Patent Publication Number: US-2017372826-A1

Title: Magnetization alignment in a thin-film device

Description:
BACKGROUND 
     Field 
     The present disclosure relates generally to spintronics and, more specifically but not exclusively, to methods and apparatus for controllably manipulating magnetization distribution(s) in thin-film devices. 
     Description of the Related Art 
     This section introduces aspects that may help facilitate a better understanding of the disclosure. Accordingly, the statements of this section are to be read in this light and are not to be understood as admissions about what is in the prior art or what is not in the prior art. 
     Some applications of thin-film magnetic devices rely on the ability to controllably generate the parallel and antiparallel magnetization alignment of two adjacent magnetic electrodes. More specifically, the parallel alignment corresponds to a situation in which the magnetization vectors of two adjacent magnetic electrodes are parallel to one another, i.e., pointing in the same direction or having the relative orientation angle of zero degrees. In contrast, the antiparallel alignment corresponds to a situation in which the magnetization vectors of two adjacent magnetic electrodes are antiparallel, i.e., pointing in the opposite directions or having the relative orientation angle of 180 degrees. While the parallel alignment can be generated in a relatively straightforward manner, the antiparallel alignment is significantly more difficult to generate, e.g., when the two magnetic electrodes have a nanometer-scale separation and/or are laterally adjacent to one another, rather than being stacked vertically. 
     SUMMARY OF SOME SPECIFIC EMBODIMENTS 
     Disclosed herein are various embodiments of a magnetic device having a pair of coplanar thin-film magnetic electrodes arranged on a substrate with a relatively small edge-to-edge separation. In an example embodiment, the magnetic electrodes have a substantially identical footprint that can be approximated by an ellipse, with the short axes of the ellipses being collinear and the edge-to-edge separation between the ellipses being smaller than the size of the short axis. In some embodiments, the magnetic electrodes may have relatively small tapers that extend toward each other from the ellipse edges in the constriction area between the electrodes. Some embodiments may also include an active element inserted into the gap between the tapers and electrical leads connected to the magnetic electrodes for passing electrical current through the active element. When subjected to an appropriate external magnetic field, the magnetic electrodes can advantageously be magnetized to controllably enter parallel and antiparallel magnetization states. 
     According to one embodiment, provided is an apparatus comprising, a substrate; and a first set of electrodes supported on the substrate, the set including a first thin-film magnetic electrode and a second thin-film magnetic electrode, each of the first and second thin-film magnetic electrodes having a substantially oval shape; wherein the substantially oval shape is characterized by a first axis having a first size and a second axis having a second size, the first and second axes being orthogonal to one another, and the second size being larger than the first size; wherein the first axis of the first thin-film magnetic electrode and the first axis of the second thin-film magnetic electrode are collinear; and wherein an edge-to-edge separation between the first thin-film magnetic electrode and the second thin-film magnetic electrode is smaller than the first size. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The patent or application file contains at least one drawing executed in color. Copies of this patent or patent application publication with color drawing(s) will be provided by the Office upon request and payment of the necessary fee. 
       Other aspects, features, and benefits of various disclosed embodiments will become more fully apparent, by way of example, from the following detailed description and the accompanying drawings, in which: 
         FIGS. 1A-1B  illustrate top and cross-sectional side views of a magnetic device according to an embodiment; 
         FIGS. 2A-2E  show enlarged schematic top views of a constriction between two magnetic electrodes in the magnetic device of  FIG. 1  according to example embodiments; 
         FIGS. 3A-3C  show enlarged schematic side views of a constriction between two magnetic electrodes in the magnetic device of  FIG. 1  according to example embodiments; 
         FIGS. 4A-4B  illustrate alternative embodiments of the magnetic device of  FIG. 1 , each having a respective active element therein; 
         FIGS. 5A-5D  show schematic top views of an array of the magnetic devices of  FIG. 1  according to example embodiments; 
         FIG. 6  shows a schematic top view of an array of magnetic devices of  FIG. 1  according to an alternative embodiment; 
         FIG. 7  pictorially illustrates a system in which an array of  FIG. 5  can be used according to an embodiment; 
         FIG. 8  shows a schematic diagram of a system in which the array of  FIG. 6  can be used according to an embodiment; 
         FIGS. 9A-9B  graphically illustrate certain magnetic properties of the magnetic device of  FIG. 1  according to an embodiment; 
         FIGS. 10A-10C  illustrate magnetization distributions in the magnetic device of  FIG. 1  according to an embodiment; 
         FIGS. 11A-11E  illustrate magnetization distributions in the magnetic device of  FIG. 1  according to an alternative embodiment; and 
         FIGS. 12A-12G  illustrate a fabrication method that can be used to make the magnetic device of  FIG. 1  according to an embodiment. 
     
    
    
     DETAILED DESCRIPTION 
       FIGS. 1A-1B  illustrate top and cross-sectional side views, respectively, of a magnetic device  100  according to an embodiment. The dashed line in  FIG. 1A  indicates the position of the cross-section plane BB corresponding to  FIG. 1B . An example fabrication process that can be used to make magnetic device  100  is described in more detail below in reference to  FIG. 12 . An example method of generating parallel and antiparallel alignment of magnetization vectors in magnetic device  100  is described in more detail below in reference to  FIGS. 9-11 . 
     Device  100  comprises a substrate  102  that supports a pair of thin-film magnetic electrodes  110   1  and  110   2 . In some embodiments, device  100  further comprises a pair of (optional) non-magnetic, electrically conducting electrodes  120   1  and  120   2  that are configured to provide electrical leads to magnetic electrodes  110   1  and  110   2 , respectively. Depending on the polarity of the voltage/current applied to electrically conducting electrodes  120   1  and  120   2 , one of magnetic electrodes  110   1 - 110   2  may be referred to as a “source” electrode, and the other electrode may be referred to as a “drain” electrode. Magnetic electrodes  110   1  and  110   2  are referred to herein as “thin-film” electrodes because the electrodes&#39; lateral dimensions indicated in  FIG. 1A  are significantly larger than the electrodes&#39; thickness or height indicated in  FIG. 1B . In an example embodiment, the lateral dimensions of magnetic electrodes  110   1  and  110   2  can be in the range between about 100 nm and about 500 nm, whereas the electrodes&#39; thickness can be smaller than about 10 nm. 
     The following materials can be used in some embodiments of device  100 . Substrate  102  may comprise silicon and/or silicon oxide. Magnetic electrodes  110   1  and  110   2  may comprise a ferromagnetic or ferrimagnetic material. One example ferromagnetic material that can be used to make magnetic electrodes  110   1  and  110   2  is supermalloy, whose chemical composition can be described by the following chemical formula: Ni 80 Fe 14 Mo 5 X, where X is another metal. Another example ferromagnetic material that can be used to make magnetic electrodes  110   1  and  110   2  is permalloy. Some ferromagnetic materials suitable for magnetic electrodes  110   1  and  110   2  may have a tendency to form native oxide layers, such as layers  112  shown in  FIG. 1B , over electrode portions exposed to ambient air for a sufficiently long period of time. Non-magnetic electrically conducting electrodes  120   1  and  120   2  may comprise gold, titanium, and/or other electrically conducting materials suitable for creating ohmic contacts. Various adhesion layers (not explicitly shown in  FIGS. 1A-1B ) can be used as known in the pertinent art to ensure good structural adhesion between the shown parts of device  100 . 
     A person of ordinary skill in the art will understand that other suitable materials can similarly be used in alternative embodiments of device  100 . 
     In an example embodiment, each of magnetic electrodes  110   1  and  110   2  has a substantially oval shape. As used herein, the term “substantially” refers to possible relatively small deviations (if any) of the shape of a magnetic electrode  110  from a Cartesian oval shape, e.g., in the general area of a constriction  114  between magnetic electrodes  110   1  and  110   2 . For example, the mass of an electrode  110  located outside of the footprint of the corresponding Cartesian oval shape near constriction  114  can be less than about 10% (or 5%, or 1%) of the total mass of that electrode. 
     In some embodiments, each of magnetic electrodes  110   1  and  110   2  can be approximately shaped as an ellipse, which is a special case of an oval. As known in the mathematical arts, an ellipse is a planar shape that has two orthogonal axes about which the ellipse is symmetric. These axes intersect at the center of the ellipse. The larger of the two axes is referred to as the major axis. The smaller of the two axes is referred to as the minor axis. The ratio of the sizes of the major and minor axes is referred to as the eccentricity of the ellipse. 
     In an example embodiment, each of the ellipses that can be used to approximate the shape of magnetic electrodes  110   1  and  110   2  can have the major and minor axes that are 200 nm and 100 nm, respectively. Alternative embodiments of magnetic electrodes  110   1  and  110   2  can be generated from this example embodiment using one or more of the following geometric modifications: (i) changing the eccentricity of the ellipses while having the size of one of the major/minor axes unchanged; (ii) uniformly scaling the ellipses by applying the same scaling factor to the major and minor axes; and (iii) changing the edge-to-edge separation, d, between the ellipses (also see  FIG. 2A ). The eccentricity can, for example, be in the range between about 1.5 and about 5. The scaling factor can, for example, be in the range between about 0.2 and about 5. The edge-to-edge separation d can, for example, be in the range between about 2 nm and about 100 nm. 
       FIGS. 2A-2E  show enlarged schematic views of constriction  114  between magnetic electrodes  110   1  and  110   2  in device  100  according to example embodiments. More specifically, the views shown in  FIGS. 2A-2E  are the top views of constriction  114  corresponding to  FIG. 1A .  FIG. 2A  also pictorially illustrates the definition of the above-mentioned edge-to-edge separation d. 
     Referring to  FIG. 2A , each of magnetic electrodes  110   1  and  110   2  comprises a respective one of trapezoid tapers  2101  and  2102 , each of which extends from the edge of the corresponding oval or ellipse. In the shown embodiment, trapezoid tapers  2101  and  2102  are separated by a gap  214 . In some alternative embodiments, gap  214  is not present, which causes tapers  210   1  and  210   2  to be connected to one another, thereby forming a physical bridge (not explicitly shown in  FIG. 2A ) between magnetic electrodes  110   1  and  110   2 . 
     In various embodiments, the bases of the trapezoids corresponding to tapers  210   1  and  210   2  can have different respective sizes, e.g., each selected from a range between about 30 nm and 0 nm. Gap  214  can have a width that is smaller than about 5 nm or smaller than about 1 nm. Although  FIG. 2A  shows tapers  210   1  and  210   2  as having a shape of an isosceles trapezoid, other trapezoid shapes are also possible, including a rectangular shape. 
     Referring to  FIG. 2B , each of magnetic electrodes  110   1  and  110   2  comprises a respective one of convex tapers  220   1  and  220   2 , each of which extends from the edge of the corresponding oval or ellipse. In some embodiments, the geometric shape of an outer edge of taper  220  can be approximated by a parabola or a semicircle. 
     Referring to  FIG. 2C , each of magnetic electrodes  110   1  and  110   2  comprises a respective one of concave or non-convex tapers  230   1  and  230   2 , each of which extends from the edge of the corresponding oval or ellipse. In some embodiments, the geometric shape of some of the outer edges of taper  230  can be approximated by a hyperbola or an exponent. 
       FIGS. 2D-2E  illustrate a variation of the embodiment shown in  FIG. 2A , in which an outer edge of each of trapezoid tapers  210   1  and  210   2  is not atomically smooth, straight, or linear. Such edges can be produced, e.g., by an electro-migration process as further explained below in reference to  FIG. 12G . As indicated in  FIG. 2D , gap  214  can have a fairly complex, irregular overall shape that causes the distance between tapers  210   1  and  210   2  (e.g., the width of gap  214 ) to vary along the length of the gap. 
       FIG. 2E  shows a further enlarged view of a portion  216  (also see  FIG. 2D ) of gap  214  in which the distance between tapers  210   1  and  210   2  reaches its minimum. Example arrangement of the electrode parts in portion  216  can be analogous to that of two STM (scanning tunneling microscope) tips nearly touching each other. For some applications of device  100 , it is expected that one or more pertinent device characteristics may be dominated by the atomic details of portion  216 , such as the smallest distance g between tapers  210   1  and  210   2  and the chemical identity of the atoms X and Y located at the distance g. 
     A person of ordinary skill in the art will understand that  FIGS. 2A-2E  show only several example shapes of the tapers that can be used in constriction  114  and that various alternative geometric shapes can similarly be used therein. 
       FIGS. 3A-3C  show additional enlarged schematic views of constriction  114  between magnetic electrodes  110   1  and  110   2  in device  100  according to example embodiments. More specifically, the views shown in  FIGS. 3A-3C  are the side views of constriction  114  corresponding to  FIG. 1B .  FIG. 3A  illustrates an embodiment in which the separation between magnetic electrodes  110   1  and  110   2  is uniform and does not depend on the distance from substrate  102 .  FIG. 3B  illustrates an embodiment in which the separation between magnetic electrodes  110   1  and  110   2  linearly increases with an increase of the distance from substrate  102 .  FIG. 3C  illustrates an example vertical profile of gap  214  in portion  216  illustrated in  FIGS. 2D-2E . 
       FIGS. 4A-4B  illustrate alternative embodiments of device  100  in which an active element  402  is located within constriction  114 . As used herein, the term “active element” refers to a nanometer-scale object intentionally placed in proximity to or inserted between the tapers of magnetic electrodes  110   1  and  110   2  (e.g., illustrated in  FIGS. 2A-2E ). In various embodiments, active element  402  may or may not be in direct physical contact with either or both of the tapers. In some embodiments, active element  402  may form one or more chemical bonds with either or both of the tapers of magnetic electrodes  110   1  and  110   2 . In some embodiments, a voltage applied between electrodes  120   1  and  120   2  (see  FIGS. 1A-1B ) causes an electrical charge to flow through active element  402 . 
     In the embodiment illustrated by  FIG. 4A , active element  402  comprises a bucky-ball molecule, C 60 . In the configuration shown in  FIG. 4A , the bucky-ball molecule of active element  402  is in direct physical contact with magnetic electrode  110   1 , but not with magnetic electrode  110   2 . Other positions of the bucky-ball molecule with respect to magnetic electrodes  110   1  and  110   2  are also possible. In alternative embodiments, other fullerene molecules can be used to make active element  402 . 
     In the embodiment illustrated by  FIG. 4B , active element  402  comprises an organic molecule—a derivative of the thiol end-capped oligophenylenevinylene molecule (OPV-5) in which five benzene rings are connected through four double bonds. In addition to a delocalized π-electron system, this derivative of OPV-5 has (i) n-C 12 H 25  side arms that make it soluble and (ii) acetyl protected thiol end groups that enable covalent bonding to metal electrodes, such as magnetic electrodes  110   1  and  110   2 . In this particular embodiment, after the covalent bonding is achieved, the organic molecule of active element  402  is bonded to metal atoms by means of two —S(CO)— linkers, in each of which the sulfur is covalently bonded to an aromatic ring of OPV-5, and the carbon is covalently bonded to a metal atom of the corresponding magnetic electrode  110 . In alternative embodiments, other organic molecules and/or chemical linkers can similarly be used. The linking chemical bonds can be covalent bonds, hydrogen bonds, or coordination bonds. 
     A person of ordinary skill in the art will understand that  FIGS. 4A-4B  show only two possible examples of active element  402  for device  100  and that other active elements can similarly be used therein. For example, alternative embodiments of active element  402  may include quantum dots, nanocrystals, biological and bioorganic molecules, polymers, metal-organic complexes, etc. 
       FIGS. 5A-5D  show schematic top views of an array  500  of magnetic devices  100  ( FIGS. 1A-1B ) according to example embodiments. In each of the shown embodiments of array  500 , magnetic devices  100  are fabricated on and share a common substrate  102  (also see  FIGS. 1A-1B ). The embodiment of array  500  shown in  FIG. 5A  includes fifteen arrayed magnetic devices  100 . Each of the embodiments of array  500  shown in  FIGS. 5B-5D  includes sixteen arrayed magnetic devices  100 . A person of ordinary skill in the art will understand that alternative embodiments of array  500  may include a different (from 15 or 16) number of arrayed magnetic devices  100 . 
     The embodiment of array  500  shown in  FIG. 5A  includes a plurality of electrically conducting tracks  502  arranged in a manner that makes each source electrode and each drain electrode of arrayed magnetic devices  100  individually addressable from the periphery of substrate  102 . 
     In the embodiment of array  500  shown in  FIG. 5B , magnetic devices  100  are arranged in a rectangular array having four rows and four columns. Electrically conducting tracks  502  are arranged in a manner that causes each column of magnetic devices  100  to share a respective common drain contact. However, each source electrode of arrayed magnetic devices  100  is still individually addressable from the periphery of substrate  102 . 
     In the embodiment of array  500  shown in  FIG. 5C , magnetic devices  100  are also arranged in a rectangular array having four rows and four columns. Electrically conducting tracks  502  are now arranged in a manner that causes each pair of columns of magnetic devices  100  to share a respective common drain contact. Each source electrode of arrayed magnetic devices  100  is still individually addressable from the periphery of substrate  102 . 
     In the embodiment of array  500  shown in  FIG. 5D , magnetic devices  100  are similarly arranged in a rectangular array having four rows and four columns. Electrically conducting tracks  502  are now arranged in a manner that causes all four columns of magnetic devices  100  to share a common drain contact. Each source electrode of arrayed magnetic devices  100  is still individually addressable from the periphery of substrate  102 . 
       FIG. 6  shows a schematic top view of an array  600  of magnetic devices  100  ( FIGS. 1A-1B ) according to an alternative embodiment. Similar to magnetic devices  100  of array  500 , magnetic devices  100  of array  600  are fabricated on and share a common substrate  102 . However, substrate  102  is now a part of a disk  610 . Magnetic devices  100  are arranged on a surface of disk  610  along three circular tracks  612   i  (i=1, 2, 3), each having a different respective radius R i , e.g., as indicated in  FIG. 6 . In alternative embodiments, the number of circular tracks  612  may be different from three. Note that magnetic devices  100  used in array  600  do not have electrodes  120 . Hence, conducting tracks similar to conducting tracks  502  ( FIG. 5 ) are not necessary and not present in array  600 . In some embodiments of array  600 , magnetic electrodes  110   1  and  110   2  of individual magnetic devices  100  may not even have tapers analogous to those described above in reference to  FIGS. 2A-2E . 
       FIG. 7  pictorially illustrates a system  700  in which array  500  ( FIG. 5 ) can be used according to an embodiment. System  700  comprises a split-coil electromagnet having a cylindrical magnetic core  710 . Array  500  is positioned within a relatively narrow gap  712  between two portions of magnetic core  710 , which are labeled in  FIG. 7  as  7101  and  7102 , respectively. A magnetic field, B, can be generated within gap  712  by passing an electrical current through one or more coils (not explicitly shown in  FIG. 7 ) wrapped around magnetic core  710 . The resulting magnetic field B is directed generally parallel to the center axis of magnetic core  710 , e.g., as indicated by the double-headed arrow B in  FIG. 7 . The direction of the magnetic field depends on the direction of the flow of the electrical current through the coil(s) and, as such, can be reversed by changing the electrical-current direction. The magnitude of the magnetic field depends on the magnitude of the electrical current and, as such, can be controllably changed by changing the latter. In an example embodiment, system  700  can be used to generate parallel and antiparallel alignment of remanent magnetization vectors in individual magnetic devices  100  of array  500 , e.g., as described in more detail below in reference to  FIG. 11 . 
       FIG. 8  shows a schematic diagram of a system  800  in which array  600  ( FIG. 6 ) can be used according to an embodiment. System  800  comprises an electromagnetic head  802  that is moveable along the radius of disk  610  in a manner that enables electromagnetic head to be positioned over any selected one of circular tracks  612  (also see  FIG. 6 ). Disk  610  is rotatably mounted in system  800  such that it can be rotated about a rotation axis  804 . This rotation enables electromagnetic head  802  to pass over any one of magnetic devices  100  of the selected circular track  612 . In some embodiments, electromagnetic head  802  can operate as a read-write head. In alternative embodiments, electromagnetic head  802  can operate as a write head only, with a separate read head (not explicitly shown in  FIG. 8 ) being used to read data written into array  600  using the shown write head. Each of magnetic devices  100  can be used to store one bit of information, e.g., such that parallel and antiparallel alignment of magnetization vectors in the magnetic device correspond to a binary “one” and a binary “zero,” respectively. 
     In an example embodiment, electromagnetic head  802  comprises a C-shaped magnetic core  810  and a coil  814  of electrical wire wound about that core as indicated in  FIG. 8 . A gap  812  of core  810  is positioned to face disk  610  as further indicated in  FIG. 8 . A magnetic field, B, generated within and in proximity to gap  812  when an electrical current is passed through coil  814  can be used to alter the alignment of magnetization vectors in the magnetic device  100  located under the gap, e.g., as described in more detail below in reference to  FIG. 11 . In the disk/head configuration shown in  FIG. 8 , the magnetic device located under gap  812  is magnetic device  100   N . As already indicated above, other magnetic devices  100  of array  600  can be brought to gap  812  by appropriately moving electromagnetic head  802  along the radius of disk  610  and rotating the disk about axis  804 . 
       FIGS. 9A-9B  graphically illustrate certain magnetic properties of magnetic device  100  ( FIG. 1 ) according to an embodiment. More specifically, the data shown in  FIG. 9  illustrate a hysteresis loop of normalized total transverse magnetization, M y , that is produced in magnetic device  100  by exposure to an external magnetic field. The data of  FIGS. 9A and 9B  correspond to the external magnetic field being parallel to the y-axis and the x-axis, respectively. The data points in  FIG. 9A  were obtained using numerical simulations of the behavior of an embodiment of magnetic device  100  in which each of magnetic electrodes  110   1  and  110   2  is an ideal ellipse having the following characteristics: (i) the sizes of the major and minor axes are 400 nm and 200 nm, respectively; (ii) the electrode thickness is 15 nm; and (iii) the ferromagnetic material is permalloy. No tapers are present in constriction  114 . The edge-to-edge separation d between magnetic electrodes  110   1  and  110   2  is 20 nm. The data points in  FIG. 9B  were obtained using numerical simulations of the behavior of an embodiment of magnetic device  100  that is the same as that used for  FIG. 9A , except that constriction  114  had trapezoid tapers  210   1  and  210   2  therein, with the gap  214  between the trapezoid tapers being 3-nm wide (also see  FIG. 2A ). 
     The coordinate frame (xy) used in the numerical simulations is defined as follows. The x-axis is parallel to the line that connects the centers of the ellipses. The y-axis is parallel to the major axes of the ellipses. This coordinate frame is also shown for reference in  FIGS. 10A, 11A, and 11E . 
     Referring to  FIG. 9A , the external magnetic field is parallel to the y-axis. The arrows in  FIG. 9A  indicate the magnetic-field sweep direction. The positive saturation state (M y =+1) is achieved by applying a relatively large (e.g., ˜60000 A/m) positive magnetic field. As the magnetic field is swept in the negative direction, M y  undergoes a step-like transition  902  at the negative critical field −H c . Further increase of the (negative) magnitude of the external magnetic field, e.g., to −60000 A/m, causes M y  to reach the negative saturation state (M y =−1). Reversal of the sweep direction causes M y  to undergo a step-like transition  904  at the positive critical field +H c . 
     Referring to  FIG. 9B , the external magnetic field is parallel to the x-axis. The arrows in  FIG. 9B  indicate the magnetic-field sweep direction. The positive saturation state (M y =+1) is achieved by applying a relatively large (e.g., ˜50000 A/m) positive magnetic field. As the magnetic field is swept in the negative direction, M y  first exits the positive saturation state and decreases gradually and then undergoes a step-like transition  912  at the negative critical field −H c . Further increase of the (negative) magnitude of the external magnetic field, e.g., to −50000 A/m, causes M y  to more or less gradually reach the negative saturation state (M y =−1). Reversal of the sweep direction causes M y  to go through similar changes, but with a corresponding step-like transition  914  now occurring at the positive critical field +H c . 
       FIGS. 10A-10C  illustrate magnetization distributions in magnetic device  100  according to an embodiment. More specifically, the shown magnetization distributions are obtained using the numerical simulations described above in reference to  FIG. 9A .  FIG. 10A  schematically shows a parallel magnetization state P y  of magnetic device  100 .  FIGS. 10B-10C  show maps of two example magnetization distributions in magnetic device  100  at different respective strengths of the external magnetic field. 
       FIG. 10A  shows individual total magnetization vectors M 1  and M 2  of magnetic electrodes  110   1  and  110   2  in the parallel magnetization state P y . Also shown is the above-mentioned xy coordinate frame. Because each of magnetization vectors M 1  and M 2  is parallel to the y-axis, and both vectors are pointing in the same positive y direction, the corresponding magnetization state of magnetic device  100  is denoted as a parallel magnetization state. 
       FIG. 10B  shows the map of the magnetization distribution corresponding to the parallel magnetization state P y  of  FIG. 10A  at remanence. The map is color-coded using the color bar shown in  FIG. 10C . The small black cones indicate the local magnetization directions. The magnetization distribution of  FIG. 10B  can be generated, e.g., by (i) applying the external magnetic field (H ext ) of about +60000 A/m and (ii) ramping down the external magnetic field to H ext =0 (also see  FIG. 9 ). In an example embodiment, the external magnetic field can be generated and changed as appropriate or necessary using system  700  ( FIG. 7 ). 
       FIG. 10C  shows the map of the magnetization distribution that can be obtained in magnetic device  100  by further sweeping the external magnetic field from H ext =0 ( FIG. 10B ) to a negative value that is just past the negative critical field −H c  (also see  FIG. 9 ). In this state, M y  has just undergone the transition  902 , and each of magnetic electrodes  110   1  and  110   2  exhibits a respective single-vortex magnetization distribution, as is evident from inspection of the shown color-coded map. An anti-parallel magnetization state is not achieved here because very similar magnetization distributions are produced in both magnetic electrodes  110   1  and  110   2 . 
       FIGS. 11A-11E  illustrate magnetization distributions in magnetic device  100  according to an alternative embodiment. More specifically, the shown magnetization distributions are obtained using the numerical simulations that are analogous to those described above in reference to  FIG. 9B , with the difference being that constriction  114  did not have trapezoid tapers  210   1  and  210   2  therein.  FIG. 11A  schematically shows a parallel magnetization state P x  of magnetic device  100 .  FIG. 11E  similarly shows an antiparallel magnetization state AP y  of magnetic device  100 .  FIGS. 11B-11D  show maps of three example magnetization distributions in magnetic device  100  at different respective strengths of the external magnetic field. The maps shown in  FIGS. 11B-11D  are color-coded using the same color bar as the color bar shown in  FIG. 10C . The small black cones in  FIGS. 11B-11D  indicate the local magnetization directions. 
       FIG. 11A  shows individual total magnetization vectors M 1  and M 2  of magnetic electrodes  110   1  and  110   2  in the parallel magnetization state P x . Also shown is the corresponding xy coordinate frame. Because each of magnetization vectors M 1  and M 2  is parallel to the x-axis, and both vectors are pointing in the same positive x direction, the corresponding magnetization state of magnetic device  100  is denoted as a parallel magnetization state. The parallel magnetization state P x  of  FIG. 11A  can be generated, e.g., by applying a positive saturating external magnetic field, H sat , that is parallel to the x-axis. 
       FIGS. 11B and 11C  show the maps of the magnetization distributions that can be obtained in magnetic device  100  by sweeping the external magnetic field from H ext =H sat  ( FIG. 11A ) to a positive value that is slightly smaller than H sat  ( FIG. 11B ) and then further to a positive value that is slightly higher than H ext =0. Comparison of the maps shown in  FIGS. 11B and 11C  reveals that the changing external magnetic field causes the local magnetization vectors in magnetic electrodes  110   1  and  110   2  to rotate in mostly opposite directions. More specifically, the local magnetization vectors in magnetic electrode  110   1  mostly rotate counterclockwise, while the local magnetization vectors in magnetic electrode  110   2  mostly rotate clockwise. 
       FIG. 11D  shows the map of the magnetization distribution that can be obtained in magnetic device  100  by further sweeping the external magnetic field from that of  FIG. 11C  to a negative value that is just past the negative critical field −H c . In this state, M y  has just undergone the transition that is analogous to transition  912  (see  FIG. 9B ). The resulting magnetization state is an anti-parallel magnetization state AP y  because the local magnetization vectors in magnetic electrode  110   1  mostly point in the positive y direction while the local magnetization vectors in magnetic electrode  110   2  mostly point in the negative y direction. 
       FIG. 11E  shows individual total magnetization vectors M 1  and M 2  of magnetic electrodes  110   1  and  110   2  in the antiparallel magnetization state AP y . Also shown is the corresponding xy coordinate frame. Each of magnetization vectors M 1  and M 2  is parallel to the y-axis, and the two vectors are pointing in opposite directions, which causes the corresponding magnetization state of magnetic device  100  to be an antiparallel magnetization state. 
     In an example embodiment, the external magnetic field needed to implement the magnetization changes indicated in  FIGS. 11A-11E  can be generated using system  700  ( FIG. 7 ) or system  800  ( FIG. 8 ). In the latter case, the parallel magnetization state P x  of  FIG. 11A  can be used to store a binary “one” in the corresponding magnetic device  100 . The antiparallel magnetization state AP y  of  FIG. 11E  can similarly be used to store a binary “zero” in the corresponding magnetic device  100 . The stored bit value can be changed by subjecting the corresponding magnetic device  100  to an appropriate external magnetic field, e.g., as explained above in reference to  FIGS. 11A-11E . 
       FIGS. 12A-12G  illustrate a fabrication method that can be used to make magnetic device  100  according to an embodiment. More specifically, each of  FIGS. 12A-12G  shows a side view of the nascent magnetic device  100  during a respective fabrication step. The views of  FIGS. 12A-12G  are generally analogous to the view shown in  FIG. 1B . 
     Referring to  FIG. 12A , substrate  102  is coated with a layer  1202  of an e-beam resist. Electron-beam lithography (EBL) is then used to expose and develop layer  1202  to create an opening  1204  therein in the general shape intended for magnetic electrodes  110   1  and  110   2 . A layer  1206  of a suitable ferromagnetic material (e.g., permalloy) is then deposited over the developed layer  1202  and into opening  1204 . 
     Referring to  FIG. 12B , layer  1202  and the portions of layer  1206  that are not in direct contact with substrate  102  are removed using a conventional solvent lift-off process involving immersion into a solvent (e.g., acetone) bath. The surface of a remaining portion  1206   r  of layer  1206  may get oxidized over time to produce thereon a relatively thin layer  1212  of the corresponding native metal oxide. 
     Referring to  FIG. 12C , the structure produced after the fabrication steps of  FIG. 12B  is coated with a layer  1214  of an e-beam resist. 
     Referring to  FIG. 12D , EBL is used to expose and develop layer  1214  to create openings  1216   1  and  1216   2  therein in the general shape intended for non-magnetic electrodes  120   1  and  120   2 , respectively. Portions of metal-oxide layer  1212  exposed by openings  1216   1  and  1216   2  are etched off. The latter can be done using wet or dry methods, e.g., a dry plasma etch or a wet chemical etch. 
     Referring to  FIG. 12E , a layer  1218  of a suitable non-magnetic metal (e.g., Au, Ti) is deposited over the developed layer  1214  and into openings  1216   1  and  1216   2 . 
     Referring to  FIG. 12F , layer  1214  is removed by immersion into the solvent bath mentioned above. The removal of layer  1214  also causes a removal of the portions of layer  1218  that are not in direct contact with substrate  102  and/or portion  1206   r . The remaining portions of layer  1218  form electrodes  120   1  and  120   2 . 
     Referring to  FIG. 12G , a suitable bias voltage, V b , is applied to electrodes  120   1  and  120   2  to induce an electro-migration process in portion  1206   r . The electro-migration process creates gap  214  (also see  FIG. 2D ), thereby splitting portion  1206   r  and the remaining portion of metal-oxide layer  1212  to produce magnetic electrodes  110   1  and  110   2  and separated layers  112  (also see  FIG. 1B ). The bias voltage V b  is removed to arrive at the final structure of magnetic device  100  (also see  FIGS. 1A-1B ). 
     In alternative embodiments, a nanometer-sized gap  214  between magnetic electrodes  110   1  and  110   2  can be created, e.g., as described in the following publications: (i) J. Tang, E. P. De Poortere, J. E. Klare, C. Nuckolls, and S. J. Wind, “Single-molecule transistor fabrication by self-aligned lithography and in situ molecular assembly” Microelectronic Engineering, 83, 1706-1709 (2006); (ii) A. Fursina, S. Lee, R. G. S. Sofin, I. V. Shvets, and D. Natelson “Nanogaps with very large aspect ratios for electrical measurements” Applied Physics Letters, 92, 113102 (2008); (iii) D. Ward, “Electrical and optical characterization of molecular nanojunctions” Thesis, Rice University (2010). Each of these publications is incorporated herein by reference in its entirety. 
     According to an example embodiment disclosed above in reference to  FIGS. 1-12 , provided is an apparatus comprising: a substrate (e.g.,  102 ,  FIG. 1 ); and a first set of electrodes supported on the substrate, the set including a first thin-film magnetic electrode (e.g.,  110   1 ,  FIG. 1 ) and a second thin-film magnetic electrode (e.g.,  110   2 ,  FIG. 1 ), each of the first and second thin-film magnetic electrodes having a substantially oval shape. The substantially oval shape is characterized by a first axis having a first size and a second axis having a second size, the first and second axes being orthogonal to one another, and the second size being larger than the first size. The first axis of the first thin-film magnetic electrode and the first axis of the second thin-film magnetic electrode are collinear, and an edge-to-edge separation between the first thin-film magnetic electrode and the second thin-film magnetic electrode is smaller than the first size. 
     In some embodiments of the above apparatus, each of the first and second thin-film magnetic electrodes comprises a ferromagnetic material. 
     In some embodiments of any of the above apparatus, the substrate comprises one or more of silicon and silicon oxide. 
     In some embodiments of any of the above apparatus, each of the first and second thin-film magnetic electrodes includes a respective taper (e.g.,  210   i / 220   i / 230   i ,  FIG. 2 ) that extends from a respective electrode edge in a constriction area (e.g.,  114 ,  FIG. 1 ) between the first and second thin-film magnetic electrodes. 
     In some embodiments of any of the above apparatus, a gap (e.g.,  214 ,  FIG. 2 ) between the respective tapers has a width that is smaller than the edge-to-edge separation. 
     In some embodiments of any of the above apparatus, the width of the gap varies along a length of the gap (e.g., as shown in  FIG. 2B or 2D ). 
     In some embodiments of any of the above apparatus, the width of the gap varies as a function of a distance from the substrate (e.g., as shown in  FIG. 3B or 3C ). 
     In some embodiments of any of the above apparatus, the apparatus further comprises an active element (e.g.,  402 ,  FIG. 4 ) at least a portion of which is located in the gap between the respective tapers. 
     In some embodiments of any of the above apparatus, the active element is one or more of a quantum dot, a nanocrystal, a single molecule, a polymer, and a metal-organic complex. 
     In some embodiments of any of the above apparatus, the active element comprises a fullerene molecule (e.g., C 60 ,  FIG. 4A ). 
     In some embodiments of any of the above apparatus, the active element comprises one or more linkers, each of which is chemically bonded to a respective metal atom of the respective taper (e.g., as shown in  FIG. 4B ). 
     In some embodiments of any of the above apparatus, the respective tapers are connected to one another to form a magnetic bridge between the first and second thin-film magnetic electrodes (e.g., as indicated in  FIG. 12F ). 
     In some embodiments of any of the above apparatus, the apparatus further comprises a plurality of additional sets of electrodes, each of the additional sets of electrodes being a nominal copy of the first set of electrodes, wherein the first set of electrodes and the plurality of additional sets of electrodes are arranged in an array (e.g.,  500 ,  FIG. 5 ;  600 ,  FIG. 6 ) on the substrate. 
     In some embodiments of any of the above apparatus, the apparatus further comprises a disk (e.g.,  610 ,  FIG. 6 ), wherein the substrate is a part of the disk; and wherein the first set of electrodes and the plurality of additional sets of electrodes are arranged along one or more circular tracks (e.g.,  612 ,  FIG. 6 or 8 ) on the disk. 
     In some embodiments of any of the above apparatus, the first set of electrodes further includes: a first non-magnetic metal electrode (e.g.,  120   1 ,  FIG. 1 ) attached to the first thin-film magnetic electrode; and a second non-magnetic metal electrode (e.g.,  120   2 ,  FIG. 1 ) attached to the second thin-film magnetic electrode; and the apparatus further comprises a plurality of electrically conducting tracks (e.g.,  502 ,  FIG. 5 ) connected to the first and second non-magnetic metal electrodes of the first set of electrodes and of the plurality of additional sets of electrodes. 
     In some embodiments of any of the above apparatus, the array comprises two or more rows and two or more columns of the sets of electrodes (e.g., as shown in  FIG. 5 ); and the plurality of electrically conducting tracks are arranged in a manner that makes each of the first thin-film magnetic electrodes individually addressable from the periphery of the substrate (e.g., as shown in  FIG. 5 ). 
     In some embodiments of any of the above apparatus, the plurality of electrically conducting tracks are further arranged in a manner that makes each of the second thin-film magnetic electrodes individually addressable from the periphery of the substrate (e.g., as shown in  FIG. 5A ). 
     In some embodiments of any of the above apparatus, the plurality of electrically conducting tracks are further arranged in a manner that makes the second thin-film magnetic electrodes in a column to be connected to a corresponding one of the electrically conducting tracks (e.g., as shown in  FIG. 5B  or  FIG. 5C  or  FIG. 5D ). 
     In some embodiments of any of the above apparatus, the first set of electrodes further includes: a first non-magnetic metal electrode (e.g.,  120   1 ,  FIG. 1 ) attached to the first thin-film magnetic electrode; and a second non-magnetic metal electrode (e.g.,  120   2 ,  FIG. 1 ) attached to the second thin-film magnetic electrode. 
     In some embodiments of any of the above apparatus, each of the first and second non-magnetic metal electrodes includes one or both of gold and titanium. 
     In some embodiments of any of the above apparatus, the apparatus further comprises means (e.g.,  710 ,  FIG. 7 ;  802 ,  FIG. 8 ) for subjecting the first set of electrodes to an external magnetic field. 
     In some embodiments of any of the above apparatus, the means for subjecting causes the external magnetic field to have a component that is parallel to the first axes (e.g., B,  FIG. 7 ). 
     In some embodiments of any of the above apparatus, the substantially oval shape is a substantially ellipse shape. 
     In some embodiments of any of the above apparatus, each of the first thin-film magnetic electrode and the second thin-film magnetic electrode has a thickness that is smaller than the first size. 
     In some embodiments of any of the above apparatus, the thickness is smaller than the edge-to-edge separation. 
     While this disclosure includes references to illustrative embodiments, this specification is not intended to be construed in a limiting sense. Various modifications of the described embodiments, as well as other embodiments within the scope of the disclosure, which are apparent to persons skilled in the art to which the disclosure pertains are deemed to lie within the principle and scope of the disclosure, e.g., as expressed in the following claims. 
     Unless explicitly stated otherwise, each numerical value and range should be interpreted as being approximate as if the word “about” or “approximately” preceded the value or range. 
     It will be further understood that various changes in the details, materials, and arrangements of the parts which have been described and illustrated in order to explain the nature of this disclosure may be made by those skilled in the art without departing from the scope of the disclosure, e.g., as expressed in the following claims. 
     Although the elements in the following method claims, if any, are recited in a particular sequence with corresponding labeling, unless the claim recitations otherwise imply a particular sequence for implementing some or all of those elements, those elements are not necessarily intended to be limited to being implemented in that particular sequence. 
     Reference herein to “one embodiment” or “an embodiment” means that a particular feature, structure, or characteristic described in connection with the embodiment can be included in at least one embodiment of the disclosure. The appearances of the phrase “in one embodiment” in various places in the specification are not necessarily all referring to the same embodiment, nor are separate or alternative embodiments necessarily mutually exclusive of other embodiments. The same applies to the term “implementation.” 
     Throughout the detailed description, the drawings, which are not to scale, are illustrative only and are used in order to explain, rather than limit the disclosure. The use of terms such as height, length, width, top, bottom, is strictly to facilitate the description of the embodiments and is not intended to limit the embodiments to a specific orientation. For example, height does not imply only a vertical rise limitation, but is used to identify one of the three dimensions of a three dimensional structure as shown in the figures. Such “height” would be vertical where the electrodes are horizontal but would be horizontal where the electrodes are vertical, and so on. Similarly, while all figures show the different layers as horizontal layers such orientation is for descriptive purpose only and not to be construed as a limitation. 
     Also for purposes of this description, the terms “couple,” “coupling,” “coupled,” “connect,” “connecting,” or “connected” refer to any manner known in the art or later developed in which energy is allowed to be transferred between two or more elements, and the interposition of one or more additional elements is contemplated, although not required. Conversely, the terms “directly coupled,” “directly connected,” etc., imply the absence of such additional elements. 
     The description and drawings merely illustrate the principles of the disclosure. It will thus be appreciated that those of ordinary skill in the art will be able to devise various arrangements that, although not explicitly described or shown herein, embody the principles of the disclosure and are included within its spirit and scope. Furthermore, all examples recited herein are principally intended expressly to be only for pedagogical purposes to aid the reader in understanding the principles of the disclosure and the concepts contributed by the inventor(s) to furthering the art, and are to be construed as being without limitation to such specifically recited examples and conditions. Moreover, all statements herein reciting principles, aspects, and embodiments of the disclosure, as well as specific examples thereof, are intended to encompass equivalents thereof.