic component for a first direction of the plane; and a second signal that includes the information indicative of the projection of the extracted second harmonic component for a second direction of the plane, where the second direction is orthogonal to the first direction, and wherein the phase angle information was used to provide the correct projection in each direction. 
     Block  812  is optional. At block  812 , a first nulling current I nulling1    415  is applied to the first drive strap  71  to generate a first nulling magnetic field H null1    425  in the magnetoresistive sensor  10  and a second nulling current I nulling2    416  is applied to the second drive strap  72  to generate a second nulling magnetic field H null2    426  in the magnetoresistive sensor  10  (see  FIG. 4B ). The first nulling magnetic field H null1    425  is parallel to and opposing a first component (e.g., the Y-component) of the magnetic field to be measured H applied    450 . The second nulling magnetic field H null2    426  is parallel to and opposing a second component (e.g., the X-component) of the magnetic field to be measured H applied    450 . The first and second nulling magnetic fields H null(1-2)    425  and  426  together reduce Barkhausen noise and increase the dynamic range of the sensor. 
     In one implementation of this embodiment, first and second nulling currents  415  and  416  are applied to the first and second respective first drive straps  71  and  72  to generate the respective first and second nulling magnetic fields  425  and  426  in the magnetoresistive sensor  10  as follows: the second harmonic signal at the initial frequency is projected onto X and Y-components by amplifiers  233  and  234 , respectively; the amplified second harmonic signals  330  and  331  are integrated to generate the second nulling current I nulling2    416  and the first nulling current I nulling1    415  that are respectively proportional to components (e.g., X and Y-components) of the extracted second harmonic components. Specifically, the first nulling current I nulling1    415  is input from the integrator  238  to the first drive strap  71 ; the second nulling current I nulling2    416  is input from the integrator  237  to the second drive strap  72 . In this manner, the first and second nulling magnetic fields  425  and  426  that are opposing the magnetic field to be measured H applied    450  are generated in the magnetoresistive sensor  10 . Block  814  is optional and occurs only if block  812  is implemented. At block  814 , voltages V 2  and V 1  are measured across fixed, temperature stable resistors R 2  and R 1 , through which the respective second and first nulling currents pass to determine the respective X and Y-components of the applied field. 
     A number of embodiments of the invention defined by the following claims have been described. Nevertheless, it will be understood that various modifications to the described embodiments may be made without departing from the spirit and scope of the claimed invention. Accordingly, other embodiments are within the scope of the following claims.