- added version of GCS extension proposal approved by SB

source/KKRnano/doc/GCS-KKRnano_extension/GCS-KKRnano_extension.tex

@@ -124,16 +124,19 @@ Institute for Advanced Simulation and Peter Gr\"unberg Institut, Forschungszentr
 
 \section{Introduction}
 \label{sec:intro}
-We have developed a unique electronic structure code, 
+We have developed a unique electronic structure code based on Density Functional Theory, 
 KKRnano \cite{zeller_towards_2008,thiess_massively_2012,bornemann_large-scale_nodate},
 specifically designed for petaFLOP computing. Our method scales linearly
 with the number of atoms, so that we can realize system sizes of up to 
 half a million atoms in a unit cell if necessary.
-Recently, we implemented a relativistic generalization of our algorithm 
-enabling us to calculate complex non-collinear magnetic structures, such as skyrmions,
+Recently, we generalized the algorithm to the vectorial spin density formulation enabling us
+to calculate complex non-collinear magnetic structures. We implemented a relativistic 
+generalization  of our algorithm  such that we are able to treat skyrmions,
 in real space. Skyrmions are two-dimensional magnetization solitons, i.e., two-dimensional
 magnetic structures localized in space, topologically protected by a non-trivial
-magnetization texture, which has particle-like properties. 
+magnetization texture, which has particle-like properties. Necessary condition for the 
+emergence of skyrmions is the spin-orbit interaction in magnets with broken inversion symmetry.
+Chiral magnetic B20 compounds are cubic crystals fulfilling the conditions above. 
 The focus of our work is on the germanide \ce{MnGe} that is particularly
 interesting among the chiral magnetic B20 compounds, as it exhibits a three-dimensional magnetic structure
 that is not yet understood (see preliminary results
@@ -146,8 +149,11 @@ we request an extension of the project period until 30th June 2019.
 \section{Complex Magnetic Textures in B20-\ce{MnGe}}
 \label{sec:mnge}
 
-B20-\ce{MnGe} was identified as a good candidate material to be investigated with the new
-version of KKRnano which now contains the feature of non-collinear magnetism and spin-orbit coupling.
+B20-\ce{MnGe} is currently the subject of extensive
+investigation
+\cite{kanazawa_large_2011,kanazawa_possible_2012,grigoriev_chiral_2013,tanigaki_real-space_2015,martin_magnetic_2016}.
+This is mainly inspired by the discovery of skyrmions as small information-carrying particles
+that could potentially be used in spintronic devices \cite{fert_magnetic_2017}.
 In a recent study \cite{tanigaki_real-space_2015}, it was 
 found by transmission electron microscopy that 3D magnetic
 objects exist in B20-\ce{MnGe}. The authors of \cite{tanigaki_real-space_2015}
@@ -169,7 +175,7 @@ remains finite \cite{feldtkeller_continuous_2017}.
 	spin spiral that propagates in (001) direction. Reprinted from \cite{rybakov_new_2016} and
 	licensed under CC BY 3.0.}
 \end{figure}
-Findings by Kanazawa \textit{et al.} suggest that the lattice is set up by a superposition of three orthogonal
+Findings by Kanazawa \textit{et al.}\ suggest that the lattice is set up by a superposition of three orthogonal
 helical structures, also referred to as 3Q state \cite{kanazawa_noncentrosymmetric_2017}. 
 Here, the local magnetization is determined by the provision
 \beq
@@ -184,16 +190,7 @@ Here, the local magnetization is determined by the provision
 where $q=\frac{2\pi}{\lambda}$ is the wavenumber given in terms of the helical wavelength $\lambda$ and
 $x$, $y$ and $z$ are the spatial coordinates within the unit cell.
 Note, that $\vec{M}(\vec{r})$ is not normalized.
-In contrast to other systems exhibiting a
-similar magnetic phase, the rather short helical wavelength in B20-\ce{MnGe} allows one to perform
-Density Functional Theory (DFT) 
-calculations with KKRnano.
-B20-\ce{MnGe} is currently the subject of extensive
-investigation
-\cite{kanazawa_large_2011,kanazawa_possible_2012,grigoriev_chiral_2013,tanigaki_real-space_2015,martin_magnetic_2016}.
-This is mainly inspired by the discovery of skyrmions as small information-carrying particles
-that could potentially be used in spintronic devices \cite{fert_magnetic_2017}.
-However, no large-scale DFT calculation seems to have been performed.
+
 At present there is a lack of a convincing explanation
 of what is observed in experiment. Research in the framework of micromagnetic models identified both
 magnetic frustration (RKKY interaction) as well as spin-orbit coupling induced Dzyaloshinskii-Moriya (DM)
@@ -219,14 +216,24 @@ is described by the relation
 \eeq
 In the following, we refer to this as the 1Q state.
 
+In summary, B20 MnGe exhibits a non-understood three-dimensional magnetic structure,
+that is different to the ones of the other chiral magnetic B20 systems, \textit{e.g.}\ FeGe,
+exhibiting two-dimensional magnetic structures.  No large-scale DFT calculation  has been performed.
+However, the relatively short  helical wavelength in B20-\ce{MnGe}  of 3--6~nm makes it ideal to perform
+a complete Density Functional Theory (DFT) 
+study with KKRnano, without involving a multiscale approach bridging length scales by atomistic spin models. 
+Thus, B20-\ce{MnGe} was identified as a prime candidate material to be investigated with the new
+version of KKRnano, since it  now contains the feature of non-collinear magnetism and spin-orbit coupling.
+
 
 \section{Selected Preliminary Results}
 
 In the following we present selected results of our investigations which give an impression
 of what has been achieved so far and which questions are still unanswered.
-All results are obtained using a 6x6x6 B20-\ce{MnGe} supercell (1728 atoms) with 
+All results are obtained using a $6\times 6\times 6$ B20-\ce{MnGe} supercell (1728 atoms) with 
 PBEsol as exchange correlation functional
-and we include only a single k-point, i.e., the $\Gamma$-point.
+and we include only a single k-point, \textit{i.e.}, the $\Gamma$-point.
+\\
 In an initial comparison of ferromagnetic (FM), 1Q and 3Q state the respective states are imposed on
 the system by forcing the atomic exchange-correlation B-fields
 to point into specific directions. 
@@ -236,7 +243,7 @@ As this contradicts experimental observations, we take into consideration that
 in experiment the crystal structure might inadvertently differ from the ideal structure.
 Such discrepancies can for instance be caused by strain that 
 originates from the manufacturing process of the sample.
-Therefore, it is reasonable to check whether a material's magnetic properties change, when the
+Therefore, it is reasonable to check whether the material's magnetic properties change, when the
 lattice constant is varied.
 \begin{figure}[htb]
   \centering
@@ -252,8 +259,8 @@ lattice constant is varied.
 }
 \label{fig:MnGe_kkrnano_comparison}
 \end{figure}
-Such a variation is performed in the upper part of \cref{fig:MnGe_kkrnano_comparison}, where
-the total energy is evaluated for FM, 1Q and 3Q state.
+The results of such a variation is displayed in the upper part of \cref{fig:MnGe_kkrnano_comparison}, where
+the total energy is evaluated for FM, 1Q and 3Q state as function of the lattice constant.
 Clearly, neither the 1Q nor the 3Q state constitutes the ground state,
 when the experimental lattice constant is assumed.
 Yet, by increasing or decreasing the lattice constant the energetic difference can be made
@@ -267,7 +274,7 @@ where by imposing the 1Q or 3Q state the energy can be made smaller than for the
 In general, for $a>5.0$ \AA \, both helical states are favored over the ferromagnetic one.
 Obviously, an artificial increase of the lattice constant by
 $0.2$ \AA \, ($\approx 4 \%$) or more is fairly large.
-However, probes in experiment are seldom if ever perfectly clean and
+However, experimental samples are seldom if ever perfectly clean and
 impurities in the sample need to be considered as a source of error in the
 final analysis. One potential
 effect of impurities is chemical pressure that causes a spatial expansion of the
@@ -278,12 +285,12 @@ Here, it was experimentally observed
 that doping can increase the melting temperature and change the magnetic properties of a B20 alloy.
 In the lower part of \cref{fig:MnGe_kkrnano_comparison}, the evolution of the magnetic moment
 with varying lattice constant is tracked.
-The resulting magnetic moment for the experimental lattice constant nicely falls 
-on top of the magnetic moment of approximately $2 \mu_{B}$/f.u. 
+For the experimental lattice constant, the resulting magnetic moment nicely falls 
+on top of the magnetic moment of approximately $2 \mu_{B}$/f.u., 
 which is reported by experimentalists \cite{yaouanc_magnetic_2017}.
 Furthermore, the high-spin/low-spin transition is recognizable between $a=4.60$ and $a=4.70$ \AA.
 It can also be observed that the magnetic moment increases, when the lattice constant is increased.
-This is a common behaviour which is often observed in metallic systems.
+This is a common behavior which is often observed in metallic systems.
 For larger lattice constants the magnetic moments of the three different
 magnetic textures differ more than for the smaller lattice constants.
 This might be connected to the observation of the differences in the total energy.
@@ -318,7 +325,7 @@ and
 \eeq
 The BP texture does not depend on $r$ and we can therefore neglect it in the following.
 Usually, the atomic positions are given in the Cartesian coordinates $x,y$ and $z$.
-In the definition above, we define the origin of the coordinate system, i.e., the tuple $(x=0, \, y=0, \, z=0)$,
+In the definition above, we define the origin of the coordinate system, \textit{i.e.}, the tuple $(x=0, \, y=0, \, z=0)$,
 to be at the center of the unit cell.
 In this frame of reference, all atoms that lay in an x-y-plane that intersects with the center
 are described by $\theta=\pi/2$.
@@ -334,10 +341,10 @@ and the azimuthal angle
 where the angles designating the atomic position enter as arguments. $\phi_{1}$ is a phase factor.
 An illustration of a BP is given in \cref{fig:mnge_blochpoint}. Note, that in contrast to
 that illustration we conduct our investigation for a BP with $\phi_{1}=\pi$, where magnetic moments
-are inverted, i.e., all moments point into instead of out of the center.
+are inverted, \textit{i.e.}, all moments point into instead of out of the center.
 \\
 For our calculations we
-again use a 6x6x6 supercell but this time with a 2x2x2 k-point-mesh and LDA as
+again use a $6\times 6\times 6$ supercell but this time with a $2\times 2\times 2$ k-point-mesh and LDA as
 exchange-correlation functional. Here, we choose LDA because it has been used extensively in all KKR codes
 in the past and 
 we want to eliminate the possibility of numerical problems that could occur when SOC is artificially enhanced.
@@ -347,7 +354,7 @@ B20 materials \cite{chizhikov_multishell_2013}.
 \begin{figure}[!htb]
   \centering
    \includegraphics[width=1.00\textwidth]{Figures/MnGe_ferro_bp.eps}
-	\caption{Effect of increased SOC on B20-\ce{MnGe} in a 6x6x6 supercell.
+	\caption{Effect of increased SOC on B20-\ce{MnGe} in a $6\times 6\times 6$ supercell.
 	Top: Total energy difference between (relaxed) Bloch point and (relaxed) ferromagnet.
 	Bottom: Magnetic moment of ferromagnet and Bloch point state.}
 \label{fig:MnGe_kkrnano_comparison_bp}
@@ -379,23 +386,27 @@ The reason for this is currently under investigation.
 \FloatBarrier
 
 \section{Justification of Extension}
-As shown in the previous section, there are promising hints to the existence of non-trivial magnetic textures in
+As shown in the previous section, there are promising hints for the existence of non-trivial magnetic textures in
 B20-\ce{MnGe} that can be found not only in experiment but also in \textit{ab initio} calculations with KKRnano.
 However, the obvious approach of imposing the experimentally reported magnetic texture on the system does not
 confirm the existence of a 1Q or 3Q ground state unless parameters like the lattice constant and the strength of 
 spin-orbit coupling are adjusted.
 It is our aim to verify the existence of non-trivial ground states without such adjustments and hence
-we spent a considerable amount of time on the investigation of B20-\ce{MnGe} by other means than KKRnano, e.g.,
-by constructing an extended Heisenberg model that is used to detect magnetic phase transitions and
-to perform Atomistic Spin Dynamics (ASD) simulations.
-A promising adjustment of our scheme, that we would like to
-look into, is to improve the quantitative description of the magnetization given in
+we spent a considerable amount of time on the investigation of B20-\ce{MnGe} employing other variants
+of the KKR method
+to extract microscopic
+parameters to construct an extended Heisenberg model that is used to detect magnetic phase transitions and
+to perform Atomistic Spin Dynamics (ASD) simulations. Here we noticed that due to the low-symmetry 
+position of the magnetic 
+atoms a canting of the atoms can emerge that goes beyond that what could be resolved experimentally so far. 
+Thus, we plan to continue along the path of finding the magnetic structure of B20-MnGe, but adjusting our scheme, 
+\textit{i.e.}\  we would like to look into an improved quantitative description of the magnetization given in
 \cref{eq:3q_formula} and \cref{eq:1q_spiral} by accounting for the aforementioned canting effect and
 other effects that arise from higher-order terms in the extended Heisenberg Hamiltonian.
-Apart from these challenges, that are related to physics,
-the occupation of Hazel Hen has been very high throughout the current accounting period.
+Apart from these challenges, that are related to nature of the underlying physics,
+Hazel Hen has been very busy and pretty occupied throughout the current accounting period.
 This prohibited us from obtaining results in a timely manner as mid-sized computing jobs of 50-100 nodes
-almost always queued for a couple of days and occasionally even for more than a week.
+were almost always queued for a couple of days and occasionally even for more than a week.
 
 
 \bibliography{references}