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Ultrafast magnetization dynamics are governed by energy flow between electronic, magnetic, and lattice degrees of freedom. A quantitative understanding of these dynamics must be based on a model that agrees with experimental results for all three subsystems. However, ultrafast dynamics of the lattice remain largely unexplored experimentally. Here, we combine femtosecond electron diffraction experiments of the lattice dynamics with energy-conserving atomistic spin dynamics (ASD) simulations and ab-initio calculations to study the intrinsic energy flow in the 3d ferromagnets cobalt (Co) and iron (Fe). The simulations yield a good description of experimental data, in particular an excellent description of our experimental results for the lattice dynamics. We find that the lattice dynamics are influenced significantly by the magnetization dynamics due to the energy cost of demagnetization. Our results highlight the role of the spin system as the dominant heat sink in the first hundreds of femtoseconds. Together with previous findings for nickel, our work demonstrates that energy-conserving ASD simulations provide a general and consistent description of the laser-induced dynamics in all three elemental 3d ferromagnets.

DFT data concerning the electronic structure and electron-phonon coupling of Co and Fe. NOT the atomistic spin simulations. NO experimental data.

Many questions are still open regarding the physical mechanisms behind the magnetic switching in Gd-Fe-Co alloys by single optical pulses. Phenomenological models suggest a femtosecond scale exchange relaxation between sublattice magnetization as the driving mechanism for switching. The recent observation of thermally induced switching in Gd-Fe-Co by using both several picosecond optical laser pulse as well as electric current pulses has questioned this previous understanding. This has raised the question of whether or not the same switching mechanics are acting at the femtosecond and picosecond scales. In this work, we aim at filling this gap in the understanding of the switching mechanisms behind thermal single-pulse switching. To that end, we have studied experimentally thermal single-pulse switching in Gd-Fe-Co alloys, for a wide range of system parameters, such as composition, laser power, and pulse duration. We provide a quantitative description of the switching dynamics using atomistic spin dynamics methods with excellent agreement between the model and our experiments across a wide range of parameters and timescales, ranging from femtoseconds to picoseconds. Furthermore, we find distinct element-specific damping parameters as a key ingredient for switching with long picosecond pulses and argue that switching with pulse durations as long as 15 ps is possible due to a low damping constant of Gd. Our findings can be easily extended to speed up dynamics in other contexts where ferrimagnetic Gd-Fe-Co alloys have been already demonstrated to show fast and energy-efficient processes, e.g., domain-wall motion in a track and spin-orbit torque switching in spintronics devices.

Many questions are still open regarding the physical mechanisms behind the magnetic switching in Gd-Fe-Co alloys by single optical pulses. Phenomenological models suggest a femtosecond scale exchange relaxation between sublattice magnetization as the driving mechanism for switching. The recent observation of thermally induced switching in Gd-Fe-Co by using both several picosecond optical laser pulse as well as electric current pulses has questioned this previous understanding. This has raised the question of whether or not the same switching mechanics are acting at the femtosecond and picosecond scales. In this work, we aim at filling this gap in the understanding of the switching mechanisms behind thermal single-pulse switching. To that end, we have studied experimentally thermal single-pulse switching in Gd-Fe-Co alloys, for a wide range of system parameters, such as composition, laser power, and pulse duration. We provide a quantitative description of the switching dynamics using atomistic spin dynamics methods with excellent agreement between the model and our experiments across a wide range of parameters and timescales, ranging from femtoseconds to picoseconds. Furthermore, we find distinct element-specific damping parameters as a key ingredient for switching with long picosecond pulses and argue that switching with pulse durations as long as 15 ps is possible due to a low damping constant of Gd. Our findings can be easily extended to speed up dynamics in other contexts where ferrimagnetic Gd-Fe-Co alloys have been already demonstrated to show fast and energy-efficient processes, e.g., domain-wall motion in a track and spin-orbit torque switching in spintronics devices.

Many questions are still open regarding the physical mechanisms behind the magnetic switching in Gd-Fe-Co alloys by single optical pulses. Phenomenological models suggest a femtosecond scale exchange relaxation between sublattice magnetization as the driving mechanism for switching. The recent observation of thermally induced switching in Gd-Fe-Co by using both several picosecond optical laser pulse as well as electric current pulses has questioned this previous understanding. This has raised the question of whether or not the same switching mechanics are acting at the femtosecond and picosecond scales. In this work, we aim at filling this gap in the understanding of the switching mechanisms behind thermal single-pulse switching. To that end, we have studied experimentally thermal single-pulse switching in Gd-Fe-Co alloys, for a wide range of system parameters, such as composition, laser power, and pulse duration. We provide a quantitative description of the switching dynamics using atomistic spin dynamics methods with excellent agreement between the model and our experiments across a wide range of parameters and timescales, ranging from femtoseconds to picoseconds. Furthermore, we find distinct element-specific damping parameters as a key ingredient for switching with long picosecond pulses and argue that switching with pulse durations as long as 15 ps is possible due to a low damping constant of Gd. Our findings can be easily extended to speed up dynamics in other contexts where ferrimagnetic Gd-Fe-Co alloys have been already demonstrated to show fast and energy-efficient processes, e.g., domain-wall motion in a track and spin-orbit torque switching in spintronics devices.

The ultrafast dynamics of magnetic order in a ferromagnet are governed by the interplay between electronic, magnetic and lattice degrees of freedom. In order to obtain a microscopic understanding of ultrafast demagnetization, information on the response of all three subsystems is required. A consistent description of demagnetization and microscopic energy flow, however, is still missing. Here, we combine a femtosecond electron diffraction study of the ultrafast lattice response of nickel to laser excitation with ab initio calculations of the electron-phonon interaction and energy conserving atomistic spin dynamics simulations. Our model is in agreement with the observed lattice dynamics and previously reported electron and magnetization dynamics. Our approach reveals that the spin system is the dominating heat sink in the initial few hundreds of femtoseconds and implies a transient non-thermal state of the spins. Our results provide a clear picture of the microscopic energy flow between electronic, magnetic and lattice degrees of freedom on ultrafast timescales and constitute a foundation for theoretical descriptions of demagnetization that are consistent with the dynamics of all three subsystems.

The ultrafast dynamics of magnetic order in a ferromagnet are governed by the interplay between electronic, magnetic and lattice degrees of freedom. In order to obtain a microscopic understanding of ultrafast demagnetization, information on the response of all three subsystems is required. A consistent description of demagnetization and microscopic energy flow, however, is still missing. Here, we combine a femtosecond electron diffraction study of the ultrafast lattice response of nickel to laser excitation with ab initio calculations of the electron-phonon interaction and energy conserving atomistic spin dynamics simulations. Our model is in agreement with the observed lattice dynamics and previously reported electron and magnetization dynamics. Our approach reveals that the spin system is the dominating heat sink in the initial few hundreds of femtoseconds and implies a transient non-thermal state of the spins. Our results provide a clear picture of the microscopic energy flow between electronic, magnetic and lattice degrees of freedom on ultrafast timescales and constitute a foundation for theoretical descriptions of demagnetization that are consistent with the dynamics of all three subsystems.

A hierarchical multiscale approach to model the magnetization dynamics of ferromagnetic random alloys is presented. First-principles calculations of the Heisenberg exchange integrals are linked to atomistic spin models based upon the stochastic Landau-Lifshitz-Gilbert (LLG) equation to calculate temperature-dependent parameters (e.g., effective exchange interactions, damping parameters). These parameters are subsequently used in the Landau-Lifshitz-Bloch (LLB) model for multisublattice magnets to calculate numerically and analytically the ultrafast demagnetization times. The developed multiscale method is applied here to FeNi (permalloy) as well as to copper-doped FeNi alloys. We find that after an ultrafast heat pulse the Ni sublattice demagnetizes faster than the Fe sublattice for the here-studied FeNi-based alloys.

A hierarchical multiscale approach to model the magnetization dynamics of ferromagnetic random alloys is presented. First-principles calculations of the Heisenberg exchange integrals are linked to atomistic spin models based upon the stochastic Landau-Lifshitz-Gilbert (LLG) equation to calculate temperature-dependent parameters (e.g., effective exchange interactions, damping parameters). These parameters are subsequently used in the Landau-Lifshitz-Bloch (LLB) model for multisublattice magnets to calculate numerically and analytically the ultrafast demagnetization times. The developed multiscale method is applied here to FeNi (permalloy) as well as to copper-doped FeNi alloys. We find that after an ultrafast heat pulse the Ni sublattice demagnetizes faster than the Fe sublattice for the here-studied FeNi-based alloys.

Micromagnetic modeling has proved itself as a widely used tool, complimentary in many respects to experimental measurements. The Landau-Lifshitz equation provides a basis for this modeling, especially where the dynamical behaviour is concerned. However, this approach is strictly valid only for zero temperature and for high temperatures must be replaced by a more thermodynamically consistent approach such as the Landau-Lifshitz-Bloch (LLB) equation. Here we review the recently derived LLB equation for two-sublattice systems and extend its derivation for temperatures above the Curie temperature. We present comparison with many-body atomistic simulations and show that this equation can describe the ultra-fast switching in ferrimagnets, observed experimentally.

The Landau-Lifshitz (LL) equation, originally proposed at the macrospin level, is increasingly used in Atomistic Spin Dynamic (ASD) models. These models are based on a spin Hamiltonian featuring atomic spins of fixed length, with the exchange introduced using the Heisenberg formalism. ASD models are proving a powerful approach to the fundamental understanding of ultrafast magnetization dynamics, including the prediction of the thermally induced magnetization switching phenomenon in which the magnetization is reversed using an ultrafast laser pulse in the absence of an externally applied field. This paper outlines the ASD model approach and considers the role and limitations of the LL equation in this context.

Using large-scale computer simulations, we thoroughly study the minimum energy required to thermally induced magnetization switching (TIMS) after the application of a femtosecond heat pulse in transition metal-rare earth ferrimagnetic alloys. We find that for an energy efficient TIMS, a low ferrimagnetic net magnetization with a strong temperature dependence is the relevant factor for the magnetic system. For the lattice and electron systems, the key physics for efficient TIMS is a large electron-phonon relaxation time. Importantly, we show that as the cooling time of the heated electrons is increased, the minimum power required to produce TIMS can be reduced by an order of magnitude. Our results show the way to low power TIMS by appropriate engineering of magnetic heterostructures.

The detailed derivation of the quantum Landau-Lifshitz-Bloch (qLLB) equation for simple spin-flip scattering mechanisms based on spin-phonon and spin-electron interactions is presented and the approximations are discussed. The qLLB equation is written in a form suitable for comparison with its classical counterpart. The temperature dependence of the macroscopic relaxation rates is discussed for both mechanisms. It is demonstrated that the magnetization dynamics is slower in the quantum case than in the classical one.

It was recently observed that the two antiferromagnetically coupled sublattices of a rare earth-transition metal ferrimagnet can temporarily align ferromagnetically during femtosecond laser heating, but always with the transition metal aligning in the rare earth direction. This behavior has been attributed to the slower magnetization dynamics of the rare earth sublattice. The aim of this work was to assess how the difference in the speed of the transition metal and rare earth dynamics affects the formation of the transient ferromagneticlike state and consequently controls its formation. Our investigation was performed using extensive atomistic spin simulations and analytic micromagnetic theory of ferrimagnets, with analysis of a large area of parameter space such as initial temperature, Gd concentration, and laser fluence. Surprisingly, we found that at high temperatures, close to the Curie point, the rare earth dynamics become faster than those of the transition metal. Subsequently we show that the transient state can be formed with the opposite polarity, where the rare earth aligns in the transition metal direction. Our findings shed light on the complex behavior of this class of ferrimagnetic materials and highlight an important feature which must be considered, or even exploited, if these materials are to be used in ultrafast magnetic devices.

There has been much interest recently in the discovery of thermally induced magnetisation switching using femtosecond laser excitation, where a ferrimagnetic system can be switched deterministically without an applied magnetic field. Experimental results suggest that the reversal occurs due to intrinsic material properties, but so far the microscopic mechanism responsible for reversal has not been identified. Using computational and analytic methods we show that the switching is caused by the excitation of two-magnon bound states, the properties of which are dependent on material factors. This discovery allows us to accurately predict the onset of switching and the identification of this mechanism will allow new classes of materials to be identified or designed for memory devices in the THz regime.

Ultrafast laser-induced magnetic switching in rare earth-transition metal ferrimagnetic alloys has recently been reported to occur by ultrafast heating alone. Using atomistic simulations and a ferrimagnetic Landau-Lifshitz-Bloch formalism, we demonstrate that for switching to occur it is necessary that angular momentum is transferred from the longitudinal to transverse magnetization components in the transition metal. This dynamical path leads to the transfer of the angular momentum to the rare earth metal and magnetization switching with subsequent ultrafast precession caused by the intersublattice exchange field on the atomic scale. © 2013 American Physical Society.

Contains fulltext : 94155.pdf (preprint version ) (Open Access)

Contains fulltext : 94155.pdf (preprint version ) (Open Access)

Contains fulltext : 94155.pdf (preprint version ) (Open Access)

El objetivo de esta tesis ha sido por tanto, avanzar en el conocimiento de los procesos microscópicos relevantes que se producen en la escala de tiempo del femtosegundo incluyendo la dinámica de los electrones, fonones y las ondas de espines de frecuencia THz. Esto nos ha permitido comprender las velocidades de desimanación ultrarrápidas: la desimanación a fs, la recuperación a ps y la amortiguación precesional a 100 ps. En resumen, en la presente tesis hemos realizado el siguiente trabajo: • Desarrollo de modelos de la dinámica de la imanación válidos en todo el rango de temperaturas. El modelo está basado en la ecuación LLB para materiales ferromagnéticos y en el modelo 2T para la evolución temporal de las temperaturas electrónicas y de la red. • Comparación del modelo con experimentos de velocidad de desimanación ultrarrápida en Ni y Gd, permitiendo dar sentido físico a las velocidades de desimanación ultrarrápidas. • Desarrollo del modelo macroscópico para materiales ferrimagnéticos y antiferromagnéticos. El modelo está basado en los mecanismos térmicos; está derivado de forma similar a la ecuación LLB para materiales ferromagnéticos y verificado mediante simulaciones atomísticas, para después aplicarlo los parámetros específicos del material ferrimagnético GdFeCo. • Introdución, en el modelo de cálculos atomísticos, de correlaciones temporales en el ruido térmico (ruido coloreado). A partir de este nuevo modelo atomístico generalizamos el modelo micromagnético basado en la ecuación LLB para ruido blanco en un modelo LLB para ruido coloreado.

Contains fulltext : 91679.pdf (publisher's version ) (Open Access)

Contains fulltext : 91679.pdf (publisher's version ) (Open Access)

We present a dynamic approach to micromagnetics based on the Landau-Lifshitz-Bloch equation and Langevin dynamics. This type of modeling will be necessary at high temperatures when the magnetization length is not conserved, especially close to the Curie temperature. We model the laser-induced magnetization dynamics with various laser pulse fluences and show that the results are consistent with both experiments and atomistic modeling. Our results show different recovery rates depending on the final demagnetized state.