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International audience; Magnetism in two-dimensional (2D) van der Waals (vdW) materials has recently emerged as one of the most promising areas in condensed matter research, with many exciting emerging properties and significant potential for applications ranging from topological magnonics to low-power spintronics, quantum computing, and optical communications. In the brief time after their discovery, 2D magnets have blossomed into a rich area for investigation, where fundamental concepts in magnetism are challenged by the behavior of spins that can develop at the single layer limit. However, much effort is still needed in multiple fronts before 2D magnets can be routinely used for practical implementations. In this comprehensive review, prominent authors with expertise in complementary fields of 2D magnetism (i.e., synthesis, device engineering, magneto-optics, imaging, transport, mechanics, spin excitations, and theory and simulations) have joined together to provide a genome of current knowledge and a guideline for future developments in 2D magnetic materials research.

We present a general approach to the derivation of the effective anisotropy field which determines the dynamical behaviour of magnetic spins according to the Landau-Lifshitz-Gilbert equation. The approach is based on the gradient in spherical polar coordinates with the final results being expressed in Cartesian coordinates as usually applied in atomistic and micromagnetic model calculations. The approach is generally valid for all orders of anisotropies including higher order combinations of azimuthal and rotational anisotropies often found in functional magnetic materials such as permanent magnets and an emerging class of antiferromagnetic materials with applications in spintronics. Anisotropies are represented in terms of spherical harmonics which have the important property of rational temperature scaling. Effective field vectors are given for anisotropies up to sixth order, presenting a unified framework for implementing higher order magnetic anisotropies in numerical simulations., 10 pages total (4 pages for references and appendix)

We have computationally studied the properties of higher-order magnetic anisotropy constants in an L10/A1-FePt coreshell system which is characterized by a strong second-order 2-ion Fe-Pt anisotropy component. We show that the coreshell structure induces an unexpected fourth-order anisotropy constant K2 the magnitude of which varies non-monotonically with the core-size ratio R reaching a peak at R = 0.50. Furthermore, we find that K2 scales with the normalized magnetization by (M/Ms)^2.2 at temperatures below the Curie temperature - a remarkable deviation from the established Callen-Callen theory which instead predicts a scaling exponent of 10. We construct an analytic model which demonstrates K2 arises from the canting of the core and shell magnetization, and successfully reproduces and justifies the scaling exponent obtained from numerical simulation., Comment: Manuscript: 6 pages, 4 figures Supplemental: 5 pages, 2 figures Submitted to Physical Review Letters

Two-dimensional magnets could potentially revolutionize information technology, but their potential application to cooling technology and magnetocaloric effect (MCE) in a material down to the monolayer limit remain unexplored. Herein, we reveal through multiscale calculations the existence of giant MCE and its strain tunability in monolayer magnets such as CrX$_3$ (X=F, Cl, Br, I), CrAX (A=O, S, Se; X=F, Cl, Br, I), and Fe$_3$GeTe$_2$. The maximum adiabatic temperature change ($\Delta T_\text{ad}^\text{max}$), maximum isothermal magnetic entropy change, and specific cooling power in monolayer CrF$_3$ are found as high as 11 K, 35 $\mu$Jm$^{-2}$K$^{-1}$, and 3.5 nWcm$^{-2}$ under a magnetic field of 5 T, respectively. A 2% biaxial and 5% $a$-axis uniaxial compressive strain can remarkably increase $\Delta T_\text{ad}^\text{max}$ of CrCl$_3$ and CrOF by 230% and 37% (up to 15.3 and 6.0 K), respectively. It is found that large net magnetic moment per unit area favors improved MCE. These findings advocate the giant-MCE monolayer magnets, opening new opportunities for magnetic cooling at nanoscale.

Dynamic simulations of spin-transfer and spin-orbit torques are increasingly important for a wide range of spintronic devices including magnetic random access memory, spin-torque nano-oscillators and electrical switching of antiferromagnets. Here we present a computationally efficient method for the implementation of spin-transfer and spin-orbit torques within the Landau–Lifshitz–Gilbert equation used in micromagnetic and atomistic simulations. We consolidate and simplify the varying terminology of different kinds of torques into a physical action and physical origin that clearly shows the common action of spin torques while separating their different physical origins. Our formalism introduces the spin torque as an effective magnetic field, greatly simplifying the numerical implementation and aiding the interpretation of results. The strength of the effective spin torque field unifies the action of the spin torque and subsumes the details of experimental effects such as interface resistance and spin Hall angle into a simple transferable number between numerical simulations. We present a series of numerical tests demonstrating the mechanics of generalised spin torques in a range of spintronic devices. This revised approach to modelling spin-torque effects in numerical simulations enables faster simulations and a more direct way of interpreting the results, and thus it is also suitable to be used in direct comparisons with experimental measurements or in a modelling tool that takes experimental values as input.

Magnetism in recently discovered van der Waals materials has opened several avenues in the study of fundamental spin interactions in truly two-dimensions. A paramount question is what effect higher-order interactions beyond bilinear Heisenberg exchange have on the magnetic properties of few-atom thick compounds. Here we demonstrate that biquadratic exchange interactions, which is the simplest and most natural form of non-Heisenberg coupling, assume a key role in the magnetic properties of layered magnets. Using a combination of nonperturbative analytical techniques, non-collinear first-principles methods and classical Monte Carlo calculations that incorporate higher-order exchange, we show that several quantities including magnetic anisotropies, spin-wave gaps and topological spin-excitations are intrinsically renormalized leading to further thermal stability of the layers. We develop a spin Hamiltonian that also contains antisymmetric exchanges (e.g., Dzyaloshinskii–Moriya interactions) to successfully rationalize numerous observations, such as the non-Ising character of several compounds despite a strong magnetic anisotropy, peculiarities of the magnon spectrum of 2D magnets, and the discrepancy between measured and calculated Curie temperatures. Our results provide a theoretical framework for the exploration of different physical phenomena in 2D magnets where biquadratic exchange interactions have an important contribution.

Domain wall motion is in the core of many information technologies ranging from storage [Beach et al., J. Magn. Magn. Mater. 320, 1272–1281 (2008)], processing [Tatara et al., Phys. Rep. 468, 213–301 (2008)], and sensing [Ralph and Stiles, J. Magn. Magn. Mater. 320, 1190–1216 (2008)] up to novel racetrack memory architectures [Parkin et al., Science 320, 190–194 (2008)]. The finding of magnetism in two-dimensional (2D) van der Waals (vdW) materials [Huang et al., Nature 546, 270 (2017); Gong et al., Nature 546, 265–269 (2017); Guguchia et al., Sci. Adv. 4, eaat3672 (2018); Klein et al., Science 360, 1218–1222 (2018)] has offered a new frontier for the exploration and understanding of domain walls at the limit of few atom-thick layers. However, to use 2D vdW magnets for building spintronics nanodevices such as domain-wall based logic [Allwood et al., Science 309, 1688–1692 (2005); Luo et al., Nature 579, 214–218 (2020); Xu et al., Nat. Nanotechnol. 3, 97–100 (2008)], it is required to gain control of their domain wall dynamics by external driving forces such as spin-polarized currents or magnetic fields, which have so far been elusive. Here, we show that electric currents as well as magnetic fields can efficiently move domain walls in the recently discovered 2D vdW magnets CrI3 and CrBr3 at low temperatures and robust down to monolayer. We realize field- and current-driven domain wall motion with velocities up to 1020 m s−1, which are comparable to the state-of-the-art materials for domain-wall based applications [Yang et al., Nat. Nanotechnol. 10, 221–226 (2015); Woo et al., Nat. Mater. 15, 501–506 (2016); Vélez et al., Nat. Commun. 10, 4750 (2019); Siddiqui et al., Phys. Rev. Lett. 121, 057701 (2018); Ryu et al., Nat. Nanotechnol. 8, 527–533 (2013)]. Domain walls keep their coherence driven by the spin-transfer torque induced by the current and magnetic fields up to large values of about [Formula: see text] A cm−2 and 5 T, respectively. For larger magnitudes of current or field, a transition to a hydrodynamic spin-liquid regime is observed with the emission of a periodic train of spin-wave solitons with modulational instability [Rabinovich and Trubetskov, Oscillations and Waves: In Linear and Nonlinear Systems, Mathematics and its Applications (Springer Netherlands, 2011)]. The emitted waveform achieves terahertz (THz) frequency in a wide range of fields and current densities, which opens up perspectives for reconfigurable magnonic devices. Moreover, we found that these spin-waves can transport spin angular momentum through the layers over distances as long as 10 μm without losses for the transport of spin information. Our results push the boundary of what is currently known about the dynamics of domain walls in 2D vdW ferromagnets and unveil strategies to design ultrathin, high-speed, and high-frequency spintronic devices.

Funding Information: The atomistic simulations were undertaken on the VIKING cluster, which is a high performance computing facility provided by the University of York. We are grateful for computational support from the University of York High Performance Computing service, VIKING, and the Research Computing team. The work of A.D. and L.S. was supported by the Ministry of Innovation and Technology and the National Research, Development and Innovation Office under Projects No. PD134579 and No. K131938, as well as within the Quantum Information National Laboratory of Hungary. Publisher Copyright: © 2021 American Physical Society. Skyrmions are topologically protected nanoscale magnetic structures with a wide range of potential applications. Here we determine the life cycle of skyrmions from their creation to their intrinsic dynamics and thermal stability to their eventual thermodynamic demise. Using atomistic simulations of Ir/Co/Pt, parameterized from ab initio calculations, we demonstrate the thermal phase transition to a skyrmion state under application of a perpendicular magnetic field. The created skyrmions exhibit Brownian particlelike dynamics driven by the underlying thermal spin fluctuations. At an elevated temperature window well below the Curie temperature, the skyrmions are metastable and can collapse to a uniform magnetic state. With application of an external magnetic field, the intrinsic local thermal spin fluctuations at this elevated temperature window are sufficiently large to allow the spontaneous formation of new skyrmions in thermodynamic equilibrium analogous to a spontaneous skyrmion gas. Such a system could be used to implement a skyrmion-based true random number generator.

We present a study of the effects of strain on the magnetocrystalline anisotropy energy and magnetic moments of Y 2 Fe 14 B bulk alloy. The study has been performed within the framework of density functional theory in its fully relativistic form under the generalized gradient approximation. We have studied seven different in-plane a lattice constant values ranging from 8.48 up to 9.08 Å with an increment of δ a = 0.1 Å. For each a value, we carried out an out-of-plane c parameter optimization, achieving the corresponding optimized lattice pair ( a , c ). We find a large variation in the site resolved magnetic moments for inequivalent Fe, Y, and B atoms for different lattice expansions and a negative contribution to the total moment from the Y sites. We find a strong variation in the magnetocrystalline anisotropy with the c / a ratio. However, the calculated variation when coupled with thermodynamic spin fluctuations is unable to explain the experimentally observed increase in the total magnetic anisotropy, suggesting that a different physical mechanism is likely to be responsible in contrast with previous interpretations. We show that opposing single- and two-ion anisotropy terms in the Hamiltonian gives good agreement with the experiment and is the probable origin of the non-monotonic temperature dependence of the net anisotropy of Y 2 Fe 14 B bulk alloy.

Anti-ferromagnetic materials have the possibility to offer ultra fast, high data density spintronic devices. A significant challenge is the reliable detection of the state of the antiferromagnet, which can be achieved using exchange bias. Here we develop an atomistic spin model of the athermal training effect, a well known phenomenon in exchange biased systems where the bias is significantly reduced after the first hysteresis cycle. We find that the setting process in granular thin films relies on the presence of interfacial mixing between the ferromagnetic and antiferromagnetic layers. We systematically investigate the effect of the intermixing and find that the exchange bias, switching field and coercivity all increase with increased intermixing. The interfacial spin state is highly frustrated leading to a systematic decrease in interfacial ordering of the ferromagnet. This metastable spin structure of initially irreversible spins leads to a large effective exchange coupling and thus large increase in the switching field. After the first hysteresis cycle these metastable spins drop into a reversible ground state that is repeatable for all subsequent hysteresis cycles, demonstrating that the effect is truly athermal. Our simulations provide new insights into the role of interface mixing and the importance of metastable spin structures in exchange biased systems which could help with the design an optimisation of antiferromagnetic spintronic devices.

Iridium manganese (IrMn) is arguably the most important antiferromagnetic material for device applications due to its metallic nature, high N\'eel temperature, and exceptionally high magnetocrystalline anisotropy. Despite its importance, its magnetic properties are poorly understood due to its intrinsic complexity and the interplay between structural and magnetic properties. Here we present a unifying atomistic model of ${\mathrm{Ir}}_{x}{\mathrm{Mn}}_{(1\ensuremath{-}x)}$ alloys which reproduces the key experimental facts of the material, while providing unprecedented understanding of the compositional and structural origins of its magnetic ground state and thermodynamic properties. We find that the N\'eel temperature is strongly dependent on the nature of the ground-state magnetic order which varies with $x$ from a triangular to tetrahedral spin structure, leading to different levels of geometric spin frustration. The N\'eel temperature increases linearly with manganese concentration for the disordered phase, while the ordered phases show a peak for ${\mathrm{Ir}}_{50}{\mathrm{Mn}}_{50}$ followed by a decrease due to increased spin frustration. The ground-state tetrahedral spin structure of the disordered phase is composition independent for manganese concentrations in the 50--95% range, while the degree of spin order varies strongly in the same range. For low manganese concentrations, we find antiferromagnetic spin-glass and ferromagnetic ground-state spin structures. The magnetic anisotropy energy exhibits a complex dependence on the lattice symmetry, presenting easy-plane, cubic, and unconventional symmetries for the principal phases, and a similarly complex variation of magnitude. The complexity of behavior represents a dual blessing and a curse in that the properties of a particular sample depend strongly on the degree of order and composition, while also providing a large state space to engineer an antiferromagnet with optimal symmetry, magnetic anisotropy, and thermal stability. Such effects are important for the future development of nanoscale sensor devices and antiferromagnetic spintronics.

We perform atomistic simulations of spin transfer torque switching dynamics in CoFeB/MgO/CoFeB magnetic tunnel junctions. We base our study on Slonczewski's model parametrized following the approach of Zhang, Levy, and Fert. We utilize excitation modes and the contour integral of the magnetization to perform a deeper analysis of the switching mechanism driven by spin transfer torque. Our results show a magnetization reversal driven by the combination of coherent and nonuniform excitation modes. These can be nonuniform and initiated by a coherent mode of the magnetization, or domain wall nucleated depending on the lateral size, temperature, and current density injected into the system. Larger current densities result in stronger excitation of nonuniform modes making the switching more easily subjected to thermal excitations and structural imperfections such as edge damage. Our findings agree with experimental works on spin transfer torque switching in similar CoFeB/MgO-based systems, and they suggest the presence of complex features in the magnetization dynamics. The analysis and the results presented here can help to gain a deeper understanding of spin transfer torque dynamics in nanoscale devices.

A unified model of molecular and atomistic spin dynamics is presented enabling simulations both in microcanonical and canonical ensembles without the necessity of additional phenomenological spin damping. Transfer of energy and angular momentum between the lattice and the spin systems is achieved by a phenomenological coupling term representing the spin-orbit interaction. The characteristic spectra of the spin and phonon systems are analyzed for different coupling strength and temperatures. The spin spectral density shows magnon modes together with the uncorrelated noise induced by the coupling to the lattice. The effective damping parameter is investigated showing an increase with both coupling strength and temperature. The model paves the way to understanding magnetic relaxation processes beyond the phenomenological approach of the Gilbert damping and the dynamics of the energy transfer between lattice and spins.

Antiferromagnetic spintronic devices have the potential to greatly outperform conventional ferromagnetic devices due to their ultrafast dynamics and high data density. A challenge in designing these devices is the control and detection of the orientation of the antiferromagnet. One of the most promising ways to achieve this is through the exchange bias effect. This is of particular importance in large-scale multigranular devices. Previously, due to the large system sizes, only micromagnetic simulations have been possible, with an assumed distribution of antiferromagnetic anisotropy directions and grain size. Here, we use an atomistic model where the distribution of antiferromagnetic anisotropy directions occurs naturally and where the exchange bias occurs due to the intrinsic disorder in the antiferromagnet. We perform large-scale simulations of exchange bias, generating realistic values of exchange bias. We find a strong temperature dependence of the exchange bias, in agreement with experimental observations, approaching zero at the blocking temperature of the antiferromagnet. We find that the experimentally observed increase in the coercivity at the blocking temperature occurs due to the superparamagnetic flipping of the antiferromagnet during the hysteresis loop cycle. We find a large discrepancy between the exchange bias predicted from a geometric model of the antiferromagnetic interface, indicating the importance of grain edge effects in multigranular exchange biased systems. The grain size dependence shows the expected peak due to a competition between the superparamagnetic nature of small grains and reduction in the statistical imbalance in the number of interfacial spins for larger grain sizes. Our simulations confirm the existence of single antiferromagnetic domains within each grain. The model gives insights into the physical origin of exchange bias and provides a route to developing optimized nanoscale antiferromagnetic spintronic devices.

Higher-order exchange interactions and quantum effects are widely known to play an important role in describing the properties of low-dimensional magnetic compounds. Here, the recently discovered 2D van der Waals (vdW) CrI3 is identified as a quantum non-Heisenberg material with properties far beyond an Ising magnet as initially assumed. It is found that biquadratic exchange interactions are essential to quantitatively describe the magnetism of CrI3 but quantum rescaling corrections are required to reproduce its thermal properties. The quantum nature of the heat bath represented by discrete electron-spin and phonon-spin scattering processes induces the formation of spin fluctuations in the low-temperature regime. These fluctuations induce the formation of metastable magnetic domains evolving into a single macroscopic magnetization or even a monodomain over surface areas of a few micrometers. Such domains display hybrid characteristics of Néel and Bloch types with a narrow domain wall width in the range of 3-5 nm. Similar behavior is expected for the majority of 2D vdW magnets where higher-order exchange interactions are appreciable.

The discovery of magnetism in two-dimensional (2D) van der Waals (vdW) materials1–4 has flourished a new endeavour of fundamental problems in magnetism as well as potential applications in computing, sensing and storage technologies5–10. Of particular interest are antiferromagnets 11, 12, which due to their intrinsic antiferromagnetic exchange coupling show several advantages in relation to ferromagnets such as robustness against external magnetic perturbations. This property is one of the cornerstones of antiferromagnets13 and implies that in formation stored in antiferromagnetic domains is invisible to applied magnetic fields preventing it from being erased or manipulated. Here we show that, despite this fundamental understanding, the magnetic domains of recently discovered 2D vdW MnPS3 antiferromagnet14, 15 can be controlled via external magnetic fields and electric currents. We realize ultrafast domain-wall dynamics with velocities up to ∼1500 m s−1 and ∼3000 m s−1 respectively to a broad range of field magnitudes (0.0001−22 T) and current densities (108 − 1010 A cm−2). Both domain wall dynamics are determined by the edge terminations which generated uncompensated spins following the underlying symmetry of the honeycomb structure. We find that edge atoms belonging to different magnetic sublattices function as geometrical constrictions preventing the displacement of the wall, whereas having atoms of the same sublattice at both edges of the material allows for the field-driven domain wall motion which is only limited by the spin-flop transition of the antiferromagnet beyond 25 T. Conversely, electric currents can induce motion of domain walls in most of the edges except those where the two sublattices are present at the borders (e.g. armchair edges). Furthermore, the orientation of the layer relative to the current flow provides an additional degree of freedom for controlling and manipulating magnetic domains in MnPS3. Our results indicate that the implementation of 2D vdW antiferromagnets in real applications requires the engineering of the layer edges which enables an unprecedented functional feature in ultrathin device platforms.

Antiferromagnetic spintronic devices could offer ultrafast dynamics and a higher data density than conventional ferromagnetic devices. One of the challenges in designing such devices is the control and detection of the magnetization of the antiferromagnet due to its lack of stray fields, and this is often achieved through the exchange bias effect. In exchange biased systems, the pinned spins are known to comprise a small fraction of the total number of interface spins, yet their exact nature and physical origin has so far been elusive. Here we show that in the technologically important disordered $\ensuremath{\gamma}\text{\ensuremath{-}}{\mathrm{IrMn}}_{3}$--CoFe structure, the pinned spins arise from the small imbalance in the number of spins in each magnetic sublattice in the antiferromagnet due to the naturally occurring atomic disorder. These pinned spins are strongly coupled to the bulk antiferromagnet, explaining their stability. Moreover, we find that the ferromagnet strongly distorts the interface spin structure of the antiferromagnet, causing a large reversible interface magnetization that does not contribute to exchange bias but does increase the coercivity. We find that the uncompensated spins are not localized spins which occur due to point defects or domain walls but instead constitute a small motion of every antiferromagnet spin at the interface. This unexpected finding resolves one of the long-standing puzzles of exchange bias and provides a route to developing optimized nanoscale antiferromagnetic spintronic devices.

Magnetic anisotropy plays an essential role in information technology applications of magnetic materials, providing a means to retain the long-term stability of a magnetic state in the presence of thermal fluctuations. Anisotropy consists of a single-ion contribution stemming from the crystal structure and two-ion terms attributed to the exchange interactions between magnetic atoms. A lack of robust theory crucially limits the understanding of the temperature dependence of the anisotropy in pure two-ion and mixed single-ion and two-ion systems. Here, we use Green's function theory and atomistic Monte Carlo simulations to determine the temperature scaling of the effective anisotropy in ferromagnets in these pure and mixed cases, from saturated to vanishing magnetization. At low temperature, we find that the pure two-ion anisotropy scales with the reduced magnetization as $k(m) \sim m^{2.28}$, while the mixed scenario describes the diversity of the temperature dependence of the anisotropy observed in real materials. The temperature dependence of the mixed anisotropy determined here is expected to considerably contribute to the understanding and the control of the thermal properties of magnetic materials., Comment: 7 pages, 4 figures

Understanding the damping mechanism in finite size systems and its dependence on temperature is a critical step in the development of magnetic nanotechnologies. In this work, nano-sized materials are modeled via atomistic spin dynamics, the damping parameter being extracted from Ferromagnetic Resonance (FMR) simulations applied for FePt systems, generally used for heat-assisted magnetic recording media (HAMR). We find that the damping increases rapidly close to Tc and the effect is enhanced with decreasing system size, which is ascribed to scattering at the grain boundaries. Additionally, FMR methods provide the temperature dependence of both damping and the anisotropy, important for the development of HAMR. Semi-analytical calculations show that, in the presence of a grain size distribution, the FMR linewidth can decrease close to the Curie temperature due to a loss of inhomogeneous line broadening. Although FePt has been used in this study, the results presented in the current work are general and valid for any ferromagnetic material., Comment: 8 pages, 7 figures

Using an atomistic spin model, we have simulated spin wave injection and propagation into antiferromagnetic IrMn from an exchange coupled CoFe layer. The spectral characteristics of the exited spin waves have a complex beating behavior arising from the non-collinear nature of the antiferromagnetic order. We find that the frequency response of the system depends strongly on the strength and frequency of oscillating field excitations. We also find that the strength of excited spin waves strongly decays away from the interfacial layer with a frequency dependent attenuation. Our findings suggest that spin waves generated by coupled ferromagnets are too weak to reverse IrMn in their entirety even with resonant excitation of a coupled ferromagnet. However, efficient spin wave injection into the antiferromagnet is possible due to the non-collinear nature of the IrMn spin ordering., 9 pages, 9 figures

Higher-order exchange interactions and quantum effects are widely known to play an important role in describing the properties of low-dimensional magnetic compounds. Here, the recently discovered 2D van der Waals (vdW) CrI

We describe the process of multiscale modelling of magnetic materials, based on atomistic models coupled parametrically to micromagnetic calculations. At the atomistic lengthscale we use Spin Dynamics (SD) to study switching mechanisms, using structures predicted by Molecular Dynamics. The process is completed using SD to calculate the cell size and temperature dependent parameters for micromagnetic calculations. We demonstrate an unusually weak cell size scaling for Nd2Fe14B and demonstrate numerically the existence of atomic scale Barkhausen jumps during magnetization switching. Scaling of magnetic properties is shown to be important in micromagnetic calculations of hysteresis, especially considering variation in micromagnetic cell size.

We describe the process of multiscale modelling of magnetic materials, based on atomistic models coupled parametrically to micromagnetic calculations. At the atomistic lengthscale we use Spin Dynamics (SD) to study switching mechanisms, using structures predicted by Molecular Dynamics. The process is completed using SD to calculate the cell size and temperature dependent parameters for micromagnetic calculations. We demonstrate an unusually strong cell size scaling for Nd2Fe14B, and demonstrate numerically the existence of atomic scale Barkhausen jumps during magnetization switching. Scaling of magnetic properties is shown to be important in micromagnetic calculations of hysteresis, especially considering variation in micromagnetic cell size.

Individual disk-shaped $\mathrm{Co}\text{\ensuremath{-}}\mathrm{Fe}\text{\ensuremath{-}}\mathrm{B}$ nanodots are driven into a superparamagnetic state by a spin-transfer torque, and their time-dependent magnetoresistance fluctuations are measured as a function of current. A thin layer of oxidation at the edges has a dramatic effect on the magnetization dynamics. A combination of experimental results and atomistic spin simulations shows that pinning to oxide grains can reduce the likelihood that fluctuations lead to reversal, and can even change the easy-axis direction. Exchange-bias loop shifts and training effects are observed even at room temperature after brief exposure to small fields. The results have implications for studies of core-shell nanoparticles and small magnetic tunnel junctions and spin-torque oscillators.

Merons are nontrivial topological spin textures highly relevant for many phenomena in solid state physics. Despite their importance, direct observation of such vortex quasiparticles is scarce and has been limited to a few complex materials. Here, we show the emergence of merons and antimerons in recently discovered two-dimensional (2D) CrCl3 at zero magnetic field. We show their entire evolution from pair creation, their diffusion over metastable domain walls, and collision leading to large magnetic monodomains. Both quasiparticles are stabilized spontaneously during cooling at regions where in-plane magnetic frustration takes place. Their dynamics is determined by the interplay between the strong in-plane dipolar interactions and the weak out-of-plane magnetic anisotropy stabilising a vortex core within a radius of 8–10 nm. Our results push the boundary to what is currently known about non-trivial spin structures in 2D magnets and open exciting opportunities to control magnetic domains via topological quasiparticles., Merons are a type of topological spin texture, with relevance for both fundamental and technological problems. In this theoretical work, Augustin et al. show that the van der Waals ferromagnetic CrCl3 can host merons and anti-merons, and explore the dynamics and interactions of these quasi-particles.

The magnetic stray field is an unavoidable consequence of ferromagnetic devices and sensors leading to a natural asymmetry in magnetic properties. Such asymmetry is particularly undesirable for magnetic random access memory applications where the free layer can exhibit bias. Using atomistic dipole-dipole calculations we numerically simulate the stray magnetic field emanating from the magnetic layers of a magnetic memory device with different geometries. We find that edge effects dominate the overall stray magnetic field in patterned devices and that a conventional synthetic antiferromagnet structure is only partially able to compensate the field at the free layer position. A granular reference layer is seen to provide near-field flux closure while additional patterning defects add significant complexity to the stray field in nanoscale devices. Finally we find that the stray field from a nanoscale antiferromagnet is surprisingly non-zero arising from the imperfect cancellation of magnetic sublattices due to edge defects. Our findings provide an outline of the role of different layer structures and defects in the effective stray magnetic field in nanoscale magnetic random access memory devices and atomistic calculations provide a useful tools to study the stray field effects arising from a wide range of defects.

Temperature-dependent magnetic properties of ${\mathrm{Nd}}_{2}{\mathrm{Fe}}_{14}\mathrm{B}$ permanent magnets, i.e., saturation magnetization ${M}_{\text{s}}(T)$, effective magnetic anisotropy constants ${K}_{i}^{\text{eff}}(T)\phantom{\rule{4pt}{0ex}}(i=1,2,3)$, domain-wall width ${\ensuremath{\delta}}_{w}(T)$, and exchange stiffness constant ${A}_{\text{e}}(T)$, are calculated by using ab initio informed atomistic spin model simulations. We construct the atomistic spin model Hamiltonian for ${\mathrm{Nd}}_{2}{\mathrm{Fe}}_{14}\mathrm{B}$ by using the Heisenberg exchange of $\mathrm{Fe}\ensuremath{-}\mathrm{Fe}$ and $\mathrm{Fe}\ensuremath{-}\mathrm{Nd}$ atomic pairs, the uniaxial single-ion anisotropy of Fe atoms, and the crystal-field energy of Nd ions, which is approximately expanded into an energy formula featured by second-, fourth-, and sixth-order phenomenological anisotropy constants. After applying a temperature rescaling strategy, we show that the calculated Curie temperature, spin-reorientation phenomenon, ${M}_{\text{s}}(T),{\ensuremath{\delta}}_{w}(T)$, and ${K}_{i}^{\text{eff}}(T)$, agree well with the experimental results. ${A}_{\text{e}}(T)$ is estimated through a general continuum description of the domain-wall profile by mapping atomistic magnetic moments to the macroscopic magnetization. ${A}_{\text{e}}$ is found to decrease more slowly than ${K}_{1}^{\text{eff}}$ with increasing temperature and approximately scale with normalized magnetization as ${A}_{\text{e}}(T)\ensuremath{\sim}{m}^{1.2}$. Specifically, the possible domain-wall configurations at temperatures below the spin-reorientation temperature and the associated ${\ensuremath{\delta}}_{w}$ and ${A}_{\text{e}}$ are identified. This work provokes a scale bridge between ab initio calculations and temperature-dependent micromagnetic simulations of Nd-Fe-B permanent magnets.

We theoretically investigate the temperature and thickness dependence of the effective Gilbert damping constant (α) in the Co-Fe-B/MgO system using atomistic spin dynamics. We consider a high damping constant at the interface layer and a low damping constant for the bulklike layers due to large interfacial spin-orbit coupling. We find a strong dependence of the effective Gilbert damping with the film thickness, in quantitative agreement with experimental data. The temperature dependence of the effective damping arising from thermal-spin fluctuations up to temperatures of 400 K is weak, with no apparent change over the studied temperature range. Interestingly, we find that the temperature produces a different effect: a statistical fluctuation of the Gilbert damping parameter for a given relaxation induced solely from the finite size of the system. This statistical variation of the Gilbert damping is an intrinsic effect and is important for spintronic devices operating at gigahertz frequencies, where the dynamic response must be carefully controlled.

Skyrmions have attracted significant interest due to their topological spin structures and fascinating physical features. The skyrmion phase arises in materials with Dzyaloshinskii-Moriya (DM) interaction at interfaces or in volume of non-centrosymmetric materials. However, although skyrmions were generated experimentally, one critical intrinsic relationship between fabrication, microstructures, magnetization and the existence of skyrmions remains to be established. Here, two series of CoFeB ultrathin films with controlled atomic scale structures are employed to reveal this relationship. By inverting the growth order, the amount of defects can be artificially tuned, and skyrmions are shown to be preferentially formed at defect sites. The stable region and the density of the skyrmions can be efficiently controlled in the return magnetization loops by utilizing first-order reversal curves to reach various metastable states. These findings establish the general and intrinsic relationship from sample preparation to skyrmion generation, offering an universal method to control skyrmion density., 25 pages, 5 figures

Increasing the data storage in next-generation hard disk drives requires a reduction in the physical dimensions of read sensors. Tunneling magnetoresistance heads yield high magnetoresistance (MR) ratio but with a high resistance-area product (RA) that is suboptimal for devices. Giant magnetoresistance (GMR) head using different materials is an alternative way to improve reader performance with high MR ratio and low RA. In this paper, we theoretically study the effect of material properties and the layer thickness on RA and MR ratio in a trilayer system via an atomistic model combined with the spin transport model. The GMR stack can be constructed by the atomistic model and the RA and MR ratio can be directly calculated by considering the spin accumulation and spin current from the spin transport model. It is found that the spin valve using the (Figure presented) Heusler alloy electrode with high spin polarization exhibits a high MR ratio and RA of 64 (Figure presented) which is better than the spin valves using conventional ferromagnets such as Co, NiFe and CoFe. Moreover, we consider the thickness dependence of the change of RA ((Figure presented)). Increasing the free layer thickness yields the increase in (Figure presented) and MR ratio because of the enhancement of the bulk spin scattering. Additionally, the results show that the (Figure presented) depends on the spin diffusion length of the nonmagnetic materials ((Figure presented)). The (Figure presented) increases from 3 up to 10 (Figure presented) when (Figure presented) increases from 35 to 1200 nm. This investigation shows the possibility for read head design of HDDs with areal density beyond 2 Tb in-2.

Anti-phase boundaries (APBs) are structural defects which have been shown to be responsible for the anomalous magnetic behavior observed in different nanostructures. Understanding their properties is crucial in order to use them to tune the properties of magnetic materials by growing APBs in a controlled way since their density strongly depends on the synthesis method. In this work we investigate their influence on magnetite (Fe3O4) thin films by considering an atomistic spin model, focussing our study on the role that the exchange interactions play across the APB interface. We conclude that the main atypical features reported experimentally in this material are well described by the model we propose here, confirming the new exchange interactions created in the APB as the responsible for this deviation from bulk properties.

The dynamic process of assisted magnetic switchings has been simulated to investigate the associated physics. The model uses a Voronoi construction to determine the physical structure of the nanogranular thin film recording media, and the Landau–Lifshitz–Bloch equation is solved to evolve the magnetic system in time. The reduction of the magnetization is determined over a range of peak system temperatures and for a number of anisotropy values. The results show that the heat-assisted magnetic recording process is not simply magnetization reversal over a thermally reduced energy barrier. To achieve full magnetization reversal (for all anisotropies investigated), an applied field strength of at least 6 kOe is required and the peak system temperature must reach at least the Curie point ( T c). When heated to T c, the magnetization associated with each grain is destroyed, which invokes the non-precessional linear reversal mode. Reversing the magnetization through this linear reversal mode is favorable, as the reversal time is two orders of magnitude smaller than that associated with precession. Under these conditions, as the temperature decreases to ambient, the magnetization recovers in the direction of the applied field, completing the reversal process. Also, the model produces results that are consistent with the concept of thermal writability; when heating the media to T c, the smaller grains require a larger field strength to reverse the magnetization.

The balance between low power consumption and high efficiency in memory devices is a major limiting factor in the development of new technologies. Magnetic random access memories (MRAMs) based on CoFeB/MgO magnetic tunnel junctions (MTJs) have been proposed as candidates to replace the current technology due to their non-volatility, high thermal stability, and efficient operational performance. Understanding the size and temperature dependence of the energy barrier and the nature of the transition mechanism across the barrier between stable configurations is a key issue in the development of MRAM. Here, we use an atomistic spin model to study the energy barrier to reversal in CoFeB/MgO nanodots to determine the effects of size, temperature, and external field. We find that for practical device sizes in the 10–50 nm range, the energy barrier has a complex behavior characteristic of a transition from a coherent to domain wall driven reversal process. Such a transition region is not accessible to simple analytical estimates of the energy barrier preventing a unique theoretical calculation of the thermal stability. The atomistic simulations of the energy barrier give good agreement with experimental measurements for similar systems, which are at the state of the art and can provide guidance to experiments identifying suitable materials and MTJ stacks with the desired thermal stability.

Gilbert damping plays a significant role in magnetic reversal processes, and it determines the timescale of the switching. Here we investigate the properties of exchange-coupled composite media and the dependence of the switching time on the damping constant of the soft layer using atomistic spin dynamics. For a bilayer Fe/FePt medium, we find an anomalous increase of the switching time with increasing soft layer damping constant. The reversal occurs via a high-temperature exchange spring, and we show that the increase in the switching time is related to a corresponding increase in the time to establish the exchange spring. This phenomenon is delicately balanced in that the switching time increase occurs only in fields close to the coercivity.

Fe3O4 nanoparticles are one of the most promising candidates for biomedical applications such as magnetic hyperthermia and theranostics due to their bio-compatibility, structural stability and good magnetic properties. However, much is unknown about the nanoscale origins of the observed magnetic properties of particles due to the dominance of surface and finite size effects. Here we have developed an atomistic spin model of elongated magnetite nanocrystals to specifically address the role of faceting and elongation on the magnetic shape anisotropy. We find that for faceted particles simple analytical formulae overestimate the magnetic shape anisotropy and that the underlying cubic anisotropy makes a significant contribution to the energy barrier for moderately elongated particles. Our results enable a better estimation of the effective magnetic anisotropy of highly crystalline magnetite nanoparticles and is a step towards quantitative prediction of the heating effects of magnetic nanoparticles.

Nd 2 Fe 14 B has generated significant interest since its discovery in the 1980s due to its impressive energy density, which makes it a prime candidate for use in permanent magnet applications. Its performance is known to suffer greatly at the high temperatures required for motor applications around 450 K. Core/shell nanocomposites provide a potential route to improve material performance by combining the highly anisotropic permanent magnet with a material with high moment and high Curie temperature. We have used an atomistic spin model to investigate the magnetic properties of Nd 2 Fe 14 B with α - F e in a core/shell nanostructure. We find that at typical motor operating temperatures, increasing α - F e content reduces the coercivity of the system while enhancing the saturation magnetization. The overall effect is that an improvement in B H max is seen with increasing α - F e up to an optimal value of 70 vol . %. This property of core/shell nanostructures would make them a suitable substitute for pure Nd 2 Fe 14 B while simultaneously lowering the raw material cost of the permanent magnet component of high-performance motors.

For the first time, we demonstrate, using an atomistic description of a 30nm diameter spin-transfer-torque magnetic random access memories (STT-MRAM), that the difference in mechanical properties of its sub-nanometer layers induces a high compressive strain in the magnetic tunnel junction (MTJ) and leads to a detrimental magnetostrictive effect. Our model explains the issues met in engineering the electrical and magnetic performances in scaled STT-MRAM devices. The resulting high compressive strain built in the stack, particularly in the MgO tunnel barrier (t-MgO), and its associated non-uniform atomic displacements, impacts on the quality of the MTJ interface and leads to strain relieve mechanisms such as surface roughness and adhesion issues. We illustrate that the strain gradient induced by the different materials and their thicknesses in the stacks has a negative impact on the tunnel magneto-resistance (TMR), on the magnetic nucleation process and on the STT-MRAM performance.