Patent Publication Number: US-2022236346-A1

Title: Magnetic sensor

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application claims the benefit of Japanese Priority Patent Application No. 2021-009817 filed on Jan. 25, 2021, the entire contents of which are incorporated herein by reference. 
     BACKGROUND 
     The technology relates to a magnetic sensor including a magnetoresistive element. 
     Magnetic sensors using magnetoresistive elements have been used for various applications in recent years. A system including a magnetic sensor may be intended to detect a magnetic field containing a component in a direction perpendicular to the surface of a substrate by using a magnetoresistive element provided on the substrate. In such a case, the magnetic field containing the component in the direction perpendicular to the surface of the substrate can be detected by providing a soft magnetic body for converting a magnetic field in the direction perpendicular to the surface of the substrate into a magnetic field in the direction parallel to the surface of the substrate or locating the magnetoresistive element on an inclined surface formed on the substrate. 
     US 2008/0169807 A1 discloses first and second magnetic sensors each including an X-axis sensor, a Y-axis sensor, and a Z-axis sensor disposed on a substrate. The first magnetic sensor has V-shaped grooves in a thick film located on its substrate. Band-like portions of giant magnetoresistive elements constituting the Z-axis sensor are disposed at locations having favorable flatness in the centers of the inclined surfaces of the grooves. The band-like portions are portions constituting the main bodies of the giant magnetoresistive elements and have a long slender band-like planar shape. 
     The second magnetic sensor has V-shaped grooves each having a first inclined surface and a second inclined surface in thick films located on its substrate. The second inclined surface constitutes a lower half of the inclined surface of the groove. An angle that the second inclined surface forms with the substrate is greater than an angle that the first inclined surface forms with the substrate. Band-like portions of giant magnetoresistive elements constituting the Z-axis sensor are disposed at locations having favorable flatness in the centers of the second inclined surfaces. The band-like portions have a long slender band-like planar shape. 
     US 2008/0169807 A1 describes the fact that the inclined surface is actually formed as a curved surface somewhat bulging out because of the manufacturing process. 
     A magnetoresistive element is typically formed by etching a layered film to be the magnetoresistive element by ion milling or reactive ion etching. This etching process uses a photoresist mask. The photoresist mask is formed at a desired position on the layered film by using photolithography. The photoresist mask has a planar shape corresponding to that of the magnetoresistive element. However, the position and dimensions of the photoresist mask can vary due to the precision of the photolithography. 
     The effect of variations in the position and dimensions of the photoresist mask appear evidently in forming the magnetoresistive element on a curved surface. To form the magnetoresistive element on a curved surface, the layered film is typically formed in the shape of the curved surface by using a so-called non-conformal film formation apparatus such as a magnetron sputtering apparatus. The thickness (dimension in a direction perpendicular to the curved surface) of the layered film thus decreases as the inclination angle of the curved surface increases. 
     Suppose that the curved surface is shaped to bulge out. The amount of change in the inclination angle when the position on the curved surface changes horizontally by a predetermined distance increases with increasing distance from the top of the curved surface. Similarly, the amount of change in the thickness of the layered film increases with increasing distance from the top of the curved surface. If the position or dimensions of the photoresist mask vary to change the position of a wall surface of the photoresist mask on a side opposite from the top of the curved surface, the thickness of the magnetoresistive element changes greatly near the edge of the magnetoresistive element located on the side opposite from the top of the curved surface. This gives rise to a problem that the desired characteristic is not obtained. 
     The foregoing problem also arises if the magnetoresistive element is formed on a curved surface of a recessed shape. 
     SUMMARY 
     A magnetic sensor according to one embodiment of the technology includes a magnetoresistive element whose resistance changes with an external magnetic field, and a support member configured to support the magnetoresistive element. The support member has an opposed surface opposed to the magnetoresistive element, and a bottom surface formed of a flat surface located opposite the opposed surface. The opposed surface includes an inclined portion inclined relative to the bottom surface. In a specific cross section of the magnetic sensor perpendicular to the bottom surface, the inclined portion is inclined relative to the bottom surface at a first angle at a first position on the inclined portion, and inclined relative to the bottom surface at a second angle at a second position on the inclined portion, the second angle being smaller than the first angle. 
     An absolute value of a curvature of the inclined portion at the first position is less than an absolute value of a curvature of the inclined portion at the second position. The magnetoresistive element has a first edge and a second edge located at both ends of the magnetoresistive element in a width direction, and is provided on the inclined portion so that the first edge is located above the first position in the cross section. 
     In the magnetic sensor according to one embodiment of the technology, the magnetoresistive element may be provided on the inclined portion so that the second edge is located above the second position in the cross section. 
     In the magnetic sensor according to one embodiment of the technology, the first position and the second position may fall within a range from a third position on the inclined portion closest to the bottom surface in the cross section to a fourth position on the inclined portion farthest from the bottom surface in the cross section. In such a case, the inclined portion may be inclined relative to the bottom surface so that the first angle is a maximum and the second angle is a minimum within a range from the first position to the second position. The absolute value of the curvature of the inclined portion may be minimized at the first position and maximized at a predetermined position other than the first position within the range from the first position to the second position. 
     In the magnetic sensor according to one embodiment of the technology, the opposed surface may include a convex surface protruding in a direction away from the bottom surface. In such a case, the inclined portion may be a part of the convex surface. Alternatively, the opposed surface may include a concave surface recessed toward the bottom surface. In such a case, the inclined portion may be a part of the concave surface. 
     In the magnetic sensor according to one embodiment of the technology, the magnetoresistive element may include a magnetic layer having a magnetization whose direction is variable depending on the external magnetic field. The magnetic layer may have a first surface and a second surface located opposite the first surface, and have a thickness that is a dimension in a direction perpendicular to the first surface of the magnetic layer. The thickness at the first edge may be smaller than the thickness at the second edge. The thickness may decrease toward the first edge from the second edge. The first surface and the second surface may each have a shape long in a direction intersecting the cross section. 
     In the magnetic sensor according to one embodiment of the technology, the inclined portion of the opposed surface of the support member is inclined relative to the bottom surface at the first angle at the first position, and inclined relative to the bottom surface at the second angle smaller than the first angle at the second position. The absolute value of the curvature of the inclined portion at the first position is less than that of the curvature of the inclined portion at the second position. The magnetoresistive element is provided on the inclined portion so that the first edge is located above the first position. According to one embodiment of the technology, a change in the thickness of the magnetoresistive element due to variations in the manufacturing process can thereby be reduced. 
     Other and further objects, features and advantages of the technology will appear more fully from the following description. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The accompanying drawings are included to provide a further understanding of the disclosure and are incorporated in and constitute a part of this specification. The drawings illustrate example embodiments and, together with the specification, serve to explain the principles of the technology. 
         FIG. 1  is an explanatory diagram showing a schematic configuration of a magnetic sensor system of a first example embodiment of the technology. 
         FIG. 2  is a circuit diagram showing the circuit configuration of a magnetic sensor according to the first example embodiment of the technology. 
         FIG. 3  is a schematic diagram showing a part of the magnetic sensor according to the first example embodiment of the technology. 
         FIG. 4  is a cross-sectional view showing a part of the magnetic sensor according to the first example embodiment of the technology. 
         FIG. 5  is a plan view showing a part of the magnetic sensor according to the first example embodiment of the technology. 
         FIG. 6  is a cross-sectional view showing a magnetoresistive element of the first example embodiment of the technology. 
         FIG. 7  is an explanatory diagram for describing a shape of an inclined portion of the first example embodiment of the technology. 
         FIG. 8  is a cross-sectional view showing a step of a manufacturing method for the magnetic sensor according to the first example embodiment of the technology. 
         FIG. 9  is a cross-sectional view showing a step that follows the step in  FIG. 8 . 
         FIG. 10  is a cross-sectional view showing a step that follows the step in  FIG. 9 . 
         FIG. 11  is a cross-sectional view showing a step that follows the step in  FIG. 10 . 
         FIG. 12  is a cross-sectional view showing a step that follows the step in  FIG. 11 . 
         FIG. 13  is a characteristic chart showing the shape and curvature of the opposed surface of the support member according to the first example embodiment of the technology. 
         FIG. 14  is an explanatory diagram for describing magnetic charges on a magnetoresistive element of a comparative example. 
         FIG. 15  is an explanatory diagram for describing magnetic charges on the magnetoresistive element of the first example embodiment of the technology. 
         FIG. 16  is a cross-sectional view showing a modification example of the magnetoresistive element of the first example embodiment of the technology. 
         FIG. 17  is a cross-sectional view showing a cross section of a magnetic sensor according to a second example embodiment of the technology. 
         FIG. 18  is an explanatory diagram for describing a shape of an inclined portion of the second example embodiment of the technology. 
     
    
    
     DETAILED DESCRIPTION 
     An object of the technology is to provide a magnetic sensor configured so that a change in the thickness of a magnetoresistive element located on an inclined portion due to variations in the manufacturing process can be reduced. 
     In the following, some example embodiments and modification examples of the technology are described in detail with reference to the accompanying drawings. Note that the following description is directed to illustrative examples of the disclosure and not to be construed as limiting the technology. Factors including, without limitation, numerical values, shapes, materials, components, positions of the components, and how the components are coupled to each other are illustrative only and not to be construed as limiting the technology. Further, elements in the following example embodiments which are not recited in a most-generic independent claim of the disclosure are optional and may be provided on an as-needed basis. The drawings are schematic and are not intended to be drawn to scale. Like elements are denoted with the same reference numerals to avoid redundant descriptions. Note that the description is given in the following order. 
     First Example Embodiment 
     Example embodiments of the technology will now be described in detail with reference to the drawings. An outline of a magnetic sensor system including a magnetic sensor according to a first example embodiment of the technology will initially be described with reference to  FIG. 1 . A magnetic sensor system  100  according to the present example embodiment includes a magnetic sensor  1  according to the present example embodiment and a magnetic field generator  5 . The magnetic field generator  5  generates a target magnetic field MF that is a magnetic field for the magnetic sensor  1  to detect (magnetic field to be detected). 
     The magnetic field generator  5  is rotatable about a rotation axis C. The magnetic field generator  5  includes a pair of magnets  6 A and  6 B. The magnets  6 A and  6 B are arranged at symmetrical positions with a virtual plane including the rotation axis C at the center. The magnets  6 A and  6 B each have an N pole and an S pole. The magnets  6 A and  6 B are located in an orientation such that the N pole of the magnet  6 A is opposed to the S pole of the magnet  6 B. The magnetic field generator  5  generates the target magnetic field MF in the direction from the N pole of the magnet  6 A to the S pole of the magnet  6 B. 
     The magnetic sensor  1  is located at a position where the target magnetic field MF at a predetermined reference position can be detected. The target magnetic field MF at the reference position is part of the magnetic fields generated by the respective magnets  6 A and  6 B. The reference position may be located on the rotation axis C. In the following description, the reference position is located on the rotation axis C. The magnetic sensor  1  detects the target magnetic field MF generated by the magnetic field generator  5 , and generates a detection value Vs. The detection value Vs has a correspondence with a relative position, or rotational position in particular, of the magnetic field generator  5  with respect to the magnetic sensor  1 . 
     The magnetic sensor system  100  can be used as a device for detecting the rotational position of a rotatable moving part in an apparatus that includes the moving part. Examples of such an apparatus include a joint of an industrial robot.  FIG. 1  shows an example where the magnetic sensor system  100  is applied to an industrial robot  200 . 
     The industrial robot  200  shown in  FIG. 1  includes a moving part  201  and a support unit  202  that rotatably supports the moving part  201 . The moving part  201  and the support unit  202  are connected at a joint. The moving part  201  rotates about the rotation axis C. For example, if the magnetic sensor system  100  is applied to the joint of the industrial robot  200 , the magnetic sensor  1  may be fixed to the support unit  202 , and the magnets  6 A and  6 B may be fixed to the moving part  201 . 
     Now, we define X, Y, and Z directions as shown in  FIG. 1 . The X, Y, and Z directions are orthogonal to one another. In the present example embodiment, a direction parallel to the rotation axis C (in  FIG. 1 , a direction out of the plane of the drawing) will be referred to as the X direction. In  FIG. 1 , the Y direction is shown as a rightward direction, and the Z direction is shown as an upward direction. The opposite directions to the X, Y, and Z directions will be referred to as −X, −Y, and −Z directions, respectively. As used herein, the term “above” refers to positions located forward of a reference position in the Z direction, and “below” refers to positions located on a side of the reference position opposite to “above”. 
     In the present example embodiment, the direction of the target magnetic field MF at the reference position is expressed as a direction within the YZ plane including the reference position on the rotation axis C. The direction of the target magnetic field MF at the reference position rotates about the reference position within the foregoing YZ plane. 
     The magnetic sensor  1  includes magnetoresistive elements (hereinafter, referred to as MR elements) whose resistances change with an external magnetic field. In the present example embodiment, the resistances of the MR elements change with a change in the direction of the target magnetic field MF. The magnetic sensor  1  generates detection signals corresponding to the resistances of the MR elements, and generates a detection value Vs based on the detection signals. 
     Next, a configuration of the magnetic sensor  1  according to the present example embodiment will be described. An example of a circuit configuration of the magnetic sensor  1  will initially be described with reference to  FIG. 2 . In the example shown in  FIG. 2 , the magnetic sensor  1  includes four resistor sections  11 ,  12 ,  13 , and  14 , two power supply nodes V 1  and V 2 , two ground nodes G 1  and G 2 , and two signal output nodes E 1  and E 2 . 
     The resistor sections  11  to  14  each include at least one MR element  30 . If each of the resistor sections  11  to  14  includes a plurality of MR elements  30 , the plurality of MR elements  30  in each of the resistor sections  11  to  14  may be connected in series. 
     The resistor section  11  is provided between the power supply node V 1  and the signal output node E 1 . The resistor section  12  is provided between the signal output node E 1  and the ground node G 1 . The resistor section  13  is provided between the power supply node V 2  and the signal output node E 2 . The resistor section  14  is provided between the signal output node E 2  and the ground node G 2 . The power supply nodes V 1  and V 2  are configured to receive a power supply voltage of predetermined magnitude. The ground nodes G 1  and G 2  are connected to the ground. 
     The potential of the connection point between the resistor section  11  and the resistor section  12  changes depending on the resistance of the at least one MR element  30  of the resistor section  11  and the resistance of the at least one MR element  30  of the resistor section  12 . The signal output node E 1  outputs a signal corresponding to the potential of the connection point between the resistor section  11  and the resistor section  12  as a detection signal S 1 . 
     The potential of the connection point between the resistor section  13  and the resistor section  14  changes depending on the resistance of the at least one MR element  30  of the resistor section  13  and the resistance of the at least one MR element  30  of the resistor section  14 . The signal output node E 2  outputs a signal corresponding to the potential of the connection point between the resistor section  13  and the resistor section  14  as a detection signal S 2 . 
     The magnetic sensor  1  further includes a detection value generation circuit  21  that generates the detection value Vs on the basis of the detection signals S 1  and S 2 . The detection value generation circuit  21  includes an application specific integrated circuit (ASIC) or a microcomputer, for example. 
     Next, the configuration of the magnetic sensor  1  will be described in more detail with attention focused on one MR element  30 .  FIG. 3  is a schematic diagram showing a part of the magnetic sensor  1 .  FIG. 4  is a cross-sectional view showing a part of the magnetic sensor  1 .  FIG. 4  shows a cross section parallel to the YZ plane and intersecting the MR element  30 .  FIG. 5  is a plan view showing a part of the magnetic sensor  1 . 
     The magnetic sensor  1  further includes a support member  60 . The support member  60  supports all the MR elements  30  included in the resistor sections  11  to  14 . As shown in  FIGS. 3 and 4 , the support member  60  includes an opposed surface  60   a  opposed, at least in part, to the MR elements  30 , and a bottom surface  60   b  formed of a flat surface located opposite the opposed surface  60   a . The opposed surface  60   a  is located at an end of the support member  60  in the Z direction. The bottom surface  60   b  is located at an end of the support member  60  in the −Z direction. The bottom surface  60   b  is parallel to the XY plane. For example, the magnetic sensor  1  may be manufactured with the bottom surface  60   b  or a surface corresponding to the bottom surface  60   b  made horizontal. For example, the magnetic sensor  1  may be installed based on the direction or tilt of the bottom surface  60   b  or the surface corresponding to the bottom surface  60   b . The bottom surface  60   b  may thus serve as a reference plane in at least either the manufacturing or the installing of the magnetic sensor  1 . 
     The opposed surface  60   a  of the support member  60  includes an inclined portion inclined relative to the bottom surface  60   b . In the present example embodiment, the opposed surface  60   a  includes a flat portion  60   a   1  parallel to the bottom surface  60   b  and at least one curved portion  60   a   2  not parallel to the bottom surface  60   b . As shown in  FIG. 4 , the curved portion  60   a   2  is a convex surface protruding in a direction away from the bottom surface  60   b . The foregoing inclined portion is a part of the convex surface. The curved portion  60   a   2  has a curved shape (arch shape) curved to protrude in a direction away from the bottom surface  60   b  (Z direction) in a given cross section parallel to the YZ plane. In a given cross section parallel to the YZ plane, the distance from the bottom surface  60   b  to the curved portion  60   a   2  is maximized at the center of the curved portion  60   a   2  in a direction parallel to the Y direction (hereinafter, referred to simply as the center of the curved portion  60   a   2 ). 
     The curved portion  60   a   2  extends along the X direction. As shown in  FIG. 3 , the overall shape of the curved portion  60   a   2  is a semicylindrical curved surface formed by moving the curved shape (arch shape) shown in  FIG. 4  along the X direction. 
     The MR element  30  is located on the curved portion  60   a   2 . A portion of the curved portion  60   a   2  from an edge at the end of the curved portion  60   a   2  in the −Y direction to the center of the curved portion  60   a   2  will be referred to as a first inclined portion and be denoted by the symbol SL 1 . A portion of the curved portion  60   a   2  from an edge at the end of the curved portion  60   a   2  in the Y direction to the center of the curved portion  60   a   2  will be referred to as a second inclined portion and be denoted by the symbol SL 2 . In  FIG. 3 , the border between the first inclined portion SL 1  and the second inclined portion SL 2  is shown by a dotted line. Both the first and second inclined portions SL 1  and SL 2  are inclined relative to the bottom surface  60   b . In the present example embodiment, the entire MR element  30  is located on the first inclined portion SL 1  or the second inclined portion SL 2 .  FIGS. 3 and 4  show the MR element  30  located on the first inclined portion SL 1 . 
     The MR element  30  has a shape that is long in the X direction. As employed herein, the lateral direction of the MR element  30  will be referred to as the width direction of the MR element  30  or simply as the width direction. The MR element  30  may have a planar shape (shape seen in the Z direction), like a rectangle, including a constant width portion having a constant or substantially constant width in the width direction regardless of the position in the X direction. The MR element  30  may have a planar shape including no constant width portion, like an ellipse. Examples of the planar shape of the MR element  30  including a constant width portion include a rectangular shape where both longitudinal ends are straight, an oval shape where both longitudinal ends are semicircular, and a shape where both longitudinal ends are polygonal.  FIGS. 3 and 5  show the case where the MR element  30  has a rectangular planar shape. In this example, the MR element  30  has a bottom surface  30   a , a top surface  30   b , a first edge  30   c , a second edge  30   d , a third edge  30   e , and a fourth edge  30   f . The bottom surface  30   a  is opposed to the curved portion  60   a   2 . The top surface  30   b  is located opposite the bottom surface  30   a . The first and second edges  30   c  and  30   d  are located at both ends in the width direction. The third and fourth edges  30   e  and  30   f  are located at both ends in the longitudinal direction. The dimension of the MR element  30  in the width direction is constant or substantially constant regardless of the position in the X direction. 
     The support member  60  includes a substrate  61  and an insulating layer  62  located on the substrate  61 . The substrate  61  is a semiconductor substrate made of a semiconductor such as Si, for example. The substrate  61  has a top surface located at an end of the substrate  61  in the Z direction, and a bottom surface located at an end of the substrate  61  in the −Z direction. The bottom surface  60   b  of the support member  60  is constituted by the bottom surface of the substrate  61 . The substrate  61  has a constant thickness (dimension in the Z direction). 
     The insulating layer  62  is made of an insulating material such as SiO 2 , for example. The insulating layer  62  includes a top surface located at an end in the Z direction. The opposed surface  60   a  of the support member  60  is constituted by the top surface of the insulating layer  62 . The insulating layer  62  has a cross-sectional shape such that the curved portion  60   a   2  is formed on the opposed surface  60   a . Specifically, the insulating layer  62  has a cross-sectional shape of bulging out in the Z direction in a given cross section parallel to the YZ plane. 
     The magnetic sensor  1  further includes a lower electrode  41 , an upper electrode  42 , and insulating layers  63 ,  64  and  65 . In  FIG. 3 , the lower electrode  41 , the upper electrode  42 , and the insulating layers  63  to  65  are omitted. In  FIG. 5 , the insulating layers  63  to  65  are omitted. 
     The lower electrode  41  is located on the opposed surface  60   a  of the support member  60  (the top surface of the insulating layer  62 ). The insulating layer  63  is located on the opposed surface  60   a  of the support member  60 , around the lower electrode  41 . The MR element  30  is located on the lower electrode  41 . The insulating layer  64  is located on the lower electrode  41  and the insulating layer  63 , around the MR element  30 . The upper electrode  42  is located on the MR element  30  and the insulating layer  64 . The insulating layer  65  is located on the insulating layer  64 , around the upper electrode  42 . 
     The magnetic sensor  1  further includes a not-shown insulating layer covering the upper electrode  42  and the insulating layer  65 . The lower electrode  41  and the upper electrode  42  are made of a conductive material such as Cu, for example. The insulating layers  63  to  65  and the not-shown insulating layer are made of an insulating material such as SiO 2 , for example. 
     The substrate  61  and the portions of the magnetic sensor  1  stacked on the substrate  61  are referred to collectively as a detection unit.  FIG. 4  can be said to show the detection unit. The detection value generation circuit  21  shown in  FIG. 2  may be integrated with or separate from the detection unit. 
     Now, the configuration of the MR element  30  will be described in detail with reference to  FIG. 6 . In particular, in the present example embodiment, the MR element  30  is a spin-valve MR element. As shown in  FIG. 6 , the MR element  30  includes a magnetization pinned layer  32  having a magnetization whose direction is fixed, a free layer  34  having a magnetization whose direction is variable depending on the direction of an external magnetic field, and a spacer layer  33  located between the magnetization pinned layer  32  and the free layer  34 . The MR element  30  may be a tunneling magnetoresistive (TMR) element or a giant magnetoresistive (GMR) element. In the TMR element, the spacer layer  33  is a tunnel barrier layer. In the GMR element, the spacer layer  33  is a nonmagnetic conductive layer. The resistance of the MR element  30  changes with an angle that the direction of the magnetization of the free layer  34  forms with respect to the direction of the magnetization of the magnetization pinned layer  32 . The resistance is minimized if the angle is 0°. The resistance is maximized if the angle is 180°. 
     The magnetization pinned layer  32 , the spacer layer  33 , and the free layer  34  are stacked in this order from the lower electrode  41  in the direction toward the upper electrode  42 . The MR element  30  further includes an underlayer  31  interposed between the magnetization pinned layer  32  and the lower electrode  41 , and a cap layer  35  interposed between the free layer  34  and the upper electrode  42 . The arrangement of the magnetization pinned layer  32 , the spacer layer  33 , and the free layer  34  in the MR element  30  may be vertically reversed from that shown in  FIG. 6 . 
     The direction of the magnetization of the magnetization pinned layer  32  is desirably orthogonal to the longitudinal direction of the MR element  30 . In the present example embodiment, the MR element  30  is located on the first inclined portion SL 1  or the second inclined portion SL 2  inclined relative to the bottom surface  60   b . The direction of the magnetization of the magnetization pinned layer  32  is thus also inclined relative to the bottom surface  60   b.    
     For the sake of convenience, in the present example embodiment, the direction of the magnetization of the magnetization pinned layer  32  located on the first inclined portion SL 1  will be referred to as a U direction or a −U direction. The U direction is a direction rotated from the Y direction toward the Z direction by a predetermined angle. The −U direction is the direction opposite to the U direction. For the sake of convenience, in the present example embodiment, the direction of the magnetization of the magnetization pinned layer  32  located on the second inclined portion SL 2  will be referred to as a V direction or a −V direction. The V direction is a direction rotated from the Y direction toward the −Z direction by a predetermined angle. The −V direction is the direction opposite to the V direction. 
     The X, U, and V directions are shown in  FIG. 2 . For the sake of convenience, in  FIG. 2 , the U direction and the V direction are indicated by the same arrow. In  FIG. 2 , the filled arrows indicate the directions of the magnetizations of the magnetization pinned layers  32  of the MR elements  30  included in the respective resistor sections  11  to  14 . The magnetic sensor  1  may be configured so that the directions of the magnetizations of the magnetization pinned layers  32  of the MR elements  30  in the resistor sections  11  and  14  are the U direction, and the directions of the magnetizations of the magnetization pinned layers  32  of the MR elements  30  in the resistor sections  12  and  13  are the −U direction. Alternatively, the magnetic sensor  1  may be configured so that the directions of the magnetizations of the magnetization pinned layers  32  of the MR elements  30  in the resistor sections  11  and  14  are the V direction, and the directions of the magnetizations of the magnetization pinned layers  32  of the MR elements  30  in the resistor sections  12  and  13  are the −V direction. 
     Alternatively, the magnetic sensor  1  may include a first circuit portion and a second circuit portion each including the resistor sections  11  to  14 . The first circuit portion may be configured so that the directions of the magnetizations of the magnetization pinned layers  32  of the MR elements  30  in the resistor sections  11  and  14  are the U direction, and the directions of the magnetizations of the magnetization pinned layers  32  of the MR elements  30  in the resistor sections  12  and  13  are the −U direction. The second circuit portion may be configured so that the directions of the magnetizations of the magnetization pinned layers  32  of the MR elements  30  in the resistor sections  11  and  14  are the V direction, and the directions of the magnetizations of the magnetization pinned layers  32  of the MR elements  30  in the resistor sections  12  and  13  are the −V direction. 
     The free layer  34  corresponds to a magnetic layer according to the technology. The free layer  34  has magnetic shape anisotropy where the direction of the easy axis of magnetization intersects the direction of the magnetization of the magnetization pinned layer  32 . In the present example embodiment, the MR element  30  is patterned to a shape that is long in the X direction. This gives the free layer  34  magnetic shape anisotropy where the direction of the easy axis of magnetization is parallel to the X direction. 
     Up to this point, the configuration of the magnetic sensor  1  has been described with attention focused on one MR element  30 . In the present example embodiment, the resistor sections  11  to  14  each include at least one MR element  30 . The magnetic sensor  1  thus includes a plurality of MR elements  30 , a plurality of lower electrodes  41 , and a plurality of upper electrodes  42 . As shown in  FIG. 5 , each of the lower electrodes  41  has a long slender shape. The MR element  30  is provided on the top surface of the lower electrode  41 , near one end in the longitudinal direction. Each upper electrode  42  has a long slender shape and is located over two lower electrodes  41  to electrically connect two adjoining MR elements  30 . 
     The number of the curved portions  60   a   2  of the opposed surface  60   a  of the support member  60  may be one or more than one. If the number of the curved portions  60   a   2  is one, the plurality of MR elements  30  are located on the one curved portion  60   a   2 . In such a case, the plurality of MR elements  30  may be located on either one of the first and second inclined portions SL 1  and SL 2  or on both the first and second inclined portions SL 1  and SL 2 . 
     If the number of curved portions  60   a   2  is more than one, one or a plurality of MR elements  30  may be located on one curved portion  60   a   2 . In such a case, the plurality of curved portions  60   a   2  may be arranged along one direction. Alternatively, the plurality of curved portions  60   a   2  may be arranged in a plurality of rows, i.e., more than one curved portion  60   a   2  in both the X and Y directions. 
     Next, the inclined portions and the MR elements  30  will be described in more detail with reference to  FIGS. 6 and 7 . The following description will be given by using the first inclined portion SL 1  as an example.  FIG. 7  is an explanatory diagram for describing the shape of the first inclined portion SL 1 . In  FIG. 7 , the underlayer  31  and the cap layer  35  of the MR element  30  are omitted. 
       FIG. 7  shows a specific cross section intersecting the MR element  30  and being perpendicular to the bottom surface  60   b  of the support member  60 . Such a cross section will hereinafter be denoted by the symbol S. The cross section S intersects the longitudinal direction of the MR element  30 . To describe the shape of the first inclined portion SL 1 , a first position P 1 , a second position P 2 , a third position P 3 , and a fourth position P 4  on the first inclined portion SL 1  in a given cross section S will be defined as follows. The first position P 1  is a position where the first inclined portion SL 1  is inclined relative to the bottom surface  60   b  at a first angle θ 1 . The second position P 2  is a position where the first inclined portion SL 1  is inclined relative to the bottom surface  60   b  at a second angle θ 2  smaller than the first angle θ 1 . In the present example embodiment, in particular, the first position P 1  is closer to the bottom surface  60   b  than is the second position P 2 . In the following description, the angle that a specific surface forms with the bottom surface  60   b  will be expressed in terms of an angle of 0° or more and not more than 90°. 
     The third position P 3  is the position on the first inclined portion SL 1  closest to the bottom surface  60   b . Specifically, the third position P 3  refers to the end of the first inclined portion SL 1  in the −Y direction, and is located at the border between the curved portion  60   a   2  and the flat portion  60   a   1 . The fourth position P 4  is the position on the first inclined portion SL 1  farthest from the bottom surface  60   b . Specifically, the fourth position P 4  refers to the end of the first inclined portion SL 1  in the Y direction, and is located at the border between the first inclined portion SL 1  and the second inclined portion SL 2 , i.e., the center of the curved portion  60   a   2 . The first position P 1  and the second position P 2  fall within the range from the third position P 3  to the fourth position P 4 . 
     Both the angle that the first inclined portion SL 1  forms with the bottom surface  60   b  at the third position P 3  and the angle that the first inclined portion SL 1  forms with the bottom surface  60   b  at the fourth position P 4  are 0°. Both the first and second angles θ 1  and  02  are greater than 0° and less than 90°. In the present example embodiment, in particular, the first inclined portion SL 1  is inclined relative to the bottom surface  60   b  so that the first angle θ 1  is maximum and the second angle θ 2  is minimum within the range from the first position P 1  to the second position P 2 . 
     The outline of the first inclined portion SL 1  in a given cross section S includes a plurality of curves where each curve has a different curvature. The absolute value of a curvature k 1  of the first inclined portion SL 1  at the first position P 1  is less than that of a curvature k 2  of the first inclined portion SL 1  at the second position P 2 . In other words, the first inclined portion SL 1  at the first position P 1  is straighter than the first inclined portion SL 1  at the second position P 2 , and curves gently. 
     In  FIG. 7 , the circular arc denoted by the symbol C 1  represents a part of a circle approximating the first inclined portion SL 1  at the first position P 1 , i.e., a first circle of curvature. The circular arc denoted by the symbol C 2  represents a part of a circle approximating the first inclined portion SL 1  at the second position P 2 , i.e., a second circle of curvature. As shown in  FIG. 7 , the first circle of curvature (symbol C 1 ) has a radius greater than that of the second circle of curvature (symbol C 2 ). 
     In the range from the first position P 1  to the second position P 2 , the absolute value of the curvature of the first inclined portion SL 1  is maximized at a predetermined position other than the first position P 1  on the first inclined portion SL 1 . The predetermined position may be the second position P 2  or a position other than the first and second positions P 1  and P 2 . The absolute value of the curvature of the first inclined portion SL 1  may increase monotonically from the first position P 1  to the second position P 2 , or may increase on a whole while increasing and decreasing repeatedly. 
     In the example shown in  FIG. 7 , the outline of the first inclined portion SL 1  in a given cross section S is a smooth curve from the first position P 1  to the second position P 2 . However, the outline of the first inclined portion SL 1  may include a point where the curvature is substantially infinite. In such a case, the outline of the first inclined portion SL 1  bends at the point where the curvature is substantially infinite. An angle θb that the first inclined portion SL 1  forms with the bottom surface  60   b  at the bending point is defined as follows. An angle that the first inclined portion SL 1  forms with the bottom surface  60   b  at a point on the first inclined portion SL 1  near the bending point and closer to the bottom surface  60   b  than is the bending point will be denoted by θa. An angle that the first inclined portion SL 1  forms with the bottom surface  60   b  at a point on the first inclined portion SL 1  near the bending point and farther from the bottom surface  60   b  than is the bending point will be denoted by θc. The angle θb is an angle smaller than the angle θa and greater than the angle θc. The angle θb may be an average of the angles θa and θc. 
     The MR element  30  is provided on the first inclined portion SL 1  so that the first edge  30   c  is located above the first position P 1  in a given cross section S. Further, in the present example embodiment, the MR element  30  is provided on the first inclined portion SL 1  so that the second edge  30   d  is located above the second position P 2  in the given cross section S. Thus, in the present example embodiment, the MR element  30  is provided on the area ranging from the first position P 1  to the second position P 2  on the first inclined portion SL 1 . 
     As shown in  FIGS. 6 and 7 , the free layer  34  of the MR element  30  includes a first surface  34   a , a second surface  34   b  opposite to the first surface  34   a , and an outer peripheral surface connecting the first surface  34   a  and the second surface  34   b . The first surface  34   a  is located farther from the opposed surface  60   a  of the support member  60  than is the second surface  34   b . The first surface  34   a  is in contact with the cap layer  35 . The second surface  34   b  is in contact with the spacer layer  33 . 
     In the present example embodiment, the MR element  30  is patterned to a shape that is long in the X direction. The first and second surfaces  34   a  and  34   b  thus each have a shape that is long in the X direction. The first surface  34   a  has a first edge Ed 1  and a second edge Ed 2  located at both lateral ends of the first surface  34   a . The first edge Ed 1  is located at the first edge  30   c  of the MR element  30 . The second edge Ed 2  is located at the second edge  30   d  of the MR element  30 . 
     As employed herein, an angle that the first surface  34   a  forms with the bottom surface  60   b  of the support member  60  will be referred to as an inclination angle and denoted by the symbol ϕ. The first surface  34   a  is inclined relative to the bottom surface  60   b  of the support member  60  so that the inclination angle ϕ is greater than 0°. 
     As employed herein, the inclination angle ϕ at the first edge Ed 1  will be referred to as an inclination angle ϕ 1 . The inclination angle ϕ at the second edge Ed 2  will be referred to as an inclination angle ϕ 2 . In a given cross section S, the inclination angle ϕ 1  at the first edge Ed 1  is greater than the inclination angle ϕ 2  at the second edge Ed 2 . In a given cross section S, the inclination angle ϕ may increase toward the first edge Ed 1  from the second edge Ed 2 . 
     The inclination angle ϕ at a given position on the first surface  34   a  changes depending on the angle θ that the first inclination portion SL 1  forms with the bottom surface  60   b . Specifically, the inclination angle ϕ at a given position on the first surface  34   a  is substantially the same as the angle θ at a position on the first inclined portion SL 1  below the given position. The inclination angle ϕ thus increases as the angle θ increases. 
     The free layer  34  has a thickness T that is a dimension in a direction perpendicular to the first surface  34   a . The thickness T can also be said to be the distance between the first and second surfaces  34   a  and  34   b  in the direction perpendicular to the first surface  34   a . As employed herein, the thickness T at the first edge Ed 1  will be referred to as a thickness T 1 . The thickness T at the second edge Ed 2  will be referred to as a thickness T 2 . The thickness T 1  is also the thickness T at the first edge  30   c  of the MR element  30 . The thickness T 2  is also the thickness T at the second edge  30   d  of the MR element  30 . For the sake of convenience, an imaginary surface is assumed by extending the second surface  34   b  along the curved portion  60   a   2 , and the thickness T 2  is defined as the distance between the first surface  34   a  and the imaginary surface in the direction perpendicular to the first surface  34   a.    
     In a given cross section S, the thickness T 1  at the first edge Ed 1  is smaller than the thickness T 2  at the second edge Ed 2 . In a given cross section S, the thickness T may decrease toward the first edge Ed 1  from the second edge Ed 2 . 
     The thickness T at a given position on the first surface  34   a  changes depending on the angle θ. Specifically, the thickness T at a given position on the first surface  34   a  decreases as the angle θ at the position on the first inclined portion SL 1  closest to the given position increases. 
     From the relationship between the inclination angle ϕ and the angle θ and the relationship between the thickness T and the angle θ, the thickness T decreases as the inclination angle ϕ increases. 
     The foregoing description has been given by using the first inclined portion SL 1  as an example. The first inclined portion SL 1  and the second inclined portion SL 2  have a shape symmetrical or substantially symmetrical about the XZ plane including the center of the curved portion  60   a   2 . The foregoing description of the first inclined portion SL 1  therefore also applies to the second inclined portion SL 2 . The foregoing description of the MR element  30  also applies to the MR element  30  provided on the second inclined portion SL 2 . 
     Now, a manufacturing method for the magnetic sensor  1  according to the present example embodiment will be described with reference to  FIG. 8  to  FIG. 12 . The manufacturing method for the magnetic sensor  1  includes steps of forming the portions of the magnetic sensor  1  shown in  FIGS. 3 to 5 , i.e., the detection unit, and steps of completing the magnetic sensor  1  by using the detection unit.  FIGS. 8 to 12  show the steps of forming the detection unit. Note that  FIGS. 8 to 12  deal with the MR element  30  formed on the first inclined portion SL 1 . 
     As shown in  FIG. 8 , in the steps of forming the detection unit, the insulating layer  62  is initially formed on the substrate  61 . The insulating layer  62  may be formed by forming a photoresist mask on the substrate  61  and then forming an insulating film. The insulating layer  62  may be formed by forming an insulating film on the substrate  61  and then etching a part of the insulating film. The formation of the insulating layer  62  completes the support member  60 . 
       FIG. 9  shows the next step. In this step, the lower electrode  41  and the insulating layer  63  are formed on the insulating layer  62 , i.e., on the support member  60 . For example, the lower electrode  41  and the insulating layer  63  are formed in the following manner. A metal film is initially formed on the insulating layer  62 . An etching mask is then formed on the metal film. The etching mask may be formed by photolithographically patterning a photoresist layer. Next, the metal film is etched using the etching mask to be made into the lower electrode  41 . The insulating layer  63  is then formed with the etching mask left unremoved. The etching mask is then removed. 
       FIG. 10  shows the next step. In this step, films that later become the layers constituting the MR element  30  are formed in order, and a layered film  30 P which later becomes the MR element  30  is formed on the lower electrode  41  and the insulating layer  63 . An etching mask  81  is then formed on the layered film  30 P. The etching mask  81  is formed by photolithographically patterning a photoresist layer. The etching mask  81  has a planar shape (shape seen from above) corresponding to that of the MR element  30 . The etching mask  81  has a first wall surface  81   a  for defining the position of the first edge  30   c  of the MR element  30 , and a second wall surface  81   b  for defining the position of the second edge  30   d  of the MR element  30 . 
       FIG. 11  shows the next step. In this step, the layered film  30 P is etched by, for example, ion milling or reactive ion etching using the etching mask  81 . The layered film  30 P is thereby made into the MR element  30 . 
       FIG. 12  shows the next step. In this step, the insulating layer  64  is initially formed with the etching mask  81  left unremoved. The etching mask  81  is then removed. The upper electrode  42  and the insulating layer  65  are then formed on the MR element  30  and the insulating layer  64 . The method for forming the upper electrode  42  and the insulating layer  65  is the same as that for forming the lower electrode  41  and the insulating layer  63 . 
     A not-shown insulating layer is then formed to cover the upper electrode  42  and the insulating layer  65 . Next, a plurality of terminals constituting the power supply nodes V 1  and V 2  and the like are formed to complete the detection unit of the magnetic sensor  1 . 
     Next, an example of the shape and curvature of the opposed surface  60   a  of the support member  60  will be described with reference to  FIG. 13 .  FIG. 13  is a characteristic chart showing the shape and curvature of the opposed surface  60   a  of the support member  60  in a predetermined cross section S.  FIG. 13  is obtained by measuring the opposed surface  60   a  of an actually manufactured support member  60  under an atomic force microscope. In  FIG. 13 , the horizontal axis indicates the position in a direction parallel to the Y direction. The vertical axis on the left indicates the curvature of the opposed surface  60   a . The curvature shown in  FIG. 13  is defined so that the curvature has a positive value if the opposed surface  60   a  is a convex surface protruding in a direction away from the bottom surface  60   b . The vertical axis on the right indicates the height of the opposed surface  60   a . In  FIG. 13 , the height of the opposed surface  60   a  refers to the position in a direction parallel to the Z direction. In  FIG. 13 , the height of the flat portion  60   a   1  of the opposed surface  60   a  is assumed to be 0. The solid line denoted by the reference numeral  71  represents the curvature of the opposed surface  60   a . The thick solid line denoted by the reference numeral  72  represents the height of the opposed surface  60   a.    
     In  FIG. 13 , the points denoted by the symbols P 1 L and P 2 L represent the positions corresponding to the first and second edges  30   c  and  30   d  of the MR element  30  provided on the first inclined portion SL 1 , respectively. The MR element  30  is provided on the area ranging from the point P 1 L to the point P 2 L on the first inclined portion SL 1 . The points P 1 L and P 2 L substantially represent the first and second positions P 1  and P 2  on the first inclined portion SL 1 . As shown in  FIG. 13 , the angle that the opposed surface  60   a  forms with the bottom surface  60   b  at the point P 1 L is greater than the angle that the opposed surface  60   a  forms with the bottom surface  60   b  at the point P 2 L. The absolute value of the curvature of the opposed surface  60   a  at the point P 1 L is less than that of the curvature of the opposed surface  60   a  at the point P 2 L. In the range from the point P 1 L to the point P 2 L, the absolute value of the curvature of the opposed surface  60   a  is minimized at the point P 1 L and maximized at a predetermined position other than the point P 1 L. 
     Similarly, in  FIG. 13 , the points denoted by the symbols P 1 R and P 2 R represent the positions corresponding to the first and second edges  30   c  and  30   d  of an MR element  30  provided on the second inclined portion SL 2 , respectively. The MR element  30  is provided on the area ranging from the point P 1 R to the point P 2 R on the second inclined portion SL 2 . The points P 1 R and P 2 R substantially represent the first and second positions P 1  and P 2  on the second inclined portion SL 2 . As shown in  FIG. 13 , the angle that the opposed surface  60   a  forms with the bottom surface  60   b  at the point P 1 R is greater than the angle that the opposed surface  60   a  forms with the bottom surface  60   b  at the point P 2 R. The absolute value of the curvature of the opposed surface  60   a  at the point P 1 R is less than that of the curvature of the opposed surface  60   a  at the point P 2 R. In the range from the point P 1 R to the point P 2 R, the absolute value of the curvature of the opposed surface  60   a  is minimized at the point P 1 R and maximized at a predetermined position other than the point P 1 R. 
     The operation and effect of the magnetic sensor  1  according to the present example embodiment will now be described. As shown in  FIG. 7 , in the present example embodiment, the first inclined portion SL 1  is inclined relative to the bottom surface  60   b  at the first angle θ 1  at the first position P 1  and inclined relative to the bottom surface  60   b  at the second angle θ 2  smaller than the first angle θ 1  at the second position P 2  in a given cross section S. The absolute value of the curvature k 1  of the first inclined portion SL 1  at the first position P 1  is less than that of the curvature k 2  of the first inclined portion SL 1  at the second position P 2 . 
     The MR element  30  provided on the first inclined portion SL 1  is disposed on the first inclined portion SL 1  so that the first edge  30   c  is located above the first position P 1  in a given cross section S. Further, in the present example embodiment, the MR element  30  is disposed on the first inclined portion SL 1  so that the second edge  30   d  is located above the second position P 2  in the given cross section S. 
     As described with reference to  FIGS. 8 to 12 , the MR element  30  is formed by etching the layered film  30 P. The etching uses the etching mask  81 . The etching mask  81  is formed at a desired position on the layered film  30 P by photolithographically patterning a photoresist layer. 
     The etching mask  81  has the first wall surface  81   a  for defining the position of the first edge  30   c  of the MR element  30  and the second wall surface  81   b  for defining the position of the second edge  30   d  of the MR element  30 . The first wall surface  81   a  is designed to be located above the first position P 1  defined in advance. The second wall surface  81   b  is designed to be located above the second position P 2  defined in advance. However, in the actual manufacturing process, the position and dimensions of the etching mask  81  can vary due to the precision of the photolithography. This changes the positions of the first and second wall surfaces  81   a  and  81   b , and the positions of the first and second edges  30   c  and  30   d  of the MR element  30  deviate from the respective designed positions. 
     The amount of deviation in the angle that the first inclined portion SL 1  forms with the bottom surface  60   b  at a predetermined position P on the first inclined portion SL 1  will now be described. Here, the angle that the first inclined portion SL 1  forms with the bottom surface  60   b  at the predetermined position P will be denoted by the symbol θ. The curvature of the first inclined portion SL 1  at the predetermined position P will be denoted by the symbol k. The amount of deviation in the angle that the first inclined portion SL 1  forms with the bottom surface  60   b  when the predetermined position P is shifted by Δy in the direction parallel to the Y direction will be denoted by the symbol Δθ. If Δy is sufficiently small, the amount of deviation Δθ can be expressed by the following Eq. (1): 
       Δθ= k*Δy /cos θ  (1)
 
     Here, the curvature k is assumed to be constant. 
     As can be seen from Eq. (1), the greater the curvature k, the greater the amount of deviation Δθ. The greater the angle θ, the greater the amount of deviation Δθ as well. 
     As described above, the thickness T of the free layer  34  of the MR element  30  changes depending on the angle θ. Thus, from Eq. (1), it can be said that the greater the curvature k, the greater the amount of change in the thickness T, and the greater the angle θ, the greater the amount of change in the thickness T. 
     In the present example embodiment, the first angle θ 1  is greater than the second angle θ 2 . Suppose, for example, that the outline of the first inclined portion SL 1  has a constant curvature k like a circular arc, and given the same Δy, the amount of deviation Δθ near the first position P 1  is greater than the amount of deviation Δθ near the second position P 2 . As a result, the amount of change in the thickness T at the first edge  30   c  is greater than the amount of change in the thickness T at the second edge  30   d.    
     By contrast, in the present example embodiment, the absolute value of the curvature k 1  of the first inclined portion SL 1  at the first position P 1  is less than that of the curvature k 2  of the first inclined portion SL 1  at the second position P 2 . In other words, in the present example embodiment, the first inclined portion SL 1  is configured to have a relatively small curvature k at the position where the amount of change in the thickness T of the free layer  34  is relatively large. As a result, according to the present example embodiment, a change in the thickness T of the free layer  34  near the first edge  30   c  due to variations in the manufacturing process can thus be reduced compared to the case where the curvature k of the first inclined portion SL 1  is constant or the absolute value of the curvature k 1  is greater than that of the curvature k 2 . 
     According to the present example embodiment, a change in the thicknesses of the layers constituting the MR element  30 , other than the free layer  34  near the first edge  30   c , due to variations in the manufacturing process can also be reduced. As a result, according to the present example embodiment, a change in the thickness of the MR element  30  (a dimension in the direction perpendicular to the first inclined portion SL 1 ) near the first edge  30   c  due to variations in the manufacturing process can be reduced. 
     In the present example embodiment, the MR element  30  is provided so that the second edge  30   d  is located above the second position P 2  where the amount of change in the thickness T of the free layer  34  is relatively small. Therefore, according to the present example embodiment, a change in the thickness T of the free layer  34  near the second edge  30   d  and the thickness of the MR element  30  near the second edge  30   d  due to variations in the manufacturing process can thus be reduced. As a result, according to the present example embodiment, a change in the thickness T of the entire free layer  34  and the thickness of the entire MR element  30  can be reduced. 
     Next, other effects of the present example embodiment will be described. In the present example embodiment, the thickness T of the free layer  34  at a given position on the first surface  34   a  decreases as the angle θ at the position on the first inclined portion SL 1  closest to the given position increases. Such a relationship between the thickness T and the angle θ can be achieved by forming the layered film  30 P using a so-called non-conformal film formation apparatus such as a magnetron sputtering apparatus. 
     In the present example embodiment, in particular, the thickness T 1  at the first edge Ed 1  is smaller than the thickness T 2  at the second edge Ed 2  in a given cross section S. Therefore, according to the present example embodiment, the concentration of magnetic charges at and near the first edge Ed 1  of the free layer  34  can thus be reduced. 
     The effect of reducing the concentration of magnetic charges will be described in detail below by comparison with an MR element  230  according to a comparative example. The MR element  230  of the comparative example will initially be described with reference to  FIG. 14 .  FIG. 14  is an explanatory diagram for describing magnetic charges on the MR element  230  of the comparative example.  FIG. 14  shows a cross section corresponding to the cross section S. Like the MR element  30  according to the present example embodiment, the MR element  230  according to the comparative example includes a magnetization pinned layer  232 , a spacer layer  233 , a free layer  234 , and a not-shown underlayer and cap layer. 
     The MR element  230  of the comparative example is located on a flat surface parallel to the bottom surface  60   b  of the support member  60 . Like the MR element  30  according to the present example embodiment, the MR element  230  is patterned to a shape that is long in the X direction. This gives the free layer  234  magnetic shape anisotropy where the direction of the easy axis of magnetization is parallel to the X direction. 
     The free layer  234  includes a first surface  234   a  located at an end in the Z direction, a second surface  234   b  opposite to the first surface  234   a , and an outer peripheral surface connecting the first surface  234   a  and the second surface  234   b . Both the first and second surfaces  234   a  and  234   b  are flat surfaces parallel to the bottom surface  60   b . The first and second surfaces  234   a  and  234   b  each have a shape that is long in the X direction. The first surface  234   a  has a first edge Ed 11  and a second edge Ed 12  located at both ends in the lateral direction of the first surface  234   a , i.e., a direction parallel to the Y direction. In particular, in the comparative example, the first edge Ed 11  is an edge located at the end of the first surface  234   a  in the −Y direction. The second edge Ed 12  is an edge located at the end of the first surface  234   a  in the Y direction. 
     If an external magnetic field is applied to the MR element  230 , the direction of the magnetic moment inside the free layer  234  rotates depending on the direction and strength of the external magnetic field. As a result, the direction of the magnetization of the free layer  234  rotates. Here, magnetic charges occur on the outer peripheral surface of the free layer  234 . 
     Now, suppose that an external magnetic field in the Y direction is applied to the MR element  230 . If the external magnetic field in the Y direction is applied, positive magnetic charges concentrate at a portion of the outer peripheral surface of the free layer  234  near the second edge Ed 12 , and negative magnetic charges concentrate at a portion of the outer peripheral surface of the free layer  234  near the first edge Ed 11 . In  FIG. 14 , the symbols “+” represent positive magnetic charges, and the symbols “−” negative magnetic charges. A demagnetizing field in the −Y direction occurs in the free layer  234  due to such magnetic charges. The strength of the demagnetizing field is higher as it is closer to the magnetic charges. The strength of the demagnetizing field in the portions of the free layer  234  near the first and second edges Ed 11  and Ed 12  is therefore high. The strength of the demagnetizing field in the midsection of the free layer  234  is low. 
     If no external magnetic field is applied, the direction of the magnetization of the free layer  234  and the direction of the magnetic moment in the free layer  234  are parallel to the X direction. If the strength of the external magnetic field is low, the direction of the magnetic moment in the midsection of the free layer  234  starts to rotate toward the Y direction. On the other hand, the direction of the magnetic moment in the portions of the free layer  234  near the first and second edges Ed 11  and Ed 12  does not rotate or hardly rotates. 
     If the strength of the external magnetic field becomes high to a certain extent, the direction of the magnetic moment in the midsection of the free layer  234  becomes the same or substantially the same as the Y direction. Meanwhile, the direction of the magnetic moment in the portions of the free layer  234  near the first and second edges Ed 11  and Ed 12  starts to rotate toward the Y direction. If the strength of the external magnetic field becomes even higher, the direction of the magnetic moment in the portions of the free layer  234  near the first and second edges Ed 11  and Ed 12  also becomes the same or substantially the same as the Y direction. 
     As described above, in the MR element  230  of the comparative example, the direction of the magnetic moment in the entire free layer  234  does not change uniformly because of the demagnetizing field. As a result, the magnetization of the free layer  234  changes nonlinearly with respect to a change in the strength of the external magnetic field. Consequently, a detection signal generated by a magnetic sensor including the MR element  230  of the comparative example changes nonlinearly with respect to a change in the strength of the external magnetic field. 
     Next, magnetic charges on the MR element  30  according to the present example embodiment will be described.  FIG. 15  is an explanatory diagram for describing magnetic charges on the MR element  30 .  FIG. 15  shows a cross section corresponding to the cross section S. In  FIG. 15 , the symbols “+” represent positive magnetic charges, and the symbols “−” negative magnetic charges. 
     In the MR element  30  according to the present example embodiment, the thickness T 1  at the first edge Ed 1  is smaller than the thickness T 2  at the second edge Ed 2 . Now, suppose that an external magnetic field in the Y direction is applied to the MR element  30 . In such a case, positive magnetic charges concentrate at a portion of the outer peripheral surface of the free layer  34  near the second edge Ed 2  as in the comparative example. By contrast, negative magnetic charges do not concentrate at a portion of the outer peripheral surface of the free layer  34  near the first edge Ed 1  but are distributed even over the first surface  34   a . This reduces a difference between the strength of the demagnetizing field at the portion of the free layer  34  near the first edge Ed 1  and that of the demagnetizing field in the midsection of the free layer  34 . As the difference decreases, the direction of the magnetic moment at the portion of the free layer  34  near the first edge Ed 1  rotates more similarly to that of the magnetic moment in the midsection of the free layer  34 . According to the present example embodiment, the magnetization of the free layer  34  can thus be prevented from changing nonlinearly with respect to a change in the strength of the external magnetic field. As a result, according to the present example embodiment, the range where the detection signal generated by the magnetic sensor  1  change linearly can be expanded. 
     To reduce variations in the thickness of the MR element  30  due to variations in the manufacturing process, the curvature k of the entire first inclined portion SL 1  can be reduced. This, however, reduces a difference between the first angle θ 1  and the second angle θ 2 , and reduces a difference between the thickness T 1  at the first edge Ed 1  and the thickness T 2  at the second edge Ed 2 . In particular, if the entire first inclined portion SL 1  has a curvature k of 0, i.e., the entire first inclined portion SL 1  is a flat surface, the first angle θ 1  and the second angle θ 2  are the same, and the thickness T 1  at the first edge Ed 1  and the thickness T 2  at the second edge Ed 2  are the same. This annihilates the effect of reducing the concentration of magnetic charges at and near the first edge Ed 1 . 
     By contrast, according to the present example embodiment, the absolute value of the curvature k 2  of the first inclined portion SL 1  at the second position P 2  where the angle θ is relatively small is made relatively large. According to the present example embodiment, the difference between the first angle θ 1  and the second angle θ 2  is thereby increased to increase the difference between the thickness T 1  at the first edge Ed 1  and the thickness T 2  at the second edge Ed 2 . According to the present example embodiment, the concentration of magnetic charges at and near the first edge Ed 1  of the free layer  34  can thus be reduced while reducing a change in the thickness T 1  at the first edge Ed 1  due to variations in the manufacturing process. 
     The effects of the present example embodiment have so far been described by using the MR element  30  provided on the first inclined portion SL 1  as an example. However, the foregoing description also applies to the MR element  30  provided on the second inclined portion SL 2  since the first inclined portion SL 1  and the second inclined portion SL 2  have a symmetrical shape. 
     Modification Example 
     Next, a modification example of the MR element  30  will be described with reference to  FIG. 16 . In the modification example, the MR element  30  is an anisotropic magnetoresistive (AMR) element. In the modification example, the MR element  30  includes a magnetic layer  36  given magnetic anisotropy, instead of the magnetization pinned layer  32 , the spacer layer  33 , and the free layer  34  shown in  FIG. 6 . The magnetic layer  36  has a magnetization whose direction is variable depending on the direction of the external magnetic field. As described above, the MR element  30  is patterned to a shape that is long in the X direction. This gives the magnetic layer  36  magnetic shape anisotropy where the direction of the easy axis of magnetization is parallel to the X direction. 
     The magnetic layer  36  has a first surface  36   a  having a shape that is long in the X direction, a second surface  36   b  opposite to the first surface  36   a , and an outer peripheral surface connecting the first surface  36   a  and the second surface  36   b . The description of the shape of the MR element  30  with reference to  FIGS. 6 and 7  also applies to the modification example. The description of the shape of the MR element  30  applies to the shape of that in the modification example, with the free layer  34 , the first surface  34   a , and the second surface  34   b  in the description replaced with the magnetic layer  36 , the first surface  36   a , and the second surface  36   b , respectively. 
     Second Example Embodiment 
     A second example embodiment of the technology will now be described. Initially, a configuration of a magnetic sensor according to the present example embodiment will be described with reference to  FIG. 17 .  FIG. 17  is a cross-sectional view showing a part of the magnetic sensor according to the present example embodiment. 
     A configuration of the magnetic sensor  101  according to the present example embodiment differs from that of the magnetic sensor  1  according to the first example embodiment in the following respect. The magnetic sensor  101  according to the present example embodiment includes MR elements  130  instead of the MR elements  30  according to the first example embodiment.  FIG. 17  shows a cross section parallel to the YZ plane and intersecting an MR element  130 . 
     The opposed surface  60   a  of the support member  60  includes at least one curved portion  60   a   3  not parallel to the bottom surface  60   b , instead of the curved portion  60   a   2  according to the first example embodiment. As shown in  FIG. 17 , the curved portion  60   a   3  is a concave surface recessed toward the bottom surface  60   b . As will be described below, the opposed surface  60   a  includes inclined portions that are a part of the concave surface (curved portion  60   a   3 ). The curved portion  60   a   3  has a curved shape (arch shape) curved to be recessed toward the bottom surface  60   b  (−Z direction) in a given cross section parallel to the YZ plane. In the given cross section parallel to the YZ plane, the distance from the bottom surface  60   b  to the curved portion  60   a   3  is the smallest at the center of the curved portion  60   a   3  in a direction parallel to the Y direction (hereinafter, referred to simply as the center of the curved portion  60   a   3 ). 
     The curved portion  60   a   3  extends along the X direction. The overall shape of the curved portion  60   a   3  is a semicylindrical curved surface formed by moving the curved shape shown in  FIG. 17  along the X direction. The insulating layer  62  of the support member  60  has a cross-sectional shape such that the curved portion  60   a   3  is formed in the opposed surface  60   a . Specifically, the insulating layer  62  has a cross-sectional shape recessed in the −Z direction in a given cross section parallel to the YZ plane. 
     A portion of the curved portion  60   a   3  from an edge at the end of the curved portion  60   a   3  in the Y direction to the center of the curved portion  60   a   3  will be referred to as a first inclined portion and be denoted by the symbol SL 11 . A portion of the curved portion  60   a   3  from an edge at the end of the curved portion  60   a   3  in the −Y direction to the center of the curved portion  60   a   3  will be referred to as a second inclined portion and be denoted by the symbol SL 12 . Both the first and second inclined portions SL 11  and SL 12  are inclined relative to the bottom surface  60   b . In the present example embodiment, the entire MR element  130  is located on the first inclined portion SL 11  or the second inclined portion SL 12 .  FIG. 17  shows how the MR element  130  is located on the first inclined portion SL 11 . 
     The MR element  130  has a shape that is long in the X direction. The MR element  130  has a rectangular planar shape. As employed herein, the lateral direction of the MR element  130  will be referred to as the width direction of the MR element  130  or simply as the width direction. The MR element  130  has a bottom surface  130   a , a top surface  130   b , a first edge  130   c , a second edge  130   d , a third edge, and a fourth edge. The bottom surface  130   a  is opposed to the curved portion  60   a   3 . The top surface  130   b  is located opposite the bottom surface  130   a . The first and second edges  130   c  and  130   d  are located at both ends in the width direction. The third and fourth edges are located at both ends in the longitudinal direction. The dimension of the MR element  130  in the width direction is constant or substantially constant regardless of the position in the X direction. 
     The MR element  130  may be a spin-valve MR element or an AMR element. The following description will be given by using the case where the MR element  130  is a spin-valve MR element as an example. Like the MR element  30  shown in  FIG. 6  of the first example embodiment, the MR element  130  includes an underlayer  31 , a magnetization pinned layer  32 , a spacer layer  33 , a free layer  34 , and a cap layer  35 . The free layer  34  has magnetic shape anisotropy where the direction of the easy axis of magnetization is parallel to the X direction. 
     Next, the inclined portions and the MR elements  130  will be described in detail with reference to  FIG. 18 . The following description will be given by using the first inclined portion SL 11  as an example.  FIG. 18  is an explanatory diagram for describing the shape of the first inclined portion SL 11 .  FIG. 18  is an enlarged view of a part of the cross section shown in  FIG. 17 . In  FIG. 18 , the underlayer  31  and the cap layer  35  of the MR element  130  are omitted. 
     A cross section intersecting the MR element  130  and being perpendicular to the bottom surface  60   b  of the support member  60  will be denoted by the symbol S. To describe the shape of the first inclined portion SL 11 , a first position P 11 , a second position P 12 , a third position P 13 , and a fourth position P 14  on the first inclined portion SL 11  in a given cross section S will be defined as follows. The first position P 11  is a position where the first inclined portion SL 11  is inclined relative to the bottom surface  60   b  at a first angle θ 11 . The second position P 12  is a position where the first inclined portion SL 11  is inclined relative to the bottom surface  60   b  at a second angle θ 12  smaller than the first angle θ 11 . In the present example embodiment, in particular, the first position P 11  is farther from the bottom surface  60   b  than is the second position P 12 . 
     The third position P 13  is the position on the first inclined portion SL 11  closest to the bottom surface  60   b . Specifically, the third position P 13  is located at the border between the first inclined portion SL 11  and the second inclined portion SL 12 , i.e., the center of the curved portion  60   a   3 . The fourth position P 14  is the position on the first inclined portion SL 11  farthest from the bottom surface  60   b . Specifically, the fourth position P 14  is located at the border between the curved portion  60   a   3  and the flat portion  60   a   1 . The first position P 11  and the second position P 12  fall within the range from the third position P 13  to the fourth position P 14 . 
     Both the angle that the first inclined portion SL 11  forms with the bottom surface  60   b  at the third position P 13  and the angle that the first inclined portion SL 11  forms with the bottom surface  60   b  at the fourth position P 14  are 0°. Both the first and second angles θ 11  and θ 12  are greater than 0° and less than 90°. 
     The outline of the first inclined portion SL 11  in a given cross section S includes a plurality of curves where each curve has a different curvature. The absolute value of a curvature k 11  of the first inclined portion SL 11  at the first position P 11  is less than that of a curvature k 12  of the first inclined portion SL 11  at the second position P 12 . 
     In  FIG. 18 , the circular arc denoted by the symbol C 11  represents a part of a circle approximating the first inclined portion SL 11  at the first position P 11 , i.e., a first circle of curvature. The circular arc denoted by the symbol C 12  represents a part of a circle approximating the first inclined portion SL 11  at the second position P 12 , i.e., a second circle of curvature. As shown in  FIG. 18 , the first circle of curvature (symbol C 11 ) has a radius greater than that of the second circle of curvature (symbol C 12 ). 
     The MR element  130  is provided on the first inclined portion SL 11  so that the first edge  130   c  is located above the first position P 11  in a given cross section S. Further, in the present example embodiment, the MR element  130  is provided on the first inclined portion SL 11  so that the second edge  130   d  is located above the second position P 12  in the given cross section S. 
     As described in the first example embodiment, the free layer  34  has a first surface  34   a , a second surface  34   b , and an outer peripheral surface. The first surface  34   a  has a first edge Ed 1  and a second edge Ed 2  located at both lateral ends of the first surface  34   a . The first edge Ed 1  is located at the first edge  130   c  of the MR element  130 . The second edge Ed 2  is located at the second edge  130   d  of the MR element  130 . 
     The relationship between the inclination angle θ 1  at the first edge Ed 1  and the inclination angle θ 2  at the second edge Ed 2  in a given cross section S is the same as in the first example embodiment. The relationship between the thickness T 1  at the first edge Ed 1  and the thickness T 2  at the second edge Ed 2  in a given cross section S is also the same as in the first example embodiment. For the sake of convenience, an imaginary surface is assumed by extending the second surface  34   b  along the curved portion  60   a   3 , and the thickness T 1  is defined as the distance between the first surface  34   a  and the imaginary surface in the direction perpendicular to the first surface  34   a.    
     The foregoing description has been given by using the first inclined portion SL 11  as an example. The first inclined portion SL 11  and the second inclined portion SL 12  have a shape symmetrical or substantially symmetrical about the XZ plane including the center of the curved portion  60   a   3 . The foregoing description of the first inclined portion SL 11  therefore also applies to the second inclined portion SL 12 . The foregoing description of the MR element  130  also applies to the MR element  130  provided on the second inclined portion SL 12 . 
     The configuration, operation and effects of the present example embodiment are otherwise the same as those of the first example embodiment. 
     The technology is not limited to the foregoing example embodiments, and various modification examples may be made thereto. For example, the number and arrangement of MR elements and the number and arrangement of curved portions are not limited to those described in the example embodiments, and may be freely chosen as long as the requirements set forth in the claims are satisfied. 
     The first and second surfaces  34   a  and  34   b  of the free layer  34  according to the technology may each have a shape long in a direction intersecting a given cross section S, not necessarily in the direction parallel to the X direction. 
     The second edge of the MR element according to the technology may be located on the flat portion  60   a   1  or a part of the curved portion parallel to the bottom surface  60   b.    
     Obviously, various modification examples and variations of the technology are possible in the light of the above teachings. Thus, it is to be understood that, within the scope of the appended claims and equivalents thereof, the technology may be practiced in other embodiments than the foregoing example embodiments.