Phase-locked spin torque oscillator array

Abstract

An array of magnetic nanoparticle (MNP) spin torque oscillators (STOs) is described. Each STO is comprised of a uniform, chemically synthesized, spherical nanoparticle which couples to current flowing along a surface. The particles are organized into an array by a self-assembly technique with uniform spacing and close proximity to allow strong electrical and magnetic coupling between particles. The coupling of the nanoparticles to the surface current drives the oscillations by spin-torque, and for phase locking and data input. The uniform, spherical shape of the particles allows the oscillations to be achieved at low currents and with low power dissipation. The MNP-STOs may be used as a basis for massively parallel computing, microwave oscillators, or other applications.

Claims

1. A magneto-electronic device comprising: a surface channel; a source and a drain that are electrically coupled to the surface channel to provide a current through the surface channel; and an array of magnetic nanoparticles in contact with the surface channel, wherein spin torque oscillations in the magnetic nanoparticles are phase-coupled with one another.

2. The magneto-electronic device of claim 1, wherein the magnetic nanoparticles are each composed of a uniform material.

3. The magneto-electronic device of claim 1, wherein each of the magnetic nanoparticles includes a core of a magnetic material and a shell of a non-magnetic material.

4. The magneto-electronic device of claim 1, wherein the magnetic nanoparticles are spherical.

5. The magneto-electronic device of claim 1, wherein each of the magnetic nanoparticles has a single magnetic domain.

6. The magneto-electronic device of claim 1, wherein the magnetic nanoparticles have their magnetic anisotropy oriented in a substantially same direction.

7. The magneto-electronic device of claim 1, wherein the surface channel is a thin heavy metal layer in a range from 5 to 10 nm.

8. The magneto-electronic device of claim 1, wherein spin-polarization in the magnetic nanoparticles is due, at least in part, to a spin-Hall effect in the surface channel.

9. The magneto-electronic device of claim 1, wherein: the source produces the current that is non-polarized at the source; and the current becomes spin-polarized, as it travels toward the drain, through proximity of the current to the magnetic nanoparticles.

10. The magneto-electronic device of claim 1, further comprising: a ferromagnetic material, including one or more of a ferromagnetic insulator and a ferromagnetic metal, that is in contact with the surface channel, on a side of the surface channel that is opposite to the array of magnetic nanoparticles, wherein the current becomes spin-polarized, as it travels toward the drain, through proximity of the current to the ferromagnetic material.

11. The magneto-electronic device of claim 1, wherein the surface channel is composed of a topological insulator that provides spin-polarization to the current.

12. The magneto-electronic device of claim 1, wherein the magnetic nanoparticles are phase-coupled with one another due to one or more of a magnetic dipole interaction, an electrical coupling through the current, and exchange coupling through the surface channel.

13. The magneto-electronic device of claim 1, wherein the magnetic nanoparticles are separated from one another by a gap that is in the range of one-tenth to ten times a diameter of the magnetic nanoparticles.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 depicts MNP-STOs with in-plane current (CIP).

(2) FIG. 2 depicts a schematic of phase-locked magnetic nanoparticle spin torque oscillators (MNP-STOs).

(3) FIG. 3 is a scanning electron micrograph (SEM) image of 18-nm Fe.sub.3O.sub.4 MNPs self-assembled on graphene.

(4) FIG. 4 shows Hall resistance versus magnetic field for a Fe.sub.3O.sub.4 MNP array on graphene at various gate biases. Nonlinearities are signatures of the anomalous Hall effect, which is attributed to proximity induced ferromagnetism in the graphene from coupling to the MNP array

(5) FIG. 5 depicts an exemplary MNP-STO array.

DETAILED DESCRIPTION

(6) Unlike CMOS and other conventional circuitry, the logic states in oscillator schemes are represented dynamically by phase (or frequency), and the gates must dissipate dynamic power to hold the state. Thus, energy efficient computing is feasible for oscillators with ultra-low power dissipation, which implies nanoscale oscillators based on an energy-efficient physical mechanism.

(7) FIG. 1 depicts an example system 100, including an array of MNP-STOs 110 with in-plane current (CIP) including spin polarized electrons 120. The MNP-STOs are arranged on a surface channel 130, and an insulator layer 140 is arranged between the surface channel 130 and a conductive substrate 150. Through an interparticle coupling 160, a magnetic coupling between the MNP-STOs, the spin torque oscillations in the MNPs are phase-coupled to one another. Stated somewhat differently, the electrical phase of spin torque oscillations in the MNPs are coupled to one another. This phase-coupling is due to a magnetic dipole interaction between the MNPs. The phase coupling may also be due to an electrical coupling through the CIP and/or an exchange coupling through the surface channel.

(8) FIG. 1 depicts spin torque oscillators (STOs) based on magnetic nanoparticles (MNPs) driven by spin-polarized surface currents. As described herein, nano-oscillator arrays including MNP-STOs may be used as a basis for microwave oscillators having enhanced output power and high spectral purity and for massively parallel computing for demanding tasks such as pattern recognition and image processing. Spin torque (ST) underlies magnetization oscillations in spin torque oscillators (STOs). For ultra-low power, minimal voltage and current are desired. The voltage drop can be reduced or minimized by using a giant magnetoresistance (GMR) configuration with conducting layers. Current can be reduced or minimized by using spherical nanoparticles as the active precessing magnetic element, thereby decreasing the size of each STO and also eliminating the large shape anisotropy, thus decreasing the spin torque required for oscillation.

(9) An exemplary configuration that demonstrates these features is depicted in FIG. 1. As depicted, spin-polarized electrons in the surface channel impart torque to the magnetic elements by scattering from the interface. The configuration in FIG. 1 also allows electrical coupling of individual STOs to be achieved in a simple, compact layout by the series connection of elements in a close packed array, as illustrated in FIG. 2. FIG. 2 shows another example schematic 200 of phase-locked MNP-STOs 110, arranged in a close packed array on the surface channel 130. As described herein, electrical coupling is one of several mechanisms for coupling phase information between STOs.

(10) STOs comprised of MNPs are driven by spin torque (ST) from a spin-polarized surface current. In the example depicted in FIG. 1, the effective field H.sub.eff of the MNP is oriented perpendicular to the plane. The effective field may also be due to anisotropy or an external field. In some examples, tuning may be accomplished through the external field. ST from the spin-polarized surface current drives precession of the magnetic moment M. Precession of M in turn induces an oscillation in the resistance and current beneath each MNP, thereby creating a microwave output signal. The phase of the magnetic precession in one MNP is coupled to others by electrical, dipolar, and exchange mechanisms, which can be tailored by physical design. In addition, the structure allows global control of electrical coupling through a back-gate electrode and local control of coupling via a 2D optical data input.

(11) Microwave oscillators with enhanced output power and spectral purity may be achieved through phase locking of a large number of coupled MNP-STOs in an array. Output power and spectral purity scale with the number of phase locked oscillators, which can be many millions and more for MNP-STOs.

(12) Energy efficient computing may be achieved by using the coupling of phase information among STOs in an MNP array. Some features and advantages of MNP-STOs for energy efficient computing are summarized in Table 1. Obtaining adequate spin torque to excite STO oscillations at ultra-low drive currents is essential for low power, and this is made possible by the ability to synthesize single-domain MNP with sizes near the superparamagnetic limit. An STO is potentially a high-Q oscillator. Robustness to noise may be improved by the abilities to synthesize small, single crystal MNPs (low loss) and to achieve cooperative phase-locking within the array. Ultra-low power is possible at least in part because of the small size of the nanoparticle, its spherical shape for minimal shape anisotropy and the low resistance for the in-plane current/giant magnetoresistance (CIP/GMR) configuration. Scalability to massively parallel computing is achieved via self-assembly of dense MNP arrays by drop casting and DNA scaffolding methods known in the art. The tailoring of MNP magnetic moment and interparticle coupling strengths can be precisely controlled by chemical synthesis of nanoparticles with the desired composition, size, and spacing. Fabrication is simplified by the use of a lateral drive current, which allows a simple 2D layout with no upper contacts. The back-gate electrode allows global modulation of electrical coupling between elements, which can be used for RF phase locking. In addition, top (or back-side) illumination can serve to control local carrier density and coupling strengths, thereby providing a means for 2D programming and data input to the array. Some details of the advantages in density, oscillation coherence and data I/O are given below.

(13) TABLE-US-00001 TABLE 1 Exemplary features and advantages of NMP-STO computing applications. Feature Advantage small MNP .fwdarw. small M .fwdarw. adequate STT with ultra-low I nearly superparamagnetic .fwdarw. single crystal MNP .fwdarw. robust to noise low loss .fwdarw. high Q .fwdarw. CIP/GMR .fwdarw. low R .fwdarw. small V .fwdarw. ultra-low power self-assembled .fwdarw. high density .fwdarw. scalable to massively parallel tailorable MNP material, controllable M and coupling size, spacing .fwdarw. lateral drive current .fwdarw. 2D layout .fwdarw. simple fabrication back-gate .fwdarw. global coupling control .fwdarw. RF phase locking (pump ref) optical input .fwdarw. control 2D data input of local coupling .fwdarw.

(14) Higher density: Implementations provide for a higher density of MNP-STOs in an array, compared to the density that is achievable using traditional lithographic methods. Self-assembly allows the fabrication of highly uniform MNP arrays at sub-lithographic dimensions. Highly uniform arrays of close-packed MNPs with 5-20 nm diameter cores and 1-10 nm thick shells can be fabricated easily and inexpensively over large areas by self-assembly. The control of the gap between inorganic cores by the thickness of the shells also enables the electrical, dipolar, and exchange coupling to be varied over wide ranges, allowing optimization of the local and collective interactions within the array.

(15) Oscillation coherence: Implementations also provide for greater oscillation coherence than is achievable using traditional techniques. Chemically synthesized MNPs are highly uniform (<5%) and comparable in size to the magnetization exchange length (5-10 nm). This provides advantages over larger patterned nanomagnets for achieving coherent and uniform oscillations. In addition, virtually each nanoparticle is a single crystal so that material defects are less likely to degrade the oscillations. The nanoparticles are substantially spherical, so that the demagnetizing fields are substantially uniform throughout the particle and they have nearly zero shape anisotropy, which also makes uniform magnetization precession easier to attain. The suppression of multiple oscillation modes in the individual MNP-STOs enhances the collective behavior in phase-locked arrays.

(16) In contrast, conventional patterned devices are polycrystalline and prone to disorder from process-induced rough edges, both of which create a greater variation in magnetic properties. Flat magnetic films also have highly non-uniform demagnetizing fields, especially near the device edges, greatly increasing the likelihood of unwanted complex modes of oscillation.

(17) Data input/output capabilities: Implementations enable data storage with data input/output capabilities that are an improvement over traditional systems. While data I/O in a 2D array can be envisioned as entering and exiting from the edges of the array with the computation taking place by local interactions within the array, the capability for addressing internal points in the array is desirable. The simple structure of an MNP-STO array, which eliminates shadowing by surface electrodes, is attractive for 2D optical access via both front-side and back-side illumination. Illumination could be used to spatially modulate the carrier density in a surface channel (e.g., graphene or MoS.sub.2) and thereby control the local interparticle electrical coupling strengths as a means for 2D data input and/or programming. The ability to self-assemble superlattice arrays comprised of two or more species of nanoparticles with different electrical, magnetic, and optical properties may also facilitate 2D I/O by optical techniques. In addition, time-resolved magneto-optical near-field imaging and readout of the array is possible, optical manipulation of magnetic properties has been demonstrated on a scale of 10 nm. Thus, computing using MNP STOs driven by in-plane spin-polarized surface currents offers advantages for fabrication simplicity, density scalability, design flexibility, logic state robustness, and data I/O capability, as well as ultra-low power consumption.

(18) In some implementations, a device includes a Fe.sub.3O.sub.4 MNP array that is self-assembled on a graphene layer on an SiO.sub.2-on-silicon substrate. A topographical atomic force microscopy (AFM) image 300 of such a MNP array is shown in FIG. 3. In this instance, electronic coupling between the MNPs and graphene was confirmed by conductive-AFM measurements. Magnetic coupling between the MNPs and the graphene was confirmed by Hall measurements on back-gated van der Pauw devices.

(19) FIG. 4 shows a graph 400 of Hall resistance 410 versus magnetic field 420 for an example Fe3O4 MNP array on graphene at various gate biases. Nonlinearities are signatures of the anomalous Hall effect, which is attributed to proximity induced ferromagnetism in the graphene from coupling to the MNP array.

(20) The Hall data is shown in FIG. 4 for different values of back-gate bias V.sub.gs. Variations in the slope in the figure reflect differences in the electron and hole densities for different biases near the Dirac point. The striking nonlinearities in R.sub.xy vs H, which are normally not seen for graphene, are a signature of the anomalous Hall effect (AHE). This shows that the graphene in the device exhibits ferromagnetic properties due to coupling with the MNP array, and therefore shows, by conservation of angular momentum, that the electron current in the graphene exerts the desired spin torque on the magnetic moment of the MNP.

(21) As described herein, MNP STOs operate at ultra-low power levels for energy efficiency, exhibit high Q factors for robustness to noise, and demonstrate lower power dissipation than conventional STOs. In addition, unlike conventional STOs, MNP-STOs generally do not require a large magnetic bias field to be applied for oscillations. The critical current I.sub.c required for spin torque oscillation in a magnetic particle is approximately given by:

(22) $I_c\left(\frac{e}{}\right)\left(\frac{}{\mathrm{.Math.}}\right){}_0{M}_s{\mathrm{VH}}_{\mathrm{eff}}$
where e is the electron charge, h is Planck's constant divided by 2 (h-bar), is the Gilbert damping constant, is the spin polarization, M.sub.s is the free layer saturation magnetization, V is the particle volume, and H.sub.eff is the effective field acting on the particle. A spherical magnetic nanoparticle has shape anisotropy by symmetry, therefore H.sub.eff will only include contributions from the intrinsic magnetic anisotropy (crystalline or from pair-ordering), dipolar interactions from other particles, and any externally applied field. The oscillator operating frequency f.sub.0 determines the required H.sub.eff, through f.sub.0=(/2).sub.0H.sub.eff where is the gyromagnetic ratio. For f.sub.0=1 GHz, then H.sub.eff350 Oe. For graphene in a CIP device, where R1 k/sq, with a nanoparticle diameter of d=5 nm, M.sub.s=400 kA/m, and a damping =0.01, then a power density of P10 W/cm.sup.2 is estimated. If instead of graphene, a metal is used in the CIP device with R1 /sq, then the device can operate at f.sub.0=10 GHz with H.sub.eff3500 Oe and have P1 W/cm.sup.2, all other parameters being the same.

(23) For comparison, a conventional nanopillar STO patterned lithographically will have a typical minimum size of d50 nm, which is 10 larger than a 5-nm nanoparticle. Since the critical current I.sub.cd.sup.2 the power will be PI.sub.c.sup.2 d.sup.410.sup.4 larger for the nanopillar, and the power density 10.sup.2 larger. In addition, the most common nanopillar/nanocontact STOs require large bias fields B.sub.s to overcome the out-of-plane anisotropy caused by the thin film demagnetizing field. This bias field is needed in addition to any field required for setting f.sub.0. Thus, nanoparticle STOs are expected to have lower power and simpler operation than previously STOs.

(24) A high Q-factor is desired for robustness to noise. The theoretical linewidth of an STO was shown to be

(25) $f~\frac{k_{b}T}{E_{\mathrm{osc}}},$
where is the Landau-Lifshitz damping parameter, k.sub.b is Boltzmann's constant, T is temperature and E.sub.osc is the energy of the oscillator. For typical nanopillars, E.sub.oscM.sub.sVH.sub.eff50-100 k.sub.bT at room temperature, giving

(26) $Q=\frac{f_0}{f}~\frac{1}{}\frac{E_{\mathrm{OSC}}}{k_{b}T}~1000-10000.$
Since a nanoparticle is much smaller in volume and E.sub.osck.sub.bT, the linewidth of an individual nanoparticle oscillator is understood to be somewhat broad with 1/100. However, when N oscillators phase-lock, there is a corresponding narrowing of the linewidth by a factor 1/N, so that N/. This narrowing occurs since E.sub.osc is effectively N times larger for the phase locked oscillators. Such linewidth narrowing has been observed for two nanocontact oscillators, with a reduction in linewidth of >2 after phase-locking. Thus, an array of N phase-locked nanoparticle oscillators is expected to demonstrate a narrower linewidth and a higher associated , thereby providing increased stability and robustness to noise.

(27) The of individual MNP STOs can also be significantly increased by using magnetic materials with lower damping constant . Typical STO free layers such as NiFe and CoFeB alloys have 0.01. However, certain FeV and CoFe alloys have been found to have much lower damping (3-5) and are therefore suitable for high Q nanoparticle oscillators.

(28) FIG. 5 depicts an exemplary MNP-STO array 500. As shown in the example of FIG. 5, the surface channel 130 may be electrically coupled to a source 510 and a drain 520, such that the current flows from the source to the drain through the surface channel.

(29) In implementations illustrated by FIG. 5, the MNP-STOs 110 include a core 550, of a diameter (d) 540, and a shell 560 that has a tunable thickness based on the chemical composition and creation of the STOs. In some implementations, the STOs 110 may be deposited onto the surface channel in a close packed array such that the shells of the STOs are in contact with each other. Accordingly, the cores 550 may be separated from one another by a gap (g) 530 that is twice the thickness of the shell 560. In implementations that employ such a core-shell design for the STOs, the core may be a different material than the shell. For example, the core is a magnetic material, and the shell is a non-magnetic material. Alternatively, the STOs may be composed of a single, magnetic material, as shown in FIG. 1.

(30) Oscillations of the MNP magnetization are driven by coupling between the MNP and spin-polarized surface currents. The following exemplary implementation are described with reference to the device structure in FIG. 5 and to nonmagnetic (NM) and ferromagnetic (FM) contacts: 1. NM source and NM drain contacts. In this implementation, an unpolarized electron current injected from the source becomes spin polarized as it travels toward the drain due to proximity induced ferromagnetism due to coupling to the MNP array. Thus, spin polarization induced by MNPs near the source provides ST to drive oscillations farther downstream. 2. FM source and NM drain contacts. Similar to (1) but the current is already spin-polarized by the FM source contact as it is injected into the device. 3. NM source and NM drain contacts with an underlying FM coupling layer. Here, spin polarization is induced continuously along the channel by proximity induced ferromagnetism from an adjacent insulating FM thin film, such as a YIG layer. 4. NM source and NM drain contacts to a spin polarized channel created by the surface states of a topological insulator, e.g., Bi.sub.2Se.sub.3. In this case, spin-momentum locking via the topological surface states provides spin-polarization continuously along the channel. 5. NM source and NM drain contacts to a spin polarized channel comprised of a heavy metal such as Tantalum in which carriers of one spin accumulate on the surface of the metal due to the spin Hall effect.

(31) Phase coupling mechanisms: In addition to a means for driving the oscillations, computing with STOs include a means for coupling phase information among oscillators, both locally (for data processing) and globally (for data reference). MNP-STO arrays provide three mechanisms for coupling the magnetic-precession: 1) electrical coupling (current modulation due to magnetoresistance oscillations in the vicinity of each STO); 2) magnetic dipole interaction (magnetostatic coupling between adjacent or nearby STOs); 3) exchange coupling (RKKY interactions via the surface electrons).

(32) MNP array design: While all three coupling mechanisms are accessible by MNP-STOs, the small size and close proximity of MNP-STOs, together with their precise tailorability by chemical synthesis, make this approach uniquely suited to controlling dipole and exchange interactions for optimizing phase locking. State-of-art chemical synthesis of functional inorganic nanoparticles allows the precise choice of composition, core diameter and organic shell thickness, which in turn allows precise design of magnetization, anisotropy, size and interparticle gaps in self-assembled arrays. Arrays comprised of MNPs with cores in the 5-20 nm diameter range and shells with thicknesses in the 1-10 nm range are studied.

(33) Implementations provide for design optimization and frequency tunability. The H.sub.eff for the MNPs can be optimized by tailoring anisotropy (shape, magnetocrystalline) and orientation (e.g., self-assembly in a magnetic field) to provide stable operation at room temperature without an external magnetic field. Additionally, the ability to vary H.sub.eff with an external field may be exploited for tuning the oscillation frequency. Frequency tuning by current bias can also be used.

(34) With regard to the chemical synthesis of NMPs, implementations use nanoparticles of tunable size, shape and properties (magnetic, electrical, optical) that can be processed into ordered 2-D arrays in a highly modular fashion. Well-defined nanoscopic building blocks are created via bottom up wet-chemical synthetic methods. Well-defined metallic nanoparticles with tunable sizes from 5-20 nm can be synthesized using established methods, including FePt and other magnetic alloy NPs in the ranges of 5-10 nm are also synthesized. Phosphonic acids ligands with tunable lengths (e.g., alkyl segments from 6-18 carbons and polymer ligands with 10-50 units) enable control of interparticle spacing over a wide range in 2D MNP arrays. The ability to control the ligand surface chemistry of magnetic NPs is advantageous.

(35) The synthesis of heterostructured magnetic colloids, with controllable placement of noble metal inclusions in the core, or outer shell of superparamagnetic NPs can be implemented to enhance the electrical properties of these materials in magneto-electronic devices.

(36) In some implementations, the surface channel is composed of graphene-based structures or other suitable conductive materials. Alternatively, a topological insulator (TI) such as Bi.sub.2Se.sub.3 is used to provide a spin-polarized surface channel. TIs have the advantage of fully spin-polarized charge carriers in the topological surface state (TSS), which persists at room-temperature. Their spin is locked to their momentum and TSS electrons appear in counter-propagating pairs. MBE allows for the precise control of the TI film thickness and the (low-temperature) growth has been established on a number of crystalline and also amorphous substrates, allowing growth on SiO.sub.2/Si wafers. This leads to 1D or 2D, fully spin-polarized surface conduction channels in the vicinity of the MNPs; and, depending on the MNP array design, to various MNP coupling regimes and macroscopic, spin-polarized states. This will promote the coupling of the STOs, reducing the required power for their operation.

(37) The fabrication of devices, according to the implementations described herein, makes use of the chemical protocols and fabrication processes in which electrical and magnetic coupling (as shown in FIG. 4) occurs between (e.g., Fe.sub.3O.sub.4) MNP arrays (as shown in FIG. 3) and a (e.g., graphene) surface channel on a (e.g., SiO.sub.2-on-silicon) substrate. For example, self-assembled arrays can be formed by drop-casting 18-nm Fe.sub.3O.sub.4 with 2-nm oleic acid shells dispersed in hexane. In some implementations, pyrolysis is used to remove organic ligands on the MNP surfaces and create electrical contact between the (e.g., Fe.sub.3O.sub.4) cores of the MNPs and the surface channel (e.g., graphene layer).

(38) In some implementations, the array of MNP-STOs may be used, e.g., as a microwave oscillator, to generate a microwave output signal. The spin torque oscillation in the nanoparticles create an oscillating resistance in the surface channel due to spin-dependent electron scattering, which in turn causes an oscillating current in the channel, thereby giving rise to a microwave output signal.

(39) The direction of the magnetization of the particles and the direction of the electron spin in the channel may be perpendicular with respect to each other. In some instances, the nanoparticle magnetization is oriented perpendicular to the surface, and the electron spin is oriented parallel to the surface. In some instances, the nanoparticle magnetization is oriented parallel to the surface, and the electron spin is oriented perpendicular to the surface. Similarly, the direction of the magnetization in the ferromagnetic contact or ferromagnetic insulator/metal layer may be oriented perpendicularly to the nanoparticle magnetization.

(40) Implementations provide a magneto-electronic device that includes an array of MNPs that is a self-assembled structure. In some implementations, the MNPs are spherical, or substantially spherical. The MNPs may be arranged in an array that is a single, two-dimensional layer on the surface channel. In some implementations, the MNPs may be uniformly composed particles that are composed of the same material throughout each MNP. Alternatively, the MNPs may have a magnetic core and a non-magnetic shell. In such instances, the shell may be electrically conductive to provide an electrical contact with the surface channel. The MNPs may be small enough to have a single magnetic domain. The MNPs are phase-locked in their oscillation.

(41) In some implementations, the surface channel is conductive, e.g., composed of graphene, MoS.sub.2, a transition metal dichalcogenide, or some other conductive material. The surface channel provides a medium for coupling the MNPs electrically and/or through an exchange interaction. The coupling may also be through magnetic dipole coupling. The current in the surface channel may drive the spin torque oscillation, and the current may in some cases be spin-polarized to provide the spin-polarization to the MNPs.

(42) The coupling between the MNPs may be provided by one or more of the following: magnetic dipole coupling between MNPs, through a magnet dipole field; electrical coupling through the current flowing in surface channel (e.g., magnetoresistance coupling); and/or exchange interaction, as a quantum mechanical coupling mechanism that occurs through the surface current. The separation between the MNPs can be tuned (e.g., through the thickness of a persistent shell of the MNPs, or through the thickness of the organic layer that is removed following placement of the MNPs) to tailor the interaction strength for each of these types of coupling.

(43) Spin torque oscillation may be applied to the MNPs through one of the following techniques: 1. The current is sourced such that the electrons are not initially spin-polarized. Spin polarization of the electrons results from their scattering off MNPs that are themselves spin polarized, such that the current gains a spin polarization as it travels from the source to drain. 2. The source electrode that is producing the electrons for the current is composed of a ferromagnetic material, and/or there is a ferromagnet in contact with the source, such that the current passing through the source only includes one spin polarization. Thus, an electron enters the channel spin-polarized, and transfers its spin-polarization to the MNPs. 3. A ferromagnetic material may be included between the insulator and the surface channel, or the insulator is a ferromagnetic insulator (e.g., YIG), such that the electrons pick up spin polarization from the ferromagnetic material and/or insulator. 4. The surface channel is made of a topological insulator (TI), e.g., Bi.sub.2Te.sub.3, Bi.sub.2Se.sub.3, that is primarily insulating but has special surface topological properties that provide spin polarization to the electrons in the surface channel.

(44) Implementations can employ MNPs that are synthesized using various suitable methods. In some implementations, the MNPs are synthesized with an organic shell, such as a shell of Oleic acid, 1 nm thick. The solution used during synthesis may prevent the MNPs from sticking together. The MNPs may be drop-cast onto the surface channel, and the shell provides for uniform spacing of the MNPs that are close-packed on the surface. In some implementations, the shell has a one molecule thickness. The shell may be removed following the drop-casting, through a pyrolytic process (e.g., heating) that degrades and vaporizes the shell, or other suitable technique. Removing the shell causes the MNPs to contact the surface channel, and provides for a uniform spacing between MNPs. In this way, the assembly of the array may be a self-assembly, such leaves the MNPs close-packed on the surface in a single layer, separated by a uniform gap (e.g., approximately twice the thickness of the removed shell). The close packing of the MNPs provides for a strong magnetic dipole coupling between the magnetic fields of the individual particles. The close packing also facilitates the coupling through the current in the surface.

(45) Implementations provide for a stronger coupling between MNPs, compared to traditional systems of coupled particles, and thus provides for an array of MNP-STOs that is less prone to noise due to the small size of the MNPs, their spherical symmetry, and their closeness. The strongly coupled array of MNP-STOs may be employed as a microwave oscillator. The phase-locking MNPs allows for a multiplication of the power output of the oscillator, which scales as the square of the number of MNPs in phase lock. The uniformity of the array, and the strong coupling between particles, leads to a high purity of the oscillator that provides output at a single frequency with minimal noise. The oscillator is highly tunable, with high spectral purity and high power, and thus is an improvement over previously available microwave oscillators.

(46) Implementations also provide an array of MNP-STOs that may be employed as an analog computer, where information is represented by the phase of the particles, and the phase coupling enables the performance of computations. To program the array, the coupling between MNPs may be modified locally through use of an optical signal that is projected onto the surface to modify certain couplings based on intensity of optical signal at different points. In this way, the array may be employed for associative, non-Boolean computing.

(47) Further modifications and alternative embodiments of various aspects will be apparent to those skilled in the art in view of this description. Accordingly, this description is to be construed as illustrative only. It is to be understood that the forms shown and described herein are to be taken as examples of embodiments. Elements and materials may be substituted for those illustrated and described herein, parts and processes may be reversed, and certain features may be utilized independently, all as would be apparent to one skilled in the art after having the benefit of this description. Changes may be made in the elements described herein without departing from the spirit and scope as described in the following claims.