# Workshops

## Ab Initio Spin Modelling

November 26, 2018 to November 28, 2018
Location : CECAM-HQ-EPFL, Lausanne, Switzerland
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### Organisers

• Jerome Jackson (STFC Daresbury Laboratory, United Kingdom)
• Martin Lueders (Daresbury Laboratory, United Kingdom)

### Description

Magnetic materials find direct application in many technologies, most importantly in power generation and transmission but also sensing, communication and computation; new technologies depending upon magnetic phenomena, together with materials that enable these technologies, can be expected to be of key importance in the future. Theoretical understanding is vital to these developments, and the materials-specific insight provided by ab initio computational methods is of particular value. The calculation of magnetic properties is not straightforward, requiring the combination of reliable band theory methods and an adequate treatment of electronic correlations, fluctuations and temperature. This is an expensive shopping list'', and a range of diverse approaches with different strengths and weaknesses have developed.

Spin-polarized band structure calculations within density functional theory (DFT) with subsequent mapping onto a Heisenberg model have become the conventional method for the treatment of magnetism in materials. Although the formulae for the ab initio calculation of exchange parameters were written down 30 years ago[1], their evaluation and extension continue to attract considerable research[2]. The Heisenberg model remains a central theme of magnetic research although its assumption of localized moments of constant magnitude interacting by static coupling parameters, may often be inappropriate[3]. Dynamics and finite-temperature behaviour of the system are treated as separate problems using the methods of statistical physics.

Magnetic exchange calculations require an atom-centred description of the band problem and have been mostly limited to certain LMTO and KKR implementations. In both cases, computation is significantly simplified by the use of the atomic sphere approximation (ASA), although it represents a severe approximation to the potential landscape. Alternative strategies based on total energy calculations in full potential codes, e.g. spin-spiral'' methods, have also been shown to be useful[4]. Significant developments based on ASA techniques have however been made in other directions, for example in the disordered local moment approach, where finite temperature effects are included at the ab initio level without recourse to a spin model[5].

Density functional theory is limited in its ability to treat strong correlation and temperature: in this context the development of GW and the combination of DFT with dynamical mean field theory, in particular, have had a significant impact in understanding complex magnetic materials[6]. Significant efforts have been directed toward the calculation of the enhanced magnetic susceptibility using a range of post-DFT theories[7]. Other state of the art research is concerned with relaxation of the spin magnitude and damping of magnetization dynamics, or to correctly model electron-magnon scattering, for example, which is vital for understanding spin dynamics on short timescales.

The purpose of the Workshop is to promote discussion on, and hopefully work towards a consensus on, the following questions in ab initio spin modelling:

- how reliable is the ASA in comparison with full-potential methods?
- can we form a clearer consensus of when and why the Heisenberg model fails?
- what is the importance of interactions beyond the bi-linear (Heisenberg) type?
- what is the most suitable theory for magnetic exchange (or the enhanced susceptibility) beyond the LDA?
- can we clarify some of the differences in conventions for key formulae with regard to spin-modelling?
- how could we describe magnetisation dynamics in the framework of electronic structure?

The Workshop is intended to provide a forum for discussion at a technical level and will bring together some of the most active workers involved in first principles method development, code implementation, and magnetism research. It is envisioned that workers from quite different parts of the electronic structure community with an interest in magnetism will attend; this crosses traditional community boundaries and it is hoped that new collaborations will start naturally as a consequence of the Workshop.

Such a meeting, explicitly focusing on these technical points, is rather unusual. We feel that this is timely because of the wealth of exciting developments taking place currently across the electronic structure community, in particular the possibility of using self-consistent GW, LDA+DMFT in real material studies, compels a critical reassessment of the methods we have applied until now. Similarly, the future use of these methods will depend increasingly upon more robust verification of our codes and our predictions; the wider field of magnetism research, also in industry, can be expected to profit considerably by the comparison of, and improvement to, our methods and codes.

To allow speakers to give some detail about their methods, we envision allowing slightly longer talks than is usual, lasting 45 minutes followed by 25 minutes of questions. This is because the diverse range of theories to be presented necessitates that each can provide some introduction. Discussion is key to the meeting; approximately 13 talks will constitute the main programme -- the remaining time will be used to host a poster session. The poster session will be a serious part of the meeting, and all non-speaking attendants (an additional ~15 people) will be expected to present a poster concerning their methods. A conference dinner will be given. In addition to the invited participants, it is hoped that equally many younger scientists (at late PhD, early postdoc stage) will also attend. These will have the opportunity to discuss directly with the high profile researchers that we have invited -- this is important for fostering a vivid community and technical excellence in this area for the future. The Workshop will end with a round-table style wrapping-up discussion.

### References

[1] A.I. Liechtenstein, M.I. Katsnelson, V.P. Antropov and V.A. Gubanov, LSDF-Approach to the thory of exchange interactions in magnetic metals, Journal of Magnetism and Magnetic Materials 54-57 (1986) 965-966.
[2] I. Turek, J. Kudrnovsky, V. Drchal and P. Bruno, Exchange interactions, spin waves, and transition temperatures in itinerant magnets, Philosophical Magazine 86 (2006) 1713-1752.
[3] V.P. Antropov, B.N. Harmon, A.N. Smirnov, Aspects of spin dynamics and magnetic interactions, Journal of Magnetism and Magnetic Materials 200 (1999) 148-166.
[4] M. Lezaic, P. Mavropoulos, G. Bihlmayer and S. Bluegel, Exchange interactions and local-moment fluctuation corrections in ferromagnets at finite temperatures based on noncollinear density-functional calculations, Physical Review B 88 (2013) 134403
[5] J.B. Staunton, L. Szunyogh, A. Buruzs, B.L. Gyorffy, S. Ostanin, and L. Udvardi, Temperature dependence of magnetic anisotropy: An ab initio approach, Physical Review B 74 (2006) 144411.
[6] I. Di Marco, J. Minar, S. Chadov, M I. Katsnelson, H. Ebert, and A I. Lichtenstein, Correlation effects in the total energy, the bulk modulus, and the lattice constant of a transition metal: Combined local-density approximation and dynamical mean-field theory applied to Ni and Mn, Physical Review B 79 (2009) 115111.
[7] L. Sponza, P. Pisanti, A. Vishina, D. Pashov, C. Weber, M. van Schilfgaarde, S. Acharya, J. Vidal and G. Kotliar, Self-energies in itinerant magnets: a focus on Fe and Ni, Physical Review B 95 (2016) 041112(R).