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The relaxation of the magnetisation in magnetic materials is of great importance from both an applied and fundamental point of view. Conventional modelling of magnetisation dynamics employs the Landau-Lifshitz-Gilbert (LLG) equation[1] where the damping is included phenomenologically by a term that describes the coupling of the magnetic modes (given primarily by the atomic spin) to the non-magnetic modes (lattice vibrations and electron orbits) which are assumed to be in equilibrium. Recent studies of the dynamics induced by THz laser pulses has highlighted the necessity of understanding magnetisation relaxation beyond this assumption. In reality the spin and lattice dynamics mutually influence one another, hence it is necessary to employ a unified model of molecular and spin dynamics [2], Spin-Lattice dynamics (SLD). The transfer of energy and angular momentum between the lattice and the spin system is realised by the pseudo-dipolar coupling [3], which arises from the spin-orbit interaction and can be parameterised by magneto-elastic experiments. Our results show that the equilibrium magnetisation is independent of the thermostat used and by coupling the spin system only to the lattice vibrations the magnetisation temperature dependence can be reproduced without the need of a phenomenological spin damping. The autocorrelation of the coupling field (which acts as an induced noise on the spin systems) shows well defined excitation peaks at nonzero frequencies corresponding to both phonon and magnon modes, proving a successful coupling between the two subsystems (Fig.1). The magnon-phonon damping is evaluated within this framework (Fig. 2) and agrees well with the damping measured in magnetic insulators where it depends more on magnon-phonon coupling than electronic effects. Our model opens the possibility to describe the distinct dynamics of spins and phonons, necessary for the understanding of ultrafast magnetisation dynamics experiments.References: [1] T. L. Gilbert, IEEE Trans. Magn. 40, 3443 (2004). [2] P.-W. Ma, C. Woo, and S. Dudarev, “Large-scale simulation of the spin-lattice dynamics in ferromagnetic iron,” Phys. Rev. B, vol. 78, no. 2, p. 024434, Jul. 2008. [3] Aßmann, Matthias, and Ulrich Nowak. &quot;Spin-lattice relaxation beyond Gilbert damping.&quot; Journal of Magnetism and Magnetic Materials 469 (2019): 217-223.

MMM 2020

Advanced Atomistic Modelling of Magnetisation Dynamics with Spin and Lattice Degrees of Freedom

The 65th Annual Conference on Magnetism and Magnetic Materials (MMM 2020) was held in a virtual form. The COVID-19 pandemic, with its associated uncertainty about international travel and the ability to gather in large groups, meant that the Steering Committee decided to cancel the face-to-face meeting that had been planned in Palm Beach, Florida November 2-6, 2020.

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The relaxation of the magnetisation in magnetic materials is of great importance from both an applied and fundamental point of view. Conventional modelling of magnetisation dynamics employs the Landau-Lifshitz-Gilbert (LLG) equation[1] where the damping is included phenomenologically by a term that describes the coupling of the magnetic modes (given primarily by the atomic spin) to the non-magnetic modes (lattice vibrations and electron orbits) which are assumed to be in equilibrium. Recent studies of the dynamics induced by THz laser pulses has highlighted the necessity of understanding magnetisation relaxation beyond this assumption. In reality the spin and lattice dynamics mutually influence one another, hence it is necessary to employ a unified model of molecular and spin dynamics [2], Spin-Lattice dynamics (SLD). The transfer of energy and angular momentum between the lattice and the spin system is realised by the pseudo-dipolar coupling [3], which arises from the spin-orbit interaction and can be parameterised by magneto-elastic experiments. Our results show that the equilibrium magnetisation is independent of the thermostat used and by coupling the spin system only to the lattice vibrations the magnetisation temperature dependence can be reproduced without the need of a phenomenological spin damping. The autocorrelation of the coupling field (which acts as an induced noise on the spin systems) shows well defined excitation peaks at nonzero frequencies corresponding to both phonon and magnon modes, proving a successful coupling between the two subsystems (Fig.1). The magnon-phonon damping is evaluated within this framework (Fig. 2) and agrees well with the damping measured in magnetic insulators where it depends more on magnon-phonon coupling than electronic effects. Our model opens the possibility to describe the distinct dynamics of spins and phonons, necessary for the understanding of ultrafast magnetisation dynamics experiments.References: [1] T. L. Gilbert, IEEE Trans. Magn. 40, 3443 (2004). [2] P.-W. Ma, C. Woo, and S. Dudarev, “Large-scale simulation of the spin-lattice dynamics in ferromagnetic iron,” Phys. Rev. B, vol. 78, no. 2, p. 024434, Jul. 2008. [3] Aßmann, Matthias, and Ulrich Nowak. "Spin-lattice relaxation beyond Gilbert damping." Journal of Magnetism and Magnetic Materials 469 (2019): 217-223.

technical paper

The observation of ultrafast manipulation and coherent control of spins in magnetic materials at room temperature [1-2] has prompted the intense experimental and theoretical efforts to understand the underlying microscopic mechanisms and relevant interactions (exchange, spin-lattice, electron-phonon, coulomb etc.) driving such magnetic phenomena at sub-picosecond timescales. Stoichiometric B2 ordered epitaxial (001) FeRh undergoes a first order magnetic phase transition from antiferromagnetic (AFM) to ferromagnetic (FM) at ≈ 380K. In the AFM phase of FeRh, only Fe has net magnetic moment, whereas in the FM phase both Fe and Rh carry net moments. The phase transition is also accompanied by a ≈ 1% isotropic lattice expansion in the bulk BCC structure, and changes in electronic structure, see [3-5] and refs. therein.Since magnetic and structural dynamics occur at different timescales, it makes FeRh an ideal candidate for disentangling relevant interaction mechanisms at different timescales. The phase transition has been extensively studied theoretically and experimentally[6-8], in thermal equilibrium and in the time domain, but a precise understanding of the roles of the electronic, phononic and spin sub-systems remains elusive. We have studied the laser-driven AFM to FM phase transition in FeRh with small angle X-ray scattering (tr-SAXS) and X-ray absorption spectroscopy (tr-XAS) around the Fe L3 edge. The experiments were performed at the SCS Instrument of the European XFEL. We also performed the time-dependent density functional theory(TD-DFT) calculations to simulate the XAS spectra at different time delays. In this contribution, we will discuss the changes of the electronic structure of FeRh on the femto- and picosecond timescales, derived from the XAS and scattering measurements at the Fe L3 absorption edge performed at European XFEL, and compare them with the theoretical simulations (see the figure) , in order to show the relation between them and the first order AFM-FM phase transition in FeRh.References: [1] E. Beaurepaire et al., Phys. Rev. Lett. 76, 4250 (1996) [2] J.-Y. Bigot et al., Nature Physics 5, 515 (2009) [3] J.-U. Thiele et al. Appl. Phys. Lett. 82, 2859 (2003) [4] A.X. Gray et al., Phys. Rev. Lett. 108, 257208 (2012). [5] C. Baldasseroni et al., Appl. Phys. Lett. 100, 262401 (2012). [6] J.-U. Thiele, M. Buess, C.H. Back, Appl. Phys. Lett 85, 2857 (2004). [7] G. Ju et al., Phys. Rev. Lett. 93, 197403 (2004) [8] I. Radu et al., PRB 81, 104415 (2010)

Probing the Laser-driven Antiferromagnetic to Ferromagnetic Phase Transition of FeRh with Femtosecond Time-resolved Small Angle X-ray Scattering (tr-SAXS) and X-ray Absorption Spectroscopy (tr-XAS)

Antiferromagnetically coupled ferromagnetic thin films have recently attracted significant attention in magnonics because of the possibility to tune the spin-wave dispersion by altering the interlayer exchange coupling, which would help to achieve the spin-wave nonreciprocity [1]. To implement such coupled films in magnonic devices, a detailed understanding of the precessional dynamics of magnetization in such systems is required. Here, we present a systematic characterization of the precessional dynamics for systems with the layer magnetization going from nearly antiparallel to parallel alignment on application of a magnetic field. Experimentally, we have measured the ultrafast-laser-induced magnetization precession in samples with different interlayer exchange coupling strengths using the time-resolved magneto-optical Kerr effect. In addition to the acoustic and optical modes, an extra mode is observed that is due to the laser-induced decoupling of the two ferromagnetic layers. The observed precessional dynamics is in good agreement with our theoretical model based on the Landau-Lifshitz-Gilbert equation, and can be separated into three different field regions determined by the relationship between the Zeeman energy and the energy associated with the interlayer exchange coupling, as shown in Fig. 1 [2]. This work gives a detailed insigth of how the interlayer exchange coupling and Zeeman energy influence the precessional dynamics, and provides an important guide to implement antiferromagnetically coupled films in functional magnonic devices.References: [1] R. A. Gallardo, et al. Phys. Rev. Appl. 12, 034012 (2019) [2] J. Zhou, et al. Phys. Rev. B, 101, 214434 (2020)

Ultrafast Laser Induced Precessional Dynamics in Antiferromagnetically Coupled Ferromagnetic Films

While chiral spin structures stabilized by Dzyaloshinskii-Moriya interaction (DMI) are candidates as novel information carriers, their dynamics on the fs-ps timescale is little known [1-4]. Since with the bulk Heisenberg exchange and the interfacial DMI two distinct exchange mechanisms are at play, the ultra-fast dynamics of the chiral order needs to be ascertained and compared to the dynamics of the conventional collinear order. Using an XUV free-electron laser we determine the fs-ps temporal evolution of the chiral order in domain walls in a magnetic thin film sample by an IR pump - X-ray magnetic scattering probe experiment. Upon demagnetisation we observe that the dichroic (CL-CR) signal connected with the chiral order correlator mzmx in the domain walls recovers significantly faster than the (CL+CR) sum signal representing the average collinear domain magnetisation mz2+mx2 [5]. We explore possible explanations based on spin structure dynamics and reduced transversal magnetisation fluctuations inside the domain walls and find that the latter can explain the experimental data leading to distinctly different dynamics for collinear magnetic order and chiral magnetic order.References: [1] Beaurepaire, E. et al., Phys. Rev. Lett. 76, 4250–4253 (1996). [2] Koopmans, B. et al., Nat. Mater. 9, 259–265 (2010). [3] Battiato, M. et al., Phys. Rev. Lett. 105, 027203 (2010). [4] Pfau, B. et al., Nat. Commun. 3, 1100 (2012). [5] Kerber N. et al., arXiv:2002.03971 (2020).

Chiral versus collinear magnetic order dynamics: faster chiral recovery after optical excitation revealed by femtosecond XUV scattering

Thermal coupling parameters between different baths (electron, phonon, and magnon) in a nanoscale ferromagnetic Ni layer is investigated. To observe the local thermal interactions, we use time-resolved pump-probe spectroscopy. We collect both thermoreflectance and magneto-optical Kerr rotation, which represent the phonon temperature and magnon temperature, respectively, in a picosecond time scale. To analyze the experimental data, we employ the three-temperature thermal model including a spatial diffusion and local coupling mechanisms. We determine the thermal coupling parameters of Ni and find that the coupling parameter between phonon and magnon baths has a comparable magnitude to that between electron and magnon. The phonon-magnon coupling is responsible for the fast restoration of magnetization right after the ultrafast demagnetization (Fig. 1). In addition, we compare the coupling parameters with direct heating of Ni and in-direct heating of Ni via Au (Fig. 1). The in-direct heating suppresses the non-thermal electrons that reach to Ni, so that we can investigate the effect of thermal electrons on the ultrafast demagnetization. Both direct and in-direct heating situations lead to similar values of the coupling parameters, and the discrepancy is less than 30 %. We conclude that the thermalized electrons play the major role in the ultrafast demagnetization of Ni.References: Kyuhwe Kang and Gyung-Min Choi, J. Magn. Magn. Mater., Vol. 514, p.167156 (2020)

Thermal coupling parameters between electron, phonon, and magnon of Nickel

All-optical spin switching and demagnetization are two sides of the same physics. We find a way to unify them through the same model that takes into account the Heisenberg exchange between spins and spin-orbit coupling. To have efficient spin switching, the electron initial momentum direction must closely follow the spin's orientation, so that the orbital angular momentum is transverse to the spin, and consequently the spin–orbit torque lies in the same direction as the spin. The demagnetization can be understood from the spin-orbit coupling-mediated spin-wave excitation. The efficiency of laser-induced demagnetization is very high. We also observe the collapse of the spin-spin correlation length within 20 fs, consistent with the experimental findings [2]. Upon laser excitation there is a massive spin wave generated. The wave starts at the center of the laser beam and propagates outwards. Figure 1(b) shows the effect of the linearly polarized light at 123 fs after laser excitation. The spins close to the center bend strongly to the –z-axis. The situation is quite different with a right-circularly polarized laser (see Fig. 1(c)), where the spins are much more strongly affected. For left-circularly polarized light, the effect is much weaker. The demagnetization results from spin misalignment across the sample. This is similar to the traditional spin wave theory, with the low-energy spin wave excitation across several hundred lattice sites, which is far beyond the capability of the time-dependent density functional theory. Our simulation shows that the spin-spin correlation is reduced within 20 fs [3], consistent with the experimental results.References: [1] G. P. Zhang and M. Murakami, Journal of Physics: Condensed Matter 31, 345802 (2019). [2] P. Tengdin et al., Science Advances 4, eaap9744 (2018). [3] G. P. Zhang , M. Murakami , Y. H. Bai, Thomas F. George, and X. S. Wu, J. Appl. Phys. 126, 103906 (2019).

Unification of ultrafast demagnetization and switching

Helicity-independent all-optical switching (HI-AOS) of rare-earth/transition metal ferrimagnets is being intensively studied [1-6] for the last few years due to its potential applications towards faster read-write spintronic devices. The underlying magnetization dynamics has been discussed using two different approaches; i) atomistic Landau-Lifshitz-Gilbert model [3-4] and ii) microscopic three temperature model (M3TM) [5]. Recently, the ultrafast switching (< 10 ps) of ferromagnetic Co/Pt stack (exchange coupled with GdFeCo ferrimagnet) has been demonstrated showing a greater potential for technological applications [6]. We have extended the M3TM approach, to investigate similar systems by including a RKKY exchange (JRKKY) coupled ferromagnetic (Co/Pt) layer along with a ferrimagnet (GdCo) alloy. JRKKY, estimated as a fraction of CoPt exchange (JCoPt = 1.26X10-21 J), depends on the thickness of the Pt spacer layer separating Co/Pt from GdCo. Positive and negative sign of JRKKY means ferromagnetic and anti-ferromagnetic type coupling respectively. The dynamics for each of the magnetic sub-lattices have been plotted in Fig. 1. MCo crosses zero in < 1 ps while MGd is still in its demagnetized state and thereby forming a transient ferromagnetic state which is a necessary condition for HI-AOS [4-5]. Co/Pt remains demagnetized and its switching depends on the strength and sign of JRKKY. The white and dark region in Fig. 2 depicts relaxed and randomly demagnetized state of the material. The light green denotes switching of both the Co/Pt and Gd23Co77, while the dark green region denotes switching of only Gd23Co77. We found that the switching time of Co/Pt significantly depends on the composition of the GdCo alloy, absorbed power and the strength of JRKKY. Our simulation qualitatively explains the switching of Co/Pt in < 10 ps as experimentally observed by Gorchon et al. [6] and establishes the role of indirect exchange coupling in such switching.References: 1. I. Radu, K. Vahaplar, C. Stamm et al., Nature 472, 205 (2011) 2. A. Ceballos, A. Pattabi, A. El-Ghazaly et al., arXiv:1911.09803 3. U. Atxitia, P. Nieves and O. Chubykalo-Fesenko, Phys. Rev. B 86, 104414 (2012) 4. F. Jakobs, T. Ostler, C. H. Lambert et al., arXiv:2004.14844 5. M. Beens, M. L. M. Lalieu, A. J. M. Deenen et al., Phys. Rev. B. 100, 220409(R) (2019) 6. J. Gorchon, C. H. Lambert, Y. Yang, et al., Appl. Phys. Lett. 111, 042401 (2017)

A simulation study of RKKY exchange mediated ultrafast all-optical switching of GdCo/[Co/Pt] heterostructures

Co1-xMgxFe2O4（x = 0.0, 0.2, 0.4, 0.6, 0.8, 1.0）nanoparticles surrounded by amorphous SiO2 with particle sizes around 5 nm were prepared by an original wet chemical method. Furthermore, in order to develop the particles for conjugation with proteins, thiol group was modified. These particles were further confirmed as an agent for hyperthermia treatment. The heat dissipation characteristics of the particles were investigated by measuring AC magnetic susceptibility and the relationship between the imaginary part of AC magnetic susceptibility χ” and the increase in temperature in the AC field was estimated. We have carried out spin echo MRI measurements for Co1-xMgxFe2O4 nanoparticles using a 0.3-T MRI system. The particles showed drastic T2 shortening effect comparing to agarose as background depending on the composition. All the particles showed effective relaxivity, R2 values and significant contrast was observed in the phantom image. These particles are expected for future agents for theranostics.References: [1] T. Kondo, K. Mori, M. Hachisu, T. Yamazaki, D. Okamoto, M. Watanabe, K. Gonda, H. Tada, Y. Hamada, M. Takano, N. Ohuchi, and Y. Ichiyanagi, J. Appl. Phys. 11717D157 (2015). [2] D. Shigeoka, T. Yamazaki, T. Ishikawa, K. Miike, K. Fujiwara, T. Ide, A. Usui, Y. Hosokai, H. Saito and Y. Ichiyanagi, IEEE Trans. Magn., 54 6100707 (2018).


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Advanced Atomistic Modelling of Magnetisation Dynamics with Spin and Lattice Degrees of Freedom

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Probing the Laser-driven Antiferromagnetic to Ferromagnetic Phase Transition of FeRh with Femtosecond Time-resolved Small Angle X-ray Scattering (tr-SAXS) and X-ray Absorption Spectroscopy (tr-XAS)

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A simulation study of RKKY exchange mediated ultrafast all-optical switching of GdCo/[Co/Pt] heterostructures

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