Enhancing the Thermal Stability of Skyrmion in Magnetic Nanowires for Nanoscale Data Storage

Abstract

Magnetic skyrmion random switching and structural stability are critical limitations for storage data applications. Enhancing skyrmions’ magnetic properties could improve their thermal structural stability. Hence, micromagnetic calculation was carried out to explore the thermal nucleation and stability of skyrmions in magnetic nanodevices. Different magnetic properties such as uniaxial magnetic anisotropy energy (Ku), saturation magnetization (Ms) and Dzyaloshinskii—Moriya interaction (DMI) were used to assess the thermal stability of skyrmions in magnetic nanowires. For some values of Ms and Ku, the results verified that the skyrmion structure is stable at temperatures above 800 K, which is higher than room temperature. Additionally, manipulating the nanowire geometry was found to have a substantial effect on the thermal structural stability of the skyrmion in storage nanodevices. Increasing the nanowire dimensions, such as length or width, enhanced skyrmions’ structural stability against temperature fluctuations in nanodevices. Furthermore, the random nucleation of the skyrmions due to the device temperature was examined. It was shown that random skyrmion nucleation occurs at temperature values greater than 700 K. These findings make skyrmion devices suitable for storage applications.

1. Introduction

Researchers have shown significant interest in magnetic skyrmions within nanostructures due to their unique properties and potential applications in various advanced technologies [1,2]. Skyrmions are stable, topologically protected spin configurations that can exist in certain magnetic materials [3,4]. They are typically on the nanometer scale, making them highly relevant for nanotechnology applications and future electronic devices [5]. Additionally, skyrmions can be used to represent bits of data [6]. Due to their small size, they offer the possibility of extremely high-density data storage [7]. Driving magnetic skyrmions using a magnetic field is an area of active research due to its potential applications in data storage, logic devices and other spintronic technologies [8,9,10]. The manipulation of skyrmions with a magnetic field involves understanding their creation, movement and annihilation within magnetic materials [11,12,13]. Another way of driving magnetic skyrmions is through spin transfer torque (STT). STT is a phenomenon where the spin angular momentum from a spin-polarized current is transferred to the local magnetic moments in a material, causing them to move [14,15,16]. This mechanism can be used to manipulate magnetic skyrmions, which are topologically protected spin structures [17,18,19]. Driving skyrmions either by a magnetic field or spin transfer torque makes skyrmions a good candidate to have the potential to serve as magnetic bits in racetrack memory, offering advantages in terms of high density, speed and energy efficiency [20,21,22,23,24]. However, in magnetic nanowires, skyrmion racetrack memory faces stability challenges due to the used magnetic field, spin transfer torque, wire defects and device temperature [25,26,27]. Additionally, the skyrmion should be pinned at specific positions within the nanowire, such as at notches [28,29,30,31], constricted areas [32,33] and magnetic defects [34,35] to construct the magnetic nanowires as memory storage. Thus, understanding the effects of various parameters on the structural stability of skyrmions at the pinning sites is essential for applications. Most research has focused on examining the impact of pinning site geometry on skyrmion stability [36,37,38,39,40,41]. However, other influenced parameters, such as device temperature, have not been extensively considered as significant factors affecting skyrmion stability defects [42]. As skyrmion-based storage devices become smaller in nanoscale and more sensitive to temperature, the skyrmion’s structural stability due to the device temperature is essential in skyrmion storage data applications. While skyrmion structures have been found to be stable at low temperatures [43,44]. The novelty of this study lies in investigating the effect of magnetic properties on the thermal stability of skyrmions. Accordingly, this work focuses on the influence of device temperature on skyrmion structural stability in planar nanowires with nanoscale dimensions, as well as the effects of enhanced magnetic properties on skyrmion thermal structural stability. The thermal stability of the skyrmion was evaluated by modifying various magnetic properties, including magnetization (Ms) and uniaxial magnetic anisotropy energy (Ku). Additionally, the effect of nanowire geometry on the switching of skyrmions’ thermal stability was studied.

2. Theoretical Model

In this study, the calculations were performed by solving the Landau–Lifshitz–Gilbert (LLG) Equation (1):

$${\displaystyle \frac{d\mathit{m}}{dt}}=-\gamma \mathit{m} \times ({\mathit{H}}_{eff}+{\mathit{H}}_{th})+\alpha \mathit{m} \times {\displaystyle \frac{d\mathit{m}}{dt}}$$

(1)

In the equation, $\mathit{m}$ represents the magnetization unit vector, $\gamma$ denotes the electron gyromagnetic ratio, $\alpha$ stands for the dimensionless damping parameter, ${\mathit{H}}_{eff}$signifies the effective field and ${\mathit{H}}_{th}$ refers to the thermal field. The relationship between the device temperature (T) and the thermal field (Hth) is defined by Equation (2):

$$\langle {\mathit{H}}_{th,i}\left(\overrightarrow{r,}t\right),{\mathit{H}}_{th,j}(\overrightarrow{\stackrel{\prime }{r}},\stackrel{\prime }{t}\rangle ={\displaystyle \frac{2\alpha k_{B}T}{\gamma {\mu }_0{M}_{s}V}}{\delta }_{ij}\delta (\overrightarrow{r}-\overrightarrow{\stackrel{\prime }{r}}\left)\delta \right(t-\stackrel{\prime }{t})$$

(2)

In this equation, $T$ represents the device temperature, $k_B$stands for the Boltzmann constant, ${\mu }_0$ denotes the permeability and $V$ indicates the computational cell volume. The simulations were performed using the Object Oriented Micromagnetic Framework (OOMMF) [45]. The initial state is shown as the blue region, where the magnetic moments are oriented towards the negative z-direction (m_z = −1), while within the skyrmion (red region), the magnetization points upwards (m_z = +1), as illustrated in Figure 1a, at device temperature of 0 K. Figure 1b illustrates the magnetization fluctuations of both the device and the skyrmion at a device temperature of 100 K. The study considers magnetic nanowires with dimensions of length (L), width (w) and thickness (th), specified as (200$\mathrm{n}\mathrm{m} \times 40\mathrm{n}\mathrm{m} \times 3\mathrm{n}\mathrm{m})$. The radius of the skyrmion (r) is 50 nm.

The spin order and specific configuration that result in a stable skyrmion within a magnetic nanowire (Figure 1a) are determined by the total magnetic free energy density, which is a combination of several energy contributions: exchange energy, Dzyaloshinskii–Moriya interaction (DMI), anisotropy energy, Zeeman energy and magnetostatic energy. The total skyrmion magnetic free energy density can be expressed as follows:

$$E=A{(\nabla M)}^2+D\left(M.\left(\nabla \times M\right)\right)+K_u{sin}^2\theta -{\mu }_{0}M.H-{\displaystyle \frac{1}{2}}{\mu }_{0}M.H_d$$

(3)

where $A$ is the exchange stiffness constant, $M$ is the magnetization vector, D is the DMI constant, K_u represents the uniaxial anisotropy constant and${\mu }_0$ is the permeability of free space [46,47,48]. However, as the device temperature increases, the spins experience more random orientation, leading to higher spin disorder and skyrmion collapse, as shown in Figure 1b [49].

3. Results and Discussion

The steady motion of the skyrmion is described by the Thiele equation:

$$\mathit{G} \times \left({\mathit{v}}^{\left(\mathit{s}\right)}-{\mathit{v}}^{\left(\mathit{d}\right)}\right)+D\left(\beta {\mathit{v}}^{\left(\mathit{s}\right)}-{\alpha \mathit{v}}^{\left(\mathit{d}\right)}\right)+\nabla \mathrm{V}\left(\mathbf{r}\right)$$

(4)

where ${\mathit{v}}^{\left(\mathit{d}\right)}$ is the drift velocity, ${\mathit{v}}^{\left(\mathit{s}\right)}$ is the velocity induced by the spin-polarized current, $\mathit{G}$ is the gyromagnetic coupling vector, $D$ represents the dissipative force and $\mathrm{V}\left(\mathbf{r}\right)$ is the confining potential induced by the sample edges [50]. The gyro-term originates from the Berry phase and causes a moving skyrmion to be deflected perpendicular to its direction of motion. However, the stability of skyrmion motion in magnetic nanowires is a crucial aspect for potential applications in spintronics and memory storage devices. Skyrmions, which are topologically stable spin textures, exhibit robust dynamic behavior when subjected to external forces such as electric currents, magnetic fields and thermal gradients. The stability of their motion is influenced by several factors, including material properties, geometric constraints and external perturbations.

Thus, the main objective of this study is to enhance skyrmion thermal stability and nucleation in magnetic nanodevices based on device temperature. The structural stability of skyrmions is first investigated by driving them to the end of a nanowire at different current densities under a simulated temperature of 0 K. It was observed that at 0 K, no change in the skyrmion diameter occurred as it moved to the end of the nanowire, as shown in Figure 2a,b.

To further confirm the skyrmions’ structural stability during their dynamics in the magnetic nanowire, a normalized magnetization component in the z-direction (m_z) was plotted as a function of time for two current density values, as shown in Figure 2c. However, as shown in Figure 3a, once the device temperature reached 150 K, the magnetization fluctuated slightly along the z-axis. Due to these magnetization fluctuations, the skyrmion lost its stability, gradually shrinking in size over time until it completely annihilated after 4 ns, as shown in Figure 3b–e.

Investigating skyrmion propagation in nanowires is essential for developing skyrmion-based devices with applications in information storage, computing and spintronic technologies. Hence, the thermal stability of skyrmions during their propagation in nanodevices was examined under different current density values. This study examines two skyrmions with radii of 30 nm and 50 nm across various device temperatures. It was found that the relationship between skyrmion annihilation temperature and driven current density is nearly linear as shown in Figure 4a. At certain device temperature and current density values, the skyrmion reached the end nanowire with high structural stability. For example, Figure 4b,c show the propagation of the skyrmion (r = 30 nm) under $J=1.2 \times {10}^{12} \mathrm{A}{\mathrm{m}}^{-2}$ at a device temperature of 100 K. However, when the device temperature was raised to 150 K, the skyrmion, driven by the same value of current density, lost its stability and annihilated before reaching the edge of the nanowire, as shown in Figure 4d.

There are different ways to enhance the thermal stability of the skyrmion, either by developing magnetic properties such as Ms and Ku or by manipulating the skyrmion and device dimensions. Therefore, the stability time of the skyrmion was investigated as a function of device temperature for three values of Ku (Figure 5a) and Ms (Figure 5b). Figure 5a shows that the stability time of the skyrmion decreases as the device temperature increases. For example, with a Ku value of $0.5 \times {10}^5 \mathrm{J}{\mathrm{m}}^{-3}$, the skyrmion was stable for 5 ns under a device’s temperature of 80 K, while at a device’s temperature of 20 K, it remained for 13 ns. The stability time shows a similar trend with Ku, as the skyrmions’ stability time increases with increasing Ku. For instance, at a device temperature of 50 K, the graph indicates that the skyrmion stability time was around 9 ns with Ku of $0.5 \times {10}^5 \mathrm{J}{\mathrm{m}}^{-3}$, while it was 20 ns with a Ku value of $1.5 \times {10}^5 \mathrm{J}{\mathrm{m}}^{-3}$.

Similarly, the skyrmion stability time increased as Ms was increased, as shown in Figure 5b. For example, at a device temperature of 30 K, the stability time was 11 ns with$Ms=1.5 \times {10}^6 \mathrm{A}{\mathrm{m}}^{-1}$, whereas it increased to 19 ns with $Ms=2.5 \times {10}^6 \mathrm{A}{\mathrm{m}}^{-1}$. The increase in the skyrmion’s structural stability by increasing Ms is attributed to an increase in exchange energy [31].

To enhance the structural stability time of the skyrmion at temperatures higher than room temperature, the skyrmion annihilation temperature was investigated by developing magnetic properties. Figure 6a shows the skyrmion annihilation temperature versus Ms for two values of skyrmion radii (r). For Ms values greater than 3.5 × 10⁶ $\mathrm{A}{\mathrm{m}}^{-1}$, the skyrmion was found to be more stable at room temperature and above. It was observed that for certain Ms values, skyrmions remain stable at temperatures up to 750 K with a skyrmion radius of 50 nm and up to 480 K with a radius of 30 nm, which is significant for storage applications. Similar results were found when increasing Ku; for Ku values greater than $6.5 \times {10}^5 \mathrm{J}{\mathrm{m}}^{-3}$, skyrmions remained stable at device temperature up to 400 K and 800 K with r = 30 nm and 50 nm, as shown in Figure 6b.

The effect of DMI interaction energy on the skyrmion’s thermal stability was investigated. It was found that the skyrmion structure becomes more stable against device temperature by increasing DMI energy. For example, at a device temperature of 100 K, the skyrmion stability time increased from 4 ns with a DMI value of 0.2 mJm⁻² to around 14 ns with a DMI value of 9 mJm⁻². Similar improvements in the skyrmions’ structural stability were observed at device temperatures of 200 K and 300 K, at which DMI values increased. Figure 7 shows the skyrmion stability time as a function of DMI for three different device temperatures.

Furthermore, skyrmion stability time against device temperature can be adjusted by manipulating device dimensions, such as length (L), width (w) and thickness (th). This study examined the relationship between skyrmion thermal stability time and w over a range of temperatures (100 K, 200 K and 300 K). The results showed that the relation between thermal stability time and w is nearly linear, as illustrated in Figure 8a. Skyrmion stability improves with increasing device width. Thermal skyrmion stability is also influenced by the nanowire length, an inherent aspect of device geometry. Therefore, nanodevices with different L values were analyzed, demonstrating significant stability, as shown in Figure 8b. These results indicate that the skyrmion thermal stability time increases linearly with device length.

The effect of device thickness (th) on skyrmion thermal stability was examined at two temperatures (100 K and 300 K). It was found that the skyrmion stability time exponentially increased for both temperatures, as shown in Figure 9a, which shows the dependence of skyrmion stability time ($t$) against device thickness (th) for the range temperatures of the device. This dependence can be described by an exponential relationship:

$$t=t_0+A{e}^{th/\rho }$$

(5)

Here, ($th$) represents the device thickness in the x-direction, while $\mathit{\rho }$ and A are fitting parameters. The values of ρ and A at both temperature values are shown in

Table 1. Parameters for fitting derived from the exponential growth function of skyrmion time stability time against th for two device temperatures, as illustrated in Figure 9.

$\mathit{T} \mathbf{\left(}\mathbf{K}\mathbf{\right)}$	${\mathit{t}}_{\mathbf{0}}$ (s)	A (s)	$\mathit{\rho }$ (nm)
100	1.11$\pm 0.05$	0.10$\pm 0.03$	9.48$\pm 0.96$
300	0.87$\pm 0.04$	0.07$\pm 0.02$	$8.63\pm 0.82$

.

Another part of this study focused on random skyrmion switching under varying device temperatures. Device failure can be attributed to random skyrmion generation caused by temperature changes. Accordingly, this study examined how device temperature affects skyrmion generation in nanoscale nanowires., as shown in Figure 10a. The thermal nucleation of skyrmions was investigated by varying saturation magnetization (Ms) under different values of current densities, as shown in Figure 10b. In Figure 10b, the nucleation temperature of a skyrmion increased sharply with an increasing Ms value in the range of 1.5 × 10⁶ Am⁻¹ ≤ Ms ≤ 3.5 × 10⁶ Am⁻¹, while remaining nearly constant for Ms values exceeding 3.5 × 10⁶ Am⁻¹. The graph indicates that random skyrmion thermal switching occurs at temperature above 700 K suggesting that skyrmions are promising candidates for storage applications at elevated temperatures.

In addition, decreasing nanowire dimensions, such as the width, decreases skyrmion thermal switching due to an increase in shape anisotropy energy. It was found that no skyrmion thermal nucleation occurred at device temperatures greater than 900 K for Ms values of $\ge 2.5 \times {10}^6 \mathrm{A}{\mathrm{m}}^{-1}$.

4. Conclusions

To conclude, this study examined how magnetic properties and device dimensions can be used to control the thermal structural stability of skyrmion. By improving magnetic properties of magnetic materials such as Ms and Ku, it is possible to control the thermal structural stability the skyrmion in magnetic nanowires. The results showed that skyrmion thermal stability increased by increasing Ms and Ku values. At temperatures around 800 K, skyrmions were found to be stable with certain magnetic material properties. making the skyrmion structure more stable above room temperature. Consequently, this has the potential to extend the lifetime of device memory. Additionally, manipulating nanowire dimensions such as length, width and thickness contributed to increased skyrmion thermal structural stability. For some nanodevice dimensions, the skyrmion structure remained stable up to 900 K. Simulations also indicated that increasing device thickness reduces skyrmion magnetization switching. These findings may support the further development of skyrmion thermal stability in nanodevices.