Patent Publication Number: US-2019178954-A1

Title: Magnetoresistance Element Having Selected Characteristics To Achieve A Desired Linearity

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     Not Applicable. 
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH 
     Not Applicable. 
     FIELD OF THE INVENTION 
     This invention relates generally to magnetoresistance elements and, more particularly, to a magnetoresistance element having layers and formed in a shape with a selected relationship between layer magnetic field strength and shape width to achieve a desired linearity. 
     BACKGROUND 
     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 such magnetic field sensing element is a magnetoresistance (MR) element. The magnetoresistance element has a resistance that changes in relation to an external 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 Indium Antimonide (InSb), a giant magnetoresistance (GMR) element, an anisotropic magnetoresistance element (AMR), and a tunneling magnetoresistance (TMR) element, also called a magnetic tunnel junction (MTJ) element. 
     Of these magnetoresistance elements, the GMR and the TMR elements operate with spin electronics (i.e., electron spins) where the resistance is related to the magnetic orientation of different magnetic layers separated by nonmagnetic layers. In spin valve configurations, the resistance is related to an angular direction of a magnetization in a so-called “free-layer” of “free-layer structure” relative to another layer so-called “reference layer” of “reference layer structure.” The free layer and the reference layer are described more fully below. 
     The magnetoresistances element may be used as a single element or, alternatively, may be used as two or more magnetoresistance elements arranged in various configurations, e.g., a half bridge or full (e.g., Wheatstone) bridge. 
     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. In a typical magnetic field sensor, the magnetic field sensing element and the other circuits can be integrated upon a common substrate, for example, a semiconductor substrate. In some embodiments, the magnetic field sensor can also include a lead frame and packaging. 
     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 rotation detector that senses passing ferromagnetic articles, for example, magnetic domains of a ring magnet or a ferromagnetic target (e.g., gear teeth) where the magnetic field sensor is used in combination with a back-biased or other magnet, and a magnetic field sensor that senses a magnetic field density of a magnetic field. 
     Various parameters characterize the performance of magnetic field sensors and magnetic field sensing elements. With regard to magnetic field sensing elements, the parameters include sensitivity, which is the change in the output signal (or resistance) of a magnetic field sensing element in response to an external magnetic field, and linearity, which is the degree to which the output signal (or resistance) of a magnetic field sensing element varies linearly (i.e., in direct proportion) to the external magnetic field. The parameters also include offset, which describes and output (or resistance) from the magnetic field sensing element that is not indicative of zero magnetic field when the magnetic field sensing element experiences a zero magnetic field. The parameters also include common mode rejection, which describes a change in behavior when the magnetic field sensor experiences a large (common mode) external magnetic field. 
     GMR and TMR elements are known to have a relatively high sensitivity, compared, for example, to Hall Effect elements. TMR elements are known to have a higher sensitivity than GMR elements, but at the expense of higher noise at low frequencies. 
     Both GMR and TMR elements (magnetoresistance elements) are known to suffer from saturation at magnetic fields above a threshold level. Thus, conventional GMR and TMR elements have one linear range in response to magnetic fields, the one linear range between upper and lower saturation regions. 
     In some applications, it would be desirable to provide a magnetoresistance element that can have a different linear range, for example, an extended linear range or more than one linear range between saturation regions. 
     SUMMARY 
     The present invention provides a magnetoresistance element that can have a different linear range, for example, an extended linear range or more than one linear range between saturation regions. 
     In accordance with an example useful for understanding an aspect of the present invention, a magnetoresistance element disposed upon a substrate can include a stack of layers. The stack of layers can include a first portion including a first bias layer structure for generating a first bias magnetic field with a first bias direction, and a first free layer structure disposed proximate to the first bias layer structure, wherein the first free layer structure is biased by the first bias magnetic field. The stack of layers can also include a second portion including a second bias layer structure for generating a second bias magnetic field with a second bias direction, and a second free layer structure disposed proximate to the second bias layer structure, wherein the second free layer structure is biased by the second bias magnetic field, and wherein the first bias direction and the second bias directions are opposite to each other. The magnetoresistance element can further include a shape having a longest dimension and a shortest dimension both parallel to the substrate, wherein the first and second bias magnetic fields are within +/− twenty-five degrees of parallel to the shortest dimension. 
     In some embodiments, the above magnetoresistance element can include one or more of the following aspects in any combination. 
     In some embodiments of the above magnetoresistance element, the first portion comprises a first resistance-to-external-magnetic-field transfer function having a first linear range of external magnetic fields and wherein the second portion comprises a second resistance-to-external-magnetic-field transfer function having a second linear range of external magnetic fields, the first and second linear ranges having an overlap in a direction of external magnetic fields, the overlap less than eighty-five percent of the first linear range and less than eighty-five percent of the second linear range, and the magnetoresistance element further includes a third resistance-to-external-magnetic-field transfer function different than the first and second resistance-to-external-magnetic-field transfer functions. 
     In some embodiments of the above magnetoresistance element, a combination of the shortest dimension and magnitudes of the first and second bias magnetic fields is selected to result in the overlap. 
     In some embodiments of the above magnetoresistance element, the first and second bias magnetic field directions are parallel to the shortest dimension. 
     In some embodiments of the above magnetoresistance element, the second portion is disposed under the first portion in a direction perpendicular to a major surface of the substrate. 
     In some embodiments of the above magnetoresistance element, the shortest dimension and magnitudes of the first and second bias magnetic fields are selected to result in the third resistance-to-external-magnetic-field transfer function having first, second, and third linear regions, the first linear region associated with a first range of external magnetic fields, the second linear region associated with a second range of external magnetic fields, and the third linear region associated with a third range of external magnetic fields, the first, second, and third ranges being different ranges, a center of the second range between the first and third ranges. 
     In some embodiments of the above magnetoresistance element, the second linear region has a slope greater than one hundred fifty percent of slopes of the first and third linear regions. 
     In some embodiments of the above magnetoresistance element, the shortest dimension and magnitudes of the first and second bias magnetic fields are selected to result in the third resistance-to-external-magnetic-field transfer function having a linear region greater than one hundred fifty percent of the first linear range of the first resistance-to-external-magnetic-field transfer function and also greater than one hundred fifty percent of the second linear range of the second resistance-to-external-magnetic-field transfer function. 
     In some embodiments of the above magnetoresistance element, the third resistance-to-external-magnetic-field transfer function has only one linear region. 
     In some embodiments of the above magnetoresistance element, the shortest dimension and magnitudes of the first and second bias magnetic fields are selected to result in the third resistance-to-external-magnetic-field transfer function having first and second linear regions, the first linear region associated with a first range of external magnetic fields and the second linear region associated with a second range of external magnetic fields, the first and second linear ranges being different and non-overlapping linear ranges, 
     In some embodiments of the above magnetoresistance element, the first and second linear regions have equal slopes. 
     In some embodiments of the above magnetoresistance element, the shape comprises a yoke shape. 
     In some embodiments of the above magnetoresistance element, the second portion is disposed under the first portion in a direction perpendicular to a major surface of the substrate. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The foregoing features of the invention, as well as the invention itself may be more fully understood from the following detailed description of the drawings, in which: 
         FIG. 1  is a block diagram showing layers of an illustrative giant magnetoresistance (GMR) element having two double pinned GMR element portions; 
         FIG. 2  is a block diagram showing a top view of a GMR element having a yoke shape; 
         FIG. 3  is a block diagram showing another top view of a GMR element having a yoke shape; 
         FIG. 4  is a graph showing a resistance-versus-external-magnetic-field transfer function and a sensitivity-versus-external-magnetic-field transfer function versus magnetic field of a conventional GMR element; 
         FIG. 5  is a graph showing a resistance-versus-external-magnetic-field transfer function and a sensitivity-versus-external-magnetic-field transfer function of an illustrative GMR element; 
         FIG. 6  is a graph showing a resistance-versus-external-magnetic-field transfer function and a sensitivity-versus-external-magnetic-field transfer function of another illustrative GMR element; 
         FIG. 7  is a graph showing a resistance-versus-external-magnetic-field transfer function and a sensitivity-versus-external-magnetic-field transfer function of another illustrative GMR element; 
         FIG. 8  is a graph showing three regions of yoke width versus bias magnetic field; 
         FIG. 9  is a graph showing two resistance-versus-external-magnetic-field transfer functions with large overlap and small separation and combined to generate another resistance-versus-external-magnetic-field field transfer function; 
         FIG. 10  is a graph showing two resistance-versus-external-magnetic-field transfer functions with a smaller overlap and larger separation, also combined to generate another resistance-versus-external-magnetic-field field transfer function; 
         FIG. 11  is a graph showing two resistance-versus-external-magnetic-field transfer functions with no overlap and still larger separation, also combined to generate another resistance-versus-external-magnetic-field field transfer function; and 
         FIG. 12  is a graph showing two resistance-versus-external-magnetic-field transfer functions also with no overlap and still larger separation, also combined to generate another resistance-versus-external-magnetic-field field transfer function. 
     
    
    
     DETAILED DESCRIPTION 
     Before describing the present invention, it should be noted that reference is sometimes made herein to GMR elements having particular shapes (e.g., yoke shaped). One of ordinary skill in the art will appreciate, however, that the techniques described herein are applicable to a variety of sizes and shapes. TMR elements having other shapes are also possible. 
     As used herein, the term “magnetic field sensing element” is used to describe a variety of different types of electronic elements that can sense a magnetic field. A magnetoresistance element is but one type of magnetic field sensing element. 
     As is known, there are different types of magnetoresistance elements, for example, a semiconductor magnetoresistance element such as Indium Antimonide (InSb), a giant magnetoresistance (GMR) element, an anisotropic magnetoresistance element (AMR), and a tunneling magnetoresistance (TMR) element, also called a magnetic tunnel junction (MTJ) element. 
     As is known, metal based or metallic magnetoresistance elements (e.g., GMR, TMR, AMR) tend to have axes of sensitivity parallel to a substrate. 
     As used herein, the term “magnetic field sensor” is used to describe a circuit that uses a magnetic field sensing element, 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 rotation detector that senses passing ferromagnetic articles, for example, magnetic domains of a ring magnet or a ferromagnetic target (e.g., gear teeth) where the magnetic field sensor is used in combination with a back-biased or other magnet, and a magnetic field sensor that senses a magnetic field density of a magnetic field. 
     The terms “parallel” and “perpendicular” are used in various contexts herein. It should be understood that the terms parallel and perpendicular do not require exact perpendicularity or exact parallelism, but instead it is intended that normal manufacturing tolerances apply, which tolerances depend upon the context in which the terms are used. 
     As used herein, the term “predetermined,” when referring to a value or signal, is used to refer to a value or signal that is set, or fixed, in the factory at the time of manufacture, or by external means, e.g., programming, thereafter. As used herein, the term “determined,” when referring to a value or signal, is used to refer to a value or signal that is identified by a circuit during operation, after manufacture. 
     While GMR elements may be used in examples herein, the same concepts apply to TMR elements, but which, rather than references yoke width, references to a smallest dimension of a shape (e.g., a rectangular shape) parallel to a substrate of a TMR pillar is possible. 
     Referring now to  FIG. 1 , a dual magnetoresistance element  100  includes a first portion  102  and also a second portion  104 , each portion being a double pinned GMR element having two pinning layers and two pinned layer structures, the two portions  102 ,  104  coupled essentially in parallel for a magnetoresistance element (e.g., a GMR element) in which current flows between right and left on the page, i.e., parallel to a substrate upon with the magnetoresistance element  100  is formed, or in series for a magnetoresistance element (e.g., a TMR element) in which current flows between top and bottom of the page. A common antiferromagnetic pinning layer  106  can be in the middle, and used in both the first and second portions  102 ,  104 . 
     The first portion  102  can include a first reference layer structure  114  and a first bias layer structure  110 . The second portion  104  can include a second reference layer structure  116  and a second bias layer structure  112 . In an alternate embodiment, the first reference layers structure  114  and the first bias layer structure  110  can be interchanged in position and the second reference layer structure  116  and the second bias layer structure  112  can also be interchanged in position. 
     The dual spin valve magnetoresistance element  100  can have two free layer structures. Spacer layers  118 ,  120  can have different thicknesses selected to result in different couplings to the free layer structures so that the two free layer structures have magnetic fields with opposite directions as shown. The directions of the magnetic fields in the two free layer structures can both be reversed from the direction shown. 
     In some embodiments, the spacer layer  120  can have a thickness that can be in one of two example ranges, e.g., about 1.0 nm to about 1.7 nm or about 2.3 nm to about 3.0 nm, to result in a ferromagnetic coupling across the spacer layer  120   
     In some embodiments, the spacer layer  118  has a thickness that can be in the other one of two example ranges, e.g., about 1.7 nm to about 2.3 nm or about 3.0 nm to about 3.7 nm, to result in an antiferromagnetic coupling across spacer layer  118 . 
     Thus, it will be appreciated that the two free layer structures experience bias magnetic fields generated by the first and second bias layer structures  110 ,  112 , respectively, with nominal directions that are parallel to each other but in opposite directions. 
     In addition, by selection of thickness of the two spacer layers  118 ,  120 , the two couplings, antiferromagnetic and ferromagnetic, the two free layer structures can experience about the same magnitude of bias magnetic fields generated by the bias layer structures  110 ,  112 , but in opposite directions. 
     It should be further appreciated that operation of the dual spin valve magnetoresistance element  100  operates very much like combination of two separate magnetoresistance elements, but where two resulting spacer layers  118 ,  120  have selected thickness to result in a ferromagnetic coupling to the one free layer structure and an antiferromagnetic coupling to the other free layer structure. Thus, in some alternate embodiments, the dual double pinned magnetoresistance element  100  can be replaced by two double pinned magnetoresistance elements electrically coupled together. 
     In some alternate embodiments, the spacer layer  118  can have the thickness of the spacer layer  120  and vice versa. 
     The dual magnetoresistance element  100  has four synthetic antiferromagnetic (SAF) pinned structures. Thus, the first and second portions  102 ,  104  are two double pinned structures within the dual magnetoresistance element  100 . 
     The four synthetic antiferromagnetic (SAF) structures are referred to herein as pinned layer structures. 
     While particular layer thicknesses are shown in  FIG. 1 , it will be understood that the thicknesses of some or all layers can be different. 
     While particular sequences of layers are shown in  FIG. 1 , it should be appreciated that there can be other interposing layers, for example, other spacer layers, between any two or more of the layers shown. Also, there can be other layers above or below the layers shown in  FIG. 1 . 
     The term “over,” when describing layers that are over each other, is used to indicate a sequence of layers, but not to indicate that layers are necessarily in direct contact. Layers that are over each other can include layers that interpose with each other. 
     Referring now to  FIG. 2 , according to one embodiment, the magnetoresistance element  100  of  FIG. 1  can be formed in the shape of a yoke  200  (top view). A section line A-A shows the perspective  FIG. 1 . 
     The yoke  200  has a main part  201 , two arms  206 ,  208  coupled to the main part  201 , and two lateral arms  212 ,  214  coupled to the two arms  206 ,  208 , respectively. In some embodiments, the main part  201 , the two arms  206 ,  208 , and the two lateral arms  212 ,  214  each have a width (w). However, in other embodiments, the widths can be different. 
     A length (L) of the yoke  200  and a length (d) of the lateral arms  212 ,  214  of the yoke  200  are each at least three times the width (w) of the yoke  200 , and the width (w) of the yoke  200  can be between about one μm and about twenty μm. 
     As used herein, when referring to magnetoresistance elements, the term “transverse” is used to refer to a magnetic field perpendicular to a longer dimension of the yoke  200  of  FIG. 2 , e.g., in a direction of the arrow  202  of  FIG. 2 . The transverse direction  202  can also be generally parallel to a direction of the bias magnetic fields experienced by the free layer structures of the dual magnetoresistance element  100  of  FIG. 1 . However, the bias magnetic fields can be within about +/− twenty-five degrees, within about +/− ten degrees or within +/− five degrees of the transverse direction.  202  (i.e., the shortest dimension, width w.). 
     As used herein, when referring to magnetoresistance elements, the term “longitudinal” is used to refer to a magnetic field parallel to a longer dimension of the yoke  200  of  FIG. 2 , e.g., in a direction of the arrow  204  of  FIG. 2 . The longitudinal direction  204  can also be generally perpendicular to a direction of the bias magnetic fields experienced by the free layer structures of the dual magnetoresistance element  100  of  FIG. 1 . 
     A maximum response axis is parallel to the arrow  202 .
         The yoke dimensions can be, for example, within the following ranges:
           the length (L) of the main part  201  of the yoke  200  can be between about ten μm and ten millimeters;   the length ( 1 ) of the arms  206 ,  208  of the yoke  200  can be at least three times the width (w);   the width (w) of the yoke  200  can be between about one hundred nanometers and about twenty μm, with particular examples described in conjunction with  FIGS. 10-12  below.   
               

     The arms  206 ,  208  of the yoke  200  are linked to the lateral arms  212 ,  214 , which are parallel to the main part  201 , and have a length  1  which is between about ¼ and ⅓ of the overall length (L). 
     In general, sensitivity of the magnetoresistance element  100  having the yoke shape  200  decreases with the width (w), and the low frequency noise of the magnetoresistance element  100  increases with the width (w). 
     The yoke shape offers better magnetic homogeneity in a longitudinally central area of the main part  201 . 
     For a GMR element, the overall stack can be designed in a yoke shape, but for a TMR element, in some embodiments, the TMR element can have a shape (e.g., rectangular) that has a longest dimension and a shortest dimension both parallel to a substrate. 
     Referring now to  FIG. 3 , a yoke  300  can have a main part  302 . Where the yoke  300  has the layers of the dual magnetoresistance element  100  of  FIG. 1 , an arrow  306  is indicative of a magnetic direction of the first and second reference layer structures  114 ,  116  of  FIG. 1 , both pointing to the left at pinned layers proximate to Cu spacer layers. Two directions of an arrow  304  are indicative of two directions of bias magnetic fields experienced by the two free layers structures of the magnetoresistance element  100  of  FIG. 1 . 
     Referring now to  FIG. 4 , a graph  400  has a horizontal axis with a scale in units of magnetic field in Oersteds of an external magnetic field. The graph  400  also has a left vertical axis with a scale in units of sensitivity in ohms per Oersted. The graph  400  also has a right vertical axis with a scale in units of resistance in ohms. 
     A curve  402  uses the right vertical scale and is indicative of a resistance-versus-external-magnetic-field transfer function (or simply a resistance transfer function) of a general GMR element. A curve  404  uses the left vertical scale and is indicative of a sensitivity-versus-external-magnetic-field transfer function (or simply a sensitivity transfer function) of the general GMR element. 
     A linear range of the curve  402  can be defined to exist in a range  410  of the curve  404  in which a sensitivity changes, for example, by twenty-five-five percent, from a baseline sensitivity, for example, from a maximum sensitivity of the GMR element, here about −0.2 ohms per Oersted, which occurs at zero Oersteds. The twenty-five percent change, or a change to seventy-five percent of the baseline, here about −0.15 ohms per Oersted, is illustrated as a line  406  and a line  410 . Thus, in this example, the linear range extends within about +/− fifty Oersteds of external magnetic field. Points  402   a ,  402   b  are along the resistance transfer function  402  at the same +/− fifty Oersteds. 
     Other percentages can also be used. 
     It should be understood that the resistance-versus-external-magnetic-field transfer function curve  402  and the sensitivity-versus-external-magnetic-field transfer function curve  404  are related by a slope, i.e., values of the sensitivity curve  404  according to slope(s) of the resistance curve  402 . 
     It has been identified the linear range and the shape of the linear range can be influenced by a width of a yoke, e.g., width W of the yoke  200  of  FIG. 2  and by magnitudes of bias magnetic fields experienced by free layer structures, e.g., the magnitude of bias magnetic fields experienced by the free layer structures of the magnetoresistance element  100  of  FIG. 1 . 
       FIGS. 5-7  show resistance-versus-external-magnetic-field transfer functions and sensitivity-versus-external-magnetic-field transfer functions for the magnetoresistance element of  100  of  FIG. 1  formed in a yoke shape according to  FIGS. 2 and 3 , but for altered magnetoresistance elements, in which the width W of the yoke  200  of  FIG. 2  and magnitude of bias magnetic fields experienced by the free layer structures of the magnetoresistance element  100  of  FIG. 1  are tailored in particular ways to achieve particular types of transfer functions. 
       FIGS. 5-7  show respective graphs  500 ,  600 ,  700 , in which each has a respective horizontal axis with a scale in units of magnetic field in Oersteds of an external magnetic field. The graphs  8500 ,  600 ,  700  also each have a respective left vertical axis with a scale in units of sensitivity in ohms per Oersted. The graphs  800 ,  900 ,  1000  also each have a respective right vertical axis with a scale in units of resistance in ohms. 
     Referring now to  FIG. 5 , a curve  504  shows a sensitivity-versus-external-magnetic-field transfer function of a particular example of a magnetoresistance element like the magnetoresistance element  100  of  FIG. 1 , where the maximum response axis of the magnetoresistance element is along the transverse direction  202  of the yoke  200  of  FIG. 2 . A curve  502  shows a resistance-to-external-magnetic-field transfer function for the magnetoresistance element  100  of  FIG. 1 . In this particular example, magnetoresistance element  100  has a yoke shape that has a width of one micron and a magnitude of bias magnetic fields experienced by the free layer structures of about seventy-five Oersteds. (see also  FIG. 8 ) 
     Using the definition of linear range according to  FIG. 4 , e.g., a change of sensitivity by +/− twenty-five percent from a baseline level (e.g., a highest or a constant sensitivity), the curve  504  can be seen to have a first linear range  506 , a second linear range  505 , and a third linear range  510 , using baseline levels at curve portions  504   a ,  504   b ,  504   c , respectively. The first linear range  506  can correspond to a first linear region  502   a , the second linear range  505  can correspond to a second linear region  502   b , and the third linear range  510  can correspond to a third linear region  502   c  of the curve  502 . 
     The first and third linear regions  502   a ,  502   c  can have a sensitivity, i.e., a slope, that is about one half of the sensitivity of the second linear region  502   b . The linear regions  502   a ,  502   b ,  502   c  are further described below in conjunction with  FIG. 10 . 
     Referring now to  FIG. 6 , a curve  604  shows a sensitivity-to-external-magnetic-field transfer function of a particular example of a magnetoresistance element like the magnetoresistance element  100  of  FIG. 1 , where the maximum response axis of the magnetoresistance element  100  is along the transverse direction  202  of the yoke  200  of  FIG. 2 . A curve  602  shows a resistance-versus-external-magnetic-field transfer function for the magnetoresistance element  100  of  FIG. 1 . In this particular example, magnetoresistance element  100  has a yoke shape that has a width of 2.6 microns and a magnitude of bias magnetic fields experienced by the free layer structures of about seventy-five Oersteds. (see also  FIG. 8 ) 
     Using the definition of linear range according to  FIG. 4 , e.g., a change of sensitivity by +/− twenty-five percent from a baseline level, the curve  602  can be seen to have a linear range  606  using a baseline level near curve portions  604   a . The linear range  606  can correspond to a linear region  602   a.    
     The linear regions  602   a  can have a sensitivity, i.e., a slope, that extends about twice as far along the horizontal axis than does a conventional magnetoresistance element. The linear region  602   a  is further described below in conjunction with  FIG. 11 . 
     Referring now to  FIG. 7 , a curve  704  shows a sensitivity-versus-external-magnetic-field transfer function of a particular example of a magnetoresistance element like the magnetoresistance element  100  of  FIG. 1 , where the maximum response axis of the magnetoresistance element  100  is along the transverse direction  202  of the yoke  200  of  FIG. 2 . A curve  702  shows a resistance-versus-external-magnetic-field transfer function for the magnetoresistance element  100  of  FIG. 1 . In this particular example, magnetoresistance element  100  has a yoke shape that has a width of ten microns and a magnitude of bias magnetic fields experienced by the free layer structures of about seventy-five Oersteds. (see also  FIG. 8 ) 
     Using the definition of linear range according to  FIG. 4 , e.g., a change of sensitivity by +/− twenty-five percent from a baseline level (near the two regions with sensitivity of about −0.55 ohms per Oersted), the curve  704  can be seen to have a first linear range  706  and a second linear range  708 . The first linear range  706  can correspond to a first linear region  702   a  and the second linear range  708  can correspond to a second linear region  702   b.    
     The linear regions  702   a ,  702   b  are further described below in conjunction with  FIG. 12 . 
     Referring now to  FIG. 8 , a graph  800  has a horizontal axis with a scale in units of bias magnetic field experienced by the free layer structures of the magnetoresistance element  100  of  FIG. 1 , in Oersteds. The graph  800  also has a vertical axis with a scale in units of yoke width according to the yoke  200  of  FIG. 2 . 
     A first region  802  can correspond to combinations of bias magnetic fields experienced by the free layer structures and yoke widths that can achieve the first, second, and third linear regions of the curve  502  of  FIG. 5 . 
     A second region  804  can correspond to combinations of free layer structure magnetic fields and yoke widths that can achieve the broader linear region of the curve  602  of  FIG. 6 . 
     A third region  806  can correspond to combinations of free layer structure magnetic fields and yoke widths that can achieve the first and second linear regions of the curve  702  of  FIG. 7 . 
       FIGS. 9-12  each show a respective resistance-versus-external-magnetic-field transfer function, namely, transfer functions for the first portion  102 , for the second portion  104 , and for the entire magnetoresistance element  100  of  FIG. 1 . In this way, it will become apparent that the separation (offset) of the transfer functions of the first and second portions  102 ,  104  can result in different linear regions for the magnetoresistance element  100  of  FIG. 1 . 
     Transfer functions shown in  FIGS. 9-12  are shown to be somewhat ideal merely for clarity, in that the transfer functions have abrupt changes of slope to upper and lower saturation regions. In accordance with  FIG. 4 , it will be understood that the transitions are more gradual in an actual magnetoresistance element. 
       FIGS. 9-12  each have a respective horizontal axis with units of external magnetic field in Oersted and a vertical axis with units of resistance in arbitrary units. 
     Referring now to  FIG. 9 , a graph  900  includes a first curve  902  indicative of a resistance transfer function of the first portion  102  of  FIG. 1 . The graph  900  also includes a second curve  904  indicative of a resistance transfer function of the second portion  104  of  FIG. 1 . The graph  900  also includes a third curve  906  indicative of a resistance transfer function of the first portion  102  and the second portion  104  taken together in series, i.e., the entire magnetoresistance element  100  of  FIG. 1 . 
     The curve  902  has a center point  902   a  midway along a linear portion of the curve  902 . The curve  904  has a center point  904   a  midway along a linear portion of the curve  904 . An arrow  908  is indicative of a separation (offset) of the center points  902   a ,  904   a.    
     The arrow  908  is indicative of a small separation between the center points  902   a ,  904   a , i.e., a small separation between the curves  902 ,  904 . 
     An arrow  910  is indicative of regions of the first and second curves  902 ,  904  for which the linear regions overlap. It should be understood that separation  908  and overlap  910 , if changed, change in opposite directions. 
     The curve  906 , within the overlapping region  910 , has a slope, i.e., a sensitivity, that is double the slopes of the curves  902 ,  904 . 
     Arrows  912 ,  914  are indicative of minor linear ranges of the curve  906  having little extent in external magnetic field. In the minor linear ranges  912 ,  914  one of the curves  902 ,  904  has a slope and the other does not. Thus, within the minor linear ranges  912 ,  914 , the slope of the curve  906  is the same as a slope of either one of the curves  902 ,  904 . 
     In this example, the minor linear ranges  912 ,  914  are insignificant. In conventional arrangements, ideally the curves  902 ,  904  would be on top of each other, in which case, the minor linear ranges  912 ,  914  would not exist. 
     Referring now to  FIG. 10 , a graph  1000  includes a first curve  1002  indicative of a resistance transfer function of the first portion  102  of  FIG. 1 . The graph  1000  also includes a second curve  1004  indicative of a resistance transfer function of the second portion  104  of  FIG. 1 . The graph  1000  also includes a third curve  1006  indicative of a resistance transfer function of the first portion  102  and the second portion  104  taken together in series, i.e., the entire magnetoresistance element  100  of  FIG. 1 . 
     The curve  1002  has a center point  1002   a  midway along a linear portion of the curve  1002 . The curve  1004  has a center point  1004   a  midway along a linear portion of the curve  1004 . 
     An arrow  1008  is indicative of a separation (offset) of the center points  1002   a ,  1004   a . The separation  1008  is larger than the separation  908  of  FIG. 9 . 
     An arrow  1012  is indicative of a linear range of the first curve  1002 . An arrow  1014  is indicative of a linear range of the second curve  1004 . 
     An arrow  1010  is indicative of regions of the first and second curves  1002 ,  1004  for which the linear regions overlap. The arrow  1010  is indicative of a small overlap of the linear regions of the curves  1002 ,  1004 . In some embodiments, the overlap  1010  is less than eighty-five percent of a linear range of both of the first and second curves  1002 ,  1004 . In some embodiments, the overlap  1010  is less than fifty percent of a linear range of both of the first and second curves  1002 ,  1004 . In some embodiments, the overlap  1010  is less than twenty-five percent of a linear range of both of the first and second curves  1002 ,  1004 . 
     The curve  1006  has first, second, and third linear regions  1006   a ,  1006   b ,  1006   c , respectively. Within the overlapping region  1010 , a slope, i.e., a sensitivity, of the second linear region  1006   b  is double the slopes of the linear regions  1012 ,  1014  of curves  1002 ,  1004 . Slopes, i.e., sensitivities, within the first and third linear regions  1006   a ,  1006   c , can be the same the slopes of the linear regions of curves  1002 ,  1004 . 
     Thus, the curve  1006  can have three linear ranges as described above in conjunction with  FIG. 5 . The curve  1006  can be a result of the magnetoresistance element  100  of  FIG. 1  having a yoke shape with a width of one micron and free layer structure magnetic fields of seventy-five Oersteds as described above in conjunction with  FIG. 5 . 
     Referring now to  FIG. 11 , a graph  1100  includes a first curve  1102  indicative of a resistance transfer function of the first portion  102  of  FIG. 1 . The graph  1100  also includes a second curve  1104  indicative of a resistance transfer function of the second portion  104  of  FIG. 1 . The graph  1100  also includes a third curve  1106  indicative of a resistance transfer function of the first portion  102  and the second portion  104  taken together in series, i.e., the entire magnetoresistance element  100  of  FIG. 1 . 
     The curve  1102  has a center point  1102   a  midway along a linear portion of the curve  1102 . The curve  1104  has a center point  1104   a  midway along a linear portion of the curve  1104 . 
     An arrow  1108  is indicative of a separation (offset) of the center points  1102   a ,  1104   a . The separation  1108  is larger than the separation  1008  of  FIG. 10 . 
     Arrows  1110 ,  1112  are indicative of linear regions of the curves  1102 ,  1104 , respectively. The linear regions of the first and second curves  1102 ,  1104  have no overlap, but are close to each other or touch. 
     An arrow  1111  is indicative of one linear range or region of the curve  1106 . The linear region of the curve  1106  can have sensitivity contributions from the two curves  1102 ,  1104  one at a time, and not combined. Thus, a slope, i.e., a sensitivity, of the curve  1106  can be the same as a slope of the first and second curves  1102 ,  1104 . 
     The curve  1106  can have one wide linear range as described above in conjunction with  FIG. 6 . The curve  1106  can be a result of the magnetoresistance element  110  of  FIG. 1  having a yoke shape with a width of 2.6 microns and free layer structure magnetic fields of seventy-five Oesrsteds as described above in conjunction with  FIG. 6 . 
     Referring now to  FIG. 12 , a graph  1200  includes a first curve  1202  indicative of a resistance transfer function of the first portion  102  of  FIG. 1 . The graph  1200  also includes a second curve  1204  indicative of a resistance transfer function of the second portion  104  of  FIG. 1 . The graph  1200  also includes a third curve  1206  indicative of a resistance transfer function of the first portion  102  and the second portion  104  taken together in series, i.e., the entire magnetoresistance element  100  of  FIG. 1 . 
     The curve  1202  has a center point  1202   a  midway along a linear portion of the curve  1202 . The curve  1204  has a center point  1204   a  midway along a linear portion of the curve  1204 . 
     An arrow  1208  is indicative of a separation (offset) of the center points  1202   a ,  1204   a . The separation  1208  is larger than the separation  1108  of  FIG. 11 . 
     An arrow  1210  is indicative of a linear range of the first curve  1202 . An arrow  1212  is indicative of a linear range of the second curve  1204 . Linear ranges of the first and second curves  1202 ,  1204  do not overlap. 
     An arrow  1214  is indicative of one linear range or region of the curve  1206 . The linear region of the curve  1206  can have sensitivity contributions from the two curves  1202 ,  1204  one at a time, and not combined. Thus, a slope, i.e., a sensitivity, of the curve  1206  can be the same as a slope of the first and second curves  1202 ,  1204 . 
     The curve  1206  has first and second linear regions  1206   a ,  1206   b , respectively. Slopes, i.e., sensitivities, within the first and second linear regions  1206   a ,  1206   b , can be the same the slopes of the linear regions of curves  1202 ,  1204 . 
     The curve  1206  can have two linear ranges as shown above in conjunction with  FIG. 7 . The curve  1206  can be a result of the magnetoresistance element  100  of  FIG. 1  having a yoke shape with a width of ten microns and free layer structure magnetic fields of seventy-five Oesrsteds as described above in conjunction with  FIG. 7 . 
     Referring again to  FIGS. 9-12  in combination with  FIG. 8 , it should be understood that, for relatively large bias magnetic fields, as in  FIGS. 11 and 12 , at zero external magnetic field, response curves  1102  and  1202  are saturated high and curves  1104 ,  1204  are saturated low. Thus, in  FIGS. 11 and 12  the bias magnetic fields experienced by respective free layers are high enough to move the magnetizations in the free layer structures toward directions of the bias magnetic fields, i.e., in the transverse direction (see, e.g.,  FIG. 2 ). However, referring to  FIGS. 9 and 10 , at zero external field, curves  902 ,  904 ,  1002  and  1004  are not saturated. Therefore, for  FIGS. 9 and 10 , a demagnetizing field (generally in the transverse direction) is strong relative to the bias magnetic fields (generally in the transverse direction) and the demagnetizing field tends to move the magnetizations in the free layer structures to be non-parallel to the bias magnetic field directions. 
     While embodiments described herein use the dual double pinned magnetoresistance element  100  of  FIG. 1 , it should be appreciated that the same or similar structures and techniques apply to separate double pinned magnetoresistance elements, for which one of the separate double pinned magnetoresistance elements is the same as or similar to the first portion  102  and the other one of the separate double pinned magnetoresistance elements is the same as or similar to the second portion  104 . Same or similar structures can also apply to TMR element, for which the smallest dimension parallel to a substrate can be used in place of the yoke widths above. 
     All references cited herein are hereby incorporated herein by reference in their entirety. 
     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 that other embodiments incorporating these concepts, structures and techniques may be used. Accordingly, it is submitted that 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. Elements of embodiments described herein may be combined to form other embodiments not specifically set forth above. Various elements, which are described in the context of a single embodiment, may also be provided separately or in any suitable subcombination. Other embodiments not specifically described herein are also within the scope of the following claims.