Atomistic Spin Dynamics Research Articles

Magnon-driven chiral charge and spin pumping and electron-magnon scattering from time-dependent quantum transport combined with classical atomistic spin dynamics

Using newly developed quantum-classical hybrid framework, we investigate interaction between spin-polarized conduction electrons and a single spin wave (SW) coherently excited within a metallic ferromagnetic nanowire. When the nanowire hosting SW is attached to two normal metal (NM) leads, with no dc bias voltage applied between them, the SW pumps chiral electronic charge and spin currents into the leads---their direction is tied to the direction of SW propagation and they scale linearly with the frequency of the precession. This is in contrast to: standard pumping by the uniform precession mode with identical spin currents flowing in both directions and no accompanying charge current; or experimentally observed [C.~Ciccarelli et al., Nat. Nanotech. 10, 50 (2014); M.~Evelt et al., Phys. Rev. B 95, 024408 (2017)] magnonic charge pumping which requires spin-orbit coupling spin-orbit coupling. The mechanism behind our prediction is nonadiabaticity due to time-retardation effects---motion of localized magnetic moment affects conduction electron spin in a retarded way, so that it takes a finite time until the electron spin reacts to the motion of the classical vector. Upon injecting dc spin-polarized charge current from the left NM lead, electrons interact with SW where outflowing charge and spin current into the right NM lead are changed due to both scattering off time-dependent potential generated by the SW and superposition with the currents pumped by the SW itself. Using Lorentzian voltage pulse to excite leviton out of the Fermi sea, which carries one electron charge with no accompanying electron-hole pairs and behaves as soliton-like quasiparticle, we describe how a single electron interacts with a single SW.

A structurally ordered spin glass

Magnetism Spin glasses that form in disordered materials such as magnetic alloys have locally varying magnetic patterns, and their spin relaxation occurs over time scales spanning many orders of magnitude. Kamber et al. used spin-polarized scanning tunneling microscopy to image the magnetism on the (0001) surface of thick, single-crystal films of neodymium as a function of temperature and magnetic field. Despite the lack of structural disorder, they found a spectral distribution of degenerate magnetic wave vectors, or Q states, that exhibited spatiotemporal variation. In this spin-Q glass, pockets of nearly degenerate spin spiral states formed with varying periodicity. Ab initio electronic structure coupled to atomistic spin dynamics calculations suggests that the double hexagonal closed packed crystal structure in neodymium drove strongly frustrated magnetism that created these pockets. Science , this issue p. [eaay6757][1] [1]: /lookup/doi/10.1126/science.aay6757

Self-induced spin glass state in elemental and crystalline neodymium.

Spin glasses are a highly complex magnetic state of matter intricately linked to spin frustration and structural disorder. They exhibit no long-range order and exude aging phenomena, distinguishing them from quantum spin liquids. We report a previously unknown type of spin glass state, the spin-Q glass, observable in bulk-like crystalline metallic neodymium thick films. Using spin-polarized scanning tunneling microscopy combined with ab initio calculations and atomistic spin-dynamics simulations, we visualized the variations in atomic-scale noncolinear order and its response to magnetic field and temperature. We quantified the aging phenomena relating the glassiness to crystalline symmetry and the energy landscape. This result not only resolves the long-standing debate of the magnetism of neodymium, but also suggests that glassiness may arise in other magnetic solids lacking extrinsic disorder.

High-frequency magnon excitation due to femtosecond spin-transfer torques

Femtosecond laser pulses can induce ultrafast demagnetization as well as generate bursts of hot electron spin currents. In trilayer spin valves consisting of two metallic ferromagnetic layers separated by a nonmagnetic one, hot electron spin currents excited by an ultrashort laser pulse propagate from the first ferromagnetic layer through the spacer reaching the second magnetic layer. When the magnetizations of the two magnetic layers are noncollinear, this spin current exerts a torque on magnetic moments in the second ferromagnet. Since this torque is acting only within the sub-ps timescale, it excites coherent high-frequency magnons as recently demonstrated in experiments. Here, we calculate the temporal shape of the hot electron spin currents using the superdiffusive transport model and simulate the response of the magnetic system to the resulting ultrashort spin-transfer torque pulse by means of atomistic spin-dynamics simulations. Our results confirm that the acting spin-current pulse is short enough to excite magnons with frequencies beyond 1 THz, a frequency range out of reach for current induced spin-transfer torques. We demonstrate the formation of thickness dependent standing spin waves during the first picoseconds after laser excitation. In addition, we vary the penetration depth of the spin-transfer torque to reveal its influence on the excited magnons. Our simulations clearly show a suppression effect of magnons with short wavelengths already for penetration depths in the range of 1 nm confirming experimental findings reporting penetration depths below $2\, {\rm nm}$.

Spin-torque switching of noncollinear antiferromagnetic antiperovskites

Antiferromagnetic (AFM) spintronics exploits the N\'eel vector as a state variable for novel electronic devices. Recent studies have demonstrated that the N\'eel vector can be switched by a spin-orbit torque. These studies however are largely limited to collinear antiferromagnets of proper magnetic space-group symmetry. There is, however, a large group of high-temperature noncollinear antiferromagnets, which are suitable for such switching. Here, we predict that spin torque can be efficiently used to switch a noncollinear AFM order in antiperovskite materials. Based on first-principles calculations and atomistic spin-dynamics modeling, we show that in antiperovskites $A\mathrm{NM}{\mathrm{n}}_{3}$ ($A=\mathrm{Ga}$, Ni, etc.) with the AFM ${\mathrm{\ensuremath{\Gamma}}}_{4\mathrm{g}}$ ground state, the AFM order can be switched on the picosecond timescale using a spin torque generated by a spin current. The threshold switching current density can be tuned by the $A\mathrm{NM}{\mathrm{n}}_{3}$ stoichiometry engineering, changing the magnetocrystalline anisotropy. The ${\mathrm{\ensuremath{\Gamma}}}_{4\mathrm{g}}$ AFM phase supports a sizable anomalous Hall effect, which can be used to detect the spin-torque switching of the AFM order. The predicted ultrafast switching dynamics and the efficient detection of the AFM order state make noncollinear magnetic antiperovskites a promising material platform for AFM spintronics.

Unveiling domain wall dynamics of ferrimagnets in thermal magnon currents: Competition of angular momentum transfer and entropic torque

Control of magnetic domain wall motion holds promise for efficient manipulation and transfer of magnetically stored information. Thermal magnon currents, generated by temperature gradients, can be used to move magnetic textures, from domain walls, to magnetic vortices and skyrmions. In the last years, theoretical studies have centered in ferro- and antiferromagnetic spin structures, where domain walls always move towards the hotter end of the thermal gradient. Here we perform numerical studies using atomistic spin dynamics simulations and complementary analytical calculations to derive an equation of motion for the domain wall velocity. We demonstrate that in ferrimagnets, domain wall motion under thermal magnon currents shows a much richer dynamics. Below the Walker breakdown, we find that the temperature gradient always pulls the domain wall towards the hot end by minimizating its free energy, in agreement with the observations for ferro- and antiferromagnets in the same regime. Above Walker breakdown, the ferrimagnetic domain wall can show the opposite, counterintuitive behavior of moving towards the cold end. We show that in this case, the motion to the hotter or the colder ends is driven by angular momentum transfer and therefore strongly related to the angular momentum compensation temperature, a unique property of ferrimagnets where the intrinsic angular momentum of the ferrimagnet is zero while the sublattice angular momentum remains finite. In particular, we find that below the compensation temperature the wall moves towards the cold end, whereas above it, towards the hot end. Moreover, we find that for ferrimagnets, there is a torque compensation temperature at which the domain wall dynamics shows similar characteristics to antiferromagnets, that is, quasi-inertia-free motion and the absence of Walker breakdown.

Spin wave excitations of magnetic metalorganic materials

The Organic Materials Database (OMDB) is an open database hosting about 22,000 electronic band structures, density of states and other properties for stable and previously synthesized 3-dimensional organic crystals. The web interface of the OMDB offers various search tools for the identification of novel functional materials such as band structure pattern matching and density of states similarity search. In this work the OMDB is extended to include magnetic excitation properties. For inelastic neutron scattering we focus on the dynamical structure factor $S(\mathbf{q},\omega)$ which contains information on the excitation modes of the material. We introduce a new dataset containing atomic magnetic moments and Heisenberg exchange parameters for which we calculate the spin wave spectra and dynamic structure factor with linear spin wave theory and atomistic spin dynamics. We thus develop the materials informatics tools to identify novel functional organic and metalorganic magnets.

Phase boundary exchange coupling in the mixed magnetic phase regime of a Pd-doped FeRh epilayer

Spin-wave resonance measurements were performed in the mixed magnetic phase regime of a Pd-doped FeRh epilayer that appears as the first-order ferromagnetic-antiferromagnetic phase transition takes place. It is seen that the measured value of the exchange stiffness is suppressed throughout the measurement range when compared to the expected value of the fully ferromagnetic regime, extracted via the independent means of a measurement of the Curie point, for only slight changes in the ferromagnetic volume fraction. This behavior is attributed to the influence of the antiferromagnetic phase: inspired by previous experiments that show ferromagnetism to be most persistent at the surfaces and interfaces of FeRh thin films, we modelled the antiferromagnetic phase as forming a thin layer in the middle of the epilayer through which the two ferromagnetic layers are coupled up to a certain critical thickness. The development of this exchange stiffness is then consistent with that expected from the development of an exchange coupling across the magnetic phase boundary, as a consequence of a thickness dependent phase transition taking place in the antiferromagnetic regions and is supported by complimentary computer simulations of atomistic spin-dynamics. The development of the Gilbert damping parameter extracted from the ferromagnetic resonance investigations is consistent with this picture.

Effect of the interplay between layering sequence permutations and thickness on the magnetic features of Fe/Ni/Gd hetero-films.

The effect of the interplay between layering sequence permutations and film thickness on the temperature-dependent magnetization and spin structure of Fe/Ni/Gd hetero-films (sizes: 10 nm × 10 nm ×d nm and 20 nm × 20 nm ×d nm, where d is the film thickness and with all possible layer sequence permutations) is investigated in the framework of an atomistic spin dynamics formalism. As the main conclusion of our work, for d = 2 and 4 nm, layering sequence permutations do not affect the evolution of the mean temperature-dependent magnetization of hetero-films. Nonetheless, dramatic magnetic modulations appear for d = 6 nm. More specifically, a Gd film sandwiched between Fe and Ni films (FeGdNi hetero-film) exhibits a depressed mean temperature-dependent magnetization in the temperature range of 150 K to 700 K. In contrast, both FeNiGd and NiFeGd hetero-films show a more or less similar magnetization evolution.

Semiquantum thermodynamics of complex ferrimagnets

High-quality magnets such as yttrium iron garnet (YIG) are electrically insulating and very complex. By implementing a quantum thermostat into atomistic spin dynamics we compute YIG's key thermodynamic properties, viz. the magnon power spectrum and specific heat, for a large temperature range. The results differ (sometimes spectacularly) from simple models and classical statistics, but agree with available experimental data.

Evidence for Magnetic Skyrmions at the Interface of Ferromagnet/Topological-Insulator Heterostructures.

The heterostructures of the ferromagnet (Cr2Te3) and topological insulator (Bi2Te3) have been grown by molecular beam epitaxy. The topological Hall effect as evidence of the existence of magnetic skyrmions has been observed in the samples in which Cr2Te3 was grown on top of Bi2Te3. Detailed structural characterizations have unambiguously revealed the presence of intercalated Bi bilayer nanosheets right at the interface of those samples. The atomistic spin-dynamics simulations have further confirmed the existence of magnetic skyrmions in such systems. The heterostructures of ferromagnet and topological insulator that host magnetic skyrmions may provide an important building block for next generation of spintronics devices.

Temperature and Thickness Dependence of Statistical Fluctuations of the Gilbert Damping in Co - Fe - B / MgO Bilayers

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.

General method for atomistic spin-lattice dynamics with first-principles accuracy

We present a computationally efficient general first-principles based method for spin-lattice simulations for solids. Our method is based on a combination of atomistic spin dynamics and molecular dynamics, expressed through a spin-lattice Hamiltonian where the bilinear magnetic term is expanded to second order in displacement, and all parameters are computed using density functional theory. The effect of first-order spin-lattice coupling on the magnon and phonon dispersion in bcc Fe is reported as an example, and is seen to be in good agreement with previous simulations performed with an empirical potential approach. In addition, we also illustrate the abilities of our method on a more conceptual level, by exploring dissipation-free spin and lattice motion in small magnetic clusters (a dimer, trimer and quadmer). Our method opens the door for quantitative description and understanding of the microscopic origin of many fundamental phenomena of contemporary interest, such as ultrafast demagnetization, magnetocalorics, and spincaloritronics.

Ultrafast generation and dynamics of isolated skyrmions in antiferromagnetic insulators

Based on atomistic spin dynamics simulations, we report the ultrafast generation of single antiferromagnetic (AFM) skyrmions in a confined geometry. This process is achieved through an effective magnetic field induced by the athermal inverse Faraday effect from a short laser pulse. The resulting field can nucleate an isolated skyrmion as a topologically protected metastable state in a collinear antiferromagnet with small Dzyaloshinskii-Moriya interaction. The radius of a single skyrmion is shown to increase by applying a uniform dc magnetic field and at increasing temperature. To investigate possible AFM spin-caloritronics phenomena, we investigate the skyrmion dynamics under an applied temperature gradient both analytically and numerically. The antiferromagnetic skyrmions move longitudinally toward the hotter region, but in contrast, small skyrmions in the very low damping regime move toward the colder side, irrespective of the staggered topological charge number, with a speed that is much faster than that of their ferromagnetic counterparts.

Anomalous damping dependence of the switching time in Fe/FePt bilayer recording media

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.

Anomalous Phonon Lifetime Shortening in Paramagnetic CrN Caused by Spin-Lattice Coupling: A Combined Spin and AbInitio Molecular Dynamics Study.

We study the mutual coupling of spin fluctuations and lattice vibrations in paramagnetic CrN by combining atomistic spin dynamics and abinitio molecular dynamics. The two degrees of freedom are dynamically coupled, leading to nonadiabatic effects. Those effects suppress the phonon lifetimes at low temperature compared to an adiabatic approach. The dynamic coupling identified here provides an explanation for the experimentally observed unexpected temperature dependence of the thermal conductivity of magnetic semiconductors above the magnetic ordering temperature.

First-principles prediction of sub-10-nm skyrmions in Pd/Fe bilayers on Rh(111)

We show that stable skyrmions with diameters of a few nanometers can emerge in atomic Pd/Fe bilayers on the Rh(111) surface. Based on density functional theory we calculate the exchange and the Dzyaloshinskii-Moriya interaction as well as the magnetocrystalline anisotropy energy. The later two terms are driven by spin-orbit coupling and significantly reduced compared to Pd/Fe bilayers on Ir(111) as expected since Rh and Ir are isoelectronic $4d$ and $5d$ transition-metals. However, there is still a spin spiral ground state at zero magnetic field. Atomistic spin dynamics simulations show that a skyrmion phase occurs at small magnetic fields of $\sim$ 1 T. Skyrmion diameters amount to 2 to 8 nm and skyrmion lifetimes are up to 1 hour at temperatures of 25 to 45 K.

A majority gate with chiral magnetic solitons

In magnetic materials, nontrivial spin textures may emerge due to the competition among different types of magnetic interactions. Among such spin textures, chiral magnetic solitons represent topologically protected spin configurations with particle-like properties. Based on atomistic spin dynamics simulations, we demonstrate that these chiral magnetic solitons are ideal to use for logical operations, and we demonstrate the functionality of a three-input majority gate, in which the input states can be controlled by applying an external electromagnetic field or spin-polarized currents. One of the main advantages of the proposed device is that the input and output signals are encoded in the chirality of solitons, that may be moved, allowing to perform logical operations using only minute electric currents. As an example we illustrate how the three input majority gate can be used to perform logical relations, such as Boolean AND and OR.

Ultrafast double magnetization switching in GdFeCo with two picosecond-delayed femtosecond pump pulses

The recently discovered thermally induced magnetization switching (TIMS) induced by single femtosecond laser pulses in ferrimagnetic GdFeCo alloys proceeds on the picosecond time-scale. The rate at which data can be changed for use of TIMS in technological devices is limited by the processes leading to thermal equilibrium. In the present work, we address the question of whether it is possible to further excite switching via TIMS well before thermal equilibrium between subsystems is reached. In particular, we investigate the conditions for double thermally induced magnetic switching by the application of two shortly delayed laser pulses. These conditions become relevant for potential applications as it sets both a limit to rewrite data and demonstrates the importance of spatial confinement of a heat pulse to bit size, as neighboring bits may be accidentally re-switched for spatially extended pulse spots. To demonstrate this effect, we theoretically study the switching behavior in a prototypical ferrimagnetic GdFeCo alloy as a function of composition. We use computer simulations based on thermal atomistic spin dynamics and demonstrate the possibility of inducing a second switching event well before thermal equilibrium is reached and define the conditions under which it can occur. Our theoretical findings could serve as a guidance for further understanding of TIMS as well as to act as a guide for future applications.

Coherent and incoherent ultrafast magnetization dynamics in 3d ferromagnets driven by extreme terahertz fields

Ultrafast spin dynamics in magnetic materials is generally associated with ultrafast heating of the electronic system by a near infrared femtosecond laser pulse, thus offering only an indirect and nonselective access to the spin order. Here we explore spin dynamics in ferromagnets by means of extremely intense THz pulses, as at these low frequencies the magnetic field provides a direct and selective route to coherently control the magnetization. We find that, at low fields, the observed off-resonantly excited spin precession is phase locked to the THz magnetic field. At extreme THz fields, the coherent spin dynamics become convoluted with an ultrafast incoherent magnetic quenching due to the absorbed energy. This demagnetization takes place upon a single shot exposure. The magnetic properties are found to be permanently modified above a THz pump fluence of $\ensuremath{\approx}100\phantom{\rule{0.28em}{0ex}}\mathrm{mJ}/{\mathrm{cm}}^{2}$. We conclude that magnetization switching cannot be reached. Our atomistic spin-dynamics simulations excellently explain the measured magnetization response. We find that demagnetization driven by THz laser-field coupling to electron charges occurs, suggesting nonconducting materials for achieving coherent THz-magnetization reversal.