Ab Initio Spin Modelling Workshop

CECAM-HQ, Lausanne, Switzerland

26–28 November 2018

Supported by:

EPFL campus:

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Location of Hotels in Lausanne Flon:

Hotel Crystal

Rue Chaucrau 5

1003 Lausanne

Tel. +41(0) 21 317 03 03

Hotel Regina

Rue Grand-St-Jean 18

1003 Lausanne

Tel. +41 21 320 24 41

Cafe Romand

Place Saint-Francois 2

1003 Lausanne

Tel. +41 21 312 63 75

Conference Dinner:

The conference dinner will take place at 19:30, Tuesday 27 November at Cafe Romand.

WIFI:

SSID: PUBLIC-EPFL

Website: Enclair.epfl.ch

Username: x-cecamguest

Password: amuban31

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Organisers:

Jerome Jackson and Martin Luders

STFC Daresbury Laboratory, Warrington, United Kingdom

E-mail: jerome.jackson@stfc.ac.ukmartin.lueders@stfc.ac.uk

Programme:

Monday 26 November

09:00–09:50 Registration

09:50–10:00 Welcome

10:00–11:00 Ilja Turek

11:00–12:00 Samir Lounis

12:00–13:30 Lunch

13:30–14:30 Arthur Ernst

14:30–15:30 Laszlo Szunyogh

15:30–16:00 Coffee Break

16:00–17:00 Julie Staunton

17:00–18:00 Hubert Ebert

Tuesday 27 November

09:00–10:00 Roy Chantrell

10:00–11:00 Igor Di Marco

11:00–11:30 Coffee Break

11:30–12:30 Poster Session

12:30–14:00 Lunch

14:00–15:00 Jan Minar

15:00–16:00 Mark van Schilfgaarde

16:00–16:30 Coffee Break

16:30–17:30 Christoph Friedrich

19:30–22:00 Social Dinner

Wednesday 28 November

09:00–10:00 Corina Etz

10:00–11:00 Joseph Barker

11:00–11:30 Coffee Break

11:30–12:30 Poster Session

12:30–13:15 Discussion

13:15–13:20 Closing Word

4

Exchange interactions and spin-wave stiffness in systems with

broken translation invariance

Ilja Turek

Institute of Physics of Materials, Czech Academy of Sciences, Brno, Czech RepublicE-mail: turek@ipm.cz

In the first part of the talk, several spin-polarized systems with local moments will be men-

tioned which exhibit pronounced sensitivity of their exchange interactions to various external

perturbations and structure modifications. These examples include: (i) pressure dependence

and its relation to the volume magnetostriction in Gd2Al compound [1], (ii) effect of substrate

on the magnetic ground state of Fe monolayer [2], and (iii) influence of structure defects on the

magnetic order in CuMnSb Heusler compound [3].

The second part of the talk is devoted to the problem of reliable determination of the spin-wave

stiffness in random ferromagnets. Two basic ways will be sketched, namely, direct total-energy

calculations for spin spirals [4] and approaches based on the real-space pair exchange interactions.

Results of both techniques will be compared and discussed for pure transition metals (bcc Fe, fcc

Ni), their random binary alloys (fcc NiFe) and the dilute magnetic semiconductors (Mn-doped

GaAs) [5]. Difficulties encountered for bcc FeAl solid solutions will be briefly mentioned as well.

[1] I. Turek et al., J. Alloy. Compd. 431 (2007) 37.

[2] J. Kudrnovsky et al., Phys. Rev. B 80 (2009) 064405.

[3] F. Maca et al., Phys. Rev. B 94 (2016) 094407.

[4] S. Mankovsky et al., Phys. Rev. B 83 (2011) 144401.

[5] I. Turek et al., Phys. Rev. B 94 (2016) 174447.

5

Transversal and longitudinal dynamical spin-excitations from

TD-DFT

Samir Lounis

Peter Grunberg Institut and Institute for Advanced Simulation, ForschungszentrumJulich and JARA, Germany

Magnetism is a fascinating correlation phenomenon with ramifications over several orders of

magnitude in length and timescale. It generates thrilling questions across multiple fields rooting

in condensed matter physics with paramount implications in information technology. The quest

for new paradigms to increase computing speed and storage capacity at reduced energy foot-

print hinges on the fundamental understanding of microscopic mechanisms underlying the sta-

bility, detection and manipulation of nanoscale magnetic elements in a material specific context.

This requires novel concepts, the development of cutting edge methodologies and surmounting

formidable computational challenges.

In this talk, I will discuss some aspects related to the extraction of parameters needed in extended

Heisenberg models from density-functional theory (DFT) and focus on the use of time dependent

density functional theory (TD-DFT). These parameters are magnetic exchange interactions,

bilinear and beyond, magnetic anisotropy energies, gyromagnetic factors, Gilbert and nutation

tensors, which are required when solving the so-called Landau-Lifshitz-Gilbert equations [1–5].

In the context of magnetization dynamics, I will address longitudinal spin-excitations besides

the usual transversal ones and possible strategies to extract relaxation times pertaining to the

Bloch equations [5,6]. I will show a few examples across different dimensionalities going from bulk

materials, thin films hosting magnetic skyrmion [7] down to individual atoms [8]. Finally, and

if time permits, I will formulate how dynamical spin-excitations and current-driven spin-state

manipulation in nano-devices can be addressed by combining time-dependent density functional

theory and many-body perturbation theory [8].

[1] S. Lounis, P. H. Dederichs, PRB (R) 82 180404 (2010).

[2] A. Khajetoorians et al., Nature Communications 7, 10620 (2016).

[3] S. Lounis, M. dos Santos Dias, B. Schweflinghaus, PRB 91, 104420 (2015).

[4] F. Guimaraes, M. dos Santos Dias, B. Schweflinghaus, S. Lounis, PRB 96, 14401 (2017).

[5] J. Ibanez-Azpiroz et al., PRB 96, 14410 (2017); J. Ibanez-Azpiroz, et al. PRL 119, 017203

(2017).

[6] J. Iban ez-Azpiroz, M. dos Santos Dias, S. Blugel, S. Lounis, Nanoletters 16, 4305 (2016).

[7] I. L. Fernandes, J. Bouaziz, S. Blugel, S. Lounis, Nature Communications 9, 4395 (2018).

[8] B. Schweflinghaus, M. dos Santos Dias, A. T. Costa, S. Lounis, PRB 89, 235439 (2014).

6

Spin waves in disordered materials

Arthur Ernst

Max-Planck-Institut fur Mikrostrukturphysik, Halle, Germany

Disordered magnetic materials attract considerable interest in condensed matter physics commu-

nity and are widely used in many applications. The spin waves or magnons are the fingerprints

of the magnetic interaction of a system and can be detected by several experimental techniques

such as the neutron scattering, the spin polarised electron energy loss or the scanning tunnelling

spectroscopy. Therewith, theoretical simulations of spin excitations play an important role to

interpret experiment, to understand the physics behind, and to design computationally new

materials with desired properties. While several efficient theoretical methods have been already

developed and are successfully applied to study magnons in ordered materials, a description of

the spin excitations in disordered systems remains still a challenge for first-principles simulations.

In my talk I present two approached to describe spin waves in disordered materials, namely, a

direct simulation of a large supercell averaging randomly over different disorder configurations

and a coherent potential approximation for the Heisenberg model. The exchange constants are

calculated from first-principles and used in both models as parameters. These approaches enable

a realistic description of spin waves in disordered systems. To demonstrate the efficiency of the

methods I discuss the impact of disorder on spin wave excitations in different dimensions for

model and realistic materials.

7

Exchange interactions from a nonorthogonal basis: A SIESTA

implementation

Laszlo Oroszlany1,2, Jaime Ferrer3, Andras Deak4,5, Laszlo Udvardi4,5 and

Laszlo Szunyogh4,5

1Department of Physics of Complex Systems, Eotvos Lorand University, Budapest,Hungary

2MTA-BME Lendulet Topology and Correlation Research Group, Budapest University ofTechnology and Economics, Hungary

3Departamento de Fisica, Universidad de Oviedo & CINN, Spain4Department of Theoretical Physics, Budapest University of Technology and Economics,

Hungary5MTA-BME Condensed Matter Research Group, Budapest University of Technology and

Economics, Hungary

The ground state and temperature dependence of magnetic systems, either characterized by

itinerant electrons or by local moments, are most commonly described by a Hamiltonian pa-

rameterized in form of a spin model where the spins – in the classical limit – are allowed to

fluctuate with their magnitude kept constant. For a given material the model parameters can

be derived from first principles, in most cases relying on the magnetic force theorem as employed

in the famous work of Liechtenstein et al. [1]. Related methods have been developed in the past

suitable to treat correlated systems [2] and relativistic effects [3,4].

In this talk we present a computational method for direct evaluation of isotropic exchange

interaction from density functional calculations using nonorthogonal basis sets. By giving some

details of the derivation we show that the expression for the exchange interactions is formally

identical with the one using orthogonal basis sets. We implemented the new method in the

SIESTA code [5] and demonstrate that in case of simple metallic ferromagnets it adequately

reproduces the Heisenberg interactions obtained from well–established computational methods.

In case of graphene ribbons and flourinated graphene representing sp-magnetism, our results are

also in good agreement with calculations employing different approaches. The described scheme

holds great promise to investigate novel hybrid systems where metallic and organic components

are integrated to form exotic magnetic patterns [6].

[1] A. I. Lichtenstein, M. I. Katsnelson, V. P. Antropov, and V. A. Gubanov, J. Magn. Magn.

Mater. 67, 65 (1987).

[2] M. I. Katsnelson and A. I. Lichtenstein, Phys. Rev. B 61, 8906 (2000); Eur. Phys. J. B 30,

9 (2002).

[3] L. Udvardi, L. Szunyogh, K. Palotas, and P. Weinberger, Phys. Rev. B 68, 10443 (2003).

[4] H. Ebert and S. Mankovsky, Phys. Rev. B 79, 045209 (2009).

[5] https://departments.icmab.es/leem/siesta/

[6] https://arxiv.org/abs/1809.09252

8

Fluctuating local moments and itinerant electrons - phase

transitions in magnetic materials described by ab-initio theory

Julie B. Staunton, Eduardo Mendive-Tapia and Christopher E. Patrick

Department of Physics, University of Warwick, Coventry, United Kingdom

When a metal goes through a change of magnetic order, the complex electronic fluid with

its emergent magnetic ‘local moments’ transforms. The coupled itinerant electron and more

localised spin degrees of freedom have a profound effect on structure, electronic transport, and

so on which can be particularly dramatic around first-order phase transitions. An ab-initio

treatment of temperature dependent spin-polarised electronic structure can therefore provide

the means to locate and characterise magnetic phase transitions and how they are affected

quantitatively by application of magnetic field, pressure or strain. In this context the Density

Functional Theory (DFT)-based Disordered Local Moment Theory (DLM) of magnetic materials

will be discussed [1-4].

Our first example will be to show how DLM-DFT produces a theoretical model for heavy rare

earth elemental magnetism and a generic magnetic phase diagram which correctly captures most

experimentally observed features [3]. The ab-initio model’s central ingredient is the common va-

lence electronic effect on and response to f-electron magnetic moment ordering. When analysed

in terms of a spin model it produces 4-site as well as 2-site exchange interactions which explain

the first order incommensurate anti-ferromagnetic to ferromagnetic transition seen in these met-

als as they cool. We show explicitly the connection between topological Fermi surface changes

and this metamagnetism. Other applications of DLM-DFT theory will include those to materi-

als with quenched static compositional disorder traversing first-order magnetic phase transitions

such as nearly stoichiometric Fe-Rh alloys [2] and the role of multi-site magnetic interactions,

antiferromagnets which manifest tricritical metamagnetism [5] and the Mn-antiperovskites [6]

whose frustrated magnetism feeds rich magnetic-strain phase diagrams and associated caloric

effects. Relativistic effects such as spin-orbit coupling can be included and results will also be

presented for the magnetic properties of rare earth - transition metal permanent magnets such

as YCo5, GdCo5 and SmCo5 [4] focusing on the ferrimagnetism of GdCo5 and how to describe

intrinsic temperature dependent magnetic anisotropy using DLM-DFT.

[1] B.L. Gyorffy et al., J.Phys. F 15, 1337, (1985).

[2] J.B. Staunton et al., Phys. Rev. B 89,054427, (2014).

[3] Eduardo Mendive Tapia and Julie B. Staunton, Phys. Rev. Lett. 118, 197202, (2017).

[4] Christopher E. Patrick et al., Phys. Rev. Lett. 120, 097202, (2018); Christopher E. Patrick

and Julie B. Staunton, Phys. Rev. B 97, 224415 (2018).

[5] J.B. Staunton et al., Phys. Rev. B 87, 060404, (2013).

[6] J. Zemen, E. Mendive-Tapia et al., Phys. Rev. B 95, 184438, (2017); D. Boldrin et al. Phys.

Rev. X in press.

This work forms part of the PRETAMAG, UK Engineering and Physical Sciences Research

Council (EPSRC), Grant no. EP/M028941/1.

9

Impact of a non-collinear spin configuration on the properties of

magnetically ordered materials

Hubert Ebert, S. Mankovsky, S. Polesya and S. Wimmer

Department of Chemistry, Ludwig-Maximilian-University Munich, Germany

E-mail: Hubert.Ebert@cup.uni-muenchen.de

A computational scheme based on multiple scattering is briefly introduced that allows dealing

with the electronic structure of magnetic systems in real as well as reciprocal space. Working

within the framework of the relativistic Dirac formalism ensures that the impact of spin-orbit

coupling is fully accounted for. By manipulating the strength of spin-orbit coupling its role for

physical properties is unambiguously identified. In particular for non-collinear spin configura-

tions, corresponding topological contributions can be clearly identified this way. We present new

results for transverse charge and spin transport as well as Gilbert damping (GD) for various

types of non-collinear magnetic systems including three-dimensional periodic solids, inhomoge-

neous systems characterized by a spin wave vector, and Bloch- as well as Neel-like domain walls.

Using as an example the non-collinear antiferromagnetic compound Mn3Ge, we investigate the

dependence of orbital moments and X-ray dichroism on the spin configuration. We further-

more demonstrate sizable chirality-induced contributions to various electric-field-driven linear

response phenomena arising upon rotation of the magnetic moments from coplanar towards

non-coplanar arrangements. Considering the wave vector q-dependent Gilbert damping (q) ac-

counting for the non-collinear character of a magnetic structure, we demonstrate the appearance

of a non-zero GD term linear in q for the non-centrosymmetric multilayer system (Pt—FexCo1-

x—Cu) [1]. This contribution to the GD, having a chiral character, provides access to an

understanding of the asymmetric field-driven domain wall motion observed experimentally in

non-centrosymmetric systems [2].

[1] S. Mankovsky, S. Wimmer, and H. Ebert, Phys. Rev. B 98, 104406 (2018).

[2] E. Jue et al., Nat. Mater. 15, 272 (2015).

10

Ab-initio/atomistic approaches to structured nanomagnets and

complex spin structures

R.W. Chantrell

Department of Physics, The University of York, United Kingdom

Nanostructured magnetic materials provide a host of physical challenges and potential applica-

tions. One such structure is CoFeB/MgO which forms the basis of MRAM cells. These have dual

functionality in firstly comprising a spin tunnel junction, which generates a spin polarised cur-

rent capable of switching the magnetisation. Secondly the hybridisation of the interfacial spins

by the MgO leads to a sufficiently large anisotropy to support a perpendicular magnetisation. A

second, highly topical, system is Pt/Co, which has a similarly strong interfacial anisotropy and

DMI which can stabilise the formation of Skyrmions. In both cases, the use of ab-initio parame-

terised atomistic calculation is a powerful approach to understanding the spin dynamics and the

thermodynamic properties of materials and structures. I will describe the import of ab-initio

information into the VAMPIRE atomistic code via the exchange tensor, which introduces the

DMI and 2-site anisotropy terms. The model is applied to an investigation of the structure of

Fe/Mgo layers. Ab-initio calculations lead to antiferromagnetic interactions within the Fe plane

coupled to the MgO and to a dominant 2-site anisotropy. The zero K ground state structure

is a spin spiral resulting from the AF interactions and DMI contribution. The temperature

dependence of the magnetic anisotropy is shown to be non-monotonic, which is related to the

temperature dependence of the spin spiral state. Spin dynamics induced by an applied field

and by a spin polarised current will also be described. Finally I will show initial results of the

formation and stability of Skyrmions in an Pt/Co system using ab-initio information.

11

DFT+DMFT calculations for finite temperature magnetism

Igor Di Marco

Department of Physics and Astronomy, Uppsala University, Sweden

In the last two decades, the combination of dynamical mean-field theory (DMFT) and density

functional theory (DFT) has emerged as a very powerful approach to investigate the electronic

structure of strongly correlated materials. This technique, labelled as the DFT+DMFT scheme,

has recently been extended to extract inter-atomic exchange parameters for mapping the mag-

netic excitations onto a Heisenberg model. This information is not only interesting from the

point of view of fundamental physics, but also needed to perform studies based on atomistic spin

dynamics. After an overview of the technical details of our implementation [1], I will present

a range of selected applications. I will first analyse the Bethe-Slater curve in transition metal

elements, emphasizing how magnetism in Fe arises as a competition between Heisenberg and

non-Heisenberg contributions [2,3], which can also be seen in surfaces [4]. I will then move to

more localized systems, as transition metal oxides and rare-earth metals [1,5,6]. In connection

to the localization, I will focus on methodological ambiguities arising during the calculations,

which are important to clarify why similar techniques seem to give very different results [7].

[1] Y. O. Kvashnin et al., Phys. Rev. B 91, 125133 (2015).

[2] Y. O. Kvashnin et al., PRL 116, 217202 (2016).

[3] R. Cardias et al., Scientific Reports 7, 4058 (2017).

[4] S. Keshavarz et al., Phys. Rev. B 92, 165129 (2015).

[5] S. Paul et al., Phys. Rev. B 97, 125120 (2018).

[6] I. L. M. Locht et al., Phys. Rev. B 94, 085137 (2016).

[7] S Keshavarz et al., Phys. Rev. B 97, 184404 (2018).

12

Temperature and spin dependent effects in ARPES

Jan Minar

New Technologies Research Center, University of West Bohemia, Plzen, Czech Republic

My presentation will be devoted to angle-resolved photoemission spectroscopy (ARPES) which

is a leading experimental probe for studying the electronic structure and complex phenomena

in quantum materials. Modern experimental arrangements consisting of new photon sources,

analyzers and detectors supply not only spin resolution but also extremely high angle and energy

resolution. Furthermore, the use of photon energies from few eV up to several keV makes this

experimental technique a rather unique tool to investigate the electronic properties of solids

and surfaces. On the theoretical side, it is quite common to interpret measured ARPES data

by simple comparison with calculated band structure. However, various important effects, like

matrix elements, the photon momentum or phonon excitations, are in this way neglected. Here,

we present a generalization of the state of the art description of the photoemission process, the

so called one-step model that describes excitation, transport to the surface and escape into the

vacuum in a coherent way. Nowadays, the one-step model allows for photocurrent calculations

for photon energies ranging from a few eV to more than 10 keV, for finite temperatures and for

arbitrarily ordered and disordered systems, and considering in addition strong correlation effects

within the dynamical mean-field theory. Application of this formalism in order to understand

ARPES response of new materials like low-dimensional magnetic structures, Rashba systems,

topological insulator materials or high TC materials will be shown. In this presentation I review

some of the recent ARPES results and discuss the future perspective in this rapidly developing

field.

13

Towards a comprehensive ab initio treatment of magnetic

phenomena

Mark van Schilfgaarde

Department of Physics, King’s College London, United Kingdom

Our ability to study magnetic phenomena from an ab initio approach has evolved dramatically

in recent years. Density-functional theory is the most popular approach, and because of its sim-

plicity it can be applied to study many kinds of magnetic phenenoma in complex environments.

We show a recent demonstration: a study of spin-orbit torques in a Co/Pt multilayer.

The precision of DFT is limited, and it is often augmented, typically by LDA+U or LDA+DMFT.

This can improve on the deficiencies of DFT, particularly in itinerant or paramagnetic systems

where spin fluctuations, a many-body effect missing in DFT, are essential. However the model-

like flavor of such additions introduces some arbitrariness in the theory. An alternative approach,

the quasiparticle self-consistent GW approximation, dramatically improves on the quality of the

effective one-body Hamiltonian while remaining in a true ab initio framework. We show examples

where QSGW can do an excellent job at predicting one-and two-particle properties of magnetic

systems.

QSGW leaves out spin fluctuations, which causes it to break down where they are important.

We illustrate this with some examples: Ni and FeSe. In principle DMFT augmenting QSGW can

handle most physically important correlations. We show the present status of QSGW+DMFT,

applying to Sr2RuO4. We show how this (nearly) ab initio treatment can provide insight into

superconductivity in a way that model descriptions cannot.

14

Electron-magnon scattering in elementary ferromagnets from

first principles: lifetime broadening and kinks

C. Friedrich

Peter Grunberg Institut and Institute for Advanced Simulation, ForschungszentrumJulich and JARA, Germany

Electronic spin excitations are low-energy excitations that influence the properties of magnetic

materials substantially. Two types of spin excitations can be identified, single-particle Stoner

excitations and collective spin-wave excitations. They can be treated on the same footing within

many-body perturbation theory [1]. In this theory, the collective spin excitations arise from the

correlated motion of electron-hole pairs with opposite spins. The pair propagation is described

by the transverse magnetic susceptibility, which we calculate from first principles within the

full-potential linearized augmented-plane-wave method employing the ladder approximation for

the T matrix. The four-point T matrix is represented in a basis of Wannier functions. By using

an auxiliary Wannier set with suitable Bloch character, the magnetic response function can be

evaluated for arbitrary k points, allowing fine details of the spin-wave spectra to be studied.

Propagating electrons and holes can scatter with the spin fluctuations and form quasiparticles or

more complex many-body states. To calculate this effect, a k-dependent self-energy [2] describing

the scattering of electrons and magnons is constructed from the solution of a Bethe-Salpeter

equation for the T matrix. Partial self-consistency is achieved by the alignment of the chemical

potentials. The resulting renormalized electronic band structures exhibit strong spin-dependent

lifetime effects close to the Fermi energy, which are strongest in Fe. The renormalization gives

rise to a band anomaly [3] at large binding energies in iron, which results from a coupling of the

quasihole with single-particle excitations that form a peak in the Stoner continuum.

[1] C. Friedrich, M.C.T.D. Muller, S. Blugel, “Spin Excitations in Solids from Many-Body Per-

turbation Theory”. In: Andreoni W., Yip S. (eds) Handbook of Materials Modeling. Springer,

Cham (2018).

[2] M.C.T.D. Muller, S. Blugel, C. Friedrich, submitted to PRB, arXiv 1809.02395.

[3] E. Mlynczak et al., submitted to Nature Communications, arXiv 1808.02682.

15

Magnetic interactions beyond the Heisenberg model

A. Jacobsson and C. Etz

Department of Engineering Sciences and Mathematics, Lulea University of Technology,Sweden

Magnetic materials are important for current technological applications and their developments.

Thus, understanding the fundamental physics governing their properties at the atomic scale

is crucial. In the view of solid-state applications, it is of utmost importance to be able to

accurately calculate magnetic exchange interactions and predict the correct critical temperatures

for all kinds of materials. For the moment, in order to describe the behaviour and properties

of magnetic materials, we usually need to use a multi-code and multi-scale approach, often

combining ab initio methods with Monte Carlo and atomistic spin dynamics simulations. The

fundamental quantity here is the magnetic interaction between atoms. We focus on developing

a method that can properly describe these interactions in a wide range of systems, with collinear

or non-collinear magnetic structures.

We present a new method based on the use of constraining fields, which gives an accurate

assessment of the short-range interactions. An extended Heisenberg model is suggested in order

to better describe finite deviations from the magnetic ground state. By employing the cross-

validation technique, we show that the suggested model gives a superior description of the

interactions for non-collinear magnetic configurations compared to the regular Heisenberg model.

We supply a fully self-consistent method for systematic investigations of exchange interactions

beyond the standard Heisenberg model. This may prove relevant to high-throughput compu-

tational materials science, e.g., in developing high moment materials for the magnetic storage

industry.

16

Atomistic spin dynamics with a quantum thermostat

Joseph Barker

School of Physics and Astronomy, University of Leeds, United Kingdom

Atomistic spin dynamics is a formalism based on the classical Heisenberg model which is often

used to study the dynamics and thermodynamics of spin models. An often-touted advantage

is the inclusion of temperature by thermostating the spin system with a Langevin equation.

However, this has generally been applied in the classical limit – using the classical fluctuation

dissipation theorem. We will argue that this is almost never the correct limit for magnets below

their ordering temperature and instead the quantum fluctuation dissipation theorem should be

used. Applying such a thermostat we should that thermodynamics can now be calculated which

agree with analytic results such as Bloch’s law. We also show complex spin models such as

yttrium iron garnet and display quantitative agreement with experimental measurements.

Fig. 1: Comparison of the magnon specific heat capacity of yttrium iron garnet calculate with

a classical and quantum thermostat compared to experimental measurements. The quantum

thermostat gives excellent quantitative agreement whereas the classical thermostat overestimates

by 5 orders of magnitude.

17

Poster Contributions

18

Graphene-mediated exchange coupling between magnetic

molecules and substrates: a DFT view

V. Bellini1, A. Candini2, V. Corradini1, F. Troiani1, S. Heinze3, U. del Pennino4 and

M. Affronte4

1CNR-NANO-S3, Modena, Italy2CNR-ISOF, Bologna, Italy

3Institute of Theoretical Physics and Astrophysics, University of Kiel, Germany4Dipartimento di Fisica, Universita di Modena e Reggio Emilia, Italy

E-mail: valerio.bellini@unimore.it

The field of molecular spintronics aims to realize molecule-based logic and storage devices, in-

terfacing magnetic molecules with opportune substrates/electrodes. The characterization of

molecule-substrate interactions is therefore very timely and has raised in the last years a broad

interest in the surface physics and chemists communities. Along this line, I will present a theoret-

ical investigation of magnetic molecule-substrate systems, and I will focus on single ion molecules,

namely TM-phthalocyanines (TM=4d and 5d transition metals) [1] and Ln double-deckers (e.g.

TbPc2) [2,3], deposited on Ni substrates. In particular I will discuss the case where a graphene

layer is interposed between the molecules and the substrate, highlighting its role in mediating

the magnetic interaction (see Figure). The calculations have been carried out by state-of-the-

art density-functional theory methods, as implemented in the VASP and Quantum Espresso

packages, comparing when possible with X-ray Magnetic Circular Dichroism experiments.

[1] P. Ferriani, S. Heinze and V. Bellini, “Designing a molecular magnetic button based on 4d

and 5d transition-metal phthalocyanines”, Sci. Rep. 7, 3647 (2017).

[2] A. Candini, et al., “Spin-communication channels between molecular nanomagnets and a

magnetic substrate: the case study of Ln(III) bis-phthalocyanines on Ni(111) surface”, Sci. Rep.

6, 21740 (2016).

[3] S. Marocchi, et al., “Relay-like exchange mechanism through a spin radical between TbPc2

molecules and graphene/Ni(111) substrates”, ACS Nano 10, 9353 (2016).

Fig. 1: XAS and XMCD experiments (left) and sketch of the TbPc2/Graphene/Ni(111) system

(right).

19

The dynamics of magnetism in Fe-Cr alloys with Cr

precipitation

Jacob Chapman

Culham Centre for Fusion Energy, Abingdon, United Kingdom

Fe-Cr alloys are versatile and technologically significant materials owing to their magnetism.

Nonetheless, fundamental questions regarding their dynamic and static magnetic properties re-

main unanswered. As an example, changes in the magnetic properties of alloys and steels under

neutron irradiation are often overlooked despite ferritic-martensitic steels being key structural

materials in the tokamak route to fusion. In this paper we perform a quantitative study explor-

ing how ageing and irradiation-induced precipitation affects the magnetic properties of Fe-Cr

alloys. Magnetic properties are simulated over a broad temperature interval using spin dynam-

ics, implemented using a Hamiltonian including longitudinal and transverse magnetic degrees

of freedom. Simulations of alloys with nominal Cr concentrations in the range from 0 to 25

at.%, and different microstructures, including disordered solid solutions and large Cr-rich pre-

cipitates, show that the Curie temperature TC is always maximum when Cr solute concentration

in the α phase is close to 5-6 at.%. The magnetisation of Fe-9 at.%Cr alloys are found to vary

by 10%, depending on the size of Cr clusters. We compute the magnetic susceptibility and

time-displaced correlation functions of α’ precipitates and (001) interfaces in Fe-Cr superlat-

tices. A Cr interface disorders the Fe magnetic moments and acts as a nucleation site for the

ferromagnetic-paramagnetic (FM-PM) transition with a lower effective TC and enhanced sus-

ceptibility. Cr moments in disordered Fe-Cr alloys are highly non-collinear at all temperatures.

Magnetic moments at interfacial Cr atoms remain correlated far above the Neel temperature,

with correlations rapidly decreasing away from the interface. Spin dynamics simulations also

offer insight into the time correlation functions and spin relaxation times in Fe-Cr alloys.

20

Weak ferromagnetism of Mn3X (X=Sn, Ge, Ga) compounds

Bendeguz Nyari, Andras Deak and Laszlo Szunyogh

Department of Theoretical Physics, Budapest University of Technology and Economics,Hungary

Based on the fully relativistic SKKR code we investigated the weak ferromagnetism of the Mn3Sn,

Mn3Ge and Mn3Ga compounds in their hexagonal phase. We calculated tensorial spin-model

parameters in terms of a spin-cluster expansion implemented within the scheme of relativistic

disordered local moments. Using this spin model we performed a group theoretical analysis

of the formation of weak ferromagnetic states. In addition, we looked for the ground-state

spin configurations by minimizing the spin model energy, both analytically and numerically.

We found that the chiral ground state is primarily determined by the Dzyaloshinsky-Moriya

interaction, but the weak ferromagnetic distortion of this chiral state is driven by in-plane

anisotropy. In terms of unconstrained LSDA calculations we compare the distortions of the

two seemingly degenerate weak ferromagnetic configurations and examine the effect of spin-

orbit coupling. Interestingly, we find that the weak ferromagnetic distortion of the orbital

moments almost strictly follows the group theoretical picture. In the particular case of Mn3Ga,

using constrained LSDA we also investigate the role of the induced moment of Ga in the weak

ferromagnetism.

21

Skyrmion dynamics beyond the frozen core approximation

Ulrike Ritzmann1, Joo-Von Kim2, Jairo Sinova3 and Bertrand Dupe3

1Department of Physics and Astronomy, Uppsala University, Sweden2Centre de Nanosciences et de Nanotechnologies CNRS, University Paris-Saclay,

Palaiseau, France3INSPIRE Group, Institute of Physics, Johannes Gutenberg University Mainz, Germany

Surfaces and interfaces can host a wide range of physical phenomena: changes of chemical po-

tential or hybridization can induce large spin orbit coupling, the breaking of inversion symmetry

allows the emergence of new transport properties or new interactions. In particular, the charge

and spin accumulations at the interface between a magnetic metal and non-magnetic heavy

metal layer create a torque [1] which can be used to reverse the magnetization or efficiently

move magnetic domain walls [2] or skyrmions [3].

Due to their unique dynamical properties, skyrmions offer attractive perspectives for future

spintronic applications [3]. Skyrmions are chiral localized non-collinear magnetic textures. Their

chirality gives rise to the topological enhancement of their stability. Skyrmions are characterized

by a skyrmion number or topological charge which can take the value +1 or -1 for the particle

and anti-particle, respectively. Skyrmions can be stabilized at surfaces, interfaces [4,5] and

in multilayers up to room temperature [6,7] due to the presence of the Dzyaloshinskii-Moriya

interaction (DMI).

Recently, we have shown via atomistic magnetization dynamics that the trajectory of skyrmions

depends on the symmetry of the DMI [8]. When the DMI favors the presence of skyrmions, a pure

spin current induced torque always leads to its linear trajectory while antiskyrmions may have

a trochroidal motion. However, this situation is reversed when DMI favors the antiskyrmions.

We explain this qualitative difference by the core deformation of the skyrmions.

[1] X. Wang, et al., Phys. Rev. Lett. 108, 117201 (2012).

[2] K. Ryu, et al., Nature Nanotech. 8, 527 (2013).

[3] A. Fert, et al., Nature Nano. 8, 152 (2013).

[4] N. Romming, et al., Science 341, 636 (2013).

[5] B. Dupe, et al., Nature Comm. 5, 4030 (2014).

[6] B. Dupe, et al., Nature Comm. 7, 11779 (2016).

[7] C. Moreau-Luchaire, et al., Nature Nano. 11, 444 (2016).

[8] U. Ritzmann, et al. Nature Electro. 1, 451 (2018).

22

Magnetic exchange interactions in multiferroic SrMnO3 and

their coupling to strain and polar order

Alexander Edstrom and Claude Ederer

Department of Materials, ETH Zurich, Switzerland

E-mail: alexander.edstrom@mat.ethz.ch

Computational [1] and experimental [2] work has shown that epitaxial strain can produce fer-

roelectricity (FE), and ferromagnetism (FM), in the otherwise paraelectric antiferromagnet

SrMnO3. Strain engineering thus allows for controlling the ferroic phases and their critical

temperatures (TC) in this material. Recently, we used computational methods combining den-

sity functional theory with Monte Carlo simulations of the Heisenberg Hamiltonian, as well as

molecular dynamics simulations of an effective Hamiltonian for FE, to investigate the strain-

temperature ferroic phase diagram of SrMnO3 [3]. While the FE TC increases with strain after

the FE onset (around 3% strain) the magnetic TC is more insensitive to strain. This enables

a situation with coinciding FE and magnetic TCs and potentially enhanced magnetoelectric

coupling. This might be of interest, e.g., in exploring multicaloric effects or other thermally

mediated magnetoelectric coupling phenomena.

Analysis of the strain dependent exchange interactions provides insight into the sequence of

magnetic orderings. While the FM state is energetically un-favoured in the non-polar structure

at all strains, a strong dependence of the out-of-plane exchange interaction on the Mn-O-Mn

bond angle causes FM to be favoured by FE at high (∼ 4-5%) strain.

The calculations of magnetic exchange interactions indicate a non-Heisenberg behaviour, in the

form of a dependence of the exchange interactions on the magnetic reference state. Furthermore,

calculations of the exchange interactions as function of strain reveal a change in sign of nearest

neighbour magnetic exchange interactions with distance, which is difficult to understand in

terms of standard theories for exchange interactions in magnetic insulators. Hence, further

investigations, leading to enhanced understanding of the exchange interactions in SrMnO3, would

be highly desirable.

[1] J. H. Lee and K. M. Rabe, Phys. Rev. Lett. 104 (2010) 207204.

[2] J. W. Guo et al., Phys. Rev. B 97 (2018) 235135.

[3] A. Edstrom and C. Ederer, Phys. Rev. Mat. 2 (2018) 104409.

23

Modeling of magneto-volume coupling in magnetocaloric

materials

Nuno Fortunato1, Joao Amaral2, Joao Goncalves2, Oliver Gutfleisch1 and

Hongbin Zhang1

1Institute of Materials Science, TU Darmstadt, Germany2CICECO, University of Aveiro, Portugal

Magnetic refrigeration is an emergent technology promising for eco-friendly and more energy

efficient refrigeration, using the magnetocaloric effect (MCE). It is well known that the magne-

tovolume effects have significant contribution to the MCE. However, the quantitative estimation

of MCE with magnetovolume effects remains a challenge. In this work, we propose to simulate

the MCE using a microscopic spin model solved by Monte Carlo methods that evaluate the

thermodynamic Joint Density of States. The magnetic interaction between local moments is pa-

rameterized using the exchange parameter Jij as a function of volume (v), together with external

field (H) and lattice volume terms: H = −1

2

∑Jij(v)Si.Sj + 1

2Kv2 − HM , where K is compress-

ibility. It is demonstrated that this methodology allows the reproduction of magnetovolume

effects, including 1st order transitions, that are known to greatly enhance the MCE.

Simulation results are compared with the experimental data of Gd, the typical benchmark

material for room-temperature magnetic cooling applications. We show that such a simple model

quantitatively reproduces experimental data for the MCE and the magnetostriction, paving

the way to a “ground-up,” fast computational approach to optimize and search for magnetic

refrigerant materials.

24

Modelling rare-earth/transition-metal magnets at finite

temperature with self-interaction-corrected relativistic

density-functional theory and disordered local moments

Christopher E. Patrick and Julie B. Staunton

Department of Physics, University of Warwick, Coventry, United Kingdom

Intermetallic rare-earth/transition-metal (RE-TM) compounds can show exceptionally hard

magnetic properties, the most famous examples being neodymium iron boride (Nd-Fe-B) and

samarium cobalt (Sm-Co) [1]. Such compounds present an interesting challenge to theory: their

magnetization and high Curie temperatures derive from the itinerant electrons of the transi-

tion metal, generally quite well described by the local spin-density approximation (LSDA) to

density-functional theory, but their magnetocrystalline anisotropy originates from the highly

localized 4f electrons of the rare earth, which are not well accounted for by the LSDA. Here we

present a scheme to calculate the finite temperature magnetic properties of RE-TM compounds

which combines relativistic disordered local moment theory [2] with the local self-interaction

correction [3], with the latter used to improve the LSDA description of the 4f electrons. We

demonstrate the scheme by calculating the magnetization vs. temperature curves and Curie

temperatures (Tc) of the RECo5 class of RE-TM magnets, RE = Y–Lu [4]. We show how the

scheme reproduces experimentally-measured trends across the lanthanide series. We also use an

order parameter analysis to investigate the effect of the RE on the Co-Co interactions, which

strongly influence Tc. We tentatively attribute the variation in these interactions with RE to a

small contribution to the density from f-character electrons located close to the Fermi level.

[1] J. M. D. Coey, IEEE Trans. Magn. 47, 4671 (2011).

[2] J. B. Staunton et al., Phys. Rev. B 74, 144411 (2006).

[3] M. Lueders et al., Phys. Rev. B 71, 205109 (2005).

[4] C. E. Patrick and J. B. Staunton, Phys. Rev. B 97, 224415 (2018).

25

Calculation of micromagnetic parameters from atomistic

simulations in presence of crystal defects

M. Rinaldi, M. Mrovec and R. Drautz

Interdisciplinary Centre for Advanced Material Simulation (ICAMS), Ruhr-UniversitatBochum, Germany

The purpose of this work is to elucidate the relationship between the microstructure and the

magnetic properties of electrical steels (Fe-Si) using scale-bridging computational techniques

that combine atomistic simulations with mesoscopic micromagnetic framework. The relevant

parameters for the micromagnetic model (build up from the Landau-Lifshitz-Gilbert equation)

will be calculated with atomistic techniques such as density functional theory (DFT) and tight-

binding (TB) models. The parameters analyzed are the spin-wave stiffness constant (originating

in the exchange interaction) and the prefactors in the expression for the magnetocrystalline

anisotropy. For the calculation of these quantities some of the available atomistic methods

will be tested in both frameworks (TB and DFT). This combination enables simulations of

extended defects (such as dislocations, grain and phase boundaries, interfaces) that are crucial

for the microstructure and the study of their influence on the micromagnetic parameters. The

micromagnetic calculations will be subsequently employed and compared with experimental

data.

26

Finding magnetic ground state of deposited clusters from first

principles

Balazs Nagyfalusi, Laszlo Udvardi and Laszlo Szunyogh

Department of Theoretical Physics, Budapest Univesity of Technology and Economics,Hungary

As the size of spintronic devices approaches the size of clusters containing few atoms magnetic

simulations which are able to describe the properties of such a systems are getting more and more

important. We performed a series of embedded cluster Green’s function calculations within the

framework of the fully relativistic screened Korringa-Kohn-Rostoker method[1] on antiferromag-

netic Fe chains deposited on (111) surface of Re and Rh. In order to find their magnetic ground

states a gradient minimization and Newton-Raphson iteration were used where the torque and

the Hessian-matrix were calculated directly from first principles[2] instead of relying on an ef-

fective spin Hamiltonian. On both substrate the calculations resulted in a complex magnetic

structures depending on the length of the chains.

[1] Lazarovits B, Szunyogh L and Weinberger P, Phys. Rev. B 65, 104441, (2002).

[2] L. Rozsa, L. Udvardi and L. Szunyogh, J. Phs. Condensed Matter, 26, 216003, (2014).

27

Competition of lattice and spin excitations in the temperature

dependence of spin-wave properties

Marco Di Gennaro1, Alonso L. Miranda2, Thomas A. Ostler3, Aldo H. Romero4,5 and

Matthieu J. Verstraete1

1 nanomat/Q-MAT/CESAM and European Theoretical Spectroscopy Facility, Universitede Liege, Belgium

2CINVESTAV, Departamento de Materiales, Unidad Queretaro, Mexico3Faculty of Arts, Computing, Engineering and Sciences, Sheffield Hallam University,

United Kingdom4Physics and Astronomy Department, West Virginia University, Morgantown, United

States of America5 Facultad de Ingenierıa, Benemerita Universidad Autnoma de Puebla, Mexico

The interplay of magnons and phonons can induce strong temperature variations in the magnetic

exchange interactions, leading to changes in the magnetothermal response. This is a central

mechanism in many magnetic phenomena, and in the new field of Spin Caloritronics, which

focuses on the combination of heat and spin currents. Boson model systems have previously

been developed to describe the magnon-phonon coupling but, until recently, studies rely on

empirical parameters. In this paper, we propose a first-principles approach to describe the

dependence of the magnetic exchange integrals on phonon renormalization, leading to changes

in the magnon dispersion as a function of temperature. The temperature enters into the spin

dynamics (by introducing fluctuations) as well as in the magnetic exchange itself. Depending on

the strength of the coupling, these two temperatures may or may not be equilibrated, yielding

different regimes. We test our approach in typical and well-known ferromagnetic materials: Ni,

Fe, and Permalloy. We compare our results to recent experiments on the spin-wave stiffness,

and discuss departures from Bloch’s law and parabolic dispersion.

Phys Rev B 97, 214417 (2018).

28

Coupled spin and lattice dynamics in a second principles

framework: the multibinit project

He Xu1, N Helbig2, A Martin1, Ph Ghosez1, E Bousquet1, MJ Verstraete1

1nanomat/Q-MAT/CESAM and European Theoretical Spectroscopy Facility, Universitede Liege, Belgium

2Peter Grunberg Institut and Institute for Advanced Simulation, ForschungszentrumJulich and JARA, Germany

We present second principles methods of coupled lattice and spin dynamics implemented in

multibinit, which is a component of the Abinit project. While density functional theory (DFT)

can predict structural, electronic, and magnetic properties of materials with high accuracy, the

high computational cost hinders its usage in large systems, which is usually needed in dynamics

simulations. We develop second principle methods to build coupled molecular and spin dynamics

models, where the parameters of the lattice and spin effective Hamiltonians and their couplings

are extracted from DFT results automatically. The strategies for building and solving the models

will be discussed. With this method, it is possible to simulate large-scale systems with both

lattice and spin degrees of freedom while keeping the DFT accuracy.

29

Tight-binding-based spin-lattice fluctuation theory for

simulations of magnetic transition metals at high temperatures

Ning Wang, Thomas Hammerschmidt, Tilmann Hickel, Jutta Rogal and Ralf Drautz

Interdisciplinary Centre for Advanced Materials Simulation (ICAMS), Ruhr-UniversitatBochum, Germany

A challenging problem in computer-aided materials design is to perform realistic simulations

at operating conditions for real-life applications, i.e., thermal excitations should be taken into

account. The situation becomes even more complicated for the magnetic transition metals as

both the spin fluctuations, the atomic vibrations and their couplings should be treated properly.

Here we present a spin-lattice fluctuation theory combining the conventional spin fluctuation

theory and the semi-empirical tight-binding model. This model is then solved with an effi-

cient Hamiltonian Monte Carlo algorithm in order to evaluate thermal-equilibrium properties.

As an application to iron, the calculated phonon spectra for fcc and bcc lattices are in a sur-

prisingly good agreement with the experimental data in a wide range of temperatures, and the

spin-fluctuation induced phonon softening is found to be the driving force for the transformation

back from the fcc to bcc phase at the high temperature. Besides, the atomic vibrations are found

to have considerable effect on the magnetic phase transition in bcc iron, which demonstrates

the insufficiency of the widely-used rigid lattice spin-interaction models to perform realistic sim-

ulations. Furthermore, we apply our theory together with an effective force constant method

developed in this work, and demonstrate the phase stability of δ-iron is determined by the

collective effect of spin fluctuations and atomic vibrations, which both play a crucial role to

stabilize the high-temperature bcc phase. The proposed model can be straightforwardly applied

to other magnetic transition metals and also structures with defects such as point defects, sur-

faces and dislocations, and can be used as a new simulation tool for computer-aided design of

microstructures of magnetic transition metals.

30

Curie temperature study of the tetragonally distorted high

anisotropy FeCo alloys with the use of Monte Carlo method

with the use of classical and quantum statistics

Bartosz Wasilewski

Institute of Molecular Physics, Polish Academy of Sciences, Poznan, Poland

In this work we compare the results in estimating the Curie temperature of the tetragonally

distorted high anisotropy FeCo system with the use of Monte Carlo simulations with classical

and quantum statistics. To obtain the ground state properties we have used the Spin Polarized

Relativistic Korringa-Kohn-Rostoker method as implemented in the SPR-KKR code from Mu-

nich in the Full Relativistic and Full Potential mode. For the Monte Carlo simulations we have

used the Uppsala Atomistic Spin Dynamics code (UppASD) from Uppsala.

31

Magnetic interactions in Iridium oxides from LDA+U

calculations

A. Yaresko

Max-Planck-Institut fur Festkorperforschung, Stuttgart, Germany

Because of strong spin-orbit coupling, magnetic interactions in Ir4+ (5d5) oxides cannot be de-

scribed by isotropic Heisenberg-like models and anisotropic exchange interactions become impor-

tant. In Sr2IrO4 and Sr3Ir2O7, with corner-sharing IrO6 octahedra, the dominant anisotropic ex-

change is the anti-symmetric Dzyaloshinskii-Moriya interaction. In α-Na2IrO3 and α-Li2IrO3, on

the other hand, where edge-sharing IrO6 octahedra form a honeycomb lattice, the Dzyaloshinskii-

Moriya interaction is not allowed by symmetry. Nevertheless, magnetic interactions in these

compounds are strongly anisotropic and were suggested to be described by the exactly solvable

Kitaev model.

In order to study the anisotropy of magnetic interactions in Sr2IrO4 and α-Na2IrO3 band struc-

ture calculations using the LMTO method combined with the rotationally invariant LDA+U

were performed for a number of distinct arrangements of Ir4+ magnetic moments constrained

by magnetic symmetry. The range of reasonable values of the screened Coulomb repulsion U

was determined by comparing calculated and experimental optical spectra. The calculations

reproduced experimental magnetic ground states for both compounds. Then, effective inter-site

magnetic interactions were estimated by mapping the total energy differences onto a model which

includes isotropic Heisenberg-like as well as bond-dependent anisotropic exchange interactions.

It is shown that in α-Na2IrO3 symmetric anisotropic terms are at least as strong as the isotropic

Heisenberg exchange.

32

Investigation of magnetic phase transitions using DFT+DMFT

Hongbin Zhang, Nuno Fortunato, and Harish K. Singh

Institute of Materials Science, TU Darmstadt, Germany

The functionalities of many magnetic materials are driven by the magneto-structural coupling,

which is significantly enhanced at magnetic phase transitions. To understand such phenomena,

the Gibbs free energies have to be evaluated at finite temperature, particularly for the param-

agnetic states. In this work, we performed state of the art calculations based on the density

functional theory plus dynamical mean-field theory (DFT+DMFT) methods. Taking Fe as an ex-

ample, the bcc–fcc transition is studied based on the total Gibbs free energy from DFT+DMFT

calculations. It is identified that the phonon softening is originated from the correlations. We

compared also the results with those obtained using DFT-based calculations and atomistic spin

modelling. Furthermore, we applied the method on the well-known FeRh with first-order phase

transition, and observed that the underlying driving force is due to the collapse of the magnetic

moments of Rh atoms. Lastly, based on our recent high throughput calculations on magnetic

antiperovskite compounds hosting frustrated noncollinear magnetic configurations [1], we ex-

tended the DFT+DMFT calculations to noncollinear regime, which helps to understand the

giant barocaloric effects previously observed experimentally [2].

[1] H.K. Singh, et al., Chem. Mater. 30, 6983 (2018).

[2] D. Matsunami, et al., Nat. Mat. 14, 73 (2015).

33