Patent Publication Number: US-11022661-B2

Title: Magnetoresistance element with increased operational range

Description:
RELATED APPLICATIONS 
     This application is a CONTINUATION-IN-PART application under 37 C.F.R. § 1.53(b)(2) and claims the benefit of and priority to U.S. patent application Ser. No. 15/600,186 (filed May 19, 2017), which is incorporated here by reference in its entirety. 
    
    
     BACKGROUND 
     As is known in the art, magnetic field sensing elements can be used in a variety of applications. In one example application, a magnetic field sensing element can be used to detect motion (e.g., rotation) of an object, such as a gear or ring magnet. A magnetic field affected by motion of the object may be detected by one or more magnetic field sensing elements, such as Hall effect elements and/or magnetoresistance elements, which provide a signal (i.e., a magnetic field signal) in response to an applied magnetic field. Motion of the object may, for example, result in variations in a distance between a perimeter of the object (or target features of the object) and the magnetic field sensing elements, which may result in variations in the applied magnetic field to which the magnetic field sensing elements are exposed, and in the magnetic field signals provided by the magnetic field sensing elements in response to the applied magnetic field. Such magnetic field signals can be processed to detect position, proximity, speed and/or direction of motion of the object, for example. 
     Various parameters characterize the performance of magnetic field sensing elements and circuits or sensors that use magnetic field sensing elements. With regard to magnetic field sensing elements, the parameters include sensitivity, which corresponds to a change in a resistance of a magnetoresistance element or a change in an output voltage from a Hall effect element, for example, in response to an applied magnetic field (e.g., a magnetic field as may be affected by motion of a ferromagnetic object). Additionally, with regard to magnetic field sensing elements, the parameters include linearity, which corresponds to a degree to which the resistance of the magnetoresistance element or the output voltage from the Hall effect element varies linearly (i.e., in direct proportion) to the applied magnetic field. 
     Magnetoresistance elements are known to have a relatively high sensitivity compared, for example, to Hall effect elements. Magnetoresistance elements are also known to have moderately good linearity, but over a restricted or limited range of magnetic fields, more restricted in range than a range over which Hall effect elements can operate. It is known that in the restricted range of magnetic fields (i.e., in a so-called “linear region” or “linear range” of a magnetoresistance element), the resistance of a magnetoresistance element is typically indicative of an applied magnetic field to which the magnetoresistance element is exposed. It is also known that outside the restricted range of magnetic fields (i.e., in so-called “saturation regions”), the resistance of a magnetoresistance element is typically not indicative of the applied magnetic field. As a result of the foregoing, an operational range of a magnetoresistance element (i.e., a range in which the magnetoresistance element has a resistance that is indicative of an applied magnetic field) is typically limited to the restricted range of magnetic fields (i.e., the linear range of the magnetoresistance element). Additionally, an operational range of a circuit or sensor (e.g., a magnetic field sensor) using the magnetoresistance element (i.e., a range in which the circuit or sensor using the magnetoresistance element is capable of generating a signal indicative of the applied magnetic field) may be limited to the operational range of the magnetoresistance element. 
     For at least the above reasons, the fundamental usage for conventional magnetoresistance elements, and circuits or sensors using conventional magnetoresistance elements, has typically been limited to applications in which sensing is needed over a restricted range of magnetic fields (e.g., low strength magnetic fields) and the relatively high sensitivity characteristics of magnetoresistance elements are desired. 
     SUMMARY 
     In an embodiment, a magnetoresistance element deposited upon a substrate comprises a first stack portion comprising a first plurality of layers, wherein the first stack portion comprises a first spacer layer having a first thickness and a first material selected to result in the first stack portion having a first sensitivity to the applied magnetic field; and a second stack portion comprising a second plurality of layers, wherein the second stack portion is disposed over the first stack portion, wherein the second stack portion has a second spacer layer having a second thickness and a second material selected to result in the second stack portion having a second sensitivity to the applied magnetic field, wherein the first thickness is different than the second thickness resulting in the first sensitivity being different than the second sensitivity. 
     In another embodiment, a magnetic field sensor comprises one or more magnetoresistance elements deposited upon a substrate comprising a first stack portion comprising a first plurality of layers, wherein the first stack portion comprises a first spacer layer having a first thickness and a first material selected to result in the first stack portion having a first sensitivity to the applied magnetic field; and a second stack portion comprising a second plurality of layers, wherein the second stack portion is disposed over the first stack portion, and wherein the second stack portion has a second spacer layer having a second thickness selected to result in the second stack portion having a second sensitivity to the applied magnetic field, wherein the first thickness is different than the second thickness resulting in the first sensitivity being different than the second sensitivity. 
     In another embodiment, a magnetic field sensor comprises a magnetoresistance element configured to generate first and second substantially linear responses to an applied magnetic field, wherein the first and second substantially linear responses have substantially zero offset with respect to an expected response of the magnetoresistance element at an applied magnetic field strength of about zero Oersteds. 
     In another embodiment, a magnetic field sensor comprises means for generating first and second substantially linear responses to an applied magnetic field, wherein the first and second substantially linear responses have substantially zero offset with respect to an expected response at an applied magnetic field strength of about zero Oersteds 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The foregoing features of the disclosure, as well as the disclosure itself may be more fully understood from the following detailed description of the drawings, in which: 
         FIG. 1  is a plot illustrating an example response characteristic of an ideal prior art magnetoresistance element; 
         FIG. 2  is a block diagram showing layers of an example prior art magnetoresistance element with a double pinned arrangement; 
         FIG. 3  is a plot illustrating example response characteristics of the prior art magnetoresistance element of  FIG. 2 ; 
         FIG. 4  is a block diagram showing layers of another example prior art magnetoresistance element with a dual double pinned arrangement; 
         FIG. 5  is a plot illustrating example response characteristics of the prior art magnetoresistance element of  FIG. 4 ; 
         FIG. 6  is a plot illustrating response characteristics of an example magnetoresistance element according to the disclosure; 
         FIG. 7  is a block diagram showing layers of a first example magnetoresistance element with a dual double pinned arrangement according to the disclosure; 
         FIG. 8  is a block diagram showing layers of a second example magnetoresistance element with a dual double pinned arrangement according to the disclosure; 
         FIG. 9  is a block diagram showing layers of a third example magnetoresistance element with a dual single pinned arrangement according to the disclosure; 
         FIG. 10  is a plot illustrating first example response characteristics of the magnetoresistance element of  FIG. 9 ; 
         FIG. 11  is a plot illustrating second example response characteristics of the magnetoresistance element of  FIG. 9 ; 
         FIG. 12  is a block diagram showing layers of a fourth example magnetoresistance element with a double and single pinned arrangement according to the disclosure; 
         FIG. 13  is a block diagram showing layers of a fifth example magnetoresistance element with a triple double pinned arrangement according to the disclosure; 
         FIG. 14  is a block diagram showing an example resistor divider arrangement that may include magnetoresistance elements according to the disclosure; 
         FIG. 14A  is a block diagram of an example bridge arrangement that may include magnetoresistance elements according to the disclosure; and 
         FIG. 15  is a block diagram of an example magnetic field sensor that may include magnetoresistance elements according to the disclosure. 
         FIG. 16  is a block diagram showing layers of a double pinned magnetoresistance element. 
         FIG. 17  is a block diagram showing layers of a dual double pinned magnetoresistance element. 
         FIG. 18  is a graph of a transfer function of a magnetoresistance element. 
         FIG. 19  is a graph of transfer functions of magnetoresistance elements. 
         FIG. 20  is a graph of transfer functions of magnetoresistance elements. 
     
    
    
     DETAILED DESCRIPTION 
     The features and other details of the concepts, systems, and techniques sought to be protected herein will now be more particularly described. It will be understood that any specific embodiments described herein are shown by way of illustration and not as limitations of the disclosure and the concepts described herein. Features of the subject matter described herein can be employed in various embodiments without departing from the scope of the concepts sought to be protected. Embodiments of the present disclosure and associated advantages may be best understood by referring to the drawings, where like numerals are used for like and corresponding parts throughout the various views. It should, of course, be appreciated that elements shown in the figures are not necessarily drawn to scale. For example, the dimensions of some elements may be exaggerated relative to other elements for clarity. 
     For convenience, certain concepts and terms used in the specification are provided. As used herein, the term “magnetic field sensing element” is used to describe a variety of electronic elements that can sense a magnetic field. One example magnetic field sensing element is a magnetoresistance or magnetoresistive (MR) element. The magnetoresistance element generally has a resistance that changes in relation to a magnetic field experienced by the magnetoresistance element. 
     As is known, there are different types of magnetoresistance elements, for example, a semiconductor magnetoresistance element such as a giant magnetoresistance (GMR) element, for example, a spin valve, a tunneling magnetoresistance (TMR) element, and a magnetic tunnel junction (MTJ). As used herein, the term “magnetoresistance element” may refer, without exclusivity, to any or all of these types of magnetoresistance elements. Depending on the device type and other application requirements, magnetoresistance elements may be a device made of a type IV semiconductor material such as Silicon (Si) or Germanium (Ge), or a type III-V semiconductor material like Gallium-Arsenide (GaAs). 
     The magnetoresistance element may be a single element or, alternatively, may include two or more magnetoresistance elements arranged in various configurations, e.g., a half bridge or full (Wheatstone) bridge. 
     As is known, magnetoresistance elements (e.g., GMR, TMR) tend to have axes of maximum sensitivity parallel to a substrate on which they are formed or otherwise provided. 
     As used herein, the term “magnetic field sensor” is used to describe a circuit that uses one or more magnetic field sensing elements, generally in combination with other circuits. Magnetic field sensors are used in a variety of applications, including, but not limited to, an angle sensor that senses an angle of a direction of a magnetic field, a current sensor that senses a magnetic field generated by a current carried by a current-carrying conductor, a magnetic switch that senses the proximity of a ferromagnetic object, a motion (e.g., rotation) detector that senses passing ferromagnetic articles, for example, magnetic domains of a ring magnet or features of a ferromagnetic target (e.g., gear teeth) where the magnetic field sensor is used in combination with a back-biased magnet or other magnet, and a magnetic field sensor that senses a magnetic field density of a magnetic field. 
     Referring to  FIG. 1 , a plot  100  shows a curve  102  (i.e., a transfer curve) representative of an example response characteristic of a prior art ideal magnetoresistance (MR) element as it is exposed to magnetic fields of varying strengths. The magnetic fields may, for example, be local and/or external magnetic fields (i.e., applied magnetic fields) which may be generated by one or more sources. 
     The plot  100  has a horizontal axis with a scale in magnetic field strength units (e.g., Oersteds (Oe)) and a vertical axis with a scale in resistance units (e.g., Ohms (Ωs)). Positive magnetic field strength units (e.g., +X) may correspond to a magnetic field experienced by the MR element in a first direction. Additionally, negative magnetic field strength units (e.g., −X) may correspond to a magnetic field experienced by the MR element in a second direction that is opposite from the first direction. 
     As illustrated, the curve  102  has a linear region  102   a  (i.e., a single linear region) between an upper saturation point  102   b  and a lower saturation point  102   c  in which an electrical resistance of the MR element characterized by curve  102  that generally changes linearly (i.e., in direct proportion) to changes in magnetic field strength of the magnetic field experienced by the MR element. In the linear region  102   a , which corresponds to an operational range (or dynamic range) of the MR element, the resistance of the MR element is generally indicative of the magnetic field strength of the magnetic field. Additionally, in the linear region  102   a , a signal produced by a circuit or sensor including the MR element may also be indicative of the strength of the magnetic field. For the prior art ideal MR element, the linear region  102   a  of curve  102  is substantially centered about a crossing of the vertical and horizontal axes of plot  100 , i.e., when the MR element experiences a nominal (or zero) magnetic field, the resistance of the of the MR element may be a value between that of the saturation regions  102   d ,  102   e  in the plot shown, as indicated by point  102   f , and the MR element is not subject to an offset error. 
     As also illustrated, the curve  102  has first and second so-called “saturation regions”  102   d ,  102   e  in which the resistance of the MR element no longer changes (or changes very little) in response to changes in the magnetic field and curve  102  correspondingly substantially levels off. A temporary large magnetic field experienced by the MR element may, for example, saturate the MR element, and place the MR element in one of the saturation regions  102   d ,  102   e.    
     In saturation region  102   d  in which the magnetic field has a negative magnetic field strength (−X), for example, the resistance of the MR element remains substantially constant at a maximum resistance value (or within a maximum resistance range). Additionally, in saturation region  102   e  in which the magnetic field has a positive magnetic field strength (+X), the resistance of the MR element remains substantially constant at a minimum resistance value (or within a minimum resistance range). In other words, in the saturation regions  102   d ,  102   e , the resistance of the MR element remains substantially constant independent of changes in the magnetic field and the MR element has substantially no signal response. It follows that in the saturation regions  102   d ,  102   e  the resistance of the MR element is generally not indicative of the magnetic field strength of the magnetic field. Additionally, in the saturation regions  102   d ,  102   e , a signal (e.g., an output signal) produced by a circuit or sensor including the MR element may also not be indicative of the magnetic field strength of the magnetic field. For example, the signal produced by the circuit or sensor may be clipped on both sides of the linear region  102   a  (i.e., in saturation regions  102   d ,  102   e ), or clipped on one side of the linear region  102   a  (i.e., in either saturation region  102   d  or  102   e ) with an offset, and remain substantially constant independent of changes in the magnetic field in saturation regions  102   d ,  102   e.    
     As a result of the foregoing, detection accuracy of the MR element and the circuit or sensor may be substantially reduced when the MR element is operating in the saturation regions  102   d ,  102   e . It follows that the MR element and the circuit or sensor are typically limited to sensing magnetic fields in the linear region  102   a  over a restricted range of magnetic fields. For at least the above reason, it may be desirable to extend or increase the linear region  102   a  (i.e., operational range) of the MR element and reduce or limit operation of the MR element in the saturation regions  102   d ,  102   e.    
     It is understood that the above-described linear region  102   a  and saturation regions  102   d ,  102   e  are representative of an ideal linear region and ideal saturation regions, respectively, and the response of real MR elements (e.g., prior art MR element  200 , shown in  FIG. 2 , as discussed below) may vary. For example, the linear region of a real (i.e., non-ideal) MR element is generally not perfectly linear. Additionally, real MR elements are also generally responsive to temperature changes and are subject to an offset error. 
     Referring to  FIGS. 2-5 , example prior art non-ideal MR elements (i.e., real MR elements) and response curves associated with the prior art MR elements are shown. It should be appreciated that the example prior art MR elements described below are but several of many potential configurations of prior art MR elements. Additionally, it should be appreciated that the example response curves described below are but several of many representative response curves of the prior art MR elements. 
     Referring now to  FIG. 2 , a first example prior art MR element  200  (e.g., a so-called “double pinned MR element”) that is representative of a real (i.e., non-ideal) MR element, is deposited or otherwise provided upon a substrate  201  (e.g., a Silicon substrate) and includes a plurality of layers (here, twelve layers). The plurality of layers includes a nonmagnetic seed layer  202  disposed over the substrate  201 , a material stack  210  (or stack portion) disposed over the nonmagnetic seed layer  202  and a nonmagnetic cap layer  204  disposed over the material stack  210 . 
     The material stack  210  includes an antiferromagnetic pinning layer  211  disposed over the nonmagnetic seed layer  202 , a ferromagnetic pinned layer  212  disposed over the antiferromagnetic pinning layer  211 , and a nonmagnetic spacer layer  213  disposed over the ferromagnetic pinned layer  212 . The material stack  210  also includes a free layer structure  214  disposed over the nonmagnetic spacer layer  213 , a nonmagnetic spacer layer  215  disposed over the free layer structure  214  and a pinned layer structure  216  disposed over the nonmagnetic spacer layer  215 . The free layer structure  214  includes a first ferromagnetic free layer  214   a  and a second ferromagnetic free layer  214   b  disposed over the first ferromagnetic free layer  214   a . Additionally, the pinned layer structure  216  includes a first ferromagnetic pinned layer  216   a , a second ferromagnetic pinned layer  216   c , and a nonmagnetic spacer layer  216   b  disposed therebetween. 
     The material stack  210  additionally includes an antiferromagnetic pinning layer  217  disposed over the pinned layer structure  216  and the cap layer  204  disposed over the pinning layer  217  (e.g., to protect the MR element  200 ). 
     Each of the plurality of layers in the prior art MR element  200  includes one or more respective materials (e.g., magnetic materials) and has a respective thickness, as shown. Materials of the layers are shown by atomic symbols. Additionally, thicknesses of the layers are shown in nanometers (nm). 
     In general, magnetic materials can have a variety of magnetic characteristics and can be classified by a variety of terms, including, but not limited to, ferromagnetic, antiferromagnetic, and nonmagnetic. Detailed descriptions of the variety of types of magnetic materials are not made herein. However, let it suffice here to say, that a ferromagnetic material (e.g., CoFe) is a material in which magnetic moments of atoms within the material tend to, on average, align to be both parallel and in a same direction, resulting in a nonzero net magnetic magnetization of the material. Additionally, a nonmagnetic or diamagnetic material (e.g., Ta, Cu or Ru) is a material which tends to present an extremely weak magnetization that is opposite and substantially proportional to a magnetic field to which the material is exposed, and does not exhibit a net magnetization. Further, an antiferromagnetic material (e.g., PtMn) is a material in which magnetic moments of atoms within the material tend to, on average, align to be parallel but in opposite directions, resulting in a zero net magnetization. 
     Within some of the plurality of layers in prior art MR element  200 , arrows are shown that are indicative of magnetization directions of the layers when the MR element  200  experiences a nominal (or zero) applied magnetic field. Arrows coming out of the page are indicated as dots within circles and arrows going into the page are indicated as crosses within circles. 
     Detailed descriptions of the various magnetization directions are not made herein. However, let it suffice here to say that, as is known in the art, some MR elements (e.g., GMR and TMR elements) operate with spin electronics (i.e., electron spins) where the resistance of the MR elements is related to the magnetization directions of certain layers in the MR elements. 
     The MR element  200  has a maximum response axis to magnetic fields which is parallel to a surface of the substrate  201  over which the MR element  200  is deposited, as indicated by arrow  199 . Additionally, the MR element  200  has a resistance that changes in response to the applied magnetic field in a direction of the maximum response axis of the MR element  200  over a limited range of magnetic field strengths, as shown in plot  300  of  FIG. 3 , as discussed below. 
     Referring now to  FIG. 3 , a plot  300  shows curves  302 ,  304  representative of example response characteristics of the MR element  200  of  FIG. 2  as it is exposed to magnetic fields of varying strengths in a direction parallel to the maximum response axis  199  of the MR element  200 . The plot  300  has a horizontal axis with a scale in magnetic field strength units (e.g., Oersteds (Oe)) and a vertical axis with a scale in resistance units (e.g., Ohms (Ωs)). Similar to plot  100  shown in  FIG. 1 , positive magnetic field strength units (e.g., +X) in plot  300  may correspond to a magnetic field experienced by the MR element  200  in a first direction. Additionally, negative magnetic field strength units (e.g., −X) in plot  300  may correspond to a magnetic field experienced by the MR element  200  in a second direction that is opposite from the first direction. 
     Curve  302  corresponds to a response characteristic of the MR element  200  as it is exposed to a magnetic field that sweeps from a positive magnetic field strength value (e.g., 500 Oe) to a negative magnetic field strength value (e.g., −450 Oe). Additionally, curve  304  corresponds to a response characteristic of the MR element  200  as it exposed to a magnetic field that sweeps from a negative magnetic field strength value (e.g., −450 Oe) to a positive magnetic field strength value (e.g., 500 Oe). 
     As illustrated, the curves  302 ,  304  have a substantially linear region  301   a  (i.e., a single linear region) and first and second saturation regions  301   b ,  301   c . In the linear region  301   a , which corresponds to an operational range of the MR element  200  characterized by curves  302 ,  304 , the MR element  200  has a resistance that generally changes in proportion to changes in magnetic field strength of the applied magnetic field, here over a magnetic field strength range  303  (e.g., from about −60 Oe to about 40 Oe). In other words, in the linear region  301   a , the MR element  200  has a substantially linear response (i.e., a single substantially linear response) corresponding to the applied magnetic field within the magnetic field strength range  303 . 
     Additionally, in the saturation regions  301   b ,  301   c , which are separated from each other by the substantially linear region  301   a , the resistance of the MR element  200  remains substantially constant independent of changes in magnetic field strength of the applied magnetic field. In other words, in the saturation regions  301   b ,  301   c , the MR element  200  has a resistance that is substantially unresponsive to changes in magnetic field strength. In particular, in saturation region  301   b , the resistance of the MR element  200  remains substantially constant at a maximum resistance value (or within a maximum resistance range). Additionally, in saturation region  301   c , the resistance of the MR element  200  remains substantially constant at a minimum resistance value (or within a minimum resistance range). It follows that in the saturation regions  301   b ,  301   c  the resistance of the MR element  200  is generally not indicative of the magnetic field strength of the magnetic field. As a result of the foregoing, the prior art MR element  200  is typically limited to measuring or sensing the magnetic field in the linear region  301   a  over magnetic field strength range  303  (i.e., a limited range of magnetic fields), which limits magnetic field input. 
     As also illustrated, unlike curve  102  of the ideal MR element shown in  FIG. 1 , curves  302 ,  304  of the MR element  200  (i.e., a real MR element) are not symmetrical about a magnetic field of about zero Oersteds. In particular, curves  302 ,  304  are horizontally offset (i.e., not substantially centered) with respect to an intersection of the vertical and horizontal axes of plot  300 , as indicated by arrow  305 . It follows that the linear region  301   a  of MR element  200  is not symmetrical about the magnetic field of about zero Oersteds and, thus, the range of magnetic field strengths to which the MR element  200  is responsive (here, range  303 ) is also offset. As a result of this offset, the MR element  200  has a resistance which is offset with respect to an expected resistance of the MR element  200  in the linear or operational range (i.e., linear region  301   a ) of the MR element  200 . Additionally, a signal (e.g., an output signal) generated by a circuit or a sensor in which the MR element  200  may be provided may be subject to an offset error if the offset of the MR element  200  is not taken into account and corrected (e.g., through offset correction circuitry in the circuit or sensor). 
     In general, the offset can be caused by design and manufacturing constraints and defects in layers and/or materials which form the MR element  200 . As one example, the offset can be caused by a misalignment of one or more portions (i.e., layers) of the pinned layer structure  216  of MR element  200  with respect to one or more portions (i.e., layers) of the free layer structure  214  of MR element  200 . The offset can also be caused by temperature excursions which may result in a change in a response of the MR element  200  at room temperature and/or magnetic field strength variation. The effect of temperature can, for example, be characterized as a temperature coefficient in units of resistance per degree temperature. 
     Referring now to  FIG. 4 , a second example prior art MR element  400  (e.g., a so-called “dual double pinned MR element”) is deposited or otherwise provided upon a substrate  401  and includes a plurality of layers. The plurality of layers includes a nonmagnetic seed layer  402  disposed over the substrate  401 , a first material stack portion  410  (also sometimes referred to herein as “a first stack portion”) disposed over the nonmagnetic seed layer  402  and an antiferromagnetic pinning layer  420  disposed over the first material stack portion  410 . The MR element  400  also includes a second material stack portion  430  (also sometimes referred to herein as “a second stack portion”) disposed over the antiferromagnetic pinning layer  420  and a nonmagnetic cap layer  404  disposed over the second material stack portion  430 . 
     The first stack portion  410 , which contains a similar ordering or arrangement of layers as the stack portion  210  of the prior art MR element  200  of  FIG. 2  (less a second antiferromagnetic pinning layer, e.g.,  217 , shown in  FIG. 2 ), includes an antiferromagnetic pinning layer  411  disposed over the nonmagnetic seed layer  402  and a ferromagnetic pinned layer  412  disposed over the antiferromagnetic pinning layer  411 . The first stack portion  410  also includes a nonmagnetic spacer layer  413  disposed over the ferromagnetic pinned layer  412  and a free layer structure  414  disposed over the nonmagnetic spacer layer  413 . The free layer structure  414  includes a first ferromagnetic free layer  414   a  and a second ferromagnetic free layer  414   b  disposed over the first ferromagnetic free layer  414   a.    
     The first stack portion  410  further includes a nonmagnetic spacer layer  415  disposed over the free layer structure  414  and a pinned layer structure  416  disposed over the nonmagnetic spacer layer  415 . The pinned layer structure  416  includes a first ferromagnetic pinned layer  416   a , a second ferromagnetic pinned layer  416   c  and a nonmagnetic spacer layer  416   b  disposed therebetween. 
     The second stack portion  430 , which is similar to the first stack portion  410  but includes layers that are in a substantially reverse order or arrangement as the layers which are shown in first stack portion  410  with respect to the seed layer  402 , includes a pinned layer structure  431  disposed over the antiferromagnetic pinning layer  420 , a nonmagnetic spacer layer  432  disposed over the pinned layer structure  431  and a free layer structure  433  disposed over the nonmagnetic spacer layer  432 . The pinned layer structure  431  includes a first ferromagnetic pinned layer  431   a , a second ferromagnetic pinned layer  431   c  and a nonmagnetic spacer layer  431   b  disposed therebetween. Additionally, the free layer structure  433  includes a first ferromagnetic free layer  433   a  and a second ferromagnetic free layer  433   b  disposed over the first ferromagnetic free layer  433   a.    
     The second stack portion  430  also includes a nonmagnetic spacer layer  434  disposed over the free layer structure  433 , a ferromagnetic pinned layer  435  disposed over the nonmagnetic spacer layer  434  and an antiferromagnetic pinning layer  436  disposed over the ferromagnetic pinned layer  435 . A nonmagnetic cap layer  204  is disposed over the antiferromagnetic pinning layer  436 . 
     Similar to prior art MR element  200  shown in  FIG. 2 , each of the layers in prior art MR element  400  includes one or more respective materials (e.g., magnetic materials) and has a respective thickness, as shown. Materials of the layers are shown by atomic symbols. Additionally, thicknesses of the layers are shown in nanometers. 
     Additionally, similar to prior art MR element  200  shown in  FIG. 2 , within some of the plurality of layers in prior art MR element  400 , arrows are shown that are indicative of magnetization directions of the layers when the MR element  700  experiences a nominal (or zero) applied magnetic field. Arrows coming out of the page are indicated as dots within circles and arrows going into the page are indicated as crosses within circles. 
     Detailed descriptions of the various magnetization directions are not made herein. However, let it suffice here to say that, as is known in the art, some MR elements (e.g., GMR and TMR elements) operate with spin electronics (i.e., electron spins) where the resistance of the MR elements is related to the magnetization directions of certain layers in the MR elements. 
     The MR element  400  has a maximum response axis to magnetic fields which is parallel to a surface of the substrate  401  over which the MR element  400  is deposited, as indicated by arrow  399 . Additionally, the MR element  400  has an electrical resistance that changes generally in proportion to an applied magnetic field in a direction of the maximum response axis of the MR element  400  over a limited range of magnetic field strengths, as shown in plot  500  of  FIG. 5 , as discussed below. 
     Referring now to  FIG. 5 , a plot  500  shows curves  502 ,  504  representative of example response characteristics of the MR element  400  of  FIG. 4  as it is exposed to magnetic fields of varying strengths in a transverse direction relative to the maximum response axis  399  of the MR element  400 . The plot  500  has a horizontal axis with a scale in magnetic field strength units (e.g., Oersteds) and a vertical axis with a scale in resistance units (e.g., Ohms (Ωs)). 
     Curve  502  corresponds to a response characteristic of the MR element  400  as it is exposed to a magnetic field that sweeps from a positive magnetic field strength value (e.g., 550 Oe) to a negative magnetic field strength value (e.g., −450 Oe). Additionally, curve  504  corresponds to a response characteristic of the MR element  400  as it exposed to a magnetic field that sweeps from a negative magnetic field strength value (e.g., −450 Oe) to a positive magnetic field strength value (e.g., 550 Oe). 
     As illustrated, the curves  502 ,  504  have a substantially linear region  501   a  (i.e., a single substantially linear region) and first and second saturation regions  501   b ,  501   c . In the linear region  501   a , which corresponds to an operational range of the MR element  400  characterized by curves  502 ,  504 , the MR element  400  has a resistance that generally changes in proportion to changes in magnetic field strength of the applied magnetic field, here over a magnetic field strength range  503  (e.g., from about −100 Oe to about 40 Oe). In other words, the MR element  400  has a substantially linear response to the applied magnetic field in the linear region  501   a . As also illustrated, the MR element  400  has a single sensitivity level (i.e., rate of change in resistance) in the linear region  501 . 
     In the saturation regions  501   b ,  501   c , the resistance of the MR element  400  remains substantially constant independent of changes in magnetic field strength. In other words, the MR element  400  has a resistance that is substantially unresponsive to changes in magnetic field strength in the saturation regions  501   b ,  501   c . In particular, in saturation region  501   b , the resistance of the MR element  400  remains substantially constant at a maximum resistance value (or within a maximum resistance range). Additionally, in saturation region  501   c , the resistance of the MR element  400  remains substantially constant at a minimum resistance value (or within a minimum resistance range). It follows that since the resistance of the prior art MR element  400  is not indicative of the magnetic field in saturation regions, MR element  400  is limited to measuring or sensing the applied magnetic field in the linear region  501   a  over the magnetic field strength range  503  (i.e., a limited range of magnetic fields). 
     As is also illustrated, similar to curves  302 ,  304  of MR element  200  (i.e., a non-ideal MR element) shown in  FIG. 3 , curves  502 ,  504  of MR element  400  (i.e., also a real MR element) are not symmetrical about a magnetic field of about zero Oersteds. In particular, curves  502 ,  504  are horizontally offset with respect to an intersection of the vertical and horizontal axes of plot  500 , as indicated by arrow  505 . It follows that the linear region  501   a  of MR element  400  is not symmetrical about the magnetic field of about zero Oersteds and, thus, the range of magnetic field strengths to which the MR element  400  is responsive (here, range  503 ) is also offset, albeit less offset than curves  302 ,  304  of MR element  200 . As a result of this offset, the MR element  400  has a resistance which is offset with respect to an expected resistance of the MR element  400  in the linear or operational range (i.e., linear region  501   a ) of the MR element  400 . Additionally, a signal (e.g., an output signal) generated by a circuit or a sensor in which the MR element  400  may be provided may be subject to an offset error if the offset of the MR element  400  is not taken into account and corrected (e.g., through offset correction circuitry in the circuit or sensor). 
     Referring to  FIGS. 6-13 , example embodiments of MR elements according to the disclosure and response curves associated with MR elements according to the disclosure are shown. It should be appreciated that the example MR elements described below are but several of many potential configurations of MR elements in accordance with the concepts, systems, circuits and techniques described herein. Additionally, it should be appreciated that the example response curves described below are but several of many representative response curves of the MR elements. 
     Referring now to  FIG. 6 , a plot  600  shows curves  602 ,  604  representative of example response characteristics of an example MR element according to the disclosure, the structure of which MR element is described further in connection with figures below. Curves  602 ,  604  correspond to response characteristics of the MR element (e.g.,  700 , shown in  FIG. 7 , with layer  713  of the MR element having a thickness of about 3.3 nm and layer  734  of the MR element having a thickness of about 2.0 nm) as it is exposed to a magnetic field of varying strengths in a direction parallel to a maximum response axis of the MR element (e.g.,  699 , shown in  FIG. 7 ). It is understood that the applied magnetic field (e.g., a local and/or external magnetic field) may be generated in various ways, for example, depending on the type of circuit or sensor in which the MR element is provided and its application. 
     The plot  600  has a horizontal axis with a scale in magnetic field strength units (e.g., Oersteds (Oe)) and a vertical axis with a scale in resistance units (e.g., Ohms (Ωs)). The plot  600  also includes lines  606 ,  608 ,  610 ,  612 ,  614 ,  616  which are representative of boundaries of various regions or sub-regions in which the MR element may operate. 
     In the illustrated embodiment, curves  602 ,  604  have a first substantially linear region  601   a  and a second substantially linear region (here, a second substantially linear region including a plurality of substantially linear sub-regions  601   b ,  601   c ,  601   d ,  601   e ) (e.g., piecewise or discrete linear regions). Additionally, curves  602 ,  604  have a first saturation region  601   f  and a second saturation region  601   g . The MR element characterized by curves  602 ,  604  has a respective response (or responses) to the magnetic field to which the MR element is exposed in each of the substantially linear and saturation regions. Additionally, each of the substantially linear and the saturation regions is associated with a particular magnetic field threshold, or range of magnetic field strengths of the applied magnetic field. 
     In particular, in first substantially linear region  601   a , the MR element has a first substantially linear response (i.e., experiences a first substantially linear change in resistance (slope)) to the applied magnetic field over a first magnetic field strength range  603   a . Additionally, in the second substantially linear region (i.e., sub-regions  601   b ,  601   c ,  601   d ,  601   e ), the MR element has a second substantially linear response (or responses) to the applied magnetic field over a second magnetic field strength range (i.e., sub-ranges  603   b ,  603   c ,  603   d ,  603   e ). Further, in first and second saturation regions  601   f ,  601   g , the MR element has substantially no response to the applied magnetic field over third and fourth magnetic field strength ranges  603   f ,  603   g , i.e., the MR element is saturated and the resistance of the MR element no longer changes (or changes very little) in response to changes in the magnetic field. 
     In embodiments, the MR element also has a respective substantially linear response in each of the sub-regions  601   b ,  601   c ,  601   d ,  601   e  of the second substantially linear region, with the substantially linear responses of the MR element in the sub-regions  601   b ,  601   c ,  601   d ,  601   e  comprising the second substantially linear response of the second substantially linear region. In particular, in sub-region  601   b , the MR element may have a fifth substantially linear response to the applied magnetic field over sub-range  603   b  of the second magnetic field strength range. Additionally, in sub-region  601   c , the MR element may have a sixth substantially linear response to the applied magnetic field over sub-range  603   c  of the second magnetic field strength range. Additionally, in sub-region  601   d , the MR element may have a seventh substantially linear response to the applied magnetic field over sub-range  603   d  of the second magnetic field strength range. Further, in sub-region  601   e , the MR element may have an eighth substantially linear response to the applied magnetic field over sub-range  603   e  of the second magnetic field strength range. 
     In embodiments, each of the substantially linear responses (e.g., fifth, sixth, seventh, etc.) of the various sub-regions  601   b ,  601   c ,  601   d ,  601   e  in the second substantially linear region of the MR element are different from each other. Additionally, in embodiments, two or more of the substantially linear responses of the sub-regions  601   b ,  601   c ,  601   d ,  601   e  are the same as or similar to each other. For example, in embodiments, the fifth and sixth substantially linear responses of the MR element may be the same as or similar to each other, but different than the seventh substantially linear response of the MR element. Additionally, in embodiments, the seventh and eighth substantially linear responses of the MR element may be the same as or similar to each other, but different than the fifth and sixth substantially linear responses of the MR element. 
     As illustrated, sub-region  601   b  of the second substantially linear region is contiguous with sub-region  601   d  of the second substantially linear region. Additionally, sub-region  601   c  of the second substantially linear region is contiguous with sub-region  601   e  of the second substantially linear region. However, sub-regions  601   b ,  601   d  are non-contiguous with sub-regions  601   c ,  601   e . It follows that in the illustrated embodiment the second substantially linear region includes a plurality of non-contiguous sub-regions. It is understood that in other embodiments the second substantially linear region may include a plurality of contiguous sub-regions (or a single sub-region). 
     As also illustrated, the MR element characterized by curves  602 ,  604  has an associated sensitivity level (or levels) to the applied magnetic field in each of the substantially linear regions and the saturation regions. As discussed above, with regard to MR elements, sensitivity corresponds to a change in the resistance of an MR element in response to an applied magnetic field. In embodiments, the respective responses (e.g., first, second, third, etc. substantially linear responses) of the MR element to the magnetic field result in the MR element having the sensitivity levels. 
     In particular, in first substantially linear region  601   a , the MR element has a first sensitivity level (i.e., a first rate of change in resistance) to changes in magnetic field strength of the applied magnetic field over the first magnetic field strength range  603   a . Additionally, in the second substantially linear region (i.e., sub-regions  601   b ,  601   c ,  601   d ,  601   e ), the MR element has a second sensitivity level to changes in magnetic field strength of the applied magnetic field over the second magnetic field strength range (i.e., sub-ranges  603   b ,  603   c ,  603   d ,  603   e ). Further, in first and second saturation regions  601   f ,  601   g , the MR element has third and fourth respective sensitivity levels to changes in magnetic field strength of the applied magnetic field over third and fourth magnetic field strength ranges  603   f ,  603   g.    
     In embodiments, the MR element also has a respective sensitivity level to changes in magnetic field strength of the applied magnetic field in each of the sub-regions  601   b ,  601   c ,  601   d ,  601   e  of the second substantially linear regions, with the sensitivity levels of the MR element in the sub-regions  601   b ,  601   c ,  601   d ,  601   e  comprising the second sensitivity level of the second substantially linear region. In particular, in sub-region  601   b , the MR element may have a fifth sensitivity level to changes in magnetic field strength of the applied magnetic field over sub-range  603   b  of the second magnetic field strength range. Additionally, in sub-region  601   c , the MR element may have a sixth sensitivity level to changes in magnetic field strength of the applied magnetic field over sub-range  603   c  of the second magnetic field strength range. Additionally, in sub-region  601   d , the MR element may have a seventh sensitivity level to changes in magnetic field strength of the applied magnetic field over sub-range  603   d  of the second magnetic field strength range. Further, in sub-region  601   e , the MR element may have an eighth sensitivity level to changes in magnetic field strength of the applied magnetic field over sub-range  603   e  of the second magnetic field strength range. 
     In embodiments, the first magnetic field strength range  603   a  associated with first substantially linear region  601   a  corresponds to relatively “low” strength applied magnetic fields (here, between about −20 Oe and +20 Oe). Additionally, in embodiments, magnetic field strength sub-ranges  603   b ,  603   c  associated with sub-regions  601   b ,  601   c  of the second substantially linear region, respectively, correspond to relatively “medium” strength magnetic fields that are greater in magnetic field strength than “low” strength magnetic fields associated with the first magnetic field strength range  603   a  of first substantially linear region  601   a . In the illustrated embodiment, magnetic field strength sub-range  603   b  comprises negative magnetic field strength values (here, between about −20 Oe and about −120 Oe) and magnetic field strength sub-range  603   c  comprises positive magnetic field strength values (here, between about 20 Oe and about 125 Oe). 
     Additionally, in embodiments, the magnetic field strength sub-ranges  603   d ,  603   e  associated with sub-regions  601   d ,  601   e  of the second substantially linear region, respectively, correspond to relatively “high” strength magnetic fields that are greater in magnetic field strength than the “medium” strength magnetic fields associated with magnetic field strength sub-ranges  603   b ,  603   c  of sub-regions  601   b ,  601   c  of the second substantially linear region. In embodiments, the “high” strength magnetic fields are not large enough to saturate the MR element. In the illustrated embodiment, the magnetic field strength sub-range  603   d  comprises negative magnetic field strength values (here, between about −120 Oe and about −430 Oe) and magnetic field strength sub-range  603   e  comprises positive magnetic field strength values (here, between about 125 Oe and about 550 Oe). 
     Further, in embodiments, the third and fourth magnetic field strength ranges  603   f ,  603   g  associated with saturation regions  601   f ,  601   g , respectively, correspond to magnetic fields that are greater in magnetic field strength than the “high” strength magnetic fields associated with magnetic field strength sub-ranges  603   d ,  603   e  of sub-regions  601   d ,  601   e  of the second substantially linear region. The magnetic fields associated with the third and fourth magnetic field strength ranges  603   f ,  603   g , unlike the magnetic fields associated with the magnetic field strength sub-ranges  603   d ,  603   e  of the second magnetic field strength range, are large enough to saturate the MR element such that the resistance of the MR element remains substantially constant in the presence of changes in the applied magnetic field. In the illustrated embodiment, the magnetic field strength range-range  603   f  comprises negative magnetic field strength values (here, between about −430 Oe and larger) and magnetic field strength sub-range  603   g  comprises positive magnetic field strength values (here, between about 550 Oe and larger). 
     In the example embodiment shown, the first sensitivity level of the MR element in first substantially linear region  601   a  is different than (here, greater than) the second sensitivity level of the MR element in the second substantially linear region (i.e., sub-regions  601   b ,  601   c ,  601   d ,  601   e ). Additionally, the second sensitivity level of the MR element in the second substantially linear region is different than (here, greater than) the third and fourth sensitivity levels of the MR element in saturation regions  601   f ,  601   g.    
     Further, in the example embodiment shown, the fifth and sixth sensitivity levels of the MR element in sub-regions  601   b ,  601   c  of the second substantially linear region are different than (here, greater than) the seventh and eighth sensitivity levels of the MR element in sub-regions  601   d ,  601   e  of the second substantially linear region. Further, the seventh and eighth sensitivity levels of the MR element in sub-regions  601   d ,  601   e  of the second substantially linear region are different than (here, greater than) the third and fourth sensitivity levels of the MR element in saturation regions  601   f ,  601   g.    
     In other words, the MR element characterized by curves  602 ,  604  is more responsive (i.e., experiences a greater change in resistance, and has a higher sensitivity) to applied magnetic fields in the first magnetic field strength range  603   a  associated with first substantially linear region  601   a  than it is to applied magnetic fields in the second magnetic field strength range (i.e., sub-ranges  603   b ,  603   c ,  603   d ,  603   e ) associated with the second substantially linear region (i.e., sub-regions  601   b ,  601   c ,  601   d ,  601   e ). Additionally, the MR element is more responsive to applied magnetic fields in the second magnetic field strength range than it is to applied magnetic fields in the third and fourth magnetic field strength ranges  603   f ,  603   g  associated with saturation regions  601   f ,  601   g.    
     Further, in the example embodiment shown, the MR element is more responsive to applied magnetic fields in the sub-ranges  603   b ,  603   c  associated with sub-regions  601   b ,  601   c  of the second substantially linear region than it is to applied magnetic fields in sub-ranges  603   d ,  603   e  associated with sub-regions  601   d ,  601   e  of the second substantially linear region. Further, the MR element is more responsive to applied magnetic fields in the sub-ranges  603   d ,  603   e  associated with sub-regions  601   d ,  601   e  of the second substantially linear region than it is to applied magnetic fields in the third and fourth magnetic field strength ranges  603   f ,  603   g  associated with saturation regions  601   f ,  601   g.    
     In embodiments, the first substantially linear response of the MR element in first substantially linear region  601   a  corresponds to a substantially linear response of a selected stack portion of the MR element. For example, the first substantially linear response may correspond to a substantially linear response of a second stack portion (e.g.,  730 , shown in  FIG. 7 ) of the MR element. Similarly, in embodiments, the second substantially linear response of the MR element in the second substantially linear region (i.e., sub-regions  601   b ,  601   c ,  601   d ,  601   e ) may correspond to a substantially linear response of a second stack portion (e.g.,  730 , shown in  FIG. 7 ) of the MR element. 
     Additionally, in embodiments, the first substantially linear response of the MR element in first substantially linear region  601   a  corresponds to a substantially linear response of a selected stack portion of the MR element, but with other stack portions of the MR element also contributing to the first substantially linear response. For example, the first substantially linear response may correspond to a substantially linear response of a second stack portion (e.g.,  730 , shown in  FIG. 7 ) of the MR element, but with a first stack portion (e.g.,  710 , shown in  FIG. 7 ) of the MR element also contributing to at least a portion of the first substantially linear response. Similarly, in embodiments, the second substantially linear response of the MR element in the second substantially linear region (i.e., sub-regions  601   b ,  601   c ,  601   d ,  601   e ) may correspond to a substantially linear response of the first stack portion of the MR element, but with the second stack portion of the MR element also contributing to at least a portion of the second substantially linear response. The foregoing may, for example, be due to the second stack portion still being responsive to applied magnetic fields over the first magnetic field strength range  603   a  associated with the first substantially linear region  601   a , but with a sensitivity level that is substantially reduced compared to a sensitivity level of the second stack portion over the second magnetic field strength range (i.e., sub-ranges  603   b ,  603   c ,  603   d ,  603   e ) associated with the second substantially linear region (i.e., sub-regions  601   b ,  601   c ,  601   d ,  601   e ). 
     The first substantially linear region  601   a  and the second substantially linear region (i.e., sub-regions  601   b ,  601   c ,  601   d ,  601   e ) correspond to an operational range of the MR element characterized by curves  602 ,  604  in the illustrated embodiment. In other words, the operational range of the MR element, which corresponds to a range of magnetic fields in which the MR element has a resistance that is indicative of a magnetic field strength of the magnetic field to which the MR element is exposed, includes a plurality of substantially linear regions (e.g., piecewise or discrete linear regions). Each of the substantially linear regions has a respective substantially linear response to the applied magnetic field, as discussed above. This is in contrast the prior art MR elements discussed in connection with figures above (e.g.,  400 , shown in  FIG. 4 ), which have an operational range with a single substantially linear region and a single substantially linear response over the substantially linear region. One example result of the foregoing is the operational range of the MR element characterized by curves  602 ,  604  may have an increased operational range compared, for example, to an operational range of the prior art MR elements, particularly where clipping may occur at much larger magnetic field strength levels of an applied magnetic field. 
     Another example result of the foregoing is that the operational range of the MR element characterized by curves  602 ,  604  includes a plurality of sensitivity levels corresponding to the plurality of substantially linear responses of the MR element. This may, for example, provide for the MR element having a first sensitivity level at relatively “low” strength fields (e.g., where SNR is relatively “low”) and a second sensitivity level that is different than the first sensitivity level at magnetic fields that are greater than the “low” strength magnetic fields (e.g., where SNR is relatively “high”), but not in saturation. 
     In embodiments, the sensitivity levels (e.g., first, second, third, etc.) and/or magnetic field strength ranges (e.g., first, second, third, etc.) associated with each of the above-described substantially linear regions and saturation regions may be adjusted through selection of one or more characteristics (e.g., construction and/or dimensions) of the MR element characterized by curves  602 ,  604 , as described further in connection with figures below. 
     Referring now to  FIG. 7 , a first example magnetoresistance (MR) element  700  according to the disclosure is shown. The MR element  700  is deposited upon a substrate  701  (e.g., a Si Substrate) and includes a first material stack portion (also sometimes referred to herein as “a first stack portion”)  710  and a second material stack portion (also sometimes referred to herein as “a second stack portion”)  730 . The first stack portion  710  has first and second opposing surfaces, with the first surface of the first stack portion  710  disposed over a seed layer  702  (e.g., a non-magnetic seed layer) and the seed layer  702  disposed between the first stack portion  710  and the substrate  701 . Additionally, the second stack portion  730  has first and second opposing surfaces, with the first surface of the second stack portion  730  disposed over a pinning layer  720  (e.g., an antiferromagnetic pinning layer) and the pinning layer  720  disposed between the second stack portion  730  and the first stack portion  710 . A cap layer  704  (e.g., a non-magnetic cap layer) is disposed over the second surface of the second stack portion  730 . 
     The first stack portion  710 , which has a first substantially linear response corresponding to an applied magnetic field over a first magnetic field strength range, as discussed further below, includes a first plurality of layers (here, 9 layers). The first plurality of layers includes a pinning layer  711 , a pinned layer  712  and a spacer layer  713 . The first stack portion  710  also includes a first free layer structure  714 , a spacer layer  715  and a pinned layer structure  716 . The first free layer structure  714  includes a first free layer  714   a  and a second free layer  714   b . Additionally, the pinned layer structure  716  includes first pinned layer  716   a , second pinned layer  716   c  and spacer layer  716   b.    
     The pinning layer  711  is disposed over the seed layer  702  and the pinned layer  712  is disposed over the pinning layer  711 . Additionally, the spacer layer  713  is disposed over the pinned layer  712  and the free layer structure  714  is disposed over the spacer layer  713 . Further, the spacer layer  715  is disposed over the free layer structure  714  and the pinned layer structure  716  is disposed over the spacer layer  715 . 
     In embodiments, pinning layer  711  may be an antiferromagnetic pinning layer and pinned layer  712  may be a ferromagnetic pinned layer, and spacer layer  713  may be a nonmagnetic spacer layer. Additionally, in embodiments, spacer layer  715  may be a nonmagnetic spacer layer and pinned layer structure  716  may include a synthetic antiferromagnetic (SAF) pinned layer structure or layer. First free layer  714   a  of free layer structure  714  may be a ferromagnetic free layer and second free layer  714   b  of free layer structure  714  may be a ferromagnetic free layer. Additionally, first pinned layer  716   a  of pinned layer structure  716  may be ferromagnetic pinned layer, second pinned layer  716   c  of pinned layer structure  716  may be a ferromagnetic pinned layer, and spacer layer  716   b  of pinned layer structure  716  may be a nonmagnetic spacer layer. In embodiments, at least one of first pinned layer  716   a  or second pinned layer  716   c  comprises a same or similar material as second free layer  714   b.    
     In the illustrated embodiment, pinning layer  711  is shown as including PtMn or IrMn and pinned layer  712  is shown as including CoFe. Additionally, spacer layer  713  is shown as including Ru, first free layer  714   a  is shown as including NiFe and second free layer  714   b  is shown as including CoFe. Further, spacer layer  715  is shown as including Cu, first pinned layer  716   a  is shown as including CoFe, spacer layer  716   b  is shown as including Ru and second pinned layer  716   c  is shown as including CoFe. However, it is understood that each of the above-described layers in the first stack portion  710  may include materials, or compositions of materials, that are different than that which is shown, as described further below. 
     In the illustrated embodiment, pinning layer  711  is also shown as having a thickness between about 5 nm and about 15 nm and pinned layer  712  is shown as having a thickness of about 2.1 nm. Additionally, spacer layer  713  is shown as having a thickness of about 3.3 nm, first free layer  714   a  is shown as having a thickness of about 5 nm and second free layer  714   b  is shown as having a thickness of about 1 nm. Further, spacer layer  715  is shown as having a thickness of about 2.4 nm, first pinned layer  716   a  is shown as having a thickness of about 2.1 nm, spacer layer  716   b  is shown as having a thickness of about 0.85 nm and second pinned layer  716   c  is shown as having a thickness of about 2.0 nm. However, it is understood that each of the above-described layers may have a layer thickness that is different than that which is shown, as described further below. 
     The second stack portion  730 , which has a second substantially linear response that is different than the first substantially linear response of the first stack portion  710 , as discussed further below, includes a second plurality of layers (here, 9 layers), i.e., a same number of layers as the first plurality of layers of first stack portion  710  in the illustrated embodiment. The second plurality of layers includes a pinned layer structure  731 , a spacer layer  732  and a free layer structure  733 . The second plurality of layers also includes a spacer layer  734  and a pinned layer  735 . The pinned layer structure  731  includes a first pinned layer  731   a , a second pinned layer  731   c  and a spacer layer  731   b . Additionally, the free layer structure  733  includes a first free layer  733   a  and a second free layer  733   b.    
     The pinned layer structure  731  is deposited over the pinning layer  720  and the spacer layer  732  is disposed over the pinned layer structure  731 . Additionally, the free layer structure  733  is disposed over the spacer layer  732  and the spacer layer  734  is disposed over the free layer structure  733 . Further, the pinned layer  735  is disposed over the spacer layer  734  and the pinning layer  736  is disposed over the pinned layer  735 . 
     In embodiments, the pinned layer structure  731  may include an SAF pinned layer structure or layer and the spacer layer  732  may be a nonmagnetic spacer layer. Additionally, in embodiments, the first pinned layer  731   a  of pinned layer structure  731  may be ferromagnetic pinned layer, the second pinned layer  731   c  of pinned layer structure  731  may be a ferromagnetic pinned layer, and the spacer layer  731   b  of pinned layer structure  731  may be a nonmagnetic spacer layer. Further, in embodiments, the first free layer  733   a  of free layer structure  733  may be a ferromagnetic free layer and the second free layer  733   b  of free layer structure  733  may be a ferromagnetic free layer. In embodiments, the spacer layer  734  may be a nonmagnetic spacer layer, the pinned layer  735  may be a ferromagnetic pinned layer and the pinning layer  736  may be an antiferromagnetic pinning layer. 
     In the illustrated embodiment, the first pinned layer  731   a  is shown as including CoFe, spacer layer  731   b  is shown as including Ru and the second pinned layer  731   c  is shown as including CoFe. Additionally, spacer layer  732  is shown as including Cu, first free layer  733   a  is shown as including CoFe and second free layer  733   b  is shown as including NiFe. Further, spacer layer  734  is shown as including Ru, pinned layer  735  is shown as including CoFe and pinning layer  736  is shown as including PtMn or IrMn. However, similar to the layers in the first stack portion  710  of MR element  700 , it is understood that each of the above-described layers in the second stack portion  730  of MR element  700  may include materials, or compositions of materials, that are different than that which is shown, as will be described further below. 
     In the illustrated embodiment, the first pinned layer  731   a  is shown as having a thickness of about 2.0 nm, spacer layer  731   b  is shown as having a thickness of about 0.85 nm, and the second pinned layer  731   c  is shown as having a thickness of about 2.1 nm. Additionally, spacer layer  732  is shown as having a thickness of about 2.4 nm, first free layer  733   a  is shown as having a thickness of about 1 nm and second free layer  733   b  is shown as having a thickness of about 5.0 nm. Further, spacer layer  734  has a thickness T 1  in one of four example ranges, e.g., about 1.6 nm to about 1.8 nm, about 2.2 nm to about 2.4 nm, about 2.9 nm to about 3.1 nm, or about 3.5 nm to about 3.7 nm. As one example, spacer layer  734  may have a thickness T 1  of about 2.0 nm. Additionally, pinned layer  735  is shown as having a thickness of about 2.1 nm and pinning layer  736  is shown as having a thickness of between about 5 nm and about 15 nm. However, similar to the layers in the first stack portion  710  of MR element  700 , it is understood that each of the above-described layers in the second stack portion  730  of MR element  700  may have a layer thickness that is different than that which is shown, as described further below. 
     Within some of the plurality of layers in MR element  700 , arrows are shown that are indicative of magnetization directions of the layers when the MR element  700  experiences a nominal (or zero) applied magnetic field. Arrows coming out of the page are indicated as dots within circles and arrows going into the page are indicated as crosses within circles. 
     Detailed descriptions of the various magnetization directions are not made herein. However, let it suffice here to say that, as is known in the art, some MR elements (e.g., GMR and TMR elements) operate with spin electronics (i.e., electron spins) where the resistance of the MR elements is related to the magnetization directions of certain layers in the MR elements. 
     The MR element  700  has a maximum response axis to magnetic fields which is parallel to a surface of the substrate  701  over which the MR element  700  is deposited, as indicated by arrow  699 . 
     As noted above, the first stack portion  710  of MR element  700  has a first substantially linear response corresponding to an applied magnetic field over a first magnetic field strength range. Additionally, as noted above, the second stack portion  730  has a second substantially linear response that is different than the first substantially linear response of the first stack portion  710 . The second substantially linear response corresponds to the applied magnetic field over a second magnetic field strength range. 
     In embodiments, the first substantially linear response of the first stack portion  710  results in the MR element  700  having a first sensitivity level (i.e., a first rate of change in resistance) to changes in magnetic field strength in response to the applied magnetic field being within the first magnetic field strength range. Additionally, in embodiments, the second substantially linear response of the second stack portion  730  results in the MR element  700  having a second sensitivity level (i.e., a second rate of change in resistance) to changes in magnetic field strength in response to the applied magnetic field being within the second magnetic field strength range. In embodiments, the first magnetic field strength range (e.g., in Oersteds) overlaps with one or more portions of the second magnetic field strength range. Additionally, in embodiments, at least one of the first or second magnetic field strength ranges includes one or more sub-ranges (e.g.,  603   b ,  603   c ,  603   d ,  603   e , shown in  FIG. 6 ), and the first and/or second substantially linear responses associated with the first and second magnetic field strength ranges includes corresponding sub-regions (e.g.,  601   b ,  601   c ,  601   d ,  601   e , shown in  FIG. 6 ). In embodiments, the first linear range of the first stack portion includes sub-ranges  603 A,  603 B, and  603 C; and the second linear range of the second stack portion includes sub-ranges  603 A,  603 B,  603 C,  603 D, and  603 E. In this example, the linear ranges overlap at  603 A,  603 B and  603 C proving those regions with double sensitivity. In sub-ranges  603 D and  603 E, where there is no overlap of the linear ranges of the stack portions, there may be normal (i.e. not double) sensitivity. 
     The first and second stack portions  710 ,  730  each have at least one characteristic (e.g., construction and/or dimensions) selected to result in the first and second stack portions  710 ,  730  having the first and second substantially linear regions, respectively. 
     For example, one or more parameters associated with the construction of the first and second stack portions  710 ,  730  may comprise the at least one characteristic selected to result in the first and second stack portions  710 ,  730  having the first and second substantially linear ranges. Illustrative construction parameters include materials, layer thickness, and an ordering of one or more of the layers (e.g., antiferromagnetic layers, pinned layers and/or non-magnetic layers) of the first and second stack portions  710 ,  730 . The construction parameters may also include a number of layers in the first and second stack portions  710 ,  730 . 
     In the illustrated embodiment, each of the layers in the first and second stack portions  710 ,  730  is shown as including one or more materials. In embodiments, materials of one or more of the layers in the first stack portion  710  are selected to result in the first stack portion having the first substantially linear response. Additionally, in embodiments, materials of one or more of the layers in the second stack portion  730  are selected to result in the second stack portion having the second substantially linear response. For example, the material(s) of spacer layer  713  in the first stack portion  710  (here, Ruthenium (Ru)) and/or the material(s) of spacer layer  715  in the first stack portion  710  (here, Copper (Cu)) may be selected to result in the first stack portion  710  having the first substantially linear range. Additionally, the material(s) of spacer layer  732  in the second stack portion  730  (here, Cu) and/or the material(s) of spacer layer  734  in the second stack portion  730  (here, Ru) may be selected to result in the second stack portion  730  having the second substantially linear response range. A spacer layer comprising Ru, for example, may provide for antiferromagnetic coupling or ferromagnetic coupling between surrounding layers, which may provide for the first and/or second substantially linear ranges, as discussed further below. 
     It is understood that the material(s) of layers other than spacer layers  713 ,  715  in the first stack portion  710  and spacer layers  732 ,  734  in the second stack portion  730  may be selected to result in the first and second stack portions  710 ,  730  having the first and second substantially linear responses. 
     In the illustrated embodiment, each of the layers in the first and second stack portions  710  is also shown having a respective thickness. In embodiments, the thickness of at least one of the layers of the first stack portion  710  is selected to result in the first stack portion having the first substantially linear range. Additionally, in embodiments, the thickness of at least one of the layers of the second stack portion  730  is selected to result in the second stack portion having the second substantially linear range. For example, spacer layer  713  in the first stack portion  710  may have a first selected thickness (here, about 3.3 nm) to result in the first stack portion  710  having the first substantially linear range. Additionally, spacer layer  734  in the second stack portion  730  may have a second selected thickness that is different than the first selected thickness to result in the second stack portion  730  having the second substantially linear range that is different than the first substantially linear range. In the example embodiment shown, spacer layer  734  has a thickness selected to be in one of four example ranges, e.g., about 1.6 nanometers (nm) to about 1.8 nm, about 2.2 nm to about 2.4 nm, about 2.9 nm to about 3.1 nm, or about 3.5 nm to about 3.7 nm. 
     In embodiments, the example ranges are determined by measuring a transfer curve associated with the MR element at different thicknesses (e.g., Ru thicknesses) of the spacer layer  734 , and selecting a thickness (or thicknesses) T 1  of the spacer layer  734  to achieve a particular substantially linear range. (e.g., a first and/or a second substantially linear range). A spacer layer  734  having a thickness T 1  in a first one of the thickness ranges (e.g., about 1.6 nm to about 1.8 nm) may, for example, have a different slope (sensitivity) parallel to response axis  699  than a spacer layer  734  having a thickness T 1  in a second one of the thickness ranges (e.g., about 2.2 nm to about 2.4 nm). 
     It is understood that thicknesses of layers other than spacer layer  713  in the first stack portion  710  and spacer layer  734  in the second stack portion  730  may be selected to result in the first and second stack portions  710 ,  730  having the first and second substantially linear ranges. It is also understood that the thicknesses of certain layers in the first and second stack portions  710 ,  730  may be selected to provide a desired amount and/or type of magnetic coupling between adjacent layers in the first and second stack portions  710 ,  730 . For example, the thickness of the spacer layer  713  in the first stack portion  710  may be selected to provide a desired amount of magnetic coupling between pinned layer  712  and free layer structure  714  in the first stack portion  710 . Additionally, the thickness of the spacer layer  713  may be selected to provide a desired type of magnetic coupling between the pinned layer  712  and the free layer structure  714 , i.e., ferromagnetic coupling or antiferromagnetic coupling, or between ferromagnetic and antiferromagnetic coupling. 
     Here, the coupling is shown to be ferromagnetic coupling, but, by selection of the thickness of the spacer layer  713 , the coupling can be antiferromagnetic or between ferromagnetic and antiferromagnetic coupling. In other words, in the absence of an applied magnetic field it is possible for a magnetization direction of the free layers  714   a ,  714   b  in the free layer structure  714  to be rotated either as shown (out of the page) or into the page, depending upon a selected thickness of the spacer layer  713 . Additionally, by selection of the thicknesses of the spacer layers  732 ,  734 , the coupling between layers adjacent to the spacer layers  732 ,  734  can be antiferromagnetic or ferromagnetic. 
     As another example, spacer layer  716   b  in the first stack portion  710  may have a first thickness (e.g., 0.85 nm) selected to provide a first magnetic coupling between surrounding layers (e.g., layers  716   a ,  716   c ) having a first coupling strength, and spacer layer  713  may have a second thickness (e.g., 3.3 nm) selected to provide a second magnetic coupling between surrounding layers (e.g., layers  712 ,  714 ) having a second coupling strength that is different than (e.g., less than) the first coupling strength. Ru may, for example, be well suited for the spacer layer  716   b  and the spacer layer  713  since it allows antiferromagnetic coupling or ferromagnetic coupling between surrounding layers according to the Ru thickness. In other words, the materials and thicknesses of layers in the first and second stack portions  710 ,  730  may be selected to achieve a particular magnetic coupling (or coupling strength) between surrounding layers. 
     In embodiments, the first and second substantially linear ranges are based, at least in part, upon the magnetic couplings occurring in the first and second stack portions  710 ,  730 . In embodiments, the magnetic couplings are the main (or a main) factor determining the first and second substantially linear responses. Additionally, in embodiments, an annealing process used to manufacture the MR element  700  may affect the magnetic couplings, especially an angle at which the coupling occurs. 
     In the illustrated embodiment, the first plurality of layers in the first stack portion  710  and the second plurality of layers in the second stack portion  730  are additionally shown arranged in a particular ordering. In embodiments, an ordering of the first plurality of layers in the first stack portion  710  corresponds to the at least one characteristic selected to result in the first stack portion  710  having the first substantially linear range. Additionally, in embodiments an ordering of the second plurality of layers in the second stack portion  730  corresponds to the at least one selected to result in the second stack portion  730  having the second substantially linear range. For example, due to the presence of the spacer layer  716   b  between the first and second pinned layers  716   a ,  716   c  in the pinned layer structure  716  of first stack portion  710 , the first pinned layer  716   a  tends to couple antiferromagnetically with the second pinned layer  716   c . As a result, the first pinned layer  716   a  has a magnetization direction that points in a direction that is different than a magnetization direction in which a magnetic field of the second pinned layer  716   b  points. In other words, an ordering of the spacer layer  716   b  and the first and second pinned layers  716   a ,  716   c  may affect a type of coupling (e.g., antiferromagnetic or ferromagnetic) which may occur between the first and second pinned layers  716   a ,  716   c , and the coupling may result in the first stack portion  710  having the first substantially linear range. 
     In general, it has been found that the arrangement and orientation of the ferromagnetic and non-ferromagnetic layers of the MR element  700  can affect the way the MR element  700  responds to the applied magnetic field. Additionally, different orientations of the ferromagnetic and non-ferromagnetic layers of the MR element  700  can produce different types of MR elements. In one embodiment, the MR element  700  is one of a giant magnetoresistance (GMR) element, a magnetic tunnel junction (MTJ) element and a tunneling magnetoresistance (TMR) element. 
     In the illustrated embodiment, the first plurality of layers in the first stack portion  710  and the second plurality of layers in the second stack portion  730  are also shown including a particular number of layers (here, nine layers). In embodiments, the number of layers provided in the first plurality of layers corresponds to the at least one characteristic selected to result in the first stack portion having the first substantially linear range. Additionally, in embodiments the number of layers provided in the second plurality of layers corresponds to the at least one characteristic selected to result in the second stack portion having the second substantially linear range. 
     In some embodiments, the first plurality of layers includes a same number of layers as the second plurality of layers, as shown in  FIG. 7 , for example. In other embodiments, the first plurality of layers includes a different number of layers than the second plurality of layers. An example MR element according to the disclosure comprising first and second stack portions having respective first and second pluralities of layers with a different number of layers is shown and described below in connection with  FIG. 12 , for example. 
     In general, it has been found that the materials, layer thicknesses, an ordering and a number of layers in the first and second stack portions  710 ,  730  can affect the manner in which the first and second stack portions  710 ,  730  of the MR element  700  respond to an applied magnetic field. 
     For example, in one embodiment the materials of spacer layer  713  in first stack portion  710  are selected to affect the manner in which the MR element  700  responds to the applied magnetic field, and provide for the various sub-regions  601   b ,  601   c ,  601   d ,  601   e  of the second substantially linear range shown in  FIG. 6 , for example. In the illustrated embodiment, for example, Ru was selected as a material for spacer layer  713  since with Ru it is possible to establish a relatively good coupling between free layer  714  and bias portions (e.g., layer  711  and/or layer  712 ) of the first stack portion  710 . With materials other than Ru (e.g., Ta) selected for spacer layer  713 , similar couplings may be achieved, but for different thicknesses of the layer  713 . In embodiments, the thickness of the Ru in spacer layer  713  may also affect the manner in which the MR element  700  responds to the applied magnetic field. For example, in some embodiments the coupling through the Ru in spacer layer  713  oscillates between ferromagnetic (F) and antiferromagnetic (AF) and for some thicknesses of Ru the coupling is close to zero. The type of the coupling (AF vs F) may not determine the linear range of a linear region (e.g., linear region  601   a ), but a strength of the coupling may determine (or at least impact) the linear range. As one example, if the thickness of the Ru in spacer layer  713  in first stack portion  710  provides for a coupling strength that is similar to a coupling strength obtained through spacer layer  734  in second stack portion  730 , the first and second stack portions  710 ,  730  may behave in a same or similar way and the desired piecewise response may not be provided. However, if one of spacer layers  713 ,  734  has a thickness (and/or material) that provides for a coupling amplitude that is lower than the other, the piecewise response may appear. In one embodiment, the lower the coupling strength, the narrower the magnetic field strength range  603   a  of linear region  601   a , for example. In embodiments in which there is substantially no coupling, there is a steep transition (i.e., a steep slope or increased sensitivity) in linear region  601   a.    
     While MR element  700  is shown as having particular layers formed from particular materials, it is understood that the MR element  700  is illustrative of one example configuration of an MR element according to the disclosure. Other layers and materials can, for example, be provided in the MR element  700 . Additionally, one or more of the above-described layers of MR element  700  may include a plurality of layers (or sub-layers) in some embodiments. Additionally, in some embodiments, one or more other layers (not shown) can be interposed between the layers of MR element  700 . 
     In embodiments, the MR element  700  is provided in a magnetic field sensor (e.g.,  1500 , shown in  FIG. 15 , as discussed below) or another sensing circuit. As discussed above, a magnetic field sensor is used to describe a circuit that uses a magnetic field sensing element, generally in combination with other circuits. In embodiments, the MR element  700  and the other circuits of the magnetic field sensor can be integrated upon a common substrate (here, substrate  701 ). 
     Additional aspects of MR elements according to the disclosure are described below. 
     Referring now to  FIG. 8 , in which like elements of  FIG. 7  are provided having like reference designations, a second example MR element  800  according to the disclosure includes a first stack portion  810  and a second stack portion  830 . The first stack portion  810  has first and second opposing surfaces, with first surface of the first stack portion  810  disposed over seed layer  702  and the seed layer  702  disposed between the first stack portion  810  and the substrate  701  on which the MR element  800  is deposited on. Additionally, the second stack portion  830  has first and second opposing surfaces, with the first surface of the second stack portion  830  disposed over pinning layer  720  and the pinning layer  720  disposed between the first stack portion  810  and the second stack portion  830 . Cap layer  704  is disposed over the second surface of the second stack portion  830 . 
     The first stack portion  810  includes a first plurality of layers (here, 9 layers). The first plurality of layers includes pinning layer  711 , pinned layer  712  and a spacer layer  813 . The first stack portion  810  also includes free layer structure  714 , spacer layer  715  and pinned layer structure  716 . The first free layer structure  714  includes first free layer  714   a  and second free layer  714   b . Additionally, the pinned layer structure  716  includes first pinned layer  716   a , second pinned layer  716   c  and spacer layer  716   b.    
     The pinning layer  711  is disposed over the seed layer  702  and the pinned layer  712  is disposed over the pinning layer  711 . Additionally, spacer layer  813  is disposed over the pinned layer  712  and free layer structure  714  is disposed over the spacer layer  813 . Further, spacer layer  715  is disposed over the free layer structure  714  and pinned layer structure  716  is disposed over the spacer layer  715 . Spacer layer  813 , which may be similar to spacer layer  713  of MR element  700  shown in  FIG. 7  but having a thickness that is different than a thickness of the spacer layer  713 , may be a nonmagnetic spacer layer. 
     The second stack portion  830  includes a second plurality of layers (here, 9 layers), i.e., a same number of layers as the first plurality of layers of first stack portion  810  in the illustrated embodiment. The second plurality of layers includes pinned layer structure  731 , spacer layer  732  and free layer structure  733 . The second plurality of layers also includes spacer layer  834  and pinned layer  735 . The pinned layer structure  731  includes first pinned layer  731   a , second pinned layer  731   c  and spacer layer  731   b . Additionally, free layer structure  733  includes first free layer  733   a  and second free layer  733   b.    
     The pinned layer structure  731  is disposed over the pinning layer  720  and the spacer layer  732  is disposed over the pinned layer structure  731 . Additionally, the free layer structure  733  is disposed over the spacer layer  732  and the spacer layer  834  is disposed over the free layer structure  733 . Further, the pinned layer  735  is disposed over the spacer layer  834  and the pinning layer  736  is disposed over the pinned layer  735 . Spacer layer  834 , which may be similar to spacer layer  734  of MR element  700  shown in  FIG. 7  but having a thickness that is different than a thickness of the spacer layer  734 , may be a nonmagnetic spacer layer comprising one or more nonmagnetic materials (e.g., Ru). 
     Similar to first stack portion  710  in MR element  700  of  FIG. 7 , the first stack portion  810  in MR element  800  has a first substantially linear response corresponding to an applied magnetic field over a first range of magnetic field strengths (i.e., a first magnetic field strength range). Additionally, similar to second stack portion  730  in MR element  700  of  FIG. 7 , the second stack portion  830  in MR element  800  has a second substantially linear response that is different than the first substantially linear response, the second substantially linear response corresponding to the applied magnetic field over a second range of magnetic field strengths (i.e., a second magnetic field strength range). In embodiments, the first magnetic field strength range overlaps with one or more portions of the second magnetic field strength range. The MR element  800  has a maximum response axis to the applied magnetic field which is parallel to the substrate surface (e.g., a first surface of the substrate  801 ) over which the MR element  800  is disposed, as indicated by arrow  799 . 
     The first stack portion  810  has at least one characteristic selected to result in the first stack portion  810  having the first substantially linear response. Additionally, the second stack portion  830  has at least one characteristic selected to result in the second stack portion  830  having the second substantially linear response. The at least one characteristic may include: materials, layer thickness and an ordering of one or more of the layers in the first and second stack portions  810 ,  830 . Additionally, the at least one characteristic may also include a number of layers in the first and second stack portions  810 ,  830 . 
     In the illustrated embodiment, the thickness of spacer layer  813  in first stack portion  810  may, for example, correspond to the at least one characteristic selected to result in the first stack portion  810  having the first substantially linear response. For example, the spacer layer  813  may have a thickness selected (here, about 1.3 nm) to result in the first stack portion  810  having a first predetermined bias (e.g., a “strong” bias) which, in turn, may result in the first stack portion  810  having the first substantially linear response. 
     Additionally, in the illustrated embodiment, the thickness T 2  of spacer layer  834  in second stack portion  830  may correspond to the at least one characteristic selected to result in the second stack portion  830  having the second substantially linear response. For example, the spacer layer  834  may have a thickness selected (e.g., about 1.7 nm) to result in the second stack portion  830  having a second predetermined bias (e.g., a “very weak” bias) which, in turn, may result in the second stack portion  830  having the second substantially linear response. 
     In embodiments, the first stack portion  810  of MR element  800  has a first substantially linear response that is different than the first substantially linear response of first stack portion  710  of MR element  700 , e.g., due to the at least one characteristic selected to result in the first stack portion  810  having the first substantially linear response. For example, in the illustrated embodiment, spacer layer  813  of first stack portion  810  having a different thickness than spacer layer  713  of first stack portion  710  may result in the first stack portion  810  of MR element  800  having a first substantially linear response that is different than the first substantially linear response of first stack portion  710  of MR element  700 . 
     Additionally, the first stack portion  810  having a first substantially linear response that is different than the first substantially linear response of first stack portion  710  of MR element  700  may, for example, result in the first stack portion  810  having a first sensitivity level (i.e., rate of change in resistance) to changes in magnetic field strengths over a first range of magnetic field strengths that is different than a first sensitivity level of the first stack portion  710  over a similar range of magnetic fields strengths as the first range of magnetic field strengths. In embodiments, the first stack portion  810  may have a first sensitivity level that is substantially the same as a first sensitivity level of the first stack portion  710 , but over a different range of magnetic field strengths, for example. As discussed above, in embodiments, the first range of magnetic field strengths may be based upon the at least one characteristic selected to result in the first stack portion (e.g.,  810 ) having the first substantially linear response. 
     Additionally, in embodiments, the second stack portion  830  of MR element  800  has a second substantially linear response that is different than the second substantially linear response of second stack portion  730  of MR element  700  due to the at least one characteristic selected to result in the second stack portion  830  having the second substantially linear response. For example, in the illustrated embodiment, spacer layer  834  of second stack portion  830  of MR element  800  having a thickness T 2  that is different from a thickness T 1  of spacer layer  734  of second stack portion  730  of MR element  700  may result in the second stack portion  830  of MR element  800  having a second substantially linear response that is different than the second substantially linear response of second stack portion  730  of MR element  700 . 
     In one embodiment, first stack portion  710  of MR element  700  has a first coupling strength and the first stack portion  810  of MR element  800  has a second coupling strength that is different from (e.g., larger than) the first coupling strength. The foregoing may be due to the first stack portion  810  of MR element  800  having one or more characteristics that are different from one or more characteristics of the first stack portion  710  of MR element  700 . For example, as illustrated, spacer layer  813  of first stack portion  810  has a thickness that is different from spacer layer  713  of first stack portion  710 . In embodiments, such may result in the second coupling strength of the first stack portion  810  of MR element  800  being larger than the first coupling strength of the first stack portion  710  of MR element  700 . The larger coupling strength of the first stack portion  810  may, for example, result in the MR element  800  having a plurality of substantially linear sub-regions that are different from a like plurality of substantially linear regions or sub-regions of MR element  700 . For example, with respect to the curves  602 ,  604  shown in  FIG. 6 , the MR element  800  may have second and third substantially linear regions (e.g.,  601   b ,  601   c ) with magnetic field strength sub-ranges (e.g.,  603   b ,  603   d ) that are different from (e.g., larger than) magnetic field strength sub-ranges associated with second and third substantially linear regions of the MR element  700 . Additionally, the MR element  800  may have fourth and fifth substantially linear regions (e.g.,  601   d ,  601   e ) with magnetic field strength sub-ranges (e.g.,  603   d ,  603   e ) that are different from (e.g., larger than) magnetic field strength sub-ranges associated with fourth and fifth substantially linear regions of the MR element  700 . Further, the MR element  800  may have a first sensitivity level over a first magnetic field strength sub-range (e.g.,  603   a ) that is different from (e.g., larger than) a first sensitivity level over the MR element  700  over a corresponding first magnetic field strength sub-range. 
     In one embodiment, the second coupling strength of the first stack portion  810  of MR element  800  corresponds to a coupling strength of about 200 Oe, which may be representative of a very strong coupling strength. One example results of the second coupling strength of first stack portion  810  of MR element  800  being so strong is that many thicknesses of spacer layer  834  in second stack portion  830  of MR element  800 , especially thicknesses of above about 2.3 nm in some embodiments, may provide for the MR element  800  having a substantially piecewise linear response. MR element  800  may, for example, have a relatively narrow first substantially linear region (e.g.,  601   a ) and a relatively high first sensitivity level over a first magnetic field strength sub-range (e.g.,  603   a ) when spacer layer  834  has a thickness of about 2.4 nm, 3.1 nm, 3.6 nm and 4.3 nm. 
     The second stack portion  830  having a second substantially linear response that is different than the second substantially linear response of first stack portion  730  of MR element  700  may also result in the second stack portion  830  having a second sensitivity level (i.e., rate of change in resistance) to changes in magnetic field strengths over a second range of magnetic field strengths that is different than a second sensitivity level of the second stack portion  730  over a similar range of magnetic fields strengths as the first range of magnetic field strengths. In embodiments, the second stack portion  830  may have a second sensitivity level that is substantially the same as a second sensitivity level of the second stack portion  730 , but over a different range of magnetic field strengths, for example. As discussed above, in embodiments, the second range of magnetic field strengths may be based upon the at least one characteristic selected to result in the second stack portion (e.g.,  830 ) having the second substantially linear response. 
     In embodiments, the MR element  800  is provided in a magnetic field sensor (e.g.,  1500 , shown in  FIG. 15 , as discussed below), and the MR element  800  is configured to generate the first and second substantially linear responses discussed above. Additionally, in embodiments, the first and second substantially linear responses have substantially zero offset with respect to an expected response of the MR element  800  at an applied magnetic field strength of about zero Oersteds (i.e., the MR element  800  is annealed for a substantially zero offset). The foregoing may, for example, result in the MR element  800  having substantially no offset, for example, when experiencing an applied magnetic field having a magnetic field strength of about zero Oersteds. Additionally, the foregoing may result in the linear range of the MR element  800  being substantially evenly distributed about zero Oersteds, as further discussed below. 
     Referring to  FIG. 9 , in which like elements of  FIG. 7  are shown having like reference designations, a third example MR element  900  includes a first stack portion  910  and a second stack portion  930 . The first stack portion  910  has first and second opposing surfaces, with the first surface of the first stack portion  910  disposed over seed layer  702  and the seed layer  702  disposed between the first stack portion  910  and the substrate  701  on which the MR element  900  is deposited upon. Additionally, the second stack portion  930  has first and second opposing surfaces, with the first surface of the second stack portion  930  disposed over pinning layer  720  and the pinning layer  720  disposed between the first stack portion  910  and the second stack portion  930 . Cap layer  704  is disposed over the second surface of the second stack portion  930 . 
     The first stack portion  910  includes a first plurality of layers (here, 6 layers), i.e., fewer layers than first stack portion  710  of MR element  700  shown in  FIG. 7  and first stack portion  810  of MR element  800  shown in  FIG. 8 . The first plurality of layers includes free layer structure  714 , spacer layer  715  and pinned layer structure  716 . The free layer structure  714  includes first free layer  714   a  and second free layer  714   b . Additionally, the pinned layer structure  716  includes first pinned layer  716   a , second pinned layer  716   c  and spacer layer  716   b.    
     The free layer structure  714  is disposed over the seed layer  702  and the spacer layer  715  is disposed over the free layer structure  714 . Additionally, the pinned layer structure  716  is disposed over the spacer layer  715 . 
     The second stack portion  930  includes a second plurality of layers (here, 6 layers), i.e., a same number of layers as the first plurality of layers of first stack portion  910  in the illustrated embodiment. The second plurality of layers includes pinned layer structure  731 , spacer layer  732  and free layer structure  733 . The pinned layer structure  731  includes first pinned layer  731   a , second pinned layer  731   c  and spacer layer  731   b . Additionally, the free layer structure  733  includes first free layer portion  733   a  and second free layer portion  733   b.    
     The pinned layer structure  731  is disposed over the pinning layer  720  and the spacer layer  732  is disposed over the pinned layer structure  731 . Additionally, the free layer structure  733  is disposed over the spacer layer  732 . 
     Similar to first stack portion  810  in MR element  800  of  FIG. 8 , the first stack portion  910  in MR element  900  has a first substantially linear response corresponding to an applied magnetic field over a first magnetic field strength range. Additionally, similar to second stack portion  830  in MR element  800  of  FIG. 8 , the second stack portion  1130  in MR element  900  has a second substantially linear response that is different than the first substantially linear response, the second substantially linear response corresponding to the applied magnetic field over a second magnetic field strength range. The MR element  900  has a maximum response axis to magnetic fields (e.g., the applied magnetic field) which is parallel to the substrate surface (e.g., a first surface of the substrate  701 ) over which the MR element  900  is disposed, as indicated by arrow  899 . 
     The first stack portion  910  has at least one characteristic selected to result in the first stack portion  910  having the first substantially linear response. Additionally, the second stack portion  930  in MR element  900  has at least one characteristic selected to result in the second stack portion  930  having the second substantially linear response. As discussed in figures above, the at least one characteristic may include: materials, layer thickness and an ordering of one or more of the layers in the first and second stack portions  910 ,  930 . Additionally, the at least one characteristic may also include a number of layers in the first and second stack portions  910 ,  930 . 
     In the illustrated embodiment, materials and/or layer thicknesses of the first and second free layers  714   a ,  714   b  of free layer structure  714  in the first stack portion  910  may, for example, correspond to the at least one characteristic selected to result in the first stack portion  910  having the first substantially linear response. For example, the first and second free layer layers  714   a ,  714   b  may have materials and/or layer thickness selected to result in the free layer structure  714  being a substantially unbiased free layer which, in turn, may result in the first stack portion  910  having the first substantially linear response. 
     Additionally, in embodiments, the number of layers in the first and second stack portions  910 ,  930  may be selected alone, or in combination with materials, layer thickness and an ordering of one or more of the layers in the first and second stack portions  910 ,  930  to result in the first and second substantially linear responses. In other words, the at least one characteristic selected to result in the first and second substantially linear responses may include the number of layers in the first and second stack portions  910 ,  930  and materials, layer thickness and an ordering of one or more of the layers in the first and second stack portions  910 ,  930 . 
     In some embodiments, the first stack portion  910  has a same or similar first substantially linear response as the first substantially linear response of the first stack portion  810  in MR element  800  of  FIG. 8  despite comprising a different number of layers than the first stack portion  810 . Additionally, in some embodiments, the second stack portion  930  has a same or similar second substantially linear response as the second substantially linear response of the second stack portion  830  in MR element  800  of  FIG. 8  despite comprising a different number of layers than the second stack portion  830 . For example, materials, layer thickness and/or an ordering of one or more of the layers in the first stack portion  910  may be selected to result in the first stack portion  910  having a same or similar substantially linear response as the first substantially linear response of the first stack portion  810 . In other words, materials, layer thickness and/or an ordering of one or more of the layers in the first stack portion  910  may comprise the at least one characteristic selected to result in the first stack portion  910  having the first substantially linear response. 
     It is understood that the first stack portion  910  may also have a first substantially linear response that is different from the first substantially linear response of the first stack portion  810 . Additionally, it is understood that the first stack portion  910  having a first substantially linear response that is different than the first substantially linear response of first stack portion  810  may, for example, result in the first stack portion  910  having a first sensitivity level (i.e., rate of change in resistance) to changes in magnetic field strengths over a first range of magnetic field strengths that is different than a first sensitivity level of the first stack portion  810  over a similar range of magnetic fields strengths as the first range of magnetic field strengths. 
     Referring now to  FIG. 10 , a plot  1000  shows curves  1002 ,  1004  representative of first example response characteristics of the MR element  900  of  FIG. 9  as it is exposed to magnetic fields of varying strengths in a transverse direction relative to the maximum response axis  899  of the MR element  900 . The plot  1000  has a horizontal axis with a scale in magnetic field strength units (here, Oersteds (Oe)) and a vertical axis with a scale in resistance units (here, Ohms). Similar to plots  300  and  500  shown in  FIGS. 3 and 5 , respectively, positive magnetic field strength units (e.g., +X) in plot  1000  may correspond to a magnetic field experienced by the MR element  900  in a first direction, such as in response to a first direction of motion (e.g., rotation) by an object (e.g., ring magnet  1510 , shown in  FIG. 15 ). Additionally, negative magnetic field strength units (e.g., −X) in plot  1000  may correspond to a magnetic field experienced by the MR element  900  in a second direction that is opposite from the first direction, such as in response to a second direction of motion by the object that is opposite from the first direction of motion of the object. 
     Curve  1002  corresponds to a response characteristic of the MR element  900  as it is exposed to a magnetic field that sweeps from a positive magnetic field strength value (e.g., 600 Oe) to a negative magnetic field strength value (e.g., −500 Oe), e.g., from the first direction of motion to the second direction of motion. Additionally, curve  1004  corresponds to a response characteristic of the MR element  900  as it exposed to a magnetic field that sweeps a negative magnetic field strength value (e.g., −500 Oe) to a positive magnetic field strength value (e.g., 600 Oe), e.g., from the second direction of motion to the first direction of motion. 
     Curves  1002 ,  1004  have a first substantially linear region  1001   a  and a second substantially linear region (here, a second substantially linear region including substantially linear sub-regions  1001   b ,  1001   c ). Curves  1002 ,  1004  also have first and second saturation regions  1001   d ,  1001   e . As is illustrated, sub-region  1001   b  of the second substantially linear region is separated from sub-region  1001   c  of the second substantially linear region by the first substantially linear region  1001   a.    
     A first end of the first substantially linear region  1001   a  occurs at a point at which the first substantially linear region  1001   a  has a slope that deviates from an average slope of a sub-region of the second substantially linear region with which it is associated, for example, sub-region  1001   b , by a predetermined amount (e.g., about five percent). Additionally, a second opposing end of the first substantially linear region  1001   a  occurs at a point at which the first substantially linear region  1001   a  has a slope that deviates from the average slope of a sub-region of the second substantially linear region with which it is associated, for example, sub-region  1001   c , by about predetermined amount (e.g., about five percent). The first and second substantially linear regions (i.e., regions  1001   a ,  1001   b ,  1001   c ) correspond to an operational range of the MR element  900  in the illustrated embodiment in which the MR element  900  has a resistance that is substantially responsive to changes in magnetic field strength of the applied magnetic field. 
     In embodiments, the first substantially linear region  1001   a  corresponds to the first substantially linear response of the first stack portion  910  of MR element  900  discussed above in connection with  FIG. 9 , with the first substantially linear response corresponding to an applied magnetic field over a first magnetic field strength range  1003   a  (here, between about −5 Oe and about 5 Oe, i.e., a limited range of magnetic field strengths). 
     Additionally, in embodiments, the second substantially linear region (i.e., sub-regions  1001   b ,  1001   c ) corresponds to the second substantially linear response of the second stack portion  930  of MR element  900  discussed above in connection with  FIG. 9 , with the second substantially linear response corresponding to the applied magnetic field over a second magnetic field strength range (here, a second magnetic field strength range including sub-ranges  1003   b ,  1003   c ). In the illustrated embodiment, sub-range  1003   b  comprises magnetic field strengths between about −5 Oe and about −100 Oe). Additionally, in the illustrated embodiment, sub-range  1003   c  comprises magnetic field strengths between about 5 Oe and about 80 Oe). 
     As discussed above, the second substantially linear response of second stack portion  930  is different than the first substantially linear response of first stack portion  910 . In the illustrated embodiment, the second substantially linear response occurs over a second range of magnetic field strengths (here, sub-ranges  1003   b ,  1003   c ) that is different than the first range of magnetic field strengths  1003   a . In embodiments, the MR element  900  has a respective substantially linear response in each of the sub-regions  1001   b ,  1001   c  of the second substantially linear region associated with the second substantially linear response, with the substantially linear responses of the MR element  900  in sub-regions  1001   b ,  1001   c  (e.g., fourth and fifth substantially linear responses) comprising the second substantially linear response of the second substantially linear region. 
     The first substantially linear response of the first stack portion  910  results in the MR element  900  having a first sensitivity level (i.e., a first rate of change in resistance) to changes in magnetic field strength when the applied magnetic field is within the first range of magnetic field strengths  1003   a . The first sensitivity level may be determined, for example, by observing an average slope of curves  1002 ,  1004  in first substantially linear region  1001   a . Additionally, the second substantially linear response of the second stack portion  930  results in the magnetoresistance element having a second sensitivity level (i.e., a second rate of change in resistance) to changes in magnetic field strength when the applied magnetic field is within the second range of magnetic field strengths (here, sub-ranges  1003   b ,  1003   c ). The second sensitivity level may be determined, for example, by observing an average slope of curves  1002 ,  1004  in the second substantially linear region (i.e., sub-regions  1001   b ,  1001   c  of the second substantially linear region). 
     The second sensitivity level is reduced in comparison to the first sensitivity level in the illustrated embodiment. It follows that the MR element  900  has a higher sensitivity to changes in magnetic field strength in the first substantially linear region  1001   a  (i.e., over a small or limited range a magnetic fields) than it does to changes in magnetic field strength in the second substantially linear region (i.e., sub-regions  1001   b ,  1001   c , which comprise a more expansive range of magnetic fields than region  1001   a ). The first sensitivity level of the MR element  900  in the illustrated embodiment (e.g., resulting in the MR element  900  having a resistance that substantially varies at a magnetic field strength of about zero) may, for example, be given by rotation of free layer  714  or other layers of the first stack portion  910  of MR element  900 . Additionally, the first sensitivity level of the MR element  900  may be due to the lack of a biasing part (e.g., layer  712 , shown in  FIG. 7 ) in the MR element  900 . The illustrated first sensitivity level of the MR element  900  may, for example, be desirable in embodiments in which an absolute field sensor is not needed, but it is desirable for the MR element  900  (e.g., an output of the MR element  900 ) to switch at a certain threshold or range of magnetic field strengths. In other embodiments, the first sensitivity level may have a reduced sensitivity (i.e., a reduced slope in region  1001   a ) from that which is shown. Additionally, in other embodiments, the first sensitivity level may be reduced in comparison to the second sensitivity level. 
     In embodiments, MR element  900  has a respective sensitivity level to changes in magnetic field strength in the applied magnetic field in each of the sub-regions  1001   b ,  1001   c  of the second substantially linear region, with the sensitivity levels of the MR element  900  in the sub-regions  1001   b ,  1001   c  (e.g., fourth and fifth sensitivity levels) comprising the second sensitivity level of the second substantially linear region. 
     Additionally, in embodiments, at least one characteristic (e.g., layer thicknesses of one or more layers) of the first and second stack portions  910 ,  930  may be selected to tune or alter one or more regions of the curves  1002 ,  1004 , similar to the at least one characteristic selected to provide the first and second substantially linear responses of the first and second stack portions  710 ,  730  of MR element  700  discussed above in connection with  FIG. 7 , for example. 
     As illustrated, unlike prior art MR element  400  of  FIG. 4 , for example, in which the first and second stack portions  410 ,  430  behave antisymmetrically (i.e., substantially equal and opposite) to an applied magnetic field, resulting in the MR element  400  having a single substantially linear response over a single substantially linear region  401   a , as shown in plot  500 , the first and second stack portions  910 ,  930  of the MR element  900  have a first and second different, respective substantially linear responses to the applied magnetic field. As a result of the foregoing, the MR element  900  has a first substantially linear response over a first substantially linear region  1001   a  and a second substantially linear response that is different than the first substantially linear response over a second substantially linear region (here, sub-regions  1001   b ,  1001   c ) that is different than the first substantially linear region  1001   a . In embodiments, the first and second substantially linear responses of MR element  900  are provided at least in part from pinning layer  720 , more particularly the crystal structure coming from the PtMn growth of pinning layer  720 . This is contrast to the MR element  400  of  FIG. 4  in which Ru spacer layers  413 ,  434  provide for the single substantially linear response of MR element  400  in embodiments, for example, due to the Ru spacer layers  413 ,  434  stabilizing free layers  414 ,  433 . 
     As also illustrated, MR element  900  has a reduced offset compared to the prior art MR element  400  and to the prior art MR element  200 , as depicted by curves  1002 ,  1004  which are less horizontally offset with an intersection of the vertical and horizontal axes of plot  1000 , than curves  502 ,  504  shown in plot  500  of  FIG. 5  and curves  304 ,  304  shown in plot  300  of  FIG. 3 . As a result of the foregoing, the range of magnetic field strengths to which the MR element  900  is responsive also has a reduced offset compared the prior art MR element  400  and to the prior art MR element  200 . 
     In embodiments, the increased operational range of the MR element  900  may also provide for increased offset drift toleration by the MR element  900 , such as that which may occur due to temperature, age and/or a misalignment or misplacement between the MR element and an object (i.e., a magnetic field) sensed by the MR element  900 , for example. In particular, due to the increased operational range of MR element  900  (i.e., a greater range of magnetic fields that may be sensed by the MR element  900 ), MR element  900  may be able to sense magnetic fields that would otherwise not be detected by conventional MR elements (e.g., MR element  200 ), making offset drift may be more tolerable. In general, a MR element according to the disclosure having a first operational range may have an increased offset drift tolerance in comparison to a conventional MR element having a second operational range that is less than the first operational range. Remaining offset errors (if any) can, for example, be corrected in signal processing circuitry coupled an output (e.g., V OUT , shown in  FIG. 14 , as discussed below) of the MR element. 
     In embodiments, the increased operational range of the MR element  900  may further provide for improved immunity to common field interference by the MR element  900 . In particular, as is known in the art, common field interference may add an offset to a magnetic field signal (i.e., an applied magnetic field) to which an MR element (e.g.,  900 ) may experience. The offset could cause the MR element to become saturated if the linear or operational range of the MR element is too small. In embodiments, the increased linear or operational range of the MR element  900  (and other MR elements according to the disclosure) substantially reduces (or ideally prevents) saturation of the MR element  900  when subjected to common field interference (and the offset resulting from common field interference). 
     Referring now to  FIG. 11 , a plot  1100  shows curves  1102 ,  1104  representative of second example response characteristics (i.e., transfer curves) of the MR element  900  of  FIG. 9  as it is exposed to magnetic fields of varying strengths in a direction substantially parallel to the maximum response axis  899  of the MR element  900 . The plot  1100  has a horizontal axis with a scale in magnetic field strength units (here, Oersteds (Oe)) and a vertical axis with a scale in resistance units (here, Ohms). 
     Curve  1102  corresponds to a response characteristic of the MR element  900  as it is exposed to a magnetic field that sweeps from a positive magnetic field strength value (e.g., 200 Oe) to a negative value magnetic field strength value (e.g., −200 Oe). Additionally, curve  1104  corresponds to a response characteristic of the MR element  900  as it exposed to a magnetic field that sweeps from the negative magnetic field strength value (e.g., −200 Oe) to the positive magnetic field strength value (e.g., 200 Oe). 
     As illustrated, the curves  1102 ,  1104  have first and second substantially linear regions  1101   a ,  1101   b  in which the MR element  900  characterized by curves  1102 ,  1104  has a relatively low resistance when exposed to lower strength magnetic fields. Additionally, the curves  1102 ,  1104  have first and second saturation regions  1101   c ,  1101   d  in which the MR element  900  has a relatively high resistance when exposed to a higher strength magnetic fields. In substantially linear region  1101   a , the MR element  900  characterized by curves  1102 ,  1104  has a first substantially linear response corresponding to the applied magnetic field greater than a first threshold, or within a first magnetic field strength range. Additionally, in substantially linear region  1101   b , the MR element  900  has a second substantially linear response that is different than the first substantially linear response, the second substantially linear response corresponding to the applied magnetic field less than a second threshold, or within a second magnetic field strength range. In the saturation regions  1101   c ,  1101   d , the MR element  900  is substantially unresponsive to the applied magnetic field. 
     As also illustrated, the curves  1102 ,  1104  have respective peaks  1102   a ,  1104   a  at about zero Oersteds. Additionally, curves  1102 ,  1104  are substantially centered around zero Oersteds, and the substantially linear ranges  1101   a ,  1101   b  of the MR element  900  are substantially uniform in magnitude of ranges of magnetic field strengths (−Oe to +Oe). In embodiments, such corresponds to the MR element characterized by curves  1102 ,  1104  having a small (ideally, nonexistent) offset. 
     In embodiments, the peaks of curves associated with MR elements according to the disclosure (similar to peaks  1102   a ,  1104   a  of curves  1102 ,  1104 ) generally appear at an amplitude corresponding to a bias field, with the bias field determined by a thickness of one or more layers (e.g., Ru spacers  713  and  734 ) of the MR element. However, the MR element  900  to which curves  1102 ,  1104  shown in  FIG. 11  are associated with, for example, does not have Ru spacers (e.g., Ru spacers  713  and  734 ) and a biasing part. One example result of the foregoing is peaks  1102   a ,  1104   a  of curves  1102 ,  1104  are substantially overlapping at about zero Oersteds. 
     Referring to  FIG. 12 , in which like elements of  FIGS. 8 and 11  are shown having like reference designations, a fourth example MR element  1200  includes a first stack portion  910  and a second stack portion  1230 . The first stack portion  910  has first and second opposing surfaces, with the first surface of the first stack portion  910  disposed over seed layer  702  and the seed layer  702  disposed between the first stack portion  910  and the substrate on which the MR element  1200  is deposited upon. Additionally, the second stack portion  1230  has first and second opposing surfaces, with the first surface of the second stack portion  1230  disposed over pinning layer  720  and the pinning layer  720  disposed between the first stack portion  910  and the second stack portion  930 . Cap layer  704  is disposed over the second surface of the second stack portion  1230 . 
     The first stack portion  910  (i.e., a same first stack portion as the first stack portion of MR element  900 ) includes a first plurality of layers (here, 6 layers). Additionally, the second stack portion  1230  includes a second plurality of layers (here, 9 layers), i.e., a different number of layers as the first plurality of layers. 
     The second plurality of layers of second stack portion  1230  includes pinned layer structure  731 , spacer layer  732  and free layer structure  733 . The second plurality of layers also includes a spacer layer  1234 , pinned layer  735  and pinning layer  736 . The pinned layer structure  731  includes first pinned layer  731   a , second pinned layer  731   c  and spacer layer  731   b . Additionally, free layer structure  733  includes first free layer  733   a  and second free layer  733   b.    
     The pinned layer structure  731  is disposed over the pinning layer  720  and the spacer layer  732  is disposed over the pinned layer structure  731 . Additionally, the free layer structure  733  is disposed over the spacer layer  732  and the spacer layer  1234  is disposed over the free layer structure  733 . Further, the pinned layer  735  is disposed over the spacer layer  1234  and the pinning layer  736  is disposed over the pinned layer  735 . Spacer layer  1234 , which may be similar to spacer layer  734  of MR element  700  shown in  FIG. 7  but having a thickness that is different than a thickness of the spacer layer  734 , may be a nonmagnetic spacer layer comprising one or more nonmagnetic materials (e.g., Ru). 
     The first stack portion  910  in the MR element  1200  has a first substantially linear response corresponding to an applied magnetic field over a first magnetic field strength range. Additionally, the second stack portion  1230  in the MR element  1200  has a second substantially linear response that is different than the first substantially linear response, the second substantially linear response corresponding to the applied magnetic field over a second magnetic field strength range. The MR element  1200  has a maximum response axis to magnetic fields (e.g., the applied magnetic field) which is parallel to the substrate surface (e.g., a first surface of the substrate  701 ) over which the MR element  1200  is disposed, as indicated by arrow  1199 . 
     The first stack portion  910  has at least one characteristic selected to result in the first stack portion  910  having the first substantially linear response. Additionally, the second stack portion  1230  has at least one characteristic selected to result in the second stack portion  1230  having the second substantially linear response. 
     In the illustrated embodiment, the thickness of spacer layer  1234  in second stack portion  1230  may, for example, correspond to the at least one characteristic selected to result in the second stack portion  1230  having the second substantially linear response. For example, the spacer layer  1234  may have a thickness selected (here, about 4 nm) to result in the second stack portion  1230  having an antiferromagnetic partial bias which, in turn, may result in the second stack portion  1230  having the second substantially linear response. 
     Referring to  FIG. 13 , in which like elements of  FIG. 8  are shown having like reference designations, a fifth example MR element  1300  includes a first stack portion  810 , a second stack portion  1330  and a third stack portion  1350 , i.e., an additional stack portion over the MR elements discussed in figures above. The first stack portion  810  has first and second opposing surfaces, with the first surface of the first stack portion  810  disposed over the seed layer  702  and the seed layer  702  disposed between the first stack portion  810  and the substrate  701  on which the MR element  1300  is deposited upon. Additionally, the second stack portion  1330  has first and second opposing surfaces, with the first surface of the second stack portion  1330  disposed over pinning layer  720  and the pinning layer  720  disposed between the first stack portion  810  and the second stack portion  1330 . Further, the third stack portion  1350  has first and second opposing surfaces, with the first surface of the third stack portion disposed over a pinning layer  1340  and the pinning layer  1340  disposed between the second stack portion  1330  and the third stack portion  1350 . Cap layer  704  is disposed over the second surface of the third stack portion  1350 . 
     The first stack portion  810  (i.e., a same stack portion as the first stack portion of MR element  800  of  FIG. 8 ) includes a first plurality of layers (here, 9 layers). Additionally, the second stack portion  1330  includes a second plurality of layers (here, 8 layers), i.e., a different number of layers than the first plurality of layers. Further, the third stack portion  1350  includes a third plurality of layers (here, 9 layers), i.e., a same number of layers as the first plurality of layers and a different number of layers than the second plurality of layers. 
     The second plurality of layers of the second stack portion  1330  includes pinned layer structure  731 , spacer layer  732  and free layer structure  733 . The second plurality of layers also includes a spacer layer  834  and pinned layer  735 . The pinned layer structure  731  includes first pinned layer  731   a , second pinned layer  731   c  and spacer layer  731   b . Additionally, free layer structure  733  includes first free layer  733   a  and second free layer  733   b.    
     The pinned layer structure  731  is disposed over the pinning layer  720  and the spacer layer  732  is disposed over the pinned layer structure  731 . Additionally, the free layer structure  733  is disposed over the spacer layer  732  and the spacer layer  834  is disposed over the free layer structure  733 . Further, the pinned layer  735  is disposed over the spacer layer  834 . 
     The third plurality of layers of third stack portion  1350  includes a pinned layer  1351 , a spacer layer  1352  and a free layer structure  1353 . The third plurality of layers also includes a spacer layer  1354 , a pinned layer structure  1355  and a pinning layer  1356 . The free layer structure  1353 , which may be the same as or similar to free layer structure  714  in the first stack portion  810  in some embodiments, includes first free layer  1353   a  and second free layer  1353   b . Additionally, the pinned layer structure  1355 , which may be the same as or similar to pinned layer structure  716  in first stack portion  810  in some embodiments, includes first pinned layer  1355   a , second pinned layer  1355   c  and spacer layer  1355   b.    
     In embodiments, pinned layer  1351  may be a ferromagnetic pinned layer, spacer layer  1352  may be a nonmagnetic spacer layer and free layer structure  1353  may be an unbiased free layer. Additionally, in embodiments, spacer layer  1354  may be a nonmagnetic spacer layer, pinned layer structure  1355  may include an SAF pinned layer structure or layer and pinning layer  1356  may be an antiferromagnetic pinning layer  1356 . First free layer  1353   a  of free layer structure  1353  may be a ferromagnetic free layer and second free layer  1353   b  of free layer structure  1353  may be a ferromagnetic free layer. Additionally, first pinned layer  1355   a  of pinned layer structure  1355  may be ferromagnetic pinned layer, second pinned layer  1355   c  of pinned layer structure  1355  may be a ferromagnetic pinned layer, and spacer layer  1355   b  of pinned layer structure  1355  may be a nonmagnetic spacer layer. 
     The first stack portion  810  has a first substantially linear response corresponding to an applied magnetic field over a first magnetic field strength range. Additionally, the second stack portion  1330  has a second substantially linear response that is different than the first substantially linear response. The second substantially linear response corresponds to the applied magnetic field over a second magnetic field strength range. The third stack portion  1350  has a third substantially linear response that is different from both the first substantially linear response and the second substantially linear response. The third substantially linear response corresponds to an applied magnetic field between, or overlapping with, the first magnetic field strength range and the second magnetic field strength range. In one embodiment, the first substantially linear response has a first bias amplitude at about 100 Oe, the second substantially linear response has a second bias amplitude of about 10 Oe and the third substantially linear response has a third bias amplitude of about 50 Oe (i.e., between the first and second bias amplitudes). In embodiments, the respective bias amplitudes correspond to magnetic field strengths at which the stack portions of the MR element are most responsive or sensitive to changes in magnetic field strength. 
     Similar to MR elements discussed in figures above, each of the stack portions  810 ,  1330 ,  1350  in MR element  1300  has at least one characteristic selected to result in the stack portions  810 ,  1330 ,  1350  having their respective substantially linear responses (e.g., first, second, third, etc. substantially linear responses, like those which occur in regions  601   a ,  601   b ,  601   c  shown in plot  600  of  FIG. 6 ) to the applied magnetic field. 
     In the illustrated embodiment, the thickness of spacer layer  813  in first stack portion  810  may, for example, correspond to the at least one characteristic selected to result in the first stack portion  810  having the first substantially linear response. For example, the spacer layer  813  may have a thickness selected (here, about 1.3 nm) to result in the first stack portion  810  having a first predetermined bias (e.g., a “strong” bias of about 200 Oe) which, in turn, may result in the first stack portion  810  having the first substantially linear response. 
     Additionally, in the illustrated embodiment, the thickness T 2  of spacer layer  834  in second stack portion  1330  may correspond to the at least one characteristic selected to result in the second stack portion  1330  having the second substantially linear response. For example, the spacer layer  834  may have a thickness T 2  selected to be a particular value (e.g., about 1.7 nm) to result in the second stack portion  1330  having a second predetermined bias (e.g., a “very weak” bias of less than about 10 Oe) which, in turn, may result in the second stack portion  1330  having the second substantially linear response. 
     Further, in the illustrated embodiment, the thickness of spacer layer  1352  in third stack portion  1350  may correspond to the at least one characteristic selected to result in the third stack portion  1350  having the third substantially linear response. For example, the spacer layer  1352  may have a thickness selected (here, about 2.6 nm) to result in the third stack portion  1350  having a third predetermined bias (e.g., a “moderate” bias of about 70 Oe) which, in turn, may result in the third stack portion  1350  having the third substantially linear response. 
     It is understood that other characteristics (e.g., materials, layer thicknesses, etc.) of the first, second and third stack portions  810 ,  1330 ,  1350  may additionally or alternatively be selected to result in the first, second and third stack portions  810 ,  1330 ,  1350  having their respective first, second and third substantially linear responses. 
     While MR elements including two or three so-called “stack portions” are shown in  FIGS. 7, 8, 9, 12 and 13 , it is understood that MR elements according to the disclosure may include more than three stack portions in some embodiments. Additionally, it is understood that the MR elements shown in  FIGS. 7, 8, 9, 12 and 13  are but five of many potential configurations of MR elements in accordance with the disclosure. As one example, at least one of the stack portions (e.g.,  1350 ) of MR element  1300  may include a greater number of layers or a fewer number of layers than that which is shown. 
     Additionally, while particular materials and thicknesses of layers in MR elements according to the disclosure are shown in  FIGS. 7, 8, 9, 12 and 13 , it is understood that the materials and thicknesses of some layers may be different than that which is shown, for example, to provide the first, second, third, etc. substantially linear responses of the first, second, third, etc. stack portions in the MR elements. 
     Further, while particular sequences of layers in MR elements according to the disclosure are shown in  FIGS. 7, 8, 9, 12 and 13 , it is understood that there can be other interposing layers, for example, other spacer layers, between any two or more of the layers shown, for example, to provide the first, second, third, etc. substantially linear responses of the first, second, third, etc. stack portions in the MR elements. Also, there can be other layers above or below the layers shown in  FIGS. 7, 8, 9, 12 and 13 . It is also understood that the MR elements can be formed in a variety of sizes and shapes. For example, the MR elements can be formed in a yoke shape such at that shown in  FIG. 15  through a manufacturing process, for example, in which the various layers of the MR elements are deposited, patterned and annealed. 
     It is also understood that the MR elements in accordance with the disclosure may be coupled in a variety of arrangements, for example, a resistor divider arrangement, as shown in  FIG. 14 , or a bridge arrangement, as shown in  FIG. 14A , which is described below. Further, it is understood that the MR elements in accordance with the disclosure may be used in a variety of applications, including, but not limited to current sensors responsive to an electrical current, proximity detectors responsive to proximity of a ferromagnetic object, for example, ferrous gear teeth, and magnetic field sensors responsive to a magnetic field external to the magnetic field sensor. One example magnetic field sensor is shown in  FIG. 15 , which is also described below. 
     Referring to  FIG. 14 , a resistor divider  1400  includes a resistor  1402  and an MR element  1404 , which may be the same as or similar to MR elements described in connection with figures above (e.g.,  800 , shown in  FIG. 8 ) that are fabricated as a material stack. The resistor divider  1400  is coupled to a voltage source  1401  and the resistor  1402  and the MR element  1404  may be driven by the voltage source  1401 . 
     An output voltage (V OUT ) may be generated at the node  1400   a  formed between the resistor  1402  and the MR element  1404  in response to an applied magnetic field (e.g., a magnetic field as may be generated in response to motion of an object, such as ring magnet  1510 , shown in  FIG. 15 , as discussed below). In particular, changes in the applied magnetic field may cause the resistance of the MR element  1404  to change. As the resistance of the MR element  1404  changes, the output voltage at node  1400   a  may also change. The output voltage may have a magnitude indicative of the applied magnetic field. In embodiments, the resistor  1402  can be a substantially fixed resistor. Additionally, in embodiments, the resistor  1402  can be an MR element (i.e., a second MR element). 
     Referring to  FIG. 14A , a bridge arrangement (e.g., a Wheatstone bridge circuit)  1450  includes MR elements  1452 ,  1454 ,  1456 ,  1458 , one or more which may be the same as or similar to MR elements described in connection with figures above (e.g.,  800 , shown in  FIG. 8 ). The bridge  1450  is coupled to a voltage source  1451  and each of magnetoresistance elements  1452 ,  1454 ,  1456 ,  1458  may be driven by the voltage source  1451 . 
     A first output voltage (V OUT1 ) may be generated at first voltage node  1450   a  formed between magnetoresistance elements  1452 ,  1454  in response to an applied magnetic field. Additionally, a second output voltage (VP OUT2 ) may be generated at a second voltage node  1450   b  formed between magnetoresistance elements  1456 ,  1458  in response to the applied magnetic field. In particular, as the resistance of the MR elements  1452 ,  1454 ,  1456 ,  1458  changes in response to the applied magnetic field, at least one of the first output voltage generated at the first voltage node  1450   a  and the second output voltage generated at the second voltage node  1450   b  may also change. A voltage difference between the first output voltage (e.g., a first magnetic field signal) and the second output voltage (e.g., a second magnetic field signal) may be indicative of the applied magnetic field. In embodiments, the bridge  1450  may include at least one substantially fixed resistor, and at least one of the MR elements  1452 ,  1454 ,  1456 ,  1458  in bridge  1450  may be replaced by the at least one substantially fixed resistor. 
     As illustrated above, the resistor divider  1400  of  FIG. 14  and the bridge arrangement  1450  of  FIG. 14A  can provide an output signal (e.g., a magnetic field signal) that is indicative of an applied magnetic field experienced by the MR elements (e.g.,  1404 , shown in  FIG. 14 ). It is understood that the resistor divider  1400  and the bridge arrangement  1450  are but two of many potential arrangements of MR elements according to the disclosure. 
     Referring to  FIG. 15 , an example magnetic field sensor  1500  including a plurality of MR elements (here, four MR elements  1502 ,  1504 ,  1506 ,  1508 ) is shown. The MR elements  1502 ,  1504 ,  1506 ,  1508 , which can be the same as or similar to MR elements described in connection with figures above (e.g.,  800 , shown in  FIG. 8 ), are each formed in the shape of a yoke and disposed over a common substrate  1501  in the illustrated embodiment. In embodiments, the MR elements  1502 ,  1504 ,  1506 ,  1508  can be coupled in resistor divider arrangements that may be the same as or similar to the resistor divider  1400  shown in  FIG. 14 . Additionally, in embodiments, the MR elements  1502 ,  1504 ,  1506 ,  1508  can be coupled in bridge arrangements (e.g., a Wheatstone bridge) that may be the same as or similar to bridge arrangement  1450  shown in  FIG. 14A . It is understood that other configurations of the MR elements  1502 ,  1504 ,  1506 ,  1508  are, of course, possible. Additionally, it is understood that other electronic components (not shown), for example, amplifiers, analog-to-digital converters (ADC), and processors, i.e., an electronic circuit, can be disposed over the substrate  1501  and coupled to one or more of the MR elements  1502 ,  1504 ,  1506 ,  1508 , for example, to process signals (i.e., magnetic field signals) produced by the MR elements  1502 ,  1504 ,  1506 ,  1508 . 
     In the illustrated embodiment, the magnetic field sensor  1500  is disposed proximate to a moving magnetic object, for example, a ring magnet  1510  having alternative north and south magnetic poles. The ring magnet  1510  is subject to motion (e.g., rotation) and the MR elements  1502 ,  1504 ,  1506 ,  1508  of the magnetic field sensor  1500  may be oriented such that maximum response axes of the MR elements  1502 ,  1504 ,  1506 ,  1508  are aligned with a magnetic field (e.g., an applied magnetic field) generated by the ring magnet  1510 . In embodiments, the maximum responses axes of the MR elements  1502 ,  1504 ,  1506 ,  1508  may also be aligned with a magnetic field (e.g., a local magnetic field) generated by a magnet (not shown) disposed proximate to or within the magnetic field sensor  1500 . With such a back-biased magnet configuration, motion of the ring magnet  1510  can result in variations of the magnetic field sensed by the MR elements  1502 ,  1504 ,  1506 ,  1508 . 
     In embodiments, the MR elements  1502 ,  1504 ,  1506 ,  1508  are driven by a voltage source (e.g.,  1451 , shown in  FIG. 14A ) and configured to generate one or more magnetic field signals (e.g., V out1 , V out2 , shown in  FIG. 14A ) in response to motion of the ring magnet  1510 , e.g., in a first direction of motion and in a second direction of motion that is different than the first direction of motion. Additionally, in embodiments, one or more electronic components (e.g., an ADC) (not shown) on the magnetic field sensor  1500  are coupled to receive the magnetic fields signals and configured to generate an output signal indicative of position, proximity, speed and/or direction of motion of the ring magnet  1510 , for example. In some embodiments, the ring magnet  1510  is coupled to a target object, for example, a cam shaft in an engine, and a sensed speed of motion of the ring magnet  1510  is indicative of a speed of motion of the target object. The output signal (e.g., an output voltage) of the magnetic field sensor  1500  generally has a magnitude related to a magnitude of the magnetic field experienced by the MR elements  1502 ,  1504 ,  1506 ,  1508 . 
     In embodiments in which the MR elements  1502 ,  1504 ,  1506 ,  1508  are provided as MR elements according to the disclosure (e.g.,  800 , shown in  FIG. 8 ), the magnetic field sensor  1500  may have improved sensing accuracy over embodiments in which the magnetic field sensor  1500  includes conventional MR elements, for example, due to the increased operational range of magnetoresistance elements according to the disclosure in comparison to conventional magnetoresistance elements. In particular, due to the increased operational range of magnetoresistance elements according to the disclosure in comparison to conventional magnetoresistance elements, the magnetic field sensor  1500  may be able to more accurately sense a wider (or increased) range of magnetic field strengths than would otherwise be possible. For example, magnetic field strengths that would otherwise saturate conventional MR elements may be detected by MR elements according to the disclosure due to the increased operational range. This may provide for an increased number of applications in which MR elements according to the disclosure may be suitable (e.g., due to the increased range of magnetic field strengths which may be accurately detected using MR elements according to the disclosure). 
     Additionally, in embodiments in which the MR elements  1502 ,  1504 ,  1506 ,  1508  are provided as MR elements according to the disclosure (e.g.,  800 , shown in  FIG. 8 ), and the magnetic field sensor  1500  includes electronic components (e.g., ADCs) coupled to receive magnetic field signals from the MR elements  1502 ,  1504 ,  1506 ,  1508  and configured to generate the output signal of the magnetic field sensor  1500 , operational requirements of the electronic components (e.g., so-called “front end electronics” or “signal processing electronics”) may, for example, be reduced in comparison to embodiments in which the magnetic field sensor  1500  includes conventional magnetoresistance elements. 
     For example, as is known, an ADC has a dynamic range corresponding to a range of signal amplitudes or strengths which the ADC can resolve (i.e., process). If an analog input signal has an amplitude that is greater than an upper threshold of the dynamic range, or an amplitude that is less than a lower threshold of the dynamic range, the ADC may not be able to accurately convert the analog signal into a corresponding digital signal. As discussed above, MR elements according to the disclosure have at least a first substantially linear response resulting in a first sensitivity level to changes in magnetic field strength and a second substantially linear response resulting in a second sensitivity level to changes in magnetic field strength. As also discussed above, at least one characteristic in the at least first and second stack portions of the MR elements according to the disclosure may be selected to provide the first and second substantially linear responses, and the first and second sensitivity levels. In other words, the first and second sensitivity levels of the MR elements may be selected based upon the at least one characteristic selected in the first and second stack portions of the MR elements. 
     In embodiments, the first and second sensitivity levels of the MR elements according to the disclosure may be selected to be reduced in comparison to the single sensitivity level of conventional MR elements and, as a result, an output of MR elements according to the disclosure (e.g., V OUT , shown in  FIG. 14 ) may increase more gradually or at a small rate (and have a reduced upper threshold) in comparison to an output of conventional MR elements. It follows than an ADC coupled to receive an output of MR elements according to the disclosure may have a dynamic range requirement which is reduced in comparison to a range requirement of an ADC coupled to receive an output of conventional MR elements. As a result of the foregoing, in embodiments in which the magnetic field sensor  1500  includes MR elements according to the disclosure, the magnetic field sensor  1500  may be able to use ADCs that have a reduced dynamic range (and that may be less costly) in comparison to embodiments in which the magnetic field sensor  1500  includes conventional MR elements. 
     It is understood that the dynamic range of an ADC is but one example operational parameter of the ADC which may benefit from the various characteristics associated with MR elements according to the disclosure. It is also understood than an ADC is but one example electrical component that may be used in the magnetic field sensor  1500 , and which may benefit from the various characteristics associated with MR elements according to the disclosure. 
     In embodiments, MR elements according to the disclosure may also provide for a magnetic field sensor  1500  having a reduced number of electrical components (e.g., signal processing components) compared, for example, to a magnetic field sensor  1500  including conventional MR elements. For example, in embodiments in which the magnetic field sensor  1500  includes conventional MR elements and is configured to sense applied magnetic fields having a plurality of magnetic field strength ranges (e.g., −10 G to 10 G, −100 G to 100 G and −300 G to 300 G), the magnetic field sensor  1500  may require a corresponding plurality of ADCs. In contrast, in embodiments in which the magnetic field sensor  1500  includes MR elements according to the disclosure and is configured to sense the plurality of magnetic field strength ranges, the magnetic field sensor  1500  may include a fewer or reduced number of ADCs than the plurality of magnetic field strength ranges. In one embodiment, the foregoing is due to MR elements according to the disclosure having an increased operational range compared to conventional MR elements. In particular, with MR elements according to the disclosure as signals (e.g., magnetic field signals) become larger, the signals may be reduced (or even muted in some embodiments) but still usable for signal processing (e.g., due to the MR elements not being forced into saturation). 
     While the magnetic field sensor  1500  is shown and described as a motion detector to motion rotation of the ring magnet  1510  in the illustrated embodiment, it is understood that other magnetic field sensors, for example, current sensors, may include one or more of the MR elements according to the disclosure. 
     Additionally, while the MR elements  1502 ,  1504 ,  1506 ,  1508  are shown and described as formed in the shape of a yoke, it is understood that in some embodiments the MR element may instead be formed in the shape of a straight bar or a number of other shapes. For example, for a GMR element, the stack portions (e.g., first and second stack portions) of the GMR element may form a yoke shape. In contrast, for a TMR element, in some embodiments, selected portions of the TMR element (e.g., free layers of the stack portions) may have a yoke shape and remaining portions of the TMR element may have another shape (e.g., a straight bar). In some embodiments, one or more dimensions (e.g., a length, width and height) of the yoke or other shaped MR element may be based upon a number of layers and/or a thickness of the layers in the MR element. 
     Referring now to  FIG. 16 , an MR element  1600  (e.g., a double pinned MR element) is deposited or otherwise provided upon a substrate  1602  (e.g., a silicon substrate) and includes a plurality of layers (here, twelve layers). The plurality of layers includes a nonmagnetic seed layer  1604  disposed over the substrate  1602 , a material stack  1606  (or stack portion) disposed over the nonmagnetic seed layer  1604  and a nonmagnetic cap layer  1608  disposed over the material stack  1606 . 
     The material stack  1606  includes an antiferromagnetic pinning layer  1610  disposed over the nonmagnetic seed layer  1604 , a ferromagnetic pinned layer  1612  disposed over the antiferromagnetic pinning layer  1610  and a nonmagnetic spacer layer  1614  disposed over the ferromagnetic pinned layer  1612 . A free layer structure  1616  may be disposed over the nonmagnetic spacer layer  1614 , a nonmagnetic spacer layer  1618  disposed over the free layer  1616  and a pinned layer structure  1620  disposed over the nonmagnetic spacer layer  1618 . The free layer structure  1616  includes a first ferromagnetic free layer  1616   a  and a second ferromagnetic free layer  1616   b  disposed over the first ferromagnetic free layer  1616   a . Additionally, the pinned layer structure  1620  includes a first ferromagnetic pinned layer  1620   a , a second ferromagnetic pinned layer  1620   c , and a nonmagnetic spacer layer  1620   b  disposed therebetween. 
     The material stack  1606  additionally includes an antiferromagnetic pinning layer  1622  disposed between the pinned layer structure  1620  and the cap layer  1608 . 
     Each of the plurality of layers in the prior art MR element  1600  includes one or more respective materials (e.g., magnetic materials) and has a respective thickness, as shown. Materials of the layers are shown by atomic symbols. Additionally, thicknesses of the layers are shown in nanometers (nm). 
     In general, magnetic materials can have a variety of magnetic characteristics and can be classified by a variety of terms, including, but not limited to, ferromagnetic, antiferromagnetic, and nonmagnetic. Detailed descriptions of the variety of types of magnetic materials are not made herein. However, let it suffice here to say, that a ferromagnetic material (e.g., CoFe) is a material in which magnetic moments of atoms within the material tend to, on average, align to be both parallel and in a same direction, resulting in a nonzero net magnetic magnetization of the material. Additionally, a nonmagnetic or diamagnetic material (e.g., Ta, Cu or Ru) is a material which tends to present an extremely weak magnetization that is opposite and substantially proportional to a magnetic field to which the material is exposed and does not exhibit a net magnetization. Further, an antiferromagnetic material (e.g., PtMn) is a material in which magnetic moments of atoms within the material tend to, on average, align to be parallel but in opposite directions, resulting in a zero-net magnetization. 
     Within some of the plurality of layers in MR element  1600 , arrows are shown that are indicative of magnetization directions of the layers when the MR element  1600  experiences a nominal (or zero) applied magnetic field. Arrows coming out of the page are indicated as dots within circles and arrows going into the page are indicated as crosses within circles. 
     Detailed descriptions of the various magnetization directions are not provided in this document. However, let it suffice here to say that, as is known in the art, some MR elements (e.g., GMR and TMR elements) operate with spin electronics (i.e., electron spins) where the resistance of the MR elements is related to the magnetization directions of certain layers in the MR elements. 
     The MR element  1600  may have a maximum response axis to magnetic fields which is parallel to a surface  1624  of the substrate  1602  over which the MR element  1600  is deposited. Additionally, the MR element  1600  has a resistance that changes in response to the applied magnetic field in a direction of the maximum response axis of the MR element  200  over a limited range of magnetic field strengths. 
     In embodiments, MR element  1600  may include a first stack portion  1626 . Stack portion  1626  may comprise a first plurality of layers, such as layers  1604 - 1618 . The first stack portion  1626  may have a substantially linear response (i.e. a substantially linear change in electrical resistance) to an applied magnetic field over a first magnetic field range. 
     First stack portion  1626  may comprise a first spacer layer (e.g. spacer layer  1614 ) having a first thickness. Although spacer layer  1614  is comprises the material Ru and having thickness of 0.1 to 5.0 nm, other materials (such as Rh) and thicknesses may be used. 
     Although shown as having a different number of layers, in other embodiments, stack portions  1626  and  1628  may each have the same number of layers. 
     Referring now to  FIG. 17 , another example of an MR element  1700  (e.g., a so-called “dual double pinned MR element”) is deposited or otherwise provided upon a substrate  1701  and includes a plurality of layers. The plurality of layers includes a nonmagnetic seed layer  1702  disposed over the substrate  1701 , a first material stack portion  1710  (also sometimes referred to herein as “a first stack portion”) disposed over the nonmagnetic seed layer  1702  and an antiferromagnetic pinning layer  1720  disposed over the first material stack portion  1710 . The MR element  1700  also includes a second material stack portion  1730  (also sometimes referred to herein as “a second stack portion”) disposed over the antiferromagnetic pinning layer  1720  and a nonmagnetic cap layer  1704  disposed over the second material stack portion  1730 . 
     The first stack portion  1710 , which contains a similar ordering or arrangement of layers as the stack portion  1606  (see  FIG. 16 ) less a second antiferromagnetic pinning layer, includes an antiferromagnetic pinning layer  1711  disposed over the nonmagnetic seed layer  1702  and a ferromagnetic pinned layer  1712  disposed over the antiferromagnetic pinning layer  1711 . The first stack portion  1710  also includes a nonmagnetic spacer layer  1713  disposed over the ferromagnetic pinned layer  1712  and a free layer structure  1714  disposed over the nonmagnetic spacer layer  1713 . The free layer structure  1714  includes a first ferromagnetic free layer  1714   a  and a second ferromagnetic free layer  1714   b  disposed over the first ferromagnetic free layer  1714   a.    
     The first stack portion  1710  further includes a nonmagnetic spacer layer  1715  disposed over the free layer structure  1714  and a pinned layer structure  1716  disposed over the nonmagnetic spacer layer  1715 . The pinned layer structure  1716  includes a first ferromagnetic pinned layer  1716   a , a second ferromagnetic pinned layer  1716   c  and a nonmagnetic spacer layer  1716   b  disposed therebetween. 
     The second stack portion  1730 , which is similar to the first stack portion  1710  but includes layers that are in a substantially reverse order or arrangement as the layers which are shown in first stack portion  1710  with respect to the seed layer  1702 , includes a pinned layer structure  1731  disposed over the antiferromagnetic pinning layer  1720 , a nonmagnetic spacer layer  1732  disposed over the pinned layer structure  1731  and a free layer structure  1733  disposed over the nonmagnetic spacer layer  1732 . The pinned layer structure  1731  includes a first ferromagnetic pinned layer  1731   a , a second ferromagnetic pinned layer  1731   c  and a nonmagnetic spacer layer  1731   b  disposed therebetween. Additionally, the free layer structure  1733  includes a first ferromagnetic free layer  1733   a  and a second ferromagnetic free layer  1733   b , disposed over the first ferromagnetic free layer  1733   a.    
     The second stack portion  1730  also includes a nonmagnetic spacer layer  1734  disposed over the free layer structure  1733 , a ferromagnetic pinned layer  1735  disposed over the nonmagnetic spacer layer  1734  and an antiferromagnetic pinning layer  1736  disposed over the ferromagnetic pinned layer  1735 . A nonmagnetic cap layer  1704  is disposed over the antiferromagnetic pinning layer  1736 . 
     Each of the layers in prior art MR element  1700  includes one or more respective materials (e.g., magnetic materials) and has a respective thickness, as shown. Materials of the layers are shown by atomic symbols. Additionally, thicknesses of the layers are shown in nanometers. In other embodiments, the material and thicknesses of the layers in MR element  1700  may be replaced with other materials and thicknesses. 
     Arrows are shown that are indicative of magnetization directions of the layers when the MR element  1700  experiences a nominal (or zero) applied magnetic field. Arrows coming out of the page are indicated as dots within circles and arrows going into the page are indicated as crosses within circles. 
     Detailed descriptions of the various magnetization directions are not provided in this document. However, let it suffice here to say that, as is known in the art, some MR elements (e.g., GMR and TMR elements) operate with spin electronics (i.e., electron spins) where the resistance of the MR elements is related to the magnetization directions of certain layers in the MR elements. 
     The MR element  1700  has a maximum response axis to magnetic fields which is parallel to a surface of the substrate  1701  over which the MR element  1700  is deposited, as indicated by arrow  1799 . Additionally, the MR element  1700  has an electrical resistance that changes generally in proportion to an applied magnetic field in a direction of the maximum response axis of the MR element  1700  over a limited range of magnetic field strengths. 
     Referring to  FIG. 18 , a graph  1800  includes a waveform  1802  representing the transfer function of an MR element (such as MR element  1600  or  1700 ) in the presence of an applied magnetic field. The horizontal axis represents arbitrary units of magnetic field strength of the applied magnetic field and the vertical axis represents resistance of the MR element in Ohms. 
     When the MR element experiences a magnetic field with zero strength, the resistance of the MR element is at an intermediate value, as shown by point  1804 . As the strength of the external magnetic field increases, the resistance of the MR element decreases as shown, for example, by point  1806 . Conversely, as the strength of the applied magnetic field increases in the other direction, the resistance of the MR element increases as shown, for example, by point  1808 . 
     The graph  1800  is divided into three regions: low sensitivity regions  1810  and  1812  where the resistance of the MR element is relatively invariable with changes to the strength of the applied magnetic field (i.e. where the slope of the resistance curve  1802  is relatively close to zero), and high sensitivity region  1814  where the resistance of MR element has a relatively large slope (i.e. where the slope of the resistance curve  1802  is relatively distant from zero). Changing the material and thickness of the spacer regions, as discussed above, may affect the size and offset (right or left) of the high sensitivity region  1814  and the shape of resistance curve  1802  within high sensitivity region  1814 . For example, changing the thickness of Copper layer  1732  may change the proportion of high and low sensitivity. As another example, changing the material and thickness of layers  1734  and/or  1713  may change the sensitivities in the high and low sensitivity zones of the MR element&#39;s transfer function. 
     Referring to  FIG. 19 , graph  1900  shows a series of waveforms  1902  representing the resistance of a double pinned MR element with different thicknesses of the spacer layer  1732  of the low sensitivity stack portion (e.g. stack portion  1730  in  FIG. 17 ). Curve A illustrates the case where the spacer layer  1732  of the low sensitivity stack portion  1730  has the same thickness and material as the spacer layer  1715  of the high sensitivity stack portion (e.g. stack portion  1710 ). Curve B illustrates the case where the spacer layer  1730  of the low sensitivity stack portion  1730  has a thickness that is about 25% higher of that of the spacer layer  1730  of the high sensitivity stack portion  1730 . As shown, increasing the thickness of the spacer layer  1732  of the low sensitivity stack portion  1730  may result in curve B having a larger sensitivity and a smaller linear range (e.g. between points  1904  and  1906 ) that than of curve A (e.g. between points  1908  and  1910 ). Other ones of the curves show other percentages and resulting different linear ranges. 
     Referring to  FIG. 20 , graph  2000  shows a series of waveforms  2002  representing the resistance of a double pinned MR element with different thicknesses of the spacer layer  1715  of the high sensitivity stack portion (e.g. stack portion  1710  in  FIG. 17 ). Curve C illustrates the case where the spacer layer  1715  of the high sensitivity stack portion  1710  has the same thickness and material as the spacer layer of the low sensitivity stack portion (e.g. stack portion  1730 ). Curve D illustrates the case where the spacer layer  1715  of the high sensitivity stack portion  1710  has a thickness that is about 25% lower of that of the spacer layer  1732  of the low sensitivity stack portion  1710 . As shown, reducing the thickness of the spacer layer  1715  of the high sensitivity stack portion  1710  may result in curve D having a lower sensitivity and a larger linear range (e.g. between points  2004  and  2006 ) that than of curve C (e.g. between points  2008  and  2010 ). 
     The MR element  1700  in  FIG. 17  may also have varying linear range and sensitivity based on the thickness of spacer layers  1715  and  1732 . Reducing the thickness of spacer layer  1715  and/or spacer layer  1732  may result in MR element  1700  having lower sensitivity and larger linear range. 
     As described above and as will be appreciated by those of ordinary skill in the art, embodiments of the disclosure herein may be configured as a system, method, or combination thereof. Accordingly, embodiments of the present disclosure may be comprised of various means including hardware, software, firmware or any combination thereof. 
     Having described preferred embodiments, which serve to illustrate various concepts, structures and techniques, which are the subject of this patent, it will now become apparent to those of ordinary skill in the art that other embodiments incorporating these concepts, structures and techniques may be used. Additionally, elements of different embodiments described herein may be combined to form other embodiments not specifically set forth above. 
     Accordingly, the scope of the patent should not be limited to the described embodiments but rather should be limited only by the spirit and scope of the following claims.