Spintronic Nano-Oscillators

Abstract

Spintronic nano-oscillators represent a novel class of nonlinear auto-oscillators that effectively convert magnetization precession into a microwave voltage signal by means of spin torque exerted through an electric current. These nano-oscillators can be categorized as either spin-torque nano-oscillators (STNOs) or spin-Hall nano-oscillators (SHNOs), depending on the driving force involved, namely, spin-transfer torque or spin-orbit torque. The present chapter offers a comprehensive review of the fundamental aspects and recent advancements in spintronic nano-oscillators. Firstly, the discussion encompasses spin torques and magnetoresistive effects. Subsequently, the underlying principles and theoretical foundations of spintronic nano-oscillators are elucidated, encompassing the Landau-Lifshitz-Gilbert-Slonczewski (LLGS) equation and nonlinear auto-oscillation theory. Additionally, the chapter outlines the structures, characteristics, and synchronization phenomena exhibited by these oscillators. Lastly, prospective applications such as microwave communication, assisted magnetic recording, and neuromorphic computing are explored. This review is poised to stimulate research interest, particularly with regard to the commercialization of promising applications.

1. Introduction

As Moore’s Law approaches its end, it is increasingly doubtful that the highly advanced complementary metal oxide semiconductor (CMOS) technology will be capable of fulfilling the growing demands for future applications. Consequently, numerous unconventional computing hardware alternatives have been proposed to address the limitations of the von Neumann architecture. Notably, spintronic nano-oscillators have attracted significant attention as a promising solution, owing to their favorable attributes such as operational feasibility at room temperature, nanoscale size, seamless integration with CMOS technology, high-speed capabilities, and minimal power consumption. As a result, these spintronic nano-oscillators have emerged as compelling candidates for the realization of artificial intelligence applications.

In 1996, Slonczewski [1] and Berger [2] proposed the spin-transfer torque (STT) effect, which provides a convenient way of manipulating the spin by direct currents. In 1999, Hirsch [3] reformulated the spin Hall effect (SHE), which can generate a purely self-selected current perpendicular to the direction of the charge current, which in turn can exert spin-orbit torque (SOT) on the adjacent magnetic layers. Both STT and SOT are capable of manipulating the magnetization in the way of switching or precession. For the magnetization switching applications, spin transfer/orbit torque-based magnetoresistive random access memory (MRAM) with the advantages of non-volatility, high speed, and low power consumption is receiving wide attention from industry and academia [4]. For the magnetization precession applications, the current-driven magnetization precession can generate radio frequency (RF) voltage signals through different magnetoresistive effects, such as anisotropic magnetoresistance (AMR) [5], giant magnetoresistance (GMR) [6, 7], tunneling magnetoresistance (TMR) [8]. This type of device is known as a spintronic nano-oscillator, and it is further subdivided into spin-torque nano-oscillators (STNOs) [9] and spin-Hall nano-oscillators (SHNOs) [10, 11, 12, 13].

In this chapter, we first examine the fundamental concepts of spin torque-related phenomena and various magnetoresistance effects. Then we introduce the theory of spintronic nano-oscillators, including the Landau-Lifshitz-Gilbert-Slonczewski equation (LLGS) and nonlinear auto-oscillation theory. We then elaborate on the devices’ structure, characteristics, and synchronization phenomena. Finally, the applications are discussed.

2. Spin torque-related phenomena and magnetoresistance effects

Spin torques and magnetoresistive effects are the fundamental theoretical basis of spintronic nano-oscillators. Therefore, this section provides an introduction to them.

2.1 Spin torques

2.1.1 Spin-transfer torque (STT)

Figure 1 shows the process of STT. When a charge current passes through a fixed layer, non-polarized electrons acquire spin angular momentum from the magnetic moment of the fixed layer, causing their spins to become partially polarized in the same direction as the magnetic moment ($\mathit{P}$). The coherence of these spin-polarized electrons can be preserved when the thickness of the middle layer (colored in yellow) is less than the length scale over which the spin orientation of the electrons changes, known as the spin-flip length (typically a few to a hundred nanometers in metals). Upon entering the free layer, the spin-polarized electrons can transfer their angular momentum to the free layer, resulting in a torque that rotates the magnetization direction ($\mathit{M}$) of the free layer.

Figure 1.

Schematic of spin-transfer torque.

2.1.2 Spin-orbit torque (SOT)

In recent years, SOT has been proposed as a new driving torque [14, 15]. The implementation of SOT requires the addition of a heavy metal film below the free layer (The fixed layer and spacer are unnecessary in this case). The basic principle of SOT can be generated by SHE [15].

The principle of SHE is shown in Figure 2b. When a current is applied to the strong spin-orbit coupling (SOC) material (such as Pt, W and Ta, et al.), the strong SOC causes the spin-up and spin-down electrons to gather in equal quantities along both sides of the vertical film direction (z-axis), that is, the current flowing through the strong SOC material will generate spin flow along the vertical direction. The spin current ${\mathbf{J}}_s$ can be written as

Figure 2.

Schematic of spin-orbit torque with spin Hall effect.

$${\mathbf{J}}_s={\theta }_{\mathit{SHE}}\sigma \times {\mathbf{J}}_c,$$E1

where ${\theta }_{\mathit{SHE}}$ is the spin Hall angle, and $\sigma$ is the electron spin unit vector injected into the free layer due to SHE.

2.2 Magnetoresistance (MR)

The magnitude of magnetoresistance directly affects the output power of the spintronic nano-oscillators, which is the crucial property of spintronics oscillators. Here, we introduce three main magnetoresistance effects.

2.2.1 Anisotropic magnetoresistance (AMR)

AMR was discovered by William Thomson in 1857 [5], which is a phenomenon in which the resistivity of a ferromagnetic material varies with the angle between the direction of magnetization and the current direction due to the transport electrons experiencing different scattering strengths in FM materials. AMR is usually defined as:

$$\mathit{MR}=\frac{\mathit{\Delta \rho }}{{\rho }_{\mathit{av}}}=\frac{{\rho }_{\parallel }-{\rho }_{\perp }}{\frac{1}{3}{\rho }_{\parallel }-\frac{2}{3}{\rho }_{\perp }},$$E2

where ${\rho }_{\mathit{av}}$ denotes the average value of resistivity. ${\rho }_{\parallel }$ and ${\rho }_{\perp }$ denote the resistivity when the magnetization direction is parallel and perpendicular to the current direction, respectively.

2.2.2 Giant magnetoresistance (GMR)

In 1988, Peter Grünberg found a 1.5% variation of magnetoresistance in the Fe/Cr/Fe triple-layer structure, which was much larger than AMR at that time [6]. In the same year, Albert Fert found a 50% variation of magnetoresistance at low temperatures in ${\left[\mathit{Fe}/\mathit{Cr}\right]}_n$ [7], which is called GMR. GMR is based on the spin valve (SV) structure, a sandwich structure with two ferromagnetic layers sandwiched by a non-magnetic metal spacer layer. The huge variation of magnetoresistance compared with AMR has attracted widespread attention in scientific research. It is widely believed that the magnetoresistance effect originates from the electron scattering associated with spin. The Mott two-current model is commonly used to understand GMR [16]. In contrast to ordinary metals, the effect of spin transport on the resistance is considered in ferromagnetic materials. There are two channels in the conductive process of ferromagnetic metals, spin-up, and spin-down channels. When the magnetization direction of the magnetic material is parallel to the electron spin direction, the electron scattering is weak and therefore the resistivity is low, denoted by ${\mathrm{R}}_{\mathrm{L}}$; when the magnetization direction of the magnetic material is anti-parallel to the electron spin direction, the electron scattering is strong and therefore the resistivity is high, denoted by ${\mathrm{R}}_{\mathrm{H}}$, as shown in Figure 3. The magnitude of the magnetoresistance can be expressed as:

Figure 3.

Principle of giant magnetoresistance effect.

$$\mathit{MR}=\frac{\mathit{\Delta R}}{R}=\frac{R_{\mathit{AP}}-R_P}{R_{\mathit{AP}}}=\frac{{\left(R_H-R_L\right)}^2}{2{\left(R_H+R_L\right)}^2},$$E3

where ${\mathrm{R}}_{\mathrm{AP}}$ and ${\mathrm{R}}_{\mathrm{P}}$ are the resistances of antiparallel and parallel states, respectively.

2.2.3 Tunneling magnetoresistance (TMR)

TMR with greater magnetoresistance is observed in magnetic tunnel junctions (MTJs), which are similar to SV, except that the potential barrier layer of MTJs is usually made of thin insulating material, such as MgO and ${\mathrm{Al}}_2{\mathrm{O}}_3$. The principle of TMR is shown in Figure 4. When the two ferromagnetic layers are magnetized in the same direction, the majority spins tunnel easily and occupy the empty band of the majority spins in the other ferromagnetic layer; at the same time, the minority spins tunnel and occupy the empty band of the minority spins in the other ferromagnetic layer, showing a low resistance state. When the two ferromagnetic layers are magnetized in opposite directions, the majority spin tunnels into the empty band of the minority spin of the other ferromagnetic layer; the minority spin tunnels into the empty band of the majority spin of the other ferromagnetic layer, resulting in a decrease in the total number of electrons tunneled, and a high resistance state [8].

Figure 4.

Principle of tunneling magnetoresistance effect.

The magnitude of the tunneling magnetoresistance is usually expressed as:

$$\mathit{MR}=\frac{R_{\mathit{AP}}-R_P}{R_P}=\frac{G_P-G_{\mathit{AP}}}{G_{\mathit{AP}}}\times 100\%,$$E4

where $G_P$ and $G_{\mathit{AP}}$ represent the conductance of the two ferromagnetic layers when the magnetization directions are parallel and antiparallel, respectively.

3. Theory of spintronic nano-oscillators

3.1 LLGS equation

In the study of magnetization dynamics problems that include STT effects, Slonczewski and Berger first extended the STT term to the Landau-Lifshitz-Gilbert (LLG) equation, called the LLGS eq. [17]:

$$\frac{d\mathbf{m}}{\mathit{dt}}=-{\mathit{\gamma \mu }}_0\left(\mathbf{m}\times \mathbf{H}\right)+\alpha \left(\mathbf{m}\times \frac{d\mathbf{m}}{\mathit{dt}}\right)+{\mathrm{\Gamma }}_{\mathit{STT}},$$E5

where the ${\mathrm{\Gamma }}_{\mathit{STT}}$ can be generally expressed as:

$${\mathrm{\Gamma }}_{\mathit{STT}}={\mathrm{\Gamma }}_{\mathit{STT}}^{\mathit{DL}}+{\mathrm{\Gamma }}_{\mathit{STT}}^{\mathit{FL}}={\mathit{\gamma \mu }}_0\eta \frac{\mathrm{\hslash }}{2}\frac{J}{e}\frac{1}{M_{s}t}\mathbf{m}\times \left(\mathbf{m}\times {\mathbf{m}}_{\mathbf{ref}}\right)+{\mathit{\gamma \mu }}_0{\eta }^{\prime }\frac{\mathrm{\hslash }}{2}\frac{J}{e}\frac{1}{M_{s}t}\mathbf{m}\times {\mathbf{m}}_{\mathbf{ref}},$$E6

where $J$ is the charge flow density, $t$ is the free layer thickness, $e$ is the unit charge, and $\mathrm{\hslash }$ is the approximate Planck constant. $\mathbf{m}$ and ${\mathbf{m}}_{\mathbf{ref}}$ are the unit magnetic moments of the free and fixed layers, respectively. The first term ${\mathrm{\Gamma }}_{\mathit{STT}}^{\mathit{DL}}$ on the right side of the above equation is called damping torque-like torque, it can lead to an increase in the magnetic moment progression angle or even flip. The second term ${\mathrm{\Gamma }}_{\mathit{STT}}^{\mathit{FL}}$ on the right side is called field-like torque or out-of-plane torque, its effect is similar to that of the effective field, which causes the magnetic moment to move around the direction of ${\mathbf{m}}_{\mathit{ref}}$.

The LLG equation in which SOT is included can be expressed as [18]:

$$\frac{d\mathbf{m}}{\mathit{dt}}=-{\mathit{\gamma \mu }}_0\left(\mathbf{m}\times \mathbf{H}\right)+\alpha \left(\mathbf{m}\times \frac{d\mathbf{m}}{\mathit{dt}}\right)+{\mathrm{\Gamma }}_{\mathit{SOT}},$$E7

where the ${\mathrm{\Gamma }}_{\mathit{SOT}}$ can be generally expressed:

$${\mathrm{\Gamma }}_{\mathit{SOT}}={\mathrm{\Gamma }}_{\mathit{SOT}}^{\mathit{DL}}+{\mathrm{\Gamma }}_{\mathit{SOT}}^{\mathit{FL}}={\mathit{\gamma \mu }}_0{H}_{\mathit{SOT}}^{\mathit{DL}}\left(\mathbf{m}\times \left(\sigma \times \mathbf{m}\right)\right)+{\mathit{\gamma \mu }}_0{H}_{\mathit{SOT}}^{\mathit{FL}}\left(\sigma \times \mathbf{m}\right),$$E8

where $\sigma$ is the direction of spin polarization, $H_{\mathit{SOT}}^{\mathit{DL}}$ and $H_{\mathit{SOT}}^{\mathit{FL}}$ are the corresponding equivalent magnetic fields, respectively. There are two modes of precession induced by ${\mathrm{\Gamma }}_{\mathit{SOT}}$. When the easy magnetization axis of the ferromagnetic layer is the y-axis, SOT and STT have the same precession mode. When the easy magnetization axis of the ferromagnetic layer is the z-axis, the magnetization precession will reverse to the spin polarization direction within one precession period.

3.2 Nonlinear auto-oscillation theory

The behaviors of spintronic oscillators exhibit rich nonlinear dynamics and nonuniform features. To further understand these behaviors, Slavin and Tiberkevich proposed the nonlinear auto-oscillation theory [19]. According to their theory, all auto-oscillatory systems share three essential elements: (1) a resonance unit that determines the oscillation frequency; (2) dissipative units or damping that are present in all practical auto-oscillating systems; (3) and active units or energy sources that compensate for energy losses in the system and sustain the oscillations. The active unit, also known as “negative damping,” typically opposes the dissipative unit and is reflected in the precession equation like the damping term, but with the opposite sign.

The majority of auto-oscillators, regardless of their specific physical implementation, can be described by a common nonlinear oscillator model:

$$\frac{\mathrm{d}c}{\mathrm{d}t}+\mathit{i\omega }\left(p\right)c+{\mathrm{\Gamma }}_{+}\left(p\right)c+{\mathrm{\Gamma }}_{-}\left(p\right)c=f\left(t\right),$$E9

where $c$ represents the complex amplitude of the oscillation, which can be determined through measurements of the oscillation’s power ($\mathrm{p}={\left|\mathrm{c}\right|}^2$) and amplitude angle ($\varphi =arg\left(\mathrm{c}\right)$). ${\mathrm{\Gamma }}_{+}\left(p\right)$ denotes the inherent damping term of the system. The negative damping term of the system is denoted by ${\mathrm{\Gamma }}_{-}\left(p\right)$. The external term $\mathrm{f}\left(\mathrm{t}\right)$ describes the interaction of the self-oscillator with the external environment, which may include external signals and/or thermal fluctuations.

The nonlinear precession frequency, $\omega \left(\mathrm{p}\right)={\omega }_0+\mathrm{Np}$, is a fundamental aspect of the auto-oscillation of spintronic oscillators. The inherent damping term of the oscillator, ${\mathrm{\Gamma }}_{+}\left(p\right)$, is related to various parameters such as the Gilbert damping coefficient, ferromagnetic resonance frequency, and power. It causes the amplitude of the oscillation to decay over time. The power source that maintains the oscillation, ${\mathrm{\Gamma }}_{-}\left(p\right)$, is related to the power and drives current and is acted upon by the spin torque. These two damping terms can be expressed separately:

$${\mathrm{\Gamma }}_{+}\left(p\right)\approx {\mathrm{\Gamma }}_G\left(1+\mathit{Qp}\right),$$E10

$${\mathrm{\Gamma }}_{-}\left(p\right)\approx \mathit{\sigma I}\left(1-p\right),$$E11

and

$${\mathrm{\Gamma }}_G={\mathit{\alpha \omega }}_0,Q=2{\omega }_M/{\omega }_0-1,$$E12

where ${\omega }_0$ is the ferromagnetic resonance (FMR) frequency; $\sigma$ is a coefficient related to spin-polarization efficiency, spectroscopic Lande factor, Bohr magneton, the thickness of the free layer, and the area of the current-carrying region. The positive and negative damping terms are equal at the threshold for generating self-oscillation in spintronic oscillators, i.e., ${\mathrm{\Gamma }}_{+}\left(p_0\right)={\mathrm{\Gamma }}_{-}\left(p_0\right)$. At this point, the energy loss of the system is fully compensated by the energy source, resulting in a steady state.

The linewidth $\mathrm{\Delta }$H, defined as the full width at half maximum of the power spectra, is a key parameter characterizing the phase noise of spintronic nano-oscillators. Nonlinear auto-oscillation theory [19] predicts that the linewidth can be expressed as:

$$\mathrm{\Delta }H={\mathrm{\Gamma }}_{+}\frac{k_{\mathrm{B}}T}{E\left(P\right)}\left[1+{\left(\frac{\mathcal{N}}{{\mathrm{\Gamma }}_{\mathrm{eff}}}\right)}^2\right],$$E13

where $k_{\mathrm{B}}$ is the Boltzmann constant and $T$ is the temperature. ${\mathrm{\Gamma }}_{+}$ and $E\left(P\right)$ are the damping functions and time-averaged oscillation energy as a function of the power $P$, respectively. ${\mathrm{\Gamma }}_{\mathrm{eff}}$ is the effective damping. The linewidth, therefore, depends on the construction of the device, the material, and the external conditions.

4. Device structures and properties

4.1 Structures

The excitation of oscillations in STNOs or SHNOs requires a high current density, typically in the order of ${10}^6\mathrm{A}/{\mathrm{cm}}^2$ to ${10}^8\mathrm{A}/{\mathrm{cm}}^2$ [20], to counteract intrinsic damping. To achieve such high current densities, researchers aim to reduce the size of the device, which has been made possible by advances in micro−/nano-fabrication technology.

As for STNOs, four patterning geometries have been mainly developed for this purpose in Figure 5 [9]. The first experimental observation of STNOs was on a point contact structure [21], where a metal probe is in contact with the surface of the electrode layer of the device to inject current in Figure 5a. However, this structure causes damage to the sample and is not reproducible. To address these issues, researchers have developed nano-contact structures [22], which involve depositing an insulating layer on the device surface, followed by opening a circular or elliptical notch with several tens to hundreds of nanometers wide in Figure 5b [20]. While both point contact and nano-contact structures suffer from lateral spreading after current injection into the device, resulting in a lower current density. To concentrate the current to a smaller volume, a nano-pillar structure has been proposed [23], where the multilayer film is patterned into a nanoscale cylindrical structure in Figure 5c. However, the smaller size of the nano-pillar makes it more sensitive to thermal perturbations and less able to withstand high temperatures without damage, resulting in a larger microwave linewidth than that of the nano-contact devices. To overcome these limitations, a hybrid structure that combines the advantages of nano-contact and nano-pillar has been demonstrated [24]. Through complex micro-nano processing, a portion of the layer is processed into a nano-pillar, while the other layers remain unpatterned in Figure 5d, significantly reducing the current lateral diffusion effect and increasing thermal stability. The extended free layer in this structure also allows for the study of magnonic-related phenomena.

Figure 5.

Architecture of (a) point contact, (b) nano-contact, (c) nano-pillar, and (d) Hybrid STNOs.

As for SHNOs, there are also four main structures [9] in Figure 6. The structure of the three-terminal nano-pillar SHNO is shown in Figure 6a and is similar to that of the two-terminal nano-pillar STNO in that their output is carried out through SV or MTJ elements containing an oscillating free layer. The difference is that the magnetization precession of the free layer in SHNO originates from the polarized spin flow generated by the in-plane current applied to the heavy metal through SHE [10]. The three-terminal nano-pillar SHNO has a longer life because the excitation current does not pass through the output elements (SV or MTJ), so it avoids the problem of device breakdown due to high currents. The second structure is the nano-gap type [25] in Figure 6b, which uses a nano-gap (on the order of hundred nanometers) between two highly conductive poles to inject the necessary high current density into the ferromagnetic/heavy metal bilayer structure, which in turn excites a stable magnetization precession of the ferromagnetic layer. The third one is the nano-constriction type, as shown in Figure 6c. The nano-constriction type is a nano-gap type in which part of the ferromagnetic/heavy metal bilayer structure is processed to nanometer size to increase the local current density and produce a stronger SHE [11]. The fourth structure is the nano-wire type [26], as shown in Figure 6d. The nano-wire type is the previous ferromagnetic/heavy metal bilayer structure processed into nano-width lines that are connected to the electrodes at both ends. This type of device suffers from poor heating dissipation.

Figure 6.

Architecture of SHNOs. (a) Nano-pillar, (b) nano-gap, (c) nano-constriction, and (d) nano-wire.

4.2 Properties

Spintronic nano-oscillators are characterized by several key properties, including oscillation frequency, output power, and linewidth (phase noise). The frequency is determined by both external conditions, such as the magnetic field, current density, and the intrinsic properties of the ferromagnetic material, as described by nonlinear auto oscillation theory [19]. Theoretically, spintronic nano-oscillators have been predicted to oscillate at frequencies from megahertz up to terahertz region [27]. Figure 7a shows a measured power spectral density of an STNO at a fixed applied field. Its frequency is tuned by the applied field from 10 to 27 GHz in Figure 7b. This frequency can be extended further by the applied fields or currents. For example, Maehara et al. has experimentally realized microwave signals up to 45 GHz with a quality factor of 1230 on a hybrid STNO [24]. Additionally, the injected current can enable frequency modulation [28]. Bonetti et al. observed current modulation of frequencies up to 300 to 400 MHz/mA in a nano-contact type STNO [29]. Typically, ferromagnetic materials have precession frequencies in the tens of gigahertz range, while ferrimagnetic and antiferromagnetic materials can reach hundreds of gigahertz due to the strong exchange coupling fields.

Figure 7.

An example of measured (a) spectrum at a field of 0.6 T, and (b) power spectral density (PSD) as a function of magnetic fields of an STNO.

The output power of STNOs is primarily determined by the device’s magnetoresistance and the injected current. Although increasing the injected current can boost the output power by enhancing the precession amplitudes, excessively high current levels can result in significant thermal losses. Therefore, increasing magnetoresistance offers a more effective means of enhancing power. Compared to SV-based STNOs, MTJ-based oscillators exhibit higher magnetoresistance, up to 1000% [30, 31]. By adjusting the free layer FeB thickness, Tsunegi et al. achieved a microwave emission power of $3.6\mu \mathrm{W}$ and a quality factor of up to 6400 in an MTJ-type STNO [32]. Moreover, exciting specific magnetodynamics can also result in increased power output. For example, Tsunegi et al. generated output powers of up to $10.1\mu \mathrm{W}$ by exciting magnetic vortex precession, albeit at the cost of a frequency below 2 GHz [33]. Another effective strategy for enhancing output power is to achieve synchronized oscillation of multiple oscillators (discussed in the next section).

The output power of SHNOs is mainly determined by MR (mostly AMR). The MR of SHNOs is commonly small, so the power is usually at the pW level. While the linewidth of SHNOs can reach MHz or even KHz, which is the same order of magnitude as STNOs. In addition, although the magnetoresistance variation rate of AMR is low, the total output power of SHNO can reach 54 pW through the synchronization of SHNOs, which is comparable to GMR devices, but still much smaller than TMR devices [12].

5. Synchronization phenomenon

The synchronization of spintronic oscillators is a state in that multiple oscillators are interacting with each other and oscillate at the same frequency. In 2005, the National Institute of Standards and Technology (NIST) experimentally demonstrated frequency locking in STNOs for the first time [34]. Frequency locking here can be understood as the synchronization (resonance) behavior between two alternating current (AC) signals or electromagnetic waves. The phase-locked synchronization technique can be applied to spintronic nano-oscillators to improve the microwave output performance of spintronic nano-oscillators, including boosting the output power of the spintronic nano-oscillator regime and reducing the linewidth of the microwave output signal.

5.1 Synchronization of STNOs

Depending on the source of the reference AC signal, the methods to achieve spintronic nano-oscillators’ synchronization are mainly classified as magnetic coupling, electrical coupling, current-based injection locking, and field-based injection locking [35].

When the spacing of two STNOs is very close (nanometer level) and the magnetic moment precession frequency is approximate, the frequencies of two STNOs will be synchronized and have little influence by external conditions in a certain range. Figure 8a shows the schematic diagram of two magnetic coupled STNOs. The current through STNO1 is kept constant, the magnetic moment precession frequency of STNO1 is held constant as the reference frequency, and when the current of STNO2 changes, the magnetic moment precession frequency changes, and when the frequency of STNO2 is close to the frequency of STNO1, the frequency of STNO2 will be locked to the frequency of STNO1 and will be maintained within a certain range. This synchronous state is maintained. This locking does not require any external signal. The schematic diagram of two electrically coupled STNOs is shown in Figure 8b. The outputs of the two STNOs are converted into currents by an additional circuit that converts the voltages of both outputs into currents, which are used as feedback signals to regulate the input currents of the two STNOs so that their magnetic moment oscillation frequencies are close to synchronization.

Figure 8.

Schematics of (a) two magnetic coupled, and (b) two electrical coupled STNOs.

In the current-induced injection locking structure, the AC and direct current (DC) pass through an STNO simultaneously. As shown in Figure 9a, frequency synchronization can occur when the frequency of the STNO is close to the frequency of the AC signal. It has been demonstrated that the locking range of the current injection locking structure is positively correlated with the peak-to-peak of the input AC signal. In field-induced injection locking, the frequency of an STNO is locked in an externally oscillating RF field, as shown in Figure 9b. A wire parallel to the membrane surface is added in the vicinity of the STNO and an RF current is passed through the wire to generate the RF field that locks the STNO. Similar to current injection locking, the magnetic field injection locking structure can increase the locking range by increasing the signal strength of the RF.

Figure 9.

Schematics of (a) current-induced injection locking, and (b) field-induced injection locking.

5.2 Synchronization of SHNOs

Similar to STNOs, the synchronization phenomenon can also be achieved when a DC and a microwave signal with frequency f are simultaneously input in an SHNO. As shown in Figure 10a, when the frequency of the microwave current is close to that of the auto-oscillation, synchronization happens [36].

Figure 10.

Structures of SHNOs synchronization. (a) External microwave signals, (b) serial SHNO, (c) SHNO array, and (d) memristive control.

By connecting multiple SHNOs in series with each SHNO spaced at a certain distance, the phenomenon of synchronization of SHNOs with each other can be observed in a certain range, as shown in Figure 10b. This synchronization phenomenon depends on the magnitude of the driving current. When the driving current is low, each individual SHNO generates a separate microwave signal, and as the driving current increases, the interaction between SHNOs increases, expanding from partial regional synchronization to full synchronization of individual SHNO [12].

Localized regions of magnetic films and nanostructure are driven into a self-oscillating process using pure spin currents. By placing SHNOs close to each other to form arrays, they can interact with each other and achieve synchronization [37]. Figure 10c shows the structure of the synchronized $4\times 4$ array of SHNOs.

The magnetization kinetics of the PMA and thus the SHNO can be influenced by the applied voltage, so the frequency synchronization between the SHNOs and the SHNO can be directly adjusted by the applied voltage. In addition, the gate exhibits the amnestic resistor characteristic, and the synchronization state can be achieved and regulated by driving the SHNO by the electric field and current in the high-resistance and low-resistance states [13], respectively, as shown in Figure 10d.

6. Applications

With their ultra-wide frequency modulation range, low power consumption, nanoscale footprint, rich nonlinear dynamics, synchronization capabilities, and high compatibility with mainstream CMOS processes, spintronic nano-oscillators have great potential for applications in frontier areas such as wireless communication, assisted magnetic recording, and neuromorphic computing.

Spintronic nano-oscillators generate high-quality microwave signals spanning megahertz to terahertz frequencies, making them ideal microwave sources for wireless communication systems. Spintronic nano-oscillators have been applied in various wireless communication schemes, including frequency shift keying (FSK) [38], amplitude shift keying (ASK) [39], and on-off keying (OOK) [40]. Figure 11a shows a typical STNO-based wireless communication system comprising two STNOs—one performing keying modulation at the transmitter and the other responsible for signal demodulation at the receiver. With their low linewidth and ultra-fast response, spintronic nano-oscillator-based wireless communication systems can achieve data rates of up to 400 Mbps [42]. Additionally, the compatibility of spintronic nano-oscillators with mainstream CMOS processes further facilitates their integration and applicability in wireless communication technologies.

Figure 11.

Schematics of (a) spintronic nano-oscillator based transceiver, (b) microwave-assisted magnetic recording structures, and (c) four spintronic nano-oscillator-coupled neural networks [41].

Magnetic recording technology relies on switching the magnetic moment, but high writing fields limit storage density improvements. To address this challenge, researchers have proposed microwave-assisted magnetic recording [43]. This technique utilizes spintronic nano-oscillators to generate an alternating magnetic field, injecting energy into the storage cell. Consequently, the magnetic moment enters a sub-stable state, enabling complete switching with a small external magnetic field. Figure 11b illustrates the structure of a magnetic head embedded with a spintronic nano-oscillator positioned between the writing pole and the trailing shield. Studies indicate that increasing the thickness (t) of the spintronic nano-oscillator film layer enhances the microwave magnetic field strength, facilitating assisted magnetic flipping. Conversely, widening (w) the spintronic nano-oscillator reduces storage density. Reducing the distance (d) between the spintronic nano-oscillator and the storage medium increases the microwave magnetic field strength. Additionally, the relative position ($\mathrm{\Delta }$y) of the spintronic nano-oscillator to the writing pole affects the write signal-to-noise ratio of microwave-assisted magnetic recording. Several specific studies have investigated and validated these effects [44, 45, 46].

The rich nonlinear dynamics and synchronization of spintronic nano-oscillators offer significant advantages and promising potential for neuromorphic computing. Researchers have explored the application of coupled spintronic nano-oscillators in various neuromorphic computing tasks, such as image edge detection, association computation, convolution computation, and speech recognition. For instance, Yogendra et al. utilized coupled spintronic nano-oscillators as building blocks to implement image edge detection, association computation, and convolution computation [35]. Their approach demonstrated higher computational efficiency compared to the traditional von Neumann model. Furthermore, Romera et al. designed a neural network consisting of four spintronic nano-oscillator couplings in Figure 11c for speech vowel recognition, achieving a remarkable success rate of 89% [41]. These studies, combined with the long lifetime and low energy consumption of spintronic nano-oscillators, pave the way for the development of neuromorphic computing systems based on oscillator networks. Recently, spintronic nano-oscillators have proved their capability of working as Ising machines [47, 48]. In 2022, Houshang et al. reported an array of SHNOs can solve several max-cut problems [48].

In the field of magneto dynamic studies, these nano-oscillators enable detailed investigations of dynamic magnetic phenomena at the nanoscale [49, 50]. Spintronic nano-oscillators have shown potential as reliable sources for generating true random numbers [51], addressing the growing need for secure and unpredictable data in various applications. Their unique nonlinear dynamics make them highly suitable for logic devices, Ising machines, and other computational paradigms [47].

7. Conclusions

State-of-the-art spintronic nano-oscillator technology features extremely wide tunability, very compact size, ultra-wide frequency range, ultra-fast switching speed, and compatibility with the CMOS process. Most importantly, the spintronic nano-oscillator technology is compatible with CMOS processes, making it easy to commercialize. The spintronic nano-oscillator is therefore expected to play an important role in microwave communication, magnetic field detection, magnetic recording technology, and brain-like computing.

Despite recent advances, some fundamental features of spintronic nano-oscillators, such as microwave signal output power and linewidth, remain unsatisfactory. It is highly desired to improve the phase noise and the emission power, which may be achieved by synchronization of large-scale oscillators with MTJ-based oscillators, or discovering high MR materials and novel structures. We believe that more attention should be paid to the continuous development of spintronics oscillators.

Acknowledgments

The authors gratefully acknowledge the financial support from the Natural Science Foundation of China (Grant 621044196) and Basic Research Programs of Taicang (Grant TC2021JC19) and Natural Science Foundation of Chongqing (Grant 2022NSCQ-MSX4891).