CROSS-REFERENCE TO RELATED APPLICATION 
     This application claims priority to U.S. Application Ser. No. 61/781,462 entitled “NANOFERRITE FLAKES” and filed on Mar. 14, 2013, which is incorporated by reference herein in its entirety. 
    
    
     BACKGROUND 
     “Ferrite” generally refers to metal oxides having a spinel cubic crystal structure with a stoichiometry represented by AB 2 O 4 , where A and B represent different lattice sites occupied by cationic species, and O represents oxygen in its own sublattice. Thin film ferrites have been formed by methods including embedding bulk ferrite into MYLAR shims and doctor blading bulk ferrite into sheets and then firing at high temperature. Ferrites have also been deposited on plastic and glass substrates to form thin films by methods including, for example, spin-spray plating, chemical solution deposition (CSD), chemical vapor deposition (CVD), plasma enhanced CVD (PECVD), physical vapor deposition (PVD), and sputtering. Certain deposition techniques, such as pulsed laser deposition and sputtering, can involve heating substrates to high temperatures (e.g., over 600° C.) to crystallize ferrite films. Thin film ferrites exhibit a wide array of properties, including high complex permeabilities, relatively high resistivity, low losses, and high resonance frequencies. In some cases, ferrite thin films are weak in saturation magnetization and high in coercivity compared to bulk ferrites. 
     SUMMARY 
     In one aspect, a ferrite layer having a columnar polycrystalline structure is formed, whereby ferrite flakes are separated from the substrate which may be any rigid flexible material that can withstand the depositions conditions. The ferrite flakes have a spinel cubic crystal structure with a stoichiometry represented by AB 2 O 4 , where A and B represent different lattice sites occupied by cationic species, and O represents oxygen in its own sublattice. 
     Implementations may include one or more of the following features. 
     Forming the ferrite layer may include spin-spraying the ferrite layer onto a substrate. In some cases, the substrate is selected from the group consisting of thermoplastic, glass, and metal. In certain cases, the substrate is a thermoplastic, and the ferrite layer is formed at a temperature less than the glass transition temperature of the thermoplastic. The ferrite flakes form during the deposition process as films that are limited in lateral size, or may form by fracturing and spalling from the initial deposit. The flakes may be annealed at a temperature less than the glass transition temperature of the thermoplastic. 
     The ferrite layer may be formed at a temperature between 50° C. and 100° C. In some cases, the ferrite layer is formed at a rate between 5 nm/min and 500 nm/min. Rotation of the substrate during spin-spraying is typically between 50 and 500 rpm. The ferrite flakes may be nanocrystalline or polycrystalline with grain sizes in a range between 20 nm and 100 nm in diameter. The ferrite flakes may include nickel, zinc, cobalt and iron as crystalline oxides. The ferrite flakes may be annealed, for example, by heating the ferrite flakes at a ramp rate of 50° C./min or less. 
     The ferrite layer, or flakes, that are produced by this method are polycrystalline in nature. In some cases, the individual grains are less than 100 microns in any one dimension. Typically, the size of the individual grains are on the order of 15 to 100 nm in at least one dimension, from which a flake or film will comprise many in a dense or nearly dense microstructure. Often, the grains appear to be columnar, or they could be equiaxed, in shape. It is implied that the occasional use of the term “nanoferrite” means that the ferrite microstructure includes crystalline grains that are sub-micron in size. In some cases, for example, the crystalline grains are less than 100 nanometers in any one dimension. 
     In some implementations, the ferrite flakes are combined with a liquid precursor material, and the liquid precursor material is solidified to embed the ferrite flakes. The liquid precursor material may be selected from the group consisting of polymers, elastomers, and epoxies. The ferrite flakes may be oriented in the liquid precursor material before solidifying the liquid precursor material. Orienting the ferrite flakes in the material may include, for example, centrifugating the material after combining the ferrite flakes with the liquid precursor material and before solidifying the liquid precursor material. In some cases, an additive is combined with the ferrite flakes and the liquid precursor material before solidifying the liquid precursor material. The additive may be selected from the group consisting of a drug, a contrast agent, and magnetic or nonmagnetic filler materials. The application of an external magnetic field may also be a way of enhancing the degree of orientation of the flakes as the matrix material polymerizes or otherwise solidifies around them. 
     Embedded ferrite flakes formed as described herein may be included in a device such as an electromagnetic noise suppression device, a semiconductor device, a magnetic sensor, an antenna, a global positioning system, a radar absorbing structure, a synthetic aperture radio, and a medical imaging device. 
     As described herein, loose ferrite flakes are formed at a rapid deposition rate. 
     The details of one or more implementations are set forth in the accompanying drawings and the description below. Other features and advantages will be apparent from the description and drawings, and from the claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1A  shows an apparatus for forming a ferrite layer on a substrate. 
         FIG. 1B  illustrates the coating process that occurs using the apparatus shown in  FIG. 1A . 
         FIG. 2A  is a scanning electron microscopy (SEM) image of a Ni 0.23 Zn 0.33 Co 0.05 Fe 2.40  ferrite layer showing columnar and bulk spinel ferrite morphology. 
         FIG. 2B  is an enlarged view of the Ni 0.23 Zn 0.33 Co 0.05 Fe 2.40  ferrite columns seen in  FIG. 2A . 
         FIG. 3  is an experimental set-up for direct formation of nanoferrite flakes. 
         FIG. 4  is an SEM image of nanoferrite flakes formed in the apparatus shown in  FIG. 3 . 
     
    
    
     DETAILED DESCRIPTION 
     As described herein, nanoferrite flakes can be obtained from a ferrite layer deposited on a substrate to form thin film ferrite. The substrate may include thermoplastic, glass, or metal. Examples of suitable thermoplastics include polyetheretherketone (PEEK), polyether imide, nylon, polyetherketoneketone, and the like. Deposition may include, for example, spin-spray plating a ferrite on the surface of a substrate.  FIG. 1A  depicts an apparatus  100  for spin-spray plating a ferrite on the surface of a substrate  102 . During deposition of the ferrite, the substrate may be heated on a rotating platform  104 . A metals solution  106  (reactant) and an oxidizer solution  108  (oxidant) are provided to the substrate  102  on the rotating platform  104 . As described, for example, in Abe et al., Jpn. J. Appl. Phys. 22 (1983) pp. L511-L513, and Itoh et al., Jpn. J. Appl. Phys. 27 (1988) pp. 839-842, both of which are incorporated by reference herein, the metals solution  106  is an aqueous solution including two or more salts, such as chlorides of iron, nickel, zinc, cobalt, copper, manganese, indium, or other metal with a valence of two; the oxidizer solution  108  can be, for example, an aqueous solution of sodium nitrite, glacial acetic acid, and ammonium hydroxide. 
     Providing the reactant and oxidant can include atomizing liquid droplets (e.g., with a nebulizer), thereby promoting a more uniform temperature on the substrate. The rotation rate, pH, fluid flow, and temperature may be adjusted to achieve a desired spinel nanostructure. In an example, a thermoplastic substrate is mounted on an 8″ disc rotating at 60 rpm. The platform on which the substrate is positioned is heated to a temperature up to 100° C., up to 200° C., or up to 300° C. (e.g., 90° C.). The flow rate of the reactant and the oxidant can be automated at a selected rate (e.g., 55 mL/min). The rotation rate and platen temperature may be monitored.  FIG. 1B  depicts the spray flux  110 , fluid flow  112 , diffusing reactants  114 , ferrite layer  116 , and heated spinning platform  118  in an exemplary experimental setup. 
     The deposition rate of the ferrite is influenced by factors including reactant concentration (metal concentration), gas pressure, and fluid flow rate of the spray, and may range from 5 to 500 nanometers/min (e.g. 300 to 400 nanometers/min). Ferrite layers formed as described herein are nanostructured, and typically include polycrystalline nanoparticles deposited in a textured columnar network, with dimensional features of between 20 nm and 1000 nm in diameter and between 0.3 μm and 12 μm in height. Reactants and deposition conditions can be selected such that the textured columnar network is flakey. In contrast, other reactants and deposition conditions yield continuous and coherent films that are relatively dense, smooth, uniform, and well-bonded to the substrate. See, for example, Subramani et al., Materials Science and Engineering: B 148(1-3) pp. 136-140 and Kondo et al., U.S. Pat. No. 7,648,774, both of which are incorporated herein by reference. In some cases, a flakey columnar network is formed for a spin rate between 50 and 500 rpm (e.g., between 90 and 350 rpm). After a nanoferrite thin film is formed, nanoferrite flakes can be separated easily from the substrate and further processed. In one example, the nanoferrite flakes are annealed (e.g., at a temperature between 300° C. and 1100° C.). Annealing the flakes typically increases the permeability and decreases the resonance frequency of the flakes. 
     The nanoferrite flakes are combined with a material (e.g., a polymer, elastomer, or epoxy), and the material is solidified/polymerized to yield a structure with embedded nanoferrite flakes. In some cases, the nanoferrite flakes are oriented within the structure (e.g., with centrifugation) to achieve desired electromagnetic properties, such as permeability, resonance frequency, and low core losses. The material can be solidified in a desired shape or solidified and then cut or otherwise shaped into selected dimensions. In certain cases, one or more additives (e.g., drug, contrast agent, nonmagnetic fillers, etc.) may be combined with the nanoferrite flakes and the material before solidifying the material. 
     In one example, (Ni—Zn—Co) x  Fe 3 -xO 4  was spin spray plated onto VICTREX APTIV PEEK substrate to a thickness of 12 μm at 90° C. at a deposition rate of 375 μm/min. After the ferrite was deposited and cleaned with deionized water, it was cooled to room temperature. Next the Ni 0.23 Zn 0.33 Co 0.05 Fe 2.40  thin film ferrite layer was pulled off the substrate. The flakes were collected and placed into a vial. The nanoferrite flakes were mounted in a low viscosity, “ultra thin” epoxy resin and centrifuged to preferentially orient the flakes in roughly a parallel configuration. A sample was cut from the dried epoxy, and the electromagnetic properties of the sample were measured.  FIG. 2A  is an SEM image of a sample cut from the dried epoxy showing columnar  200  and bulk  202  spinel ferrite morphology.  FIG. 2B  is an enlarged view of Ni 0.23 Zn 0.33 Co 0.05 Fe 2.40  ferrite columns  200  shown in  FIG. 2A . 
     In another example, nanoferrite flakes were formed directly as a powder rather than as a flaky layer. The experimental set-up is shown in  FIG. 3 . In the process, a metal chloride solution and an oxidant solution were sprayed separately by nebulizers  300  and  302  into a pressurized glass vessel  304  with a magnetic stir bar and heated to 90° C. While the nebulizers  300  and  302  were spraying, powder was removed from the glass vessel  304  via application of a vacuum and collected in situ in glass vessel  306 . The magnetic powder was later separated using neodymium magnets and a centrifuge, then washed at least 3 times and dried in a drying furnace set to 70-100° C.  FIG. 4  is an SEM image of the resulting nanoferrite flakes  400 . This procedure simplified the process, while maintaining the permeability, resonance frequency, and low core losses. 
     Advantages of the low temperature processes described herein (e.g., below 100° C.) include the use of plastic substrates, including plastic substrates unsuitable for high temperature processes, to form thin film ferrites in a range of sizes. Depending on the raw material composition and processing conditions, embedded nanoferrite flakes formed as described herein exhibit a wide array of properties, including high complex permeabilities (e.g., in the MHz and GHz range), relatively high resistivity, low losses, and high resonance frequencies. Applications for embedded nanoferrite flakes include sensing and actuation applications, miniaturized low-microwave inductors, antennas (e.g., wireless and mobile applications, as well as dual- and tri-band antennas in global positioning systems (GPS), radar absorbing structure (RAS), synthetic aperture radar (SAR)), high-density perpendicular recording layers, semiconductor devices, noise suppression, filters, dielectric materials, composites, and magnetic sensors. Embedded nanoferrite flakes may also be used in a variety of medical applications, including medical imaging devices, contrasting agents, and drug delivery, Advantages of ferrites formed as described herein include light weight, low volume, low cost, and large-scale production, as well as flexible design, low sensitivity to manufacturing tolerances, and easy installation. 
     A number of embodiments have been described. Nevertheless, it will be understood that various modifications may be made without departing from the spirit and scope of the disclosure. Accordingly, other embodiments are within the scope of the following claims.
A ferrite layer having a columnar structure is formed, and ferrite flakes are separated from the ferrite layer. The ferrite flakes include a metal oxide having a spinel cubic crystal structure with a stoichiometry represented by AB 2 O 4, where A and B represent different lattice sites occupied by cationic species, and O represents oxygen in its own sublattice.