Ultrafast demagnetizing fields from first principles
Summary (2 min read)
Introduction
- The authors examine the ultrafast demagnetization process of iron-based materials, namely, Fe6 clusters and bulk bcc.
- The magnetization continuity equation is reformulated and the torque due to the spin-current divergence is written in terms of an effective time-dependent kinetic magnetic field, an object already introduced in the literature.
- In a standard pump- experiment the system is initially excited by an optical pulse (pump) and then the magnetization dynamics is monitored by analyzing a second signal [4,5].
- This becomes more clear through evaluation of material derivatives.
II. THEORY
- The authors consider the TDSDFT problem within the ALSDA for a spin-polarized system excited by an electric-field pulse.
- In DFT there is a set of zero-force theorems stating that the interaction between the particles cannot generate a net force [22].
III. ANALYZING SPIN DYNAMICS FROM TDSDFT
- Here the authors present the results of TDSDFT calculations, performed with the OCTOPUS code [31], where they simulate the ultrafast demagnetization process in iron-based ferromagnetic systems.
- Moving from an analysis of global quantities to probing locally the spin dynamics, in Fig. 1(d) the authors compare the magnetization and the electron density around atomic site 6 at the tip of the cluster [see inset of Fig. 1(a) for the numbering labels of all the cluster atoms].
- This suggests that the spin-sink mechanism is not directly related to the coupling of the system to the laser field, but is rather intrinsic to the electron dynamics following the pulse.
- By applying the latter in Eq. (12) the authors finally obtain a relation that can be considered approximately valid in this spatial region of the simulation box, d dt m(r,t) −∇ · D + μBm × Bkin + TSO, (22) where the contribution to the spin dynamics due to the velocity-field term has been neglected.
- In fact, the average change following the excitation pulse is larger for site 6 (the one experiencing the larger demagnetization), but the fluctuations are more pronounced for site 1 [the one experiencing the larger fluctuations in SIz(t)].
IN THE Fe6 CLUSTER
- In the previous sections the authors have revisited the concept of kinetic field, its derivation within DFT, and its properties as a major source of torque for the spin dynamics within the ALSDA.
- In this section the authors seek to extend the evidential base for the connection between the torque due to Bkin and the rate of demagnetization.
- Together with that the authors report a situation where the direction of the polarization vector of the electric field of the laser pulse alone has a significant effect on the demagnetization of a material (the Fe6 cluster).
- Notably, there is a change in the symmetry between Figs. 5(c) and 5(e):.
- In both cases no significant spin noncollinearity arises in the plane parallel to the field connecting the atomic centers.
V. DEMAGNETIZATION OF bcc Fe
- Finally, the authors present results of analogous simulations in bulk materials, namely, in bcc Fe, with the aim of demonstrating the qualitative universal role played by Bkin in the ultrafast demagnetization process.
- Fe in its ferromagnetic phase with total spin in the unit cell S = 4.85 /2 and with two atoms in it.
- In Fig. 6(c) the authors show the demagnetization rate of the single unit cell after it has been excited with the electric-field pulse [Fig. 6(a)].
- Similarly to the case of Fe6, the role played by ∇ · D(r,t) is dominant during the action of the pulse, but after this initial phase the dynamics is dominated by intraband transitions and the interplay between the spin-orbit coupling and the effective field Beff becomes dominant.
- The level of correlation among the two quantities confirms the importance of the kinetic field in the evolution of the spin noncollinearity.
VI. CONCLUSION
- In conclusion, the authors state the central result of their work, namely, that the equation of motion for the spin dynamics within the ALSDA of TDSDFT [see Eq. (8)] can be rewritten in the form of Eq. (12), by using a formalism borrowed from magnetohydrodynamics.
- The role of this field is particularly significant for processes far from equilibrium, such as the ultrafast demagnetization observed in transition metals.
- As Ai describes the degree of spin rotation per infinitesimal spatial translation, it also provides a measure for the misalignment between the kinetic field and the spin texture.
- The authors analysis has shown a significant increase in the noncollinearity between Bkin(r,t) and the spin density in the fast demagnetizing case.
- Fe the magnetization loss is more prominent after the laser pulse has been reduced to zero.
Did you find this useful? Give us your feedback
Citations
207 citations
68 citations
52 citations
Cites background from "Ultrafast demagnetizing fields from..."
...For the first few fs, the fundamental magnetic parameters are also strongly time and temperature dependent due to the effects of the laser on the underlying electronic structure (Simoni et al. 2017)....
[...]
27 citations
24 citations
References
6,874 citations
1,920 citations
1,449 citations
868 citations
788 citations
Related Papers (5)
Frequently Asked Questions (11)
Q2. What have the authors stated for future works in "Ultrafast demagnetizing fields from first principles" ?
The authors have found that clusters will demagnetize about twice as fast if the polarization vector is in the base plane and not vertical ( through the apex atoms ). During the application of the laser pulse, the rise of spin noncollinearity may be enhanced by the particular polarization direction of the laser pulse through the spin-orbit coupling and this effect combined with the collapse of the kinetic field may explain the initial spin loss.
Q3. What is the effect of the laser pulse on the spin density?
During the application of the laser pulse, the rise of spin noncollinearity may be enhanced by the particular polarization direction of the laser pulse through the spin-orbit coupling and this effect combined with the collapse of the kinetic field may explain the initial spin loss.
Q4. What is the effect of the SO enhanced by the collapse of the effective field?
The first fast decay may be attributed to the effect of the SO enhanced by the collapse of the effective field Beff following the action of the laser pulse.
Q5. What is the effect of the pulse on the spin dynamics?
Hence the long-term spin dynamics is not the result of a net charge displacement from the region close to the ions to the interstitial space.
Q6. What is the role of the effective field in the evolution of the spin vector?
The role of this field is particularly significant for processes far from equilibrium, such as the ultrafast demagnetization observed in transition metals.
Q7. Why does the laser pulse excit the currents?
This is due to the fact that the laser pulse directly excites currents, through the term −∇ · D(r,t) in Eq. (12), which in turn produces a modification of the gradients of the charge/spin density, even on a global scale since they are not conserved.
Q8. What is the result of the interplay between the SO coupling and Bkin(r,?
In both systems studied the spin dynamics is the result of the interplay between the SO coupling and Bkin(r,t), which,024412-7in general, is strongly coupled to the external pulse and highly nonuniform in space.
Q9. What is the kinetic field of Eq. 13?
By using the previous expression to rewrite the first- and second-order spatial derivatives, the kinetic field of Eq. (13) can be divided into two componentsBkin(r,t) = B0kin(r,t) + δBkin(r,t). (24)
Q10. What is the role of D(r,t) during the action of the pulse?
Similarly to the case of Fe6, the role played by ∇ · D(r,t) isdominant during the action of the pulse, but after this initial phase the dynamics is dominated by intraband transitions and the interplay between the spin-orbit coupling and the effective field Beff becomes dominant.
Q11. What is the kinetic field of the ALSDA?
In the previous sections the authors have revisited the concept of kinetic field, its derivation within DFT, and its properties as a major source of torque for the spin dynamics within the ALSDA.