Skyrmions exhibit topologically nontrivial spin textures [1] and can be motioned by comparably small spin-polarized currents [2]. This renders them promising for the use as information carriers in future magnetic data storage and processing technologies, referred to as Skyrmionics. To better understand the physics of Skyrmions, a detailed knowledge of the real space magnetic structure of these spin solitons is mandatory. We have therefore studied the 3D magnetic textures of Skyrmion tubes (SkTs) using in-line and off-axis electron holography (EH). While the orientation of the in-plane magnetic induction B obtained from a Fe0.95Co0.05Ge nanoplate using in-line EH shows the expected hexagonal vortex-like pattern (Fig. 1), a thorough quantitative analysis implies that the underlying 3D texture deviates from that of homogeneously extended Bloch Skyrmions [3]. Low temperature holographic vector field electron tomography (VFET [4]) in an external magnetic field was therefore used to quantitatively reconstruct the full 3D magnetic texture of SkTs in an FeGe needle [5]. The resulting high-resolution 3D magnetic images (Fig. 2) reveal various previously unseen details of the SkTs. Our findings include the occurrence of local deviations from a homogeneous Bloch character within the tubes. They highlight the collapse of the Skyrmion texture upon approaching the surfaces of the needle, provide evidence for the coexistence of longitudinal and transverse Skyrmion textures, and reveal an axial modulation of the SkTs that is found to be strongly correlated among neighboring tubes in the needle. Based on the quantitative 3D magnetic induction data, we have calculated spatially resolved energy density maps across the SkTs that provide experimental evidence for the energetic stabilization of these magnetic solitons through an energy gain due to the Dzyaloshinskii-Moryia interaction, which overcompensates the exchange energy in the tube centers.

![](https://assets.underline.io/uploads/markdown_image/1/image/95d4498ede230bdf211fb866fabb1ce2.jpg)

Orientation map of the projected in-plane component of the magnetic induction in the hexagonal Skyrmion lattice of a Fe0.95Co0.05Ge nanoplate.

![](https://assets.underline.io/uploads/markdown_image/1/image/a445af1acb5f54ffe8123e81a66772df.jpg)

Morphology of an FeGe needle (left) and direction of the 3D magnetic induction B (right) as determined from holographic VFET experiments.

Unravelling the details of the magnetic texture of skyrmion tubes in three dimensions

As a promising non-volatile memory, Spin Transfer Torque Magnetic Random Access Memory (STT-MRAM) suffers from high error rate due to stochastic switch [1]. Some papers use Error Correcting Code (ECC) with powerful error correction capabilities to suppress high error rate, which lead to high delays and high check bit consumption. According to published reports, the error occurring of STT-MRAM is a serious asymmetry phenomenon [2]. The write error rate of 0 → 1 is much higher than that of 1 → 0 since 0 → 1 transition requires higher energy to ensure reliably commute the value. The traditional ECC approaches for other kinds of memories are designed for symmetric error correcting, which are not suitable for STT-MRAM. A weighted error correction mechanism is proposed and fulfilled in the paper, which can be used for the asymmetric error situation. Firstly, the codewords are weighed by estimating the different probabilities of error in state 0 and 1. In STT-MRAM, the error occurrence rate on state 0 is much higher than that on state 1. Through the check matrix, the words can be preliminarily judged to determine which bits may be wrong. Through the different weights of data 0 and 1, a bit with the highest error probability can be calculated. Then this bit is flipped to get a new codeword, which is substituted into the check matrix again to get a new error situation. The process of WECC is shown in Fig.1. If situation improves, the new codeword can be kept. Otherwise, the previous substitution operation is cancelled. In order to ensure the effectiveness of the error correction mechanism, the assistance of other ECCs such as BCH or LDPC is usually required. The error correction mechanism proposed in the paper can effectively reduce the error correction delay and decrease the check bit consumption. A virtual system in GEM5 is built up to evaluate the proposed WECC mechanism. The simulation results are used for the analysis of the error correction algorithm, showing the effectiveness of the WECC proposed in the paper for STT-MRAM.

![](https://assets.underline.io/uploads/markdown_image/1/image/fa6a1883b97a9ef7b919f61da0895f72.jpg)

Fig.1 Process of WECC

Weighted Error Correcting Code (WECC) against Asymmetric Error of STT-MRAM

**Session chair:** Aisha Aqeel, University of Munich



GOG - Fundamental Interactions in Skyrmions and Novel Phases

technical paper

The 15th Joint MMM-INTERMAG Conference (2022 Joint) is sponsored jointly by AIP Publishing and the IEEE Magnetics Society. Members of the international scientific and engineering communities interested in recent developments in fundamental and applied magnetism are invited to attend and contribute to the technical sessions. The technical program will include invited and contributed papers in oral and poster sessions, invited symposia, a plenary session, and an evening session, with about 1500 presentations overall. This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

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Please register for the Joint MMM-Intermag conference to join the event.

2022 Joint MMM-INTERMAG

This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

**Session chairs:** Manfred Albrecht, University of Augsburg and Michal Krupinski, Polish Academy of Sciences


Bernd Rellinghaus

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Unravelling the details of the magnetic texture of skyrmion tubes in three dimensions

Weighted Error Correcting Code (WECC) against Asymmetric Error of STT-MRAM

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