Abstract text (incl. figure legends and references)

Introduction

The latest monochromator and spectrometer improvements in scanning transmission electron microscopy (STEM) currently allow energy resolutions below 10 meV [1-4]. This has extended the capabilities of STEM electron energy loss spectroscopy (EELS) to perform, for example, vibrational spectroscopy with high spatial resolution in STEM [3, 4].

The energy losses due to magnons are in the same range as the typical energies of vibrational modes (tens or few hundreds of meV) [5]. Hence, it might be possible to probe magnons with STEM-EELS at both high-spatial and high-energy resolutions. This would bring new possibilities for studying magnetic ordering phenomena, benefiting fields such as spintronics and spin caloritronics.

Probing magnons with STEM-EELS is technically challenging, especially since the vibrational (phonon) signal, due to thermal diffuse scattering (TDS) of electrons, can be four orders of magnitude greater than the magnon diffuse scattering (MDS) signal [5]. However, there are circumstances in which the relative strengths of the magnetic signals can reach a few percent [6–8]. Therefore, it is important to find conditions in which MDS and TDS signals can be separated. For this, temperature could play a key role: it is likely that temperature dependence of magnon and phonon signals qualitatively differ.

Objectives

In this work, we will present STEM MDS simulations for BCC iron at different temperatures. We will compare our results with TDS calculations, focusing on the distinguishability of the signals.

Materials & methods

We will follow the methodology of Ref. [5], in which the MDS signal is computed from the magnon analog of the frozen phonon multislice (FPMS) method [9, 10], combining the magnetic-fields-aware multislice method [6] and atomistic spin dynamics (ASD) simulations [11].

Results

We will present results using classic and quantum thermostats in ASD simulations. In particular, we will show that the MDS signal increases up to T_c and then decreases. We will discuss the implications of our results for experimental measurements of MDS signals.

Conclusions:

We will show that temperature could be a key factor in successful MDS measurements in STEM. In particular, as for the case of BCC iron, temperatures close to T_c might enhance MDS signals, potentially allowing for the separation of MDS and TDS signals.

References

[1] O. L. Krivanek et al., Nature 514, 209 (2014).

[2] O. L. Krivanek et al., Ultramic. 203, 60 (2019).

[3] M. J. Lagos et al., Microscopy 71, i174 (2022).

[4] N. Dellby et al., Microsc. Microanal. 28(S1), 2640 (2022).

[5] K. Lyon et al., Phys. Rev. B 104, 214418 (2021).

[6] A. Edström et al., Phys. Rev. Lett. 116, 127203 (2016).

[7] A. Edström et al., Phys. Rev. B 94, 174414 (2016).

[8] A. Edström et al., Phys. Rev. B 99, 174428 (2019).

[9] R. F. Loane et al., Acta Cryst. A47, 267 (1991).

[10] P. M. Zeiger and J. Rusz, Phys. Rev. Lett. 124, 025501 (2020).

[11] O. Eriksson et al., Atomistic Spin Dynamics: Foundations and Applications (Oxford University Press, Oxford, 2017).