France



Spin-torque nano-oscillators (STNO) are nanoscale spintronic devices in which applied currents drive self-sustained magnetization oscillations. Heusler compounds are promising materials for spintronics as they exhibit low Gilbert damping for magnetization dynamics and large spin polarizations due to their (almost) half-metallic nature [1,2]. As such, they are ideal for devices such as spin-torque nano-oscillators, where critical currents can be reduced by the lower damping values and output signals enhanced by stronger magnetoresistances. This idea has been explored in vortex-based systems involving Co&lt;sub&gt;2&lt;/sub&gt;Fe&lt;sub&gt;x&lt;/sub&gt;Mn&lt;sub&gt;1-x&lt;/sub&gt;Si where large output powers and large quality factors have been reported [3].&lt;br/&gt;&lt;br/&gt;A unique feature of nanocontact vortex oscillators is the onset of periodic core reversal above a critical current [4-6]. This reversal occurs concurrently with the steady-state gyration around the nanocontact, giving rise to various behaviors we have previously studied: chaotic core reversal [4,5], phase-locking or modulation phenomena [6] in permalloy-based spin valves. These dynamics are driven primarily by currents flowing in the film plane (CIP), resulting in spin-transfer torques of the Zhang-Li form, rather than the Slonczewski torques associated with currents perpendicular to the film plane in nanopillar geometries. Here, we will discuss how the dynamics changes when all Heusler spin valves are used instead. We fabricated 20-nm nanocontacts on Co&lt;sub&gt;2&lt;/sub&gt;MnGe/Au/Co&lt;sub&gt;2&lt;/sub&gt;MnGe films grown by molecular beam epitaxy, with a nano-indentation technique [7].&lt;br/&gt;&lt;br/&gt;&lt;br/&gt;We investigated the vortex dynamics in the time and frequency domain at room temperature. An example of the measured current-dependence of the power spectral density is given in Fig. 1. We observe a rich harmonic content with oscillations that persist down to 4.5 mA, which is lower than previous cases [4-6]. Moreover, the power spectra comprise broad bands that are reminiscent of a chirped signal. Other frequency domains measurements show single frequency signal, broad spectral lines or extinction of the signal over current intervals.&lt;br/&gt;&lt;br/&gt;Time domain measurements enable us to observe other behavior, such as mode hopping, which can be seen on Fig. 2 for different currents. Other measurements have exhibit other behaviors, such as mode coexistence, intermittent signal or signal fluctuations. We attribute the rich dynamics to the coupled motion of vortices in the free and reference layers. This hypothesis is supported by some simulations.

**References:**

[1] T. Graf &lt;i&gt;et al&lt;/i&gt;., IEEE Trans. on Magn., 47, 367-373 (2011)&lt;br/&gt;[2] C. Guillemard &lt;i&gt;et al&lt;/i&gt;., Phys. Rev. Appl., 11, 064009 (2019)&lt;br/&gt;[3] T. Yamamoto &lt;i&gt;et al.&lt;/i&gt;, Phys. Rev. B 94, 094419 (2016)&lt;br/&gt;[4] S. Petit-Watelot &lt;i&gt;et al&lt;/i&gt;., Nat. Phys., 8, 682-687 (2012)&lt;br/&gt;[5] T. Devolder &lt;i&gt;et al&lt;/i&gt;., Phys. Rev. Lett. 123, 147701 (2019)&lt;br/&gt;[6] J. Létang &lt;i&gt;et al&lt;/i&gt;., Phys. Rev. B 100, 144414 (2019)&lt;br/&gt;[7] J. Létang &lt;i&gt;et al&lt;/i&gt;., arXiv:1906.08492 (2019)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/ddb04ce76b79671646bb2ba3d9c34278.jpg)
Figure 1: Power spectral density of vortex oscillations with applied dc current. The frequency bands are suggestive of a chirped signal.

![](https://assets.underline.io/uploads/markdown_image/1/image/07722c5e6c04a690cdd33ac59038bde8.jpg)
Figure 2: (a) Power spectral density computed from time-domain measurements. (b-d) Time-domain measurements for different dc current. Mode hopping between two frequencies is visible.

INTERMAG 2021

 Heusler-compound nanocontact vortex oscillators

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Spin-torque nano-oscillators (STNO) are nanoscale spintronic devices in which applied currents drive self-sustained magnetization oscillations. Heusler compounds are promising materials for spintronics as they exhibit low Gilbert damping for magnetization dynamics and large spin polarizations due to their (almost) half-metallic nature [1,2]. As such, they are ideal for devices such as spin-torque nano-oscillators, where critical currents can be reduced by the lower damping values and output signals enhanced by stronger magnetoresistances. This idea has been explored in vortex-based systems involving Co2FexMn1-xSi where large output powers and large quality factors have been reported [3]. A unique feature of nanocontact vortex oscillators is the onset of periodic core reversal above a critical current [4-6]. This reversal occurs concurrently with the steady-state gyration around the nanocontact, giving rise to various behaviors we have previously studied: chaotic core reversal [4,5], phase-locking or modulation phenomena [6] in permalloy-based spin valves. These dynamics are driven primarily by currents flowing in the film plane (CIP), resulting in spin-transfer torques of the Zhang-Li form, rather than the Slonczewski torques associated with currents perpendicular to the film plane in nanopillar geometries. Here, we will discuss how the dynamics changes when all Heusler spin valves are used instead. We fabricated 20-nm nanocontacts on Co2MnGe/Au/Co2MnGe films grown by molecular beam epitaxy, with a nano-indentation technique [7]. We investigated the vortex dynamics in the time and frequency domain at room temperature. An example of the measured current-dependence of the power spectral density is given in Fig. 1. We observe a rich harmonic content with oscillations that persist down to 4.5 mA, which is lower than previous cases [4-6]. Moreover, the power spectra comprise broad bands that are reminiscent of a chirped signal. Other frequency domains measurements show single frequency signal, broad spectral lines or extinction of the signal over current intervals. Time domain measurements enable us to observe other behavior, such as mode hopping, which can be seen on Fig. 2 for different currents. Other measurements have exhibit other behaviors, such as mode coexistence, intermittent signal or signal fluctuations. We attribute the rich dynamics to the coupled motion of vortices in the free and reference layers. This hypothesis is supported by some simulations.

**References:**

[1] T. Graf et al., IEEE Trans. on Magn., 47, 367-373 (2011) [2] C. Guillemard et al., Phys. Rev. Appl., 11, 064009 (2019) [3] T. Yamamoto et al., Phys. Rev. B 94, 094419 (2016) [4] S. Petit-Watelot et al., Nat. Phys., 8, 682-687 (2012) [5] T. Devolder et al., Phys. Rev. Lett. 123, 147701 (2019) [6] J. Létang et al., Phys. Rev. B 100, 144414 (2019) [7] J. Létang et al., arXiv:1906.08492 (2019)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/ddb04ce76b79671646bb2ba3d9c34278.jpg)
Figure 1: Power spectral density of vortex oscillations with applied dc current. The frequency bands are suggestive of a chirped signal.

![](https://assets.underline.io/uploads/markdown_image/1/image/07722c5e6c04a690cdd33ac59038bde8.jpg)
Figure 2: (a) Power spectral density computed from time-domain measurements. (b-d) Time-domain measurements for different dc current. Mode hopping between two frequencies is visible.

technical paper

Atomically thin, magnetic materials have gained a lot of attention since 2017, when the first 2D ferromagnet was reported [1]. This breakthrough has triggered research on 2D magnetic materials [2]. They are not only important from a fundamental point of view -to understand the theory of magnetism in reduced dimensions-, but also for technological applications. However, probing the magnetic order of the 2D systems by conventional magnetic experimental setups is very challenging. On the other hand, it is well known, that even in the single layer limit, semiconducting two-dimensional materials strongly absorb light. Therefore, optical spectroscopy is a good method for their characterization. Here we present the results of the comprehensive theoretical investigation of the binding energy of the 2D magnetic crystal MnPS3 based on the density functional theory and versatile formalism of the Bethe-Salpeter equation. The MnPS3 is one important example from the large family of transition metal phosphorus trisulfide (MPS3) [3]. We demonstrate that the large binding energy of the exciton equal to more than 1 eV and obtained for monolayer of MnPS3 [4], is two times greater than in the case of transition metal dichalcogenides. We also highlight the role of the magnetic orderings in electronic and optical properties. In particular, the strong impact of the magnetic ordering on the binding energy of excitons in the monolayer limit is demonstrated, as well as its substantial influence on effective mass of the carriers. In addition, we have shown that the magnetic state of the monolayer samples is sensitive to the polarization of light. Aforementioned results indicate the possibility of indirect probing of magnetic properties via optical or transport measurements. The study was accomplished thanks to the funds allotted by the National Science Centre, Poland within the framework of the research project ‘SONATA12’ no. UMO-2016/23/D/ST3/03446. Financial support from theDeutsche Forschungsgemeinschaft (DFG, German Re-search Foundation) under Project-ID 314695032 (SFB1277) is acknowledged by P.E.F.J. and J.F. and un-der Project-ID 317551441 by J.K. Access to computing facilities of TU Dresden ZIH for the project ”TransPheMat”, PL-Grid Polish Infrastructure for Supporting Computational Science in the European Research Space, and of the Interdisciplinary Center of Modeling (ICM), University of Warsaw are gratefully acknowledged.

**References:**

[1] B. Huan et al., Nature, Vol. 546, p. 270-273 (2017) [2] M. Gibertini et al., Nature Nanotechnology, Vol. 14, p. 408 (2019). [3] R. Brec, Solid State Ionics vol. 22, p. 3-30 (1986). [4] M. Birowska, Paulo E. Faria Junior, J. Fabian, J. Kunstmann, http://arxiv.org/abs/2009.05030.

**Images:**

 2D magnetic crystals: Can we probe magnetic order? Theoretical study of vdW layered MnPS3 crystals exhibiting large exciton binding energy.

The behaviour of any physical system is governed by the order parameter, determined by the geometry of the physical space of the object, namely their dimensionality and curvature. Usually, the effects of curvature are described using local interactions only, e.g. local spin-orbit- or curvature-induced Rashba and Dzyaloshinskii-Moriya interactions (DMI). In the specific case of ferromagnetism, until recently, there was no analytical framework, which was treating curvature effects stemming from local [1] and non-local [2] interactions on the same footing. The lack of a proper theoretical foundation impedes the description of essential micromagnetic textures like magnetic domains, skyrmion-bubbles and vortices. Here, we present a micromagnetic theory of curvilinear ferromagnetic shells, which allows to describe the geometry-driven effects stemming from exchange and magnetostatics within the same framework [3]. A general description of magnetic curvilinear shells can be done using tangential derivatives of the unit magnetization vector. Tangential derivatives are represented by the covariant derivatives of in-surface components and the regular derivative of the normal magnetization component, normalized by the square root of the corresponding metric tensor coefficient. This allows to separate the explicit effects of curvature and spurious effects of the reference frame. The shape of a given thin shell can be determined by two principal curvatures k1 and k2, which are functions of coordinate. The respective classification of curvilinear surfaces operates with (i) developable surfaces, where one of the principal curvatures equals to zero; (ii) minimal ones, where the mean curvature k1 + k2 = 0; and (iii) the general case. The local geometry-driven energy contributions are represented by the DMI and anisotropy, whose coefficients are determined by powers of the principal curvatures. This allows to cancel the influence of one of the DMI terms for the developable surfaces for any magnetic texture. The magnetostatic interaction is a source of new chiral effects, which are essentially non-local in contrast to the conventional DMI. The physical origin is the non-zero mean curvature of a shell and the non-equivalence between the top and bottom surfaces of the shell. We demonstrate that the analysis of non-local effects in curvilinear thin shells can become more straightforward when introducing three magnetostatic charges. In this respect, in contrast to the classical approach by Brown [4], we split a conventional volume magnetostatic charge into two terms: (i) magnetostatic charge, governed by the tangent to the sample's surface, and (ii) geometrical charge, given by the normal component of magnetization and the mean curvature. In addition to the shape anisotropy (local effect), there appear four additional non-local terms, determined by the surface curvature. Three of them are zero for any magnetic texture in shells with the geometry of minimal surfaces. The fourth term is determined by the non-equivalence of the top and bottom surfaces of the shell and becomes zero only for the special symmetries of magnetic textures. The discovered non-local magnetochiral effects introduce handedness in an intrinsically achiral material and enables the design of magneto-electric and ferro-toroidic responses. This will stimulate to rethink the origin of chiral effects in different systems, e.g. in fundamentally appealing and technologically relevant skyrmionic systems, and further theoretical investigations in the field of curvilinear magnetism as well as experimental validation of these theoretical predictions. These developments will pave the way towards new device ideas relying on curvature effects in magnetic nanostructures. The impact of effects predicted in this work goes well beyond the magnetism community. Our description of the vector field behaviour can be applied to different emergent field of studies of curvature effects. The prospective applications include curved superconductors [5], twisted graphene bilayers [6], flexible ferroelectrics [7], curved liquid crystals [8].

**References:**

[1] Yu. Gaididei, V. P. Kravchuk, D. D. Sheka, Phys. Rev. Lett., 112, 257203 (2014); D. D. Sheka, V. P. Kravchuk, Yu. Gaididei, J. Phys. A: Math. Theor., 48, 125202 (2015); O. V. Pylypovskyi, V. P. Kravchuk, D. D. Sheka et al, Phys. Rev. Lett., 114, 197204 (2015); V. P. Kravchuk, D. D. Sheka, A. Kakay et al, Phys. Rev. Lett., 120, 067201 (2018) [2] P. Landeros, A. S. Nunez, J. Appl. Phys. Vol. 108, p. 033917 (2010); J. A. Otalora, M. Yan, H. Schultheiss et al, Phys. Rev. Lett., 117, 227203 (2016); J. A. Otalora, M. Yan, H. Schultheiss et al, Phys. Rev. B, 95, 184415 (2017) [3] D. D. Sheka, O. V. Pylypovskyi, P. Landeros et al., Comm. Phys. 3, 128 (2020) [4] W. F. Brown Jr. Micromagnetics (Wiley, New York, 1963) [5] V. Vitelly, A. M. Turner, Phys. Rev. Lett., 93, 215301 (2004) [6] W. Yan, W.-Y. He, Z.-D. Chu et al, Nat. Comm., 4, 2159 (2013) [7] M. Owczarek, K. A. Hujsak, D. P. Ferris et al, Nat. Comm., 7, 13108 (2016) [8] G. Napoli, L. Vergori, Phys. Rev. Lett., 108, 207803 (2012)

**Images:**

 Micromagnetic description of symmetry-breaking effects in curvilinear ferromagnetic shells

We investigate the effects of the competition between exchange (J) and dipolar (D) interactions on the magnetization reversal mechanisms of ferromagnetic nanotubes. Using atomistic Monte Carlo simulations for a model with Heisenberg spins on a cylindrical surface, we study how the competition between both interactions influences the low temperature magnetic order of the nanotubes as well as the thermal-driven transitions involved, showing that helical (H) states become stable for a range of intermediate values of γ=D/J and establishing phase diagrams for the stability of FM, H and vortex states as a function of the radius R and length L of the nanotube, see Fig. 1 [1]. We also study the reversal behavior under application of a magnetic field, showing that for which helical (H) states are energetically favorable at zero applied field, we show that the hysteresis loops can occur in four different classes that are combinations of two reversal modes with well-differentiated coercivities with probabilities that depend on R and L. This variety in the reversal modes is found to be linked to the metastability of the H states during the reversal that induces different paths followed along the energy landscape as the field is changed. We further demonstrate that reversal by either of the two modes can be induced by tailoring the nanotube initial state so circular states with equal or contrary chirality are formed at the ends (Fig. 2), thus achieving low or high coercive fields at will without changing γ. Finally, the results of additional micromagnetic simulations performed on tubes with a similar aspect ratio show that dual switching modes and its tailoring can also be observed in tubes of microscopic dimensions [2]. Acknowledgements: Work supported by Spanish MINECO (PGC2018-097789-B-I00), Catalan DURSI (2017SGR0598) and EU FEDER funds (Una manera de hacer Europa), Colciencias Beca de Doctorados Nacionales, ConvocatoriaNo. 727, Project No. CODIUdeA 2017-16253, also CSUC for supercomputer facilities.

**References:**

[1] H. D. Salinas, J. Restrepo, Òscar Iglesias, Sci. Rep. 8, 10275 (2018). [2] H. D. Salinas, J. Restrepo, Òscar Iglesias, Phys. Rev. B 101, 054419 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/4c95db4a71866b9df94625a04b88cb42.jpg)
Fig. 1: Typical phase diagram.

![](https://assets.underline.io/uploads/markdown_image/1/image/7cb117a7f970c0aa3b067c1bece94d70.jpg)
Fig. 2: Snapshots of spin configurations during a reversal mode.

 Magnetic phase diagrams and helicity control of reversal modes in ferromagnetic nanotubes

Recently, it was demonstrated that confined helimagnetic nanostructures, composed of grains of different chirality (and consequently, a different sign of Dzyaloshinskii-Moriya energy constant), can host stable Bloch points [1]. In addition, it was shown that Bloch points undergo hysteretic behaviour and that their type can be changed using an external magnetic field. In this work, using Ubermag [2] micromagnetic simulations with OOMMF [3] as a computational backend, we explore if Bloch point magnetisation states can be manipulated using spin-polarized currents in nano-disk and nano-strip FeGe samples. We start by showing that a zero-field stable Bloch point emerges not only in thin-film disk samples [1] but also in an extensive range of planar geometries, including nanostrips. We then explore whether Bloch point's type can be switched using spin-polarized current pulses. We simulate a FeGe [4] nanodisk with 150 nm diameter, 20 nm thickness of the bottom layer with D&lt;0 and 10 nm thickness of the top layer with D&gt;0. We begin by relaxing a uniform +z magnetisation state, which results in a head-to-head Bloch point. To a relaxed head-to-head Bloch point, we apply a spin-polarised current pulse with current density J and duration T, polarised in the negative z-direction. We vary current density J and pulse duration T and observe whether the type of Bloch point changes. In Fig. 1 we show a diagram depicting J-T regions for which Bloch point type switching occurs from head-to-head to tail-to-tail. In the second part of our work, we simulate nanostrips with 450 nm length and 90 nm width. Similar to nanodisks previously simulated, the thickness of the bottom layer with negative Dzyaloshinskii-Moriya constant is 20 nm and the thickness of the top layer with positive DM constant is 10 nm. We apply current polarised in -y-direction and track both x and y positions of the Bloch point. In Fig. 2, we show how Bloch point moves in the x-direction for different current densities J. Our findings demonstrate that Bloch points can be manipulated using spin-polarized currents. Using current pulses polarised in -z-direction, we were able to switch the Bloch point's type, whereas, with currents polarised in the negative y-direction, we managed to move Bloch point in the x-direction. Our results, in addition to being of interest to fundamental physics, bring Bloch points one step closer to being potential candidates for future data storage and information processing devices.

**References:**

[1] M. Beg et al. Stable and manipulable Bloch point. Scientific Reports 5, 17137 (2015). [2] M. Beg et al. User interfaces for computational science: A domain-specific language for OOMMF embedded in Python. AIP Advances, 7, 056025 (2017). [3] M. J. Donahue and D. G. Porter, OOMMF User’s Guide, Version 1.0, Interag. Rep. NISTIR 6376, Natl. Inst. Stand. Technol. Gaithersburg, MD, 1999. [4] M. Beg et al. Ground state search, hysteretic behaviour, and reversal mechanism of skyrmionic textures in confined helimagnetic nanostructures. Scientific Reports, 5, 17137 (2015).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/640e10a6e4df4a9d468372576f020ff1.jpg)
Switching diagram of a head-to-head Bloch point in a 150 nm FeGe diameter disk using current pulse polarised in negative z-direction, with current density J and pulse duration T.

![](https://assets.underline.io/uploads/markdown_image/1/image/55c492a4be70dde428d04bd6e85f4c49.jpg)
Bloch point's x-coordinate as a function of time for different current densities J polarised in the negative y-direction.

 Spin-Polarised Current Bloch Point Manipulation

Understanding magnetization dynamics in nanosized systems is a key condition not only to realize innovative new applications, but also to further expand our comprehension of the underlying fundamental physics. Only recently has it been possible to image magnetic objects such as domain walls (DWs) with high temporal and spatial resolution and versatile environments or excitations, using, for example time resolved x-ray magnetic circular dichroism with scanning transmission x-ray microscopy (XMCD STXM). Continuous developments of this technique have allowed for a shift of interest from simple systems such as flat nanostrips, that lend themselves more readily to magnetic imaging, to more intricate systems such as three dimensional nanostructures, with added complexity from the volume [1,2]. A textbook case for such an investigation is provided by cylindrical magnetic nanowires (NWs) featuring a novel type of DW, the Bloch-point wall (BPW) [3] which exhibits azimuthal curling of magnetic moments around a Bloch-point on the NW axis. The dynamics of these walls stand out compared to DWs in flat nanostrips due to fascinating theoretical predictions of fast, stable speeds and the controlled emission of spin waves [4]. Recent experiments in NWs indicate that the Œrsted field induced by nanosecond pulses of current plays a key role in stabilising walls exclusively of the BPW type and further switches the azimuthal circulation to be parallel to the field [5]. This allows controlling the wall structure and enables fast DW motion with speeds &gt; 600 m/s and an absence of Walker breakdown. The importance of the Œrsted field in NWs was further studied with simulations to determine a strong radial dependence, scaling as one-over radius cubed, and a complex mechanism of the BPW switching process, involving nucleation and annihilation of pairs of Bloch-points [6]. In the case of longitudinally magnetised domains, the peripheral magnetic moments also tend to align with the Œrsted field with the degree of tilt related to a competition between magnetic exchange and Zeeman energy. It is clear that the Œrsted field has a major influence on magnetization dynamics in NWs, yet few predictions have been confirmed experimentally due to the complexity of such experiments. Further, without time resolved measurements, no quantitative comparisons of eg. tilt angles in magnetization may be made with the simulations. Verifications of these effects are therefore strongly required in order to control the system and employ it in possible future applications. Here, we make use of time resolved XMCD STXM to image the magnetization dynamics in NWs subjected to nanosecond pulses of electrical current. Time resolved images were acquired with a temporal resolution of 200 ps, to image the effect of positive and negative polarity 3 ns duration voltage pulses of chosen amplitude applied to magnetically soft Co30Ni70 NWs with diameters 93, 97 and 101 nm. We first observed the tilting of magnetization towards the applied Œrsted field direction in longitudinally magnetized domains (Fig. 1a) and created a model based on the absorptivity of x-rays and a description of the magnetization in a NW cross section to accurately reproduce the observed magnetic contrast and extract quantitative information. We find that the degree of tilt on the surface of these NW samples is of the order of 18±8° per 1012 A/m2 applied (Fig. 1b), which is in agreement with theoretical predictions from ref. [6]. We then observe the expansion (Fig. 2b,d) and compression (Fig. 2a,c) of the BPW width due to the application of a parallel and antiparallel Œrsted field, respectively. This effect, previously predicted by simulations, occurs when the applied current density is insufficiently strong to induce the BPW circulation switching. The magnetic contrast of the phenomenon is again reproduced with our simple model giving quantitative information about this “breathing” of the BPW. We expect that this work lays the foundation for and provides an incentive to further studying complex magnetisation dynamics in NWs. With increased control of the NW materials, the predicted ultrafast DW motion and associated spin wave emissions [4] may be visualized using this technique. Further, the quantitative analysis provided herein shows the depth of information obtainable with time resolved XMCD STXM and that a direct comparison of the observed dynamics to ie. simulations and theory is possible. This type of direct collaboration will significantly grow the understanding of three dimensional magnetic nanosized systems and enable better control over them.

**References:**

[1] C. Donnelly et al., Time-resolved imaging of three-dimensional nanoscale magnetization dynamics. Nat. Nanotech. 15 p.356-360 (2020) [2] A. Fernández-Pacheco et al., Three-dimensional nanomagnetism. Nat. Comm. 8 p.15756 (2017) [3] S. Da Col et al., Observation of Bloch-point domain walls in cylindrical magnetic nanowires. Phys. Rev. B. 89 p.180405 (2014) [4] R. Wieser et al., Current-driven domain wall motion in cylindrical nanowires. Phys. Rev. B. 82, p.1-7 (2010) [5] M. Schöbitz et al. Fast Domain Wall Motion Governed by Topology and Œrsted Fields in Cylindrical Magnetic Nanowires. Phys. Rev. Lett. 123 p.217201 (2019) [6] A. De Riz et al. Mechanism of current-assisted Bloch-point wall stabilization for ultra fast dynamics. arxiv: 2011.14869v1

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/dad38862b68e88e07ac7345f1feba12e.jpg)
Figure 1: (a) Time resolved imaging of the tilting of magnetization in cylindrical NWs due to an applied Oersted field with white arrows indicating the direction of the Œrsted field. (b) Tilt angle calculated from the magnetic images for three different NW diameters and compared with theoretical predictions.

![](https://assets.underline.io/uploads/markdown_image/1/image/266b1bac51bb6fd30599e47d72aee2f6.jpg)
Figure 2: (a) Time resolved images of the compression (a) and expansion (b) of a Bloch-point DW in cylindrical NWs due to an applied Oersted field. Illustrations of the compressed (c) and expanded (d) DW from (a,b) with the Oersted field direction indicated.

 Time resolved imaging of Œrsted field induced magnetization dynamics in cylindrical magnetic nanowires

Current-driven domain wall dynamics in circular cross-section nanowires is a key phenomenon to be studied with a view to designing three-dimensional magnetic memory devices. The information stored in this type of device would be encoded by magnetic domains separated by magnetic domain walls. Two types of domain walls exist in magnetically soft cylindrical nanowires: the transverse-vortex wall (TVW) and the Bloch-point wall (BPW). The latter has a distinct topology and exhibits azimuthal curling of magnetic moments (also called circulation) around a Bloch point – a micromagnetic singularity. This micromagnetic object is expected to prevent the usual Walker breakdown, and thus enable high domain wall speed. The Walker breakdown is expected to not occur in the case of the Bloch-point wall, as it would require a too large energy of dipolar origin with a head-on magnetization configuration along all three directions. We showed recently [1] that the previously overlooked Oersted field associated with an electric current is a key in experiments to stabilize the BPW and reach speed above 600m/s with spin-transfer. Here we use micromagnetic simulations, analytical modeling and topological arguments to understand in detail and quantitatively the underlying phenomena, in particular the switching from negative to positive circulation of the BPW, with respect to the applied current [2]. The switching of the azimuthal circulation of the BPW to match that of the OEersted field occurs above a threshold current which we quantify as a function of geometry and material parameters. The key result is a 1/R3 dependence of the switching threshold, with R the wire radius, with the effect of the OErsted field becoming predominant for wire radius above typically 30nm. To the contrary, the speed of walls remains largely determined by spin-transfer alone, in a below-Walker regime. Thanks to a generalized micromagnetic scaling of lengths and densities of current, the present result can be applied to wires made of any magnetically soft material. We also highlight the complexity of BPW transformation involving the nucleation and/or annihilation of the topological objects at the surface (vortex/antivortex pairs) and in the volume (Bloch points) [Fig.1].

**References:**

[1] M. Schöbitz, A. de Riz, S. Martin et al., Phys. Rev. Lett. 123, 217201 (2019) [2] A. De Riz, J. Hurst, M. Schöbitz, C. Thirion, J. Bachmann, J. C. Toussaint, O. Fruchart, D. Gusakova, arXiv:2011.14869 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/639b0dd3d6b4627fa77ee50fcccf7ce4.jpg)
Figure 1: Snapshots illustrating the switching mechanism of BPW circulation in a permalloy wire under applied current. Top row: unrolled maps of radial magnetization, wire axis along z, periphery along φ. Bottom row: same surface maps of radial magnetization seen from inside of the wire as a 3D view. A, V and B labels highlight surface vortex and antivortex as well as Bloch point.

 Mechanism of current-assisted Bloch-point wall stabilization for ultra fast dynamics

Cylindrical magnetic nanowires are a three-dimensional system in which magnetization may be manipulated by spin-polarized currents in order to controllably nucleate, move and pin magnetic domain walls (DWs). Such control makes them excellent candidates for three-dimensional storage devices such as in the well-known concept of Racetrack memories [1]. Due to their geometry, cylindrical nanowires can host a DW with curling magnetization not subject to the Walker breakdown limitation [2], and thus that can reach velocities over 1 km/s. This kind of DW is known as the Bloch-Point wall (BPW) [3] [4] and it was experimentally reported under static conditions for the first time in 2014 [5]. Recently, velocities above 600 m/s driven by spin-transfer torques have been also reported [6]. In order to achieve the desired control of DW motion, effective pinning sites need to be set along the wire’s axis. Here, we propose a system based on cylindrical Permalloy (Fe20Ni80) nanowires with evenly spaced chemical barriers: Fe-rich segments (Fe80Ni20) of length ranging from 20 to 100 nm and 1 μm separation. We present an overview of their static micromagnetic configuration as well as their response to applied field and nano-second electric current pulses. This is a prerequisite to investigating and understanding the interplay of DWs with chemical modulations. Quantitative understanding is achieved combining magnetic imaging by means of X-ray Magnetic Circular Dichroism (XMCD) coupled to PhotoEmission Electron Microscopy (PEEM), Scanning Transmission X-ray Microscopy (STXM) or X-ray ptychography with &lt;15 nm spatial resolution (Figure 1), and micromagnetic simulations with mumax3 and feeLLGood codes, as well analytical modelling. In addition, Transmission Electron Microscopy (TEM) combined with electron holography was used to extract valuable qualitative and quantitative information on the local magnetic behavior. The Fe-rich barriers have a spontaneous magnetization of 1.4 T whereas the Permalloy segments of 0.8 T. Such magnetization change at the interface generates volume charges and thus a dipolar energy increase. This energy cost can be overcome with a vortex state at the chemical barrier where the magnetization remains axial at the core and curling at the shell. The XMCD images indeed show a curling magnetic state at the chemical barriers (Figure 2). In addition, magnetic images are supported by a quantitative post processing code that simulates the magnetic contrast coming from XMCD-PEEM technique for a specific three dimensional magnetization texture, allowing us to extract the curling angle of the magnetization with respect to the wire’s axis. The strength of curling increases with both the modulation length and wire diameter, with a clear analogy with the vortex state in flat magnetic disks. The strength of curling was assessed by imaging under large axial magnetic field. The chirality of curling is random at rest but can be switched deterministically by means of the Oersted field of nanosecond current pulses, showing again a clear correlation between the strength of curling and the geometry of the modulations.

**References:**

 [1] S. S. P. Parkin et al, Science, vol. 320, no. 5873, p. 190 (2008). [2] R. Hertel, Journal of Physics: Condensed Matter, vol. 28, no. 48, p. 483002 (2016). [3] H. Forster et al., Journal of Applied Physics, vol. 91, no. 10, pp. 6914–6919 (2002). [4] A. Thiaville and Y. Nakatani, ‘Spin dynamics in confined magnetic structures III’, vol. 101 pp. 161–205 (2006). [5] S. Da Col et al., Phys. Rev. B, vol. 89, no. 18, p. 180405 (2014). [6] M. Schöbitz et al., Phys. Rev. Lett., vol. 123, no. 21, p. 217201 (2019).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/0655064c9bacad1f07583fcda00e9f63.jpg)
Figure 1: Reconstructed amplitude ptychographic XAS image at Fe L3 edge of a permalloy cylindrical nanowire of 140 nm of diameter with a Fe-rich chemical barrier (Fe80Ni20) of 100 nm in length (dark region).

![](https://assets.underline.io/uploads/markdown_image/1/image/2e86f6a91ded7f93aaa462b2471792da.jpg)
Figure 2: Reconstructed XMCD ptychographic image of the chemical barrier shown in Fig. 1. The curling magnetization is indicated by the dark and light bipolar contrasts.

 Micromagnetics of Chemical Barriers Inserted within Permalloy Cylindrical Nanowires: Towards the Control of Domain Wall Motion

Nanowires and nanotubes are one-dimensional conduits, providing an ideal playground to investigate the fundamentals of domain-wall motion and spin-wave propagation. While simulations have been dominating for two decades, the first experiments are emerging. In particular, a peculiar class of domains were observed recently in nanotubes – domains with azimuthal (flux-closure) magnetization [1] (CoNiB, 400nm diameter). Azimuthal magnetization relates to the curvature-induced magnetic anisotropy resulting from the anisotropy of the granular structure, combined with inverse magnetostriction and/or inter-grain interface anisotropy. Interestingly, besides the conventional spin-transfer torques, a significant OErsted field directly coupled to the azimuthal magnetization through Zeeman energy may exist in a tubular geometry. This opens new possibilities for the manipulation of the domain walls in such geometries. Curvature-induced anisotropy together with OErsted field effects suggest that according to the domain wall type their dynamical features may be very different from the case of thin flat strips, now well established theoretically and experimentally. Given that, we report a theoretical overview [2] of the magnetic domain wall behavior under an electric current in infinitely long nanotubes with azimuthal magnetization, combining the one-dimensional analytic model and micromagnetic simulations. We derive a phase diagram predicting the stable azimuthal domains versus the anisotropy strength and the tube geometry, see Fig. 1. In addition, we predict the types of stable walls, either Néel or Bloch, pictured in Fig. 2, resulting from the competition between the curvature induced exchange energy, the demagnetization energy and the anisotropy energy. We also draw the panorama of the impact of the OErsted field on wall motion in tubes with azimuthal domains, pointing at curiosities such as opposite directions of motion below and above the Walker current and dramatic contrast between Néel and Bloch walls. In particular, we show the existence of spin-transfer torque and/or Oersted dominated regime for both domain wall structures and we predict large domain wall speeds reaching potentially 800 m/s, before the occurrence of a so-called Walker breakdown, see Fig. 2. We show how the domain wall speed and the walker field depend on the anisotropy and the geometrical parameter of the magnetic tubes and highlight the most suitable parameters to achieve high domain wall speed. Our study may guide the experimental realization of magnetic tubes, targeting the optimal parameters to get the desired properties.

**References:**

[1] M.Stano, O. Fruchart, Magnetic Nanowires and Nanotubes, Handbook of Magnetic Materials, Elsevier, v. 27, pp.155-267, (2018). [2] J. Hurst, A. De Riz, M. Stano, J.-C. Toussaint, O. Fruchart, D. Gusakova, arXiv:2010.01966, (2020) [Accepted for publication in PRB].

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/4b1cb2080f81d841fe83ecf93d78ffdb.jpg)
Fig. 1 : Threshold values of the anisotropy strength separating axial monodomain (below the curve) from azimuthal monodomain (above the curve) as a function of the tube thickness for three different external tube radius. The markers indicate an estimation of the threshold anisotropy value obtained with feeLLGood simulations [2].

![](https://assets.underline.io/uploads/markdown_image/1/image/ca8308c0d13e791df5240097cefc75c7.jpg)
Fig. 2 : Time-averaged domain wall speed for a Néel wall (left panel) and a Bloch wall (right panel) versus the applied current density for two nanotube thicknesses: ΔR=10 nm (full lines) and ΔR=20 nm (dashed lines). Three different configurations are considered: disconsidering spin-transfer torques~(black curves), with spin-transfer torque and Oersted field cooperating~(red curve), and with spin-transfer torque and Oersted competing~(blue curve).

 Theoretical study of current induced domain wall motion in magnetic nanotubes with azimuthal magnetization

Vortex-based spin torque nano-oscillators (STNOs) are nanoscale tunable multifunctional radio-frequency devices which have been proposed for a diverse variety of applications, ranging from novel wireless communications paradigms [1, 2], random number generators [3] and more recently the building blocks of novel bio-inspired computing architectures for neuromorphic computing [4]. The competitiveness of STNOs as an emerging technology lies in several key characteristics relative to conventional electronics, including tunability, multi-functionality, scalability and radiation hardness. Vortex-based STNOs have been shown to demonstrate superior performance parameters in terms of output power emission and signal linewidth to other STNO-based radio frequency devices, operating in the 50 MHz to 1 GHz regime. By harnessing the rich dynamics associated with non-homogeneous magnetisation configurations in confined nanostructures, the free layer of a magnetic tunnel junction (MTJ) can be forced, via a localised magnetic field, to transition between two magnetic states: the quasi-uniform and vortex states. In this report we demonstrate that such transitions can be driven back and forth to a dynamic equilibrium by exciting an MTJ with alternating magnetic fields close to the resonant modes of the magnetic vortex. The induced magnetic state transitions leads to a strong dependence of the resistance of the MTJ to the incoming signal, resulting in nominally identical devices which can act as both high frequency sources and detectors. In this presentation we will show how this dynamic behaviour can have exciting potential for future emerging paradigms, such as novel analogue wideband communication, integrated rf source/sensors and the building blocks for neuromorphic computing architectures.

**References:**

[1] - A. S. Jenkins, L. San Emeterio Alvarez, R. Dutra, R. L. Sommer, P. P. Freitas, and R. Ferreira, “Wideband High-Resolution Frequency-to-Resistance Converter Based on Nonhomogeneous Magnetic-State Transitions,” Phys. Rev. Appl., vol. 13, no. 1, p. 014046, Jan. 2020. [2] - A. S. Jenkins, L. San Emeterio Alvarez, P. P. Freitas, and R. Ferreira, “Digital and analogue modulation and demodulation scheme using vortex-based spin torque nano-oscillators”, Scientific Reports, vol. 10, 11181 (2020) [3] - A. S. Jenkins, L. S. E. Alvarez, P. P. Freitas, and R. Ferreira, “Nanoscale true random bit generator based on magnetic state transitions in magnetic tunnel junctions,” Sci. Rep., vol. 9, no. 1, p. 15661, Dec. 2019. [4] - H. Farkhani, T. Boehnert, M. Tarequzzaman, J. D. Costa, A. Jenkins, R. Ferreira, J. Madsen, F. Moradi, “LAO-NCS: Laser Assisted Spin Torque Nano Oscillator-Based Neuromorphic Computing System,” Front. Neurosci., vol. 13, Jan. 2020.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/7d7e9cca455acdd32d033ea720d9662d.jpg)
Figure 1 – (a) Schematic representation of the modulation and demodulation scheme and (b) single device schematic and (c) transfer curve showing possible magnetisation states of the free layer, (insets are micromagnetic simulations).

![](https://assets.underline.io/uploads/markdown_image/1/image/988030636d76b85869977f368b1cf864.jpg)
Figure 2- (a) schematic circuit showing how the signal created by MTJsource is fed into the antenna of MTJdetector. The (b) spectral properties of MTJsource alongside the c) resultant resistance response of MTJdetector as a function of the current applied to the MTJsource (IMTJS). The insets in (c) show example time traces, where the free layer is transitioning between the vortex (green) and QUP (blue) states.

 Dynamic state transitions in vortex-based magnetic tunnel junctions for high frequency data transmission

Heusler magnetic compounds offer a wide variety of electronic properties very promising for spintronics and magnonics. Some of them exhibit a spin gap in their band structure at the Fermi energy. This peculiar electronic property was denominated as Half-Metal Magnetic (HMM) behavior [1]. This leads to two very interesting properties for spintronics, i.e. fully polarized current together with ultra-low magnetic damping, two key-points for spin-transfer-torque based devices. The full polarization was experimentally reported in Co2MnSi [2,3], and we measured a magnetic damping in the 10-4 range on this compounds. Recently, we reported magnetic damping in the same range for other Heusler compounds [4]. In this talk, we show that a key experimental point to get ultra-low magnetic damping (in the 10-4 range) is to control the compound stoichiometry as best as possible. Single-crystalline Co2MnZ thin films with Z=Al, Si, Ga, Ge, Sn and Sb were grown by using Molecular Beam Epitaxy [4]. We developed a process to control the Co, Mn and Z fluxes with accuracy lower than 1% [5]. The electronic properties of these Co2MnZ compounds were examined by using in situ techniques like electron diffraction during the growth, and spin resolved photoemission (SR-PES performed at SOLEIL synchrotron), and ex situ techniques like x-ray diffraction, transmission electron microscopy and ferromagnetic resonance. Electron diffraction during the growth (RHEED) allowed us to verify the stoichiometry after fluxes calibration [5]. This consists in recording diffracted intensity during deposition : if the growth is 2-dimensional, intensity oscillations are observed (called RHEED oscillations) due to interferences between electron scattered by the nth grown atomic plane, and n+1th plane that is growing (fig.1). We observed this behavior for the Co2MnZ series grown at 250C on a V or Cr buffer layers. Interestingly, a bilayer by bi layer growth mode was observed. Bilayer growth mode is well-known for MBE-grown semiconductors and is associated to the growth of basic blocks of the zinc blend or diamond structures. Similarly, the basic block for Co2MnZ Heusler compounds is a cube with Co atoms at its 8 corners, and Mn or Z in the center of the cube. These Heusler compounds thus want to develop these basic blocks during the growth, leading to bilayer growth. This is a clear experimental proof of chemical ordering during the growth [5]. Finally, the excellent agreement between the delay to complete 2 atomic planes measured by RHEED and the time deduced from fluxes calibration allows us to confirm stoichiometry accuracy around 1% for each element. The spin (half-) gaps obtained by SR-PES on Co2Mn-Si, -Ge and –Sn were found to be in very good agreement with ab initio calculations. The lowest magnetic damping values were obtained for these former HMM compounds, and are greater for Co2Mn – Al and Ga where no spin gap was observed (Table I). The control of the stoichiometry also offered us a robust experimental demonstration of the correlation between the spin polarization and the magnetic damping in Co2MnSixAl1-x epitaxial thin films [6]. Finally, we show that single crystalline thin films are not mandatory, since we observed spin gap and magnetic damping values as low as 10-3 in polycrystalline Co2Mn-Si and –Ge grown on glass [7]. This highlights the key role of the stoichiometry control for getting low damping, more importantly than structural defects like grain boundaries for instance.

**References:**

[1] New Class of Materials: Half-Metallic Ferromagnets, R. A. de Groot et al, Phys. Rev. Lett. 50, 2024 (1983) [2] Direct observation of half-metallicity in the Heusler compound Co2MnSi, M. Jourdan et al., Nat. Commun. 5, 3974 (2014) [3] Direct evidence for minority spin gap in the Co2MnSi Heusler compound, S. Andrieu et al, Phys. Rev. B 93, 094417 (2016) [4] Ultra-low magnetic damping in Co2Mn-based Heusler compounds promising materials for spintronic, C. Guillemard et al, Phys. Rev. Appl.. 11, 064009 (2019) [5] Issues in growing Heusler compounds in thin films for spintronic applications, C. Guillemard et al, Invited Tutorial, J.Appl. Phys., 128, 241102 (2020) [6] Engineering Co2MnAlxSi1-x Heusler compounds as a model system to correlate spin polarization, intrinsic Gilbert damping and ultrafast demagnetization, C. Guillemard et al, Adv. Mat. 1908357 (2020) [7] Polycrystalline Co2Mn-based Heusler thin films with high spin polarization and low magnetic damping, C. Guillemard et al, Appl. Phys. Lett. 115, 172401 (2019)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/18b04372cf1e5ed6b2c6e20c3c5b575f.jpg)
Fig.1 : Electron Diffraction Intensity oscilaltions during the growth of Co2MnGa on a V(001) buffer layer. The oscilaltions correspond to a bilayer by bilayer growth mode [5].

![](https://assets.underline.io/uploads/markdown_image/1/image/b0ed917652ad898d0b349c40287d4b7e.jpg)
Table I : reviiew of the structural and electronic properties observed on the Co2MnZ series. The crystalline structures were determined using transmission electron microscopy, spin polarization and gap using spin-resolved photoemission, and magnetic properties using feromagnetic resonance (FMR) [5].

Heusler-compound nanocontact vortex oscillators

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