Temperature scaling of the Dzyaloshinsky-Moriya interaction in the spin wave spectrum

The temperature scaling of the micromagnetic Dzyaloshinsky-Moriya exchange interaction is calculated for the whole range of temperature. We use Green's function theory to derive the finite-temperature spin wave spectrum of ferromagnetic systems described by a classical atomistic spin model Hamiltonian. Within this model, we find universal expressions for the temperature scaling not only of the Dzyaloshinsky-Moriya interaction but also of the Heisenberg exchange stiffness and the single-ion anisotropy. In the spirit of multiscale models, we establish a clear connection between the atomistic interactions and the temperature-dependent coefficients in the spin wave spectrum and in the micromagnetic free energy functional. We demonstrate that the corrections to mean-field theory or the random phase approximation for the temperature scaling of Dzyaloshinsky-Moriya and Heisenberg exchange interactions assume very similar forms. In the presence of thermal fluctuations and Dzyaloshinsky-Moriya interaction an anisotropy-like term emerges in the spin wave spectrum which, at low temperature, increases with temperature, in contrast to the decreasing single-ion anisotropy. We evaluate the accuracy of the theoretical method by comparing it to the spin wave spectrum calculated from Monte Carlo simulations.Comment: 11 pages, 4 figure

Temperature dependence of spin-model parameters in antiferromagnets

The temperature dependence of mesoscopic spin-model parameters is derived in two-sublattice antiferromagnetically aligned systems based on Green's function theory. It is found that transversal spin correlations decrease the anisotropy terms while increasing the Heisenberg and Dzyaloshinsky--Moriya exchange interactions and the latter's contribution to the anisotropy. The obtained temperature dependences show quantitative agreement with the results for ferromagnets, and they also agree well with numerical atomistic simulations which treat the spin correlations without approximations. Possible applications of the results in multiscale modelling are discussed.Comment: 13 pages, 7 figure

Bridging atomistic spin dynamics methods and phenomenological models of single-pulse ultrafast switching in ferrimagnets

We bridge an essential knowledge gap on the understanding of all-optical ultrafast switching in ferrimagnets, namely, the connection between atomistic spin dynamics methods and macroscopic phenomenological models. All-optical switching of the magnetization occurs after the application of a single femtosecond laser pulse to specific ferrimagnetic compounds. This strong excitation puts the involved degrees of freedom, electrons, lattice, and spins out-of-equilibrium between each other. Atomistic spin models have quantitatively described all-optical switching in a wide range of experimental conditions, while having failed to provide a simple picture of the switching process. Phenomenological models are able to qualitatively describe the dynamics of the switching process. However, a unified theoretical framework is missing that describes the element-specific spin dynamics as atomistic spin models with the simplicity of phenomenology. Here, we bridge this gap and present an element-specific macrospin dynamical model which fully agrees with atomistic spin dynamics simulations and symmetry considerations of the phenomenological models

Electron-phonon mediated spin-flip as driving mechanism for ultrafast magnetization dynamics in 3dd ferromagnets

Despite intense experimental effort, theoretical proposals and modeling approaches, a lack of consensus exists about the intrinsic mechanisms driving ultrafast magnetization dynamics in 3$d$ ferromagnets. In this work, we find evidence of electron-phonon mediated spin-flip as the driving mechanism for the ultrafast magnetization dynamics in all three 3$d$ ferromagnets; nickel, iron and cobalt. We use a microscopic three temperature model with parameters calculated from first-principles, which has been validated by direct comparison to the electron and lattice dynamics extracted from previous experiments. By direct comparison to the experimentally measured magnetization dynamics for different laser fluence, we determine the spin-flip probability of each material. In contrast to previous findings but in agreement to ab-initio predictions, we find that relatively small values of the spin-flip probability enable ultrafast demagnetization in all three 3$d$ ferromagnets

Reduced thermal stability of antiferromagnetic nanostructures

Antiferromagnetic materials hold promising prospects in novel types of spintronics applications. Assessing the stability of antiferromagnetic nanostructures against thermal excitations is a crucial aspect of designing devices with a high information density. Here we use theoretical calculations and numerical simulations to determine the mean switching time of antiferromagnetic nanoparticles in the superparamagnetic limit. It is demonstrated that the thermal stability is drastically reduced compared to ferromagnetic particles in the limit of low Gilbert damping, attributed to the exchange enhancement of the attempt frequencies. It is discussed how the system parameters have to be engineered in order to optimize the switching rates in antiferromagnetic nanoparticles.Comment: 12 pages, 6 figures. Supplemental Videos available with the published versio

Temperature scaling of two-ion anisotropy in pure and mixed anisotropy systems

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)∼m2.28, while the mixed scenario describes the diversity of the temperature dependence of the anisotropy observed in real materials. The deviation of the scaling exponent of the mixed anisotropy from previous mean-field results is ascribed to correlated thermal spin fluctuations, and its value determined here is expected to considerably contribute to the understanding and the control of the thermal properties of magnetic materials

Realistic micromagnetic description of all-optical ultrafast switching processes in ferrimagnetic alloys

[EN]Both helicity-independent and helicity-dependent all-optical switching processes driven by single ultrashort laser pulse have been experimentally demonstrated in ferrimagnetic alloys as GdFeCo. Although the switching has been previously reproduced by atomistic simulations, the lack of a robust micromagnetic framework for ferrimagnets limits the predictions to small nanosystems, whereas the experiments are usually performed with lasers and samples of tens of micrometers. Here we develop a micromagnetic model based on the extended Landau-Lifshitz-Bloch equation, which is firstly validated by directly reproducing atomistic results for small samples and uniform laser heating. After that, the model is used to study ultrafast single shot all-optical switching in ferrimagnetic alloys under realistic conditions.We find that the helicity-independent switching under a linearly polarized laser pulse is a pure thermal phenomenon, in which the size of inverted area directly correlates with the maximum electron temperature in the sample. On the other hand, the analysis of the helicity-dependent processes under circular polarized pulses in ferrimagnetic alloys with different composition indicates qualitative differences between the results predicted by the magnetic circular dichroism and the ones from inverse Faraday effect. Based on these predictions, we propose experiments that would allow one to resolve the controversy over the physical phenomenon that underlies these helicity-dependent all optical processes.This work was supported by Projects No. MAT2017- 87072-C4-1-P funded by Ministerio de Educacion y Ciencia and No. PID2020117024GB-C41 funded by Ministerio de Ciencia e Innovacion, both from the Spanish government, Projects No. SA299P18 and No. SA114P20 from Consejeria de Educacion of Junta de Castilla y León, and project MagnEFi, Grant Agreement No. 860060, (H2020-MSCAITN- 2019) funded by the European Commission. U.A. would like to acknowledge funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—Project- ID 328545488—TRR 227, Project No. A08

Accelerating double pulse all-optical write/erase cycles in metallic ferrimagnets

All-optical switching of magnetic order presents a promising route toward faster and more energy efficient data storage. However, a realization in future devices is ultimately dependent on the maximum repetition rates of optically induced write/erase cycles. Here, we present two strategies to minimize the temporal separation of two consecutive femtosecond laser pulses to toggle the out-of-plane direction of the magnetization of ferrimagnetic rare-earth transition metal alloys. First, by systematically changing the heat transfer rates using either amorphous glass, crystalline silicon, or polycrystalline diamond substrates, we show that efficient cooling rates of the magnetic system present a prerequisite to accelerate the sequence of double pulse toggle switching. Second, we demonstrate that replacing the transition metal iron by cobalt leads to a significantly faster recovery of the magnetization after optical excitation allowing us to approach terahertz frequency of write/erase cycles with a minimum pulse-to-pulse separation of 7 ps

Breaking through the Mermin-Wagner limit in 2D van der Waals magnets

The Mermin-Wagner theorem states that long-range magnetic order does not exist in one- (1D) or two-dimensional (2D) isotropic magnets with short-ranged interactions. Here we show that in finite-size 2D van der Waals magnets typically found in lab setups (within millimetres), short-range interactions can be large enough to allow the stabilisation of magnetic order at finite temperatures without any magnetic anisotropy. We demonstrate that magnetic ordering can be created in 2D flakes independent of the lattice symmetry due to the intrinsic nature of the spin exchange interactions and finite-size effects. Surprisingly we find that the crossover temperature, where the intrinsic magnetisation changes from superparamagnetic to a completely disordered paramagnetic regime, is weakly dependent on the system length, requiring giant sizes (e.g., of the order of the observable universe ~ 1026 m) to observe the vanishing of the magnetic order as expected from the Mermin-Wagner theorem. Our findings indicate exchange interactions as the main ingredient for 2D magnetism