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Thermally induced creation and annihilation of a single skyrmion. (a) Triangular spin lattice with a hexagonal boundary shape containing a single skyrmion at kBT=0.05 J and μB=0.1 J. (b) The inset displays the DM energy as a function of the Monte Carlo step (MCS) for different magnetic field strengths at kBT=0.61 J exhibiting a two-state behaviour due to the ongoing creation and annihilation of a single skyrmion. The size of the system is such that it contains a maximum of one skyrmion at a given MCS. The histogram of the DM energy shows two peaks corresponding to the FM and Sk states. The Sk and FM states are populated with equal probability at the critical field Bc and the areas underneath the peaks of the histogram are equal.
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The switching between topologically distinct skyrmionic and ferromagnetic states has been proposed as a bit operation for information storage. While long lifetimes of the bits are required for data storage devices, the lifetimes of skyrmions have not been addressed so far. Here we show by means of atomistic Monte Carlo simulations that the field-de...
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Magnetic skyrmions are intensively explored for potential applications in ultralow-energy data storage and computing. To create practical skyrmionic memory devices, it is necessary to electrically create and manipulate these topologically protected information carriers in thin films, thus realizing both writing and addressing functions. Although ro...
Citations
... The switching between skyrmionic and non-topological states is well established as a promising bit operation for information transport and storage [37]. Understanding the temperature, thickness, and field dependence of the nucleation and collapse processes of magnetic skyrmions is therefore crucial to the development of novel tech-nological applications. ...
While the transition between skyrmionic and non-topological states has been widely explored as a bit operation for information transport and storage in spintronic devices, the ultrafast dynamics of such transitions remains challenging to observe and understand. Here, we utilize spin-dynamics simulations and harmonic transition state theory (HTST) to provide an in-depth analysis of the nucleation of skyrmionic states in helimagnets. We reveal a persistent blinking (creation-annihilation) phenomenon of these topological states under specific conditions near the phase boundary between skyrmion and conical states. Through a minimum-energy path analysis, we elucidate that this blinking behavior is favored by the formation of chiral bobber (CB) surface states and that the collapse of CBs differs from that of skyrmions in thin films due to their different oscillation modes. We further employ HTST to estimate the typical blinking time as a function of the applied magnetic field and temperature. Finally, we illustrate the practical use of skyrmion blinking for controlled probabilistic computing, exemplified by a skyrmion-based random-number generator.
... Skyrmions stable at room temperature was found in ultrathin Pt/Co/MgO nanostructures [9]. Stability of Sk in Fe monolayer on an Ir(111) substrate was demonstrated in [10], and is theoretically predicted in [11,12]. Creation of Sk can be achieved by several means, among which local heating using laser irradiation [13], applying local magnetic field [14] or by injection of current [15,16]. ...
... The summation i, j in (1) runs over all pairs of nearest neighbor atoms. We studied Neel-type skyrmions on triangular lattice with the lattice constant a = 2.7Å and parameters K = 0.49 meV, |D ij | = 2.24 meV, J = 7 meV, µ = 3µ B , which corresponds to the Pd/Fe bilayer on the Ir(111) substrate [12]. This system maintains skyrmions of radius 3.95a, defined as distance from skyrmion center to the ring S z = 0 . ...
Magnetic skyrmions are considered promising candidates for coding bits of information in racetrack memory devices. Information recording in such devices is assumed to occur by creating skyrmions. This work is devoted to finding solutions to make this process as energy-efficient as possible. One of the factors influencing the creation of skyrmions is the geometry of the track on which recording takes place. We study the influence of the shape and size of track boundary notches on the energy barriers of skyrmion nucleation. We show that skyrmions generation is facilitated by the presence of irregularities at the track boundary and the best solution is a deep narrow notch. On the other hand the skyrmion nucleation rate is smaller for smooth boundaries and skyrmions generation can be suppressed by their interaction with the track boundary, if notch size is smaller than the skyrmion radius. These results can be used in development of future memory devices based on skyrmions.
... Magnetic skyrmions, as shown in Fig. 1, are topologically protected nanoscale spin solitions [1][2][3][4][5][6][7]. Skyrmions have many good properties including low threshold current and high mobility, which suggests a promising future for skyrmions in information storage and processing [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. However, due to their nonzero topological charge, skyrmions experience topology-dependent Magnus forces that occur under certain external stimulus; for instance, spin-polarized currents may lead to the deflection of a skyrmion during its motion. ...
... The stability of skyrmioniums is essential for the applications of skyrmioniums as a nonvolatile information carrier and as a sensor in spintronic information storage and processing devices [34,[36][37][38][39][40][41][42][43][44][45][46]. With the assistance of thermal noise, topologically protected nanoscale magnetic structures like skyrmions and skyrmioniums can generate, evolve in Brownian particlelike dynamics driven by thermal fluctuations, respond to external stimulus like spin waves, and annihilate through topological transition under various conditions [8][9][10][11][12][13][14]26,[50][51][52][53][54][55][56][57][58][59][60][61][62]. Especially, the stability of skyrmioniums has been studied through the geodesic nudged elastic band (GNEB) method based atomic spin simulation and extension of harmonic transition state theory of skyrmions [26,50,59]. ...
... where C 2 = A 2 1−2AB and D = A 1−2AB are defined forconvenience. Note that Eq. (14) only applies to the case with D > 0, or with L limited so some integrals remain convergent: ...
Skyrmioniums are doughnutlike topological spin textures in chiral magnets, which are able to move with zero skyrmion Hall effect. The annihilation of a skyrmionium involves the topological transition through singularity formation at the continuum level. Here we analytically and numerically study a type of thermal annihilation of a skyrmionium under the framework of micromagnetism. The skyrmionium initially exists in an ultrathin ferromagnetic film in the exchange-dominated regime and is stabilized under a uniform perpendicular magnetic field. The thermal annihilation of the “skyrmion” inside the skyrmionium results in the transformation of the skyrmionium to a skyrmion. We derive an analytical formula in the Arrhenius form describing the annihilation rate of this process. We find that the analytical solutions agree well with the micromagnetic simulation results. Besides, from the large deviation point of view, we derive the dynamical path for the collapse of a skyrmionium. Our results are useful for understanding the thermal stability of skyrmioniums and may lead to spintronic applications based on the thermal manipulation of skyrmioniums.
... Spin textures such as skyrmions are classified by their nonzero topological charge Q ¼ 1=4π RR mð ∂m ∂x ∂m ∂y Þd 2 r 1,2 , where m is the magnetization unit vector. According to a topological viewpoint, a continuous transformation between topologically distinct spin textures with different Q values is not allowed; thus, spin textures with Q ≠ 0 have high stability in magnetic medium despite their small size [3][4][5][6] . Due to the topology-associated intriguing physical behaviors and unique features of spin textures with Q ≠ 0, such as skyrmion Hall effects 7,8 and topological protection [3][4][5][6] , the topological transition from topologically trivial spin textures (Q = 0) to non-trivial textures (Q ≠ 0) has not only attracted significant scientific interest but also been considered important in the development of advanced spin-based electronic devices such as memory, logic, and bioinspired computing devices [9][10][11][12] . ...
... According to a topological viewpoint, a continuous transformation between topologically distinct spin textures with different Q values is not allowed; thus, spin textures with Q ≠ 0 have high stability in magnetic medium despite their small size [3][4][5][6] . Due to the topology-associated intriguing physical behaviors and unique features of spin textures with Q ≠ 0, such as skyrmion Hall effects 7,8 and topological protection [3][4][5][6] , the topological transition from topologically trivial spin textures (Q = 0) to non-trivial textures (Q ≠ 0) has not only attracted significant scientific interest but also been considered important in the development of advanced spin-based electronic devices such as memory, logic, and bioinspired computing devices [9][10][11][12] . ...
Revolutionising Electronics: Controlling Magnetic Monopole Injection in Spin Textures
In the nanomagnetism realm, scientists are intrigued by minuscule magnetic formations known as spin textures, possessing unique characteristics that could transform electronic devices. However, there’s a knowledge gap in controlling these structures’ transformation, especially creating stable formations called skyrmions. In a recent study, Mi-Young Im and team devised a technique to control the injection of a magnetic monopole a crucial step in forming skyrmions, in a ferrimagnetic multilayer film. They performed experiments and simulations demonstrating that a slight in-plane magnetic field can focus energy favoring MP injection, leading to skyrmion formation. The results indicated that the controlled injection of MPs is vital for the topological transition from stripe domains to skyrmions. The study concludes that the strength of the in-plane magnetic field is a critical factor in this process, offering a new method to manipulate magnetic structures for advanced technologies. This summary was initially drafted using artificial intelligence, then revised and fact-checked by the author.
... Therefore, it is significant to study the nucleation and stability of vortexantivortex pairs [25], which defines the dynamic of magnetic structures. However, the research on the nucleation and stability is mainly focused on the topological magnetic textures, such as skyrmions [32,33]. Moreover, very short time scale characteristic to evolution of magnetic structures complicates considerably the possibility of experimental observation [6]. ...
Vortex-antivortex pairs have shown great potential in spintronics, where they can be used for information storage and logical devices. However, the physical mechanism for the nucleation of vortex-antivortex pairs is still unclear due to its metastability. We report on spontaneous nucleation of vortex-antivortex pairs in patterned Fe20Ni80 films (circular, square, hexagonal islands). By using a complex approach involving micromagnetic simulations, more in-depth understanding of vortex pair nucleation was achieved. A large amount of vortex-antivortex pairs appear in the as-grown magnetic film, which is the unstable high-energy state. Then, vortex and antivortex moves towards each other and annihilate, transforming magnetic structures and lowering the total energy of the system. With the decrease of sizes of microstructures, isolated vortex becomes stabilized due to confinement effect. These results provide a physical view for the nucleation of vortex-antivortex pairs and may be useful for design and optimization of magnetic microstructures for future spintronic applications.
... 32 The stability of a skyrmion to thermal fluctuations capable of kicking it out of a metastable state has been studied by several authors. [33][34][35][36][37][38][39][40][41][42] Similar effect due to quantum fluctuations 43 has been investigated as well. [44][45][46] These works addressed the lifetime of a skyrmion in a metastable state but did not study its evolution in time after it goes over or under the energy barrier. ...
Contraction and expansion of skyrmions in ferromagnetic films are investigated. In centrosymmetric systems, the dynamics of a collapsing skyrmion is driven by dissipation. The collapse time has a minimum on the damping constant. In systems with broken inversion symmetry, the evolution of skyrmions toward equilibrium size is driven by the Dzyaloshinskii–Moriya interaction. Expressions describing the time dependence of the skyrmion size are derived and their implications for skyrmion-based information processing are discussed.
... As presented in Fig. 1f, we find that the skyrmion annihilation energy barrier ΔE Sk→FM is significantly larger than that for antiskyrmions, ΔE Ask→FM , for all magnetic fields. Surprisingly, the antiskyrmion barrier of about 150 meV at B ¼ 0 T is of the same order of magnitude as the barrier for the skyrmion collapse reported for Pd/Fe/Ir(111) 43 , a well-studied system for which experiment 4,12,51,53,58 and first-principles based theory 43,50,53,59 are in good agreement. This suggests that antiskyrmions in Rh/Co/ Ir(111) could possess a similar stability as that observed for skyrmions in Pd/Fe/Ir(111) at low temperatures 4,12,51,53,58 . ...
... Surprisingly, the antiskyrmion barrier of about 150 meV at B ¼ 0 T is of the same order of magnitude as the barrier for the skyrmion collapse reported for Pd/Fe/Ir(111) 43 , a well-studied system for which experiment 4,12,51,53,58 and first-principles based theory 43,50,53,59 are in good agreement. This suggests that antiskyrmions in Rh/Co/ Ir(111) could possess a similar stability as that observed for skyrmions in Pd/Fe/Ir(111) at low temperatures 4,12,51,53,58 . ...
... Remarkably, the lifetime of Ask in Rh/Co/Ir(111) is even larger than that of Sk in Pd/Fe/Ir(111). Note, that the calculated Sk lifetimes 52,61 are in good agreement with experiments for Pd/Fe/Ir(111) 51,53 . We have also calculated the lifetime of antiskyrmions in Pd/Fe/Ir(111) at B ¼ 3:9 T. ...
Magnetic skyrmions have raised high hopes for future spintronic devices. For many applications, it would be of great advantage to have more than one metastable particle-like texture available. The coexistence of skyrmions and antiskyrmions has been proposed in inversion-symmetric magnets with exchange frustration. However, so far only model systems have been studied and the lifetime of coexisting metastable topological spin structures has not been obtained. Here, we predict that skyrmions and antiskyrmions with diameters below 10 nm can coexist at zero magnetic field in a Rh/Co bilayer on the Ir(111) surface—an experimentally feasible system. We show that the lifetimes of metastable skyrmions and antiskyrmions in the ferromagnetic ground state are above one hour for temperatures up to 75 and 48 K, respectively. The entropic contribution to the nucleation and annihilation rates differs for skyrmions and antiskyrmions. This opens the route to the thermally activated creation of coexisting skyrmions and antiskyrmions in frustrated magnets with Dzyaloshinskii–Moriya interaction.
... This hierarchy of the timescales makes it challenging to study the thermal stability of the solitons. Consistently with the Néel-Brown theory of thermally activated magnetization reversal [2,3], experimental observations [4] and numerical simulations [5] of magnetic skyrmions identified Arrhenius dependency of their nucleation/annihilation rates k on temperature T: ...
... Nevertheless, the presence of discrete magnetic moments and thermal fluctuation can disrupt and overcome these barriers. Skyrmions are stable (Hagemeister et al., 2015) under applied fields and at low temperatures, but their practical use in devices is still limited. They have been found stabilized in Bose-Einstein condensates (Al Khawaja and Stoof, 2001), superconductors (Mascot et al., 2021), liquid crystals (Fukuda and Žumer, 2011), acoustic systems (Ge et al., 2021), photonic systems (Du et al., 2019) and other magnetic materials. ...
... Theoretical studies have also discussed various mechanisms for the nucleation of skyrmions by electric current pulses in nanodisks (Lin et al., 2013), circulating spin current (Tchoe and Han, 2012), local heating , thermal fluctuations (Hagemeister et al., 2015), and time-dependent magnetic fields (Heo et al., 2016). One such breakthrough was made by N. Romming et al. in 2013(Romming et al., 2013, they used a scanning tunneling microscope (STM) to inject spin-polarized current(∼ 1 nA) into a Pd/Fe bilayer to write a skyrmion [FIG. ...
Skyrmionic devices exhibit energy-efficient and high-integration data storage and computing capabilities due to their small size, topological protection, and low drive current requirements. So, to realize these devices, an extensive study, from fundamental physics to practical applications, becomes essential. In this article, we present an exhaustive review of the advancements in understanding the fundamental physics behind magnetic skyrmions and the novel data storage and computing technologies based on them. We begin with an in-depth discussion of fundamental concepts such as topological protection, stability, statics and dynamics essential for understanding skyrmions, henceforth the foundation of skyrmion technologies. For the realization of CMOS-compatible skyrmion functional devices, the writing and reading of the skyrmions are crucial. We discuss the developments in different writing schemes such as STT, SOT, and VCMA. The reading of skyrmions is predominantly achieved via two mechanisms: the Magnetoresistive Tunnel Junction (MTJ) TMR effect and topological resistivity (THE). So, a thorough investigation into the Skyrmion Hall Effect, topological properties, and emergent fields is also provided, concluding the discussion on skyrmion reading developments. Based on the writing and reading schemes, we discuss the applications of the skyrmions in conventional logic, unconventional logic, memory applications, and neuromorphic computing in particular. Subsequently, we present an overview of the potential of skyrmion-hosting Majorana Zero Modes (MZMs) in the emerging Topological Quantum Computation and helicity-dependent skyrmion qubits.
... The stability of a skyrmion to thermal fluctuations capable of kicking it out of a metastable state has been studied by several authors [33][34][35][36][37][38][39][40][41][42] . Similar effect due to quantum fluctuations 43 has been investigated as well [44][45][46] . ...
Contraction and expansion of skyrmions in ferromagnetic films are investigated. In centrosymmetric systems, the dynamics of a collapsing skyrmion is driven by dissipation. The collapse time has a minimum on the damping constant. In systems with broken inversion symmetry, the evolution of skyrmions toward equilibrium size is driven by the Dzyaloshinskii-Moriya interaction. Expressions describing the time dependence of the skyrmion size are derived and their implications for skyrmion-based information processing are discussed.
