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Half-metallic ferromagnets (HMFs) have attracted much interest as promising materials in spintronics devices since they generate highly spin-polarized current due to the absence of one spin-channel at the Fermi level (&lt;i&gt;E&lt;/i&gt;&lt;sub&gt;F&lt;/sub&gt;). Among the known HMFs, the use of Co&lt;sub&gt;2&lt;/sub&gt;-based Heusler alloys enables enhancing the giant-magnetoresistance, tunnel-magnetoresistance, and spin-accumulation effects, thereby improving the performance of spintronic devices [1-3]. Despite the large magnetoresistance (MR) ratio observed in Heusler based devices, the structural disorder is still one of the remaining issues which lower the &lt;i&gt;P&lt;/i&gt;. Therefore, it is essential to have a highly ordered Heusler structure to realize the half-metallicity. The structural order (&lt;i&gt;B2→L2&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;) of the Heusler alloys e.g., Co&lt;sub&gt;2&lt;/sub&gt;MnSi [4] and Co&lt;sub&gt;2&lt;/sub&gt;FeGe&lt;sub&gt;0.5&lt;/sub&gt;Ga&lt;sub&gt;0.5&lt;/sub&gt; [1] have been promoted by annealing at high temperatures (&amp;gt;500°C) resulting in an enhanced MR ratio. However, for various applications, the permissible maximum annealing temperature is restricted, e.g., for a magnetic read head in a hard disk drive (HDD) the annealing temperature is limited to 300°C because of the temperature tolerance of the NiFe shield. Therefore, it is desirable to search for other Heusler alloys that crystallize in &lt;i&gt;L2&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;-order below 300°C. The present work is motivated by Okubo &lt;i&gt;et al&lt;/i&gt;. [5]’s report, where the &lt;i&gt;L2&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt; to &lt;i&gt;B2&lt;/i&gt;-order transition temperature of Co&lt;sub&gt;2&lt;/sub&gt;Mn&lt;i&gt;Z&lt;/i&gt; (&lt;i&gt;Z&lt;/i&gt; = Ge, Sn) Heusler alloys is very high (&amp;gt;1500K) suggesting high energetical stability of &lt;i&gt;L2&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;-structure; and hence &lt;i&gt;L2&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;-order is expected to appear even in the as-deposited state or by low-temperature annealing.&lt;br/&gt;Co&lt;sub&gt;2&lt;/sub&gt;Mn&lt;i&gt;Z&lt;/i&gt; (&lt;i&gt;Z&lt;/i&gt; = Ge, Sn) and reference Co&lt;sub&gt;2&lt;/sub&gt;FeGe&lt;sub&gt;0.5&lt;/sub&gt;Ga&lt;sub&gt;0.5&lt;/sub&gt; films were deposited on MgO (001) single crystal substrate using an ultra-high vacuum magnetron sputter system at room temperature and then post-annealed &lt;i&gt;in-situ&lt;/i&gt; at &lt;i&gt;T&lt;/i&gt;&lt;sub&gt;ann&lt;/sub&gt; = 200-700°C to induce the atomic-ordering. Here, Co&lt;sub&gt;50&lt;/sub&gt;Fe&lt;sub&gt;50&lt;/sub&gt; (3nm) was used as a buffer layer to deposit Co&lt;sub&gt;2&lt;/sub&gt;Mn&lt;i&gt;Z&lt;/i&gt; films to suppress a phase separation. Co&lt;sub&gt;2&lt;/sub&gt;MnSn films with two different compositions Co:Mn:Sn = 53.4:29.3:17.3 and 47.4:25.5:27.1 were deposited, which we refer to as Sn-poor and Sn-rich films, respectively. The crystal structure of the films was analyzed using a high-resolution X-ray diffractometer with Cu-&lt;i&gt;K&lt;/i&gt;&lt;sub&gt;α&lt;/sub&gt; radiation. Finally, to quantify the &lt;i&gt;P&lt;/i&gt; of the conduction electron in the bulk region, Co&lt;sub&gt;2&lt;/sub&gt;Mn&lt;i&gt;Z&lt;/i&gt; and Co&lt;sub&gt;2&lt;/sub&gt;FeGe&lt;sub&gt;0.5&lt;/sub&gt;Ga&lt;sub&gt;0.5&lt;/sub&gt; films were microfabricated into a non-local spin valve (NLSV) device using electron-beam lithography, Ar-ion milling, and the lift-off techniques.&lt;br/&gt;X-ray diffraction revealed that Co&lt;sub&gt;2&lt;/sub&gt;Mn&lt;i&gt;Z&lt;/i&gt; and Co&lt;sub&gt;2&lt;/sub&gt;FeGe&lt;sub&gt;0.5&lt;/sub&gt;Ga&lt;sub&gt;0.5&lt;/sub&gt; films are epitaxially grown along (001) direction. The degree of &lt;i&gt;L2&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;-ordering (&lt;i&gt;S&lt;/i&gt;&lt;sub&gt;L21&lt;/sub&gt;) as a function of &lt;i&gt;T&lt;/i&gt;&lt;sub&gt;ann&lt;/sub&gt; of Co&lt;sub&gt;2&lt;/sub&gt;Mn&lt;i&gt;Z&lt;/i&gt;, Co&lt;sub&gt;2&lt;/sub&gt;FeGe&lt;sub&gt;0.5&lt;/sub&gt;Ga&lt;sub&gt;0.5&lt;/sub&gt;, and Co&lt;sub&gt;2&lt;/sub&gt;MnSi [4] films are shown in Fig.1(a). In the case of Co&lt;sub&gt;2&lt;/sub&gt;FeGe&lt;sub&gt;0.5&lt;/sub&gt;Ga&lt;sub&gt;0.5&lt;/sub&gt; and Co&lt;sub&gt;2&lt;/sub&gt;MnSi, &lt;i&gt;L2&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;-ordering was observed above 500°C. Interestingly, in Co&lt;sub&gt;2&lt;/sub&gt;Mn&lt;i&gt;Z&lt;/i&gt; films, &lt;i&gt;L2&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;-ordering appeared even in the as-deposited state and it enhances systematically with increasing &lt;i&gt;T&lt;/i&gt;&lt;sub&gt;ann&lt;/sub&gt;. Figure 2(a) shows a scanning electron microscopy (SEM) image of a typical NLSV device using Co&lt;sub&gt;2&lt;/sub&gt;MnGe and Cu and the schematic of non-local measurement. We observed a clear spin-accumulation signal (△&lt;i&gt;R&lt;/i&gt;&lt;sub&gt;S&lt;/sub&gt;) in all our NLSV devices, which decays with increasing the gap-length (&lt;i&gt;d&lt;/i&gt;); as Fig.2(b) shows a representative &lt;i&gt;△R&lt;/i&gt;&lt;sub&gt;S&lt;/sub&gt;-&lt;i&gt;d&lt;/i&gt; curve of Co&lt;sub&gt;2&lt;/sub&gt;MnGe film (&lt;i&gt;T&lt;/i&gt;&lt;sub&gt;ann&lt;/sub&gt; = 300°C). To evaluate &lt;i&gt;P&lt;/i&gt;, the measured &lt;i&gt;△R&lt;/i&gt;&lt;sub&gt;S&lt;/sub&gt; in the Cu channel was analyzed by one-dimensional spin diffusion model [6]. The evaluated &lt;i&gt;P&lt;/i&gt; of the films are displayed in Fig.1(b), which varies systematically with increasing &lt;i&gt;T&lt;/i&gt;&lt;sub&gt;ann&lt;/sub&gt;. The spin-polarization &lt;i&gt;P&lt;/i&gt; of Co&lt;sub&gt;2&lt;/sub&gt;MnGe at &lt;i&gt;T&lt;/i&gt;&lt;sub&gt;ann&lt;/sub&gt; = 300°C is higher (~0.65) than that of Co&lt;sub&gt;2&lt;/sub&gt;MnSn and Co&lt;sub&gt;2&lt;/sub&gt;FeGe&lt;sub&gt;0.5&lt;/sub&gt;Ga&lt;sub&gt;0.5&lt;/sub&gt; due to a higher &lt;i&gt;S&lt;/i&gt;&lt;sub&gt;L21&lt;/sub&gt;, suggesting that Co&lt;sub&gt;2&lt;/sub&gt;MnGe is a promising material for various practical applications. For Co&lt;sub&gt;2&lt;/sub&gt;MnSn, however, low &lt;i&gt;P&lt;/i&gt; was found in both compositions, despite high &lt;i&gt;S&lt;/i&gt;&lt;sub&gt;L21&lt;/sub&gt;. Because first-principle calculations predict highly spin-polarized electronic structure in the Sn-rich composition, it is desirable to check the microstructure by transmission-electron microscopy to understand the origin of low &lt;i&gt;P&lt;/i&gt;. In conclusion, we elucidated that Co&lt;sub&gt;2&lt;/sub&gt;MnGe is a promising material to obtain high atomic order and large &lt;i&gt;P&lt;/i&gt; in the sputtered film without high-temperature annealing. Since the present Co&lt;sub&gt;2&lt;/sub&gt;MnGe film has a slightly Co-rich composition which is not suitable to obtain high &lt;i&gt;P&lt;/i&gt; due to the formation of the Co antisite disorder, optimization of the composition ratio is expected to lead to higher &lt;i&gt;P&lt;/i&gt;.

**References:**

[1] S. Li &lt;i&gt;et al&lt;/i&gt;., Appl. Phys. Lett. 103, 042405 (2013).&lt;br/&gt;[2] H. Liu&lt;i&gt; et al&lt;/i&gt;., Appl. Phys. Lett. 101, 132418 (2012).&lt;br/&gt;[3] Ikhtiar&lt;i&gt; et al&lt;/i&gt;., J. Appl. Phys. 115, 173912 (2014).&lt;br/&gt;[4] Y. Sakuraba&lt;i&gt; et al&lt;/i&gt;., Phys. Rev. B 82, 094444 (2010).&lt;br/&gt;[5] A. Okubo&lt;i&gt; et al&lt;/i&gt;., Appl. Phys. Lett. 96, 222507 (2010).&lt;br/&gt;[6] S. Takahashi and S. Maekawa, Phys. Rev. B 67, 052409 (2003).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/8902ea3d787672d1d6b6265fa50d0219.jpg)
Fig.1. &lt;i&gt;T&lt;/i&gt;&lt;sub&gt;ann&lt;/sub&gt; dependence of (a). &lt;i&gt;S&lt;/i&gt;&lt;sub&gt;L21&lt;/sub&gt;, and (b). bulk spin-polarization &lt;i&gt;P&lt;/i&gt; measured in NLSV devices. &lt;i&gt;S&lt;/i&gt;&lt;sub&gt;L21&lt;/sub&gt; exceeding 1 is expected to be caused by off-stoichiometry in the films.

![](https://assets.underline.io/uploads/markdown_image/1/image/1c520a3f468d3d48a7c2ba59af666eb7.jpg)
Fig.2. (a). An SEM image of a typical NLSV device using Co&lt;sub&gt;2&lt;/sub&gt;MnGe and Cu, and the schematic of non-local measurement. (b). The gap-length (&lt;i&gt;d&lt;/i&gt;) dependence of △&lt;i&gt;R&lt;/i&gt;&lt;sub&gt;S&lt;/sub&gt; of NLSV based on Co&lt;sub&gt;2&lt;/sub&gt;MnGe film (&lt;i&gt;T&lt;/i&gt;&lt;sub&gt;ann&lt;/sub&gt; = 300°C). The solid line indicates the fitting curve using one-dimensional spin diffusion model [6].

INTERMAG 2021

 Enhancement of L21-atomic order and spin-polarization in Co2MnZ (Z = Ge, Sn) Heusler thin films by low-temperature annealing process

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Half-metallic ferromagnets (HMFs) have attracted much interest as promising materials in spintronics devices since they generate highly spin-polarized current due to the absence of one spin-channel at the Fermi level (EF). Among the known HMFs, the use of Co2-based Heusler alloys enables enhancing the giant-magnetoresistance, tunnel-magnetoresistance, and spin-accumulation effects, thereby improving the performance of spintronic devices [1-3]. Despite the large magnetoresistance (MR) ratio observed in Heusler based devices, the structural disorder is still one of the remaining issues which lower the P. Therefore, it is essential to have a highly ordered Heusler structure to realize the half-metallicity. The structural order (B2→L21) of the Heusler alloys e.g., Co2MnSi [4] and Co2FeGe0.5Ga0.5 [1] have been promoted by annealing at high temperatures (&gt;500°C) resulting in an enhanced MR ratio. However, for various applications, the permissible maximum annealing temperature is restricted, e.g., for a magnetic read head in a hard disk drive (HDD) the annealing temperature is limited to 300°C because of the temperature tolerance of the NiFe shield. Therefore, it is desirable to search for other Heusler alloys that crystallize in L21-order below 300°C. The present work is motivated by Okubo et al. [5]’s report, where the L21 to B2-order transition temperature of Co2MnZ (Z = Ge, Sn) Heusler alloys is very high (&gt;1500K) suggesting high energetical stability of L21-structure; and hence L21-order is expected to appear even in the as-deposited state or by low-temperature annealing. Co2MnZ (Z = Ge, Sn) and reference Co2FeGe0.5Ga0.5 films were deposited on MgO (001) single crystal substrate using an ultra-high vacuum magnetron sputter system at room temperature and then post-annealed in-situ at Tann = 200-700°C to induce the atomic-ordering. Here, Co50Fe50 (3nm) was used as a buffer layer to deposit Co2MnZ films to suppress a phase separation. Co2MnSn films with two different compositions Co:Mn:Sn = 53.4:29.3:17.3 and 47.4:25.5:27.1 were deposited, which we refer to as Sn-poor and Sn-rich films, respectively. The crystal structure of the films was analyzed using a high-resolution X-ray diffractometer with Cu-Kα radiation. Finally, to quantify the P of the conduction electron in the bulk region, Co2MnZ and Co2FeGe0.5Ga0.5 films were microfabricated into a non-local spin valve (NLSV) device using electron-beam lithography, Ar-ion milling, and the lift-off techniques. X-ray diffraction revealed that Co2MnZ and Co2FeGe0.5Ga0.5 films are epitaxially grown along (001) direction. The degree of L21-ordering (SL21) as a function of Tann of Co2MnZ, Co2FeGe0.5Ga0.5, and Co2MnSi [4] films are shown in Fig.1(a). In the case of Co2FeGe0.5Ga0.5 and Co2MnSi, L21-ordering was observed above 500°C. Interestingly, in Co2MnZ films, L21-ordering appeared even in the as-deposited state and it enhances systematically with increasing Tann. Figure 2(a) shows a scanning electron microscopy (SEM) image of a typical NLSV device using Co2MnGe and Cu and the schematic of non-local measurement. We observed a clear spin-accumulation signal (△RS) in all our NLSV devices, which decays with increasing the gap-length (d); as Fig.2(b) shows a representative △RS-d curve of Co2MnGe film (Tann = 300°C). To evaluate P, the measured △RS in the Cu channel was analyzed by one-dimensional spin diffusion model [6]. The evaluated P of the films are displayed in Fig.1(b), which varies systematically with increasing Tann. The spin-polarization P of Co2MnGe at Tann = 300°C is higher (~0.65) than that of Co2MnSn and Co2FeGe0.5Ga0.5 due to a higher SL21, suggesting that Co2MnGe is a promising material for various practical applications. For Co2MnSn, however, low P was found in both compositions, despite high SL21. Because first-principle calculations predict highly spin-polarized electronic structure in the Sn-rich composition, it is desirable to check the microstructure by transmission-electron microscopy to understand the origin of low P. In conclusion, we elucidated that Co2MnGe is a promising material to obtain high atomic order and large P in the sputtered film without high-temperature annealing. Since the present Co2MnGe film has a slightly Co-rich composition which is not suitable to obtain high P due to the formation of the Co antisite disorder, optimization of the composition ratio is expected to lead to higher P.

**References:**

[1] S. Li et al., Appl. Phys. Lett. 103, 042405 (2013). [2] H. Liu et al., Appl. Phys. Lett. 101, 132418 (2012). [3] Ikhtiar et al., J. Appl. Phys. 115, 173912 (2014). [4] Y. Sakuraba et al., Phys. Rev. B 82, 094444 (2010). [5] A. Okubo et al., Appl. Phys. Lett. 96, 222507 (2010). [6] S. Takahashi and S. Maekawa, Phys. Rev. B 67, 052409 (2003).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/8902ea3d787672d1d6b6265fa50d0219.jpg)
Fig.1. Tann dependence of (a). SL21, and (b). bulk spin-polarization P measured in NLSV devices. SL21 exceeding 1 is expected to be caused by off-stoichiometry in the films.

![](https://assets.underline.io/uploads/markdown_image/1/image/1c520a3f468d3d48a7c2ba59af666eb7.jpg)
Fig.2. (a). An SEM image of a typical NLSV device using Co2MnGe and Cu, and the schematic of non-local measurement. (b). The gap-length (d) dependence of △RS of NLSV based on Co2MnGe film (Tann = 300°C). The solid line indicates the fitting curve using one-dimensional spin diffusion model [6].

technical paper

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

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

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

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.

 Heusler-compound nanocontact vortex oscillators

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].

 The Crucial Role of Stoichiometry to get Ultra-low Magnetic Damping in Heusler Compounds

The control of magnetization by electric current plays an important role in the applications of magnetic recording, nonvolatile memories, etc. As a key way to realize the manipulation of magnetization efficiently, the application of spin transfer torque (STT) and spin-orbit torques (SOT) requires materials with high spin polarization in electron transport.1-3 Besides, magnetic materials with low magnetization could reduce the critical switching current effectively due to the switching current is proportional to the saturation magnetization.4 Antiperovskite type Mn4N films have attracted a lot of attention due to the perpendicular magnetic anisotropy (PMA) and low saturation magnetization.5,6 However, the details about electronic transport properties in Mn4N films are not yet clear. Thus, the electronic transport properties of the Mn4N films with different thicknesses on MgO substrates have been investigated systematically. Fig. 1(a) presents the ρxx(T)/ρxx(300 K) of Mn4N films with different thicknesses on MgO(001) substrates. It is obvious that the resistivity continuously increases as the temperature increases in most films, showing a metallic conductance mechanism for the Mn4N films. However, there is an abnormal trend in the 4.7-nm-thick Mn4N films whose resistivity decreases as the temperature increases. In order to evaluate the purity and integrity of the Mn4N films, the residual resistivity ρxx0 at 0 K originated from impurity scattering is extracted from the ρxx-T curves.7 Fig. 1(b) shows the ρxx-T and fitting curve of the 78.8-nm-thick Mn4N film. The ρxx0 is obtained by fitting the ρxx-T at low temperatures using the expression as ρxx(T) = ρxx0+αTβ, where ρxx0 and T are the residual resistivity and temperature, and the coefficient α and β will change with the scattering model. The calculated ρxx0 of the 78.8-nm-thick Mn4N film is 30.56 μΩ cm, which is slightly less than ρxx(2 K) = 30.95 μΩ cm. The calculated β is 2.014 below 85 K, which is closely proportional to 2 for the ferromagnets. And the ρxx0 of other thicknesses were obtained by fitting the ρxx-T curves with the thickness from 7.8 to 47.3 nm in the same way. The thickness-dependent ρxx0(t) curve is shown in the inset of Fig. 1(b). It is obvious that the ρxx0 increases with the decrease of the film thickness, which imply the enhancement of the electron-electron interaction effects and interfacial scattering.8 Anomalous Hall effect of the Mn4N films were measured in the temperature range of 5-300K and in magnetic fields to 7 T. The Hall bars were used for measuring the Hall resistivity ρxy of Mn4N films with the thickness of 4.7-78.8 nm. The AHE is analyzed by the expression as ρxy=ρOH+ρAH=R0H+RsM, where R0 and Rs are ordinary and anomalous Hall coefficients, respectively. Fig. 2(a)-(h) shows the hysteretic property of the Hall resistivity ρxy for the different thickness as a function of applied magnetic field H at the temperatures of 5-300 K. The hysteretic property of ρxy due to the AHE caused by quantum mechanical spin-orbit interaction, and the linear property at the high-field regions due to the ordinary Hall effect (OHE) originated from the Lorentz force.9 The definition of MR is [ρxx(H)-ρxx(0)]/ρxx(0)×100%, where ρxx(0) is the resistivity of the film at 0 T. MR of the Mn4N film displays a negative signal and butterfly shape. The films with the thickness of 47.3 nm and 23.6 nm show a sudden lift as the magnetic field increases from 0 to 0.5 T, and the sign of MR is positive. Then, MR gradually decreases and sign turns negative with the increasing magnetic field above 0.5 T. The MR of 11.0 nm and 7.8 nm thick films shows the same trend except for the turning point at about 1 T. The upturn of MR in the low fields is mainly due to the Lorentz force effect, which causes a decline of mean free paths and a rise of the scattering rates.10 And the downturn of MR at high fields could be attributed to the enhancement of ferrimagnetic order and the reduction of electron scattering by spin-wave excitations and local magnetic anisotropy.11 At a certain temperature, MR of the Mn4N films increases with the increase of film thickness. These results provide experimental basis for application of SOT devices. This work is supported by National Natural Science Foundation of China (51871161 and 52071233).

**References:**

[1] S. Picozzi, A. Continenza, and A. J. Freeman, Phys. Rev. B 66, 094421 (2002). [2] Y. Takahashi, A. Srinivasan, B. Varaprasad, et al, Appl. Phys. Lett. 98, 152501 (2011). [3] A. Schmehl, V. Vaithyanathan, A. Herrnberger, S. Thiel, et al, Nature Mater. 6, 882-887 (2007). [4] K. Yamada, K. Oomaru, S. Nakamura, et al, Appl. Phys. Lett. 106, 042402 (2015). [5] Y. Yasutomi, K. Ito, T. Sanai, K. Toko, et al, J. Appl. Phys. 115, 17A935 (2014). [6] K. Ito, Y. Yasutomi, K. Kabara, et al, AIP Adv. 6, 056201 (2016). [7] G. Su, Y. Li, D. Hou, et al, Phys. Rev. B 90, 214410 (2014). [8] A. Cottey, Thin Solid Films 1, 297-307 (1968). [9] S. Onoda, N. Sugimoto, and N. Nagaosa, Phys. Rev. B 77, 165103 (2008). [10] X. Feng, W. Mi, and H. Bai, J. Appl. Phys. 110, 053911 (2011). [11] B. Raquet, M. Viret, E. Sondergard, O. Cespedes, and R. Mamy, Phys. Rev. B 66, 024433 (2002).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/33b2abbb653ccc1887899b2f70a1a699.jpg)
Figure 1. (a) Temperature-dependent ρxx(T)/ρxx(300 K) of Mn4N films with different thicknesses on MgO substrates. (b) The longitudinal resistivity ρxx(T) of the 78.8-nm-thick Mn4N film and the fitting curve obtained below 85 K (blue line). The inset shows the thickness-dependent ρxx0

![](https://assets.underline.io/uploads/markdown_image/1/image/10105250aa2ccde783d9f5ac35cb2723.jpg)
Figure 2. Magnetic field-dependent Hall resistivity ρxy(H) of the (a) 78.8 nm, (b) 47.3 nm, (c) 31.5 nm, (d) 23.6 nm, (e) 15.8 nm, (f) 11.0 nm, (g) 7.8 nm and (h) 4.7 nm thick Mn4N films at different temperatures

 Electronic transport properties of antiperovskite Mn4N epitaxial films

Co-based Heusler compounds are promising candidates for many emerging spintronic applications regarding the potential full spin polarization and ultra-low magnetic damping, together with their high Curie temperature (900 – 1000 K) and tunable electronic properties [1]. In particular, the existence of a minority spin gap and 100% spin polarization has been demonstrated by spin-resolved photoemission spectroscopy (SR-PES) for Co2MnSi thin films, and an ultra-low magnetic damping coefficient of 4.6*10-4 was obtained for this compound, which is the lowest value reported so far for a conductive material [2]. Tunnel magnetoresistance (TMR) ratios as high as 1995 % and 354 % has been reported for epitaxial Co2MnSi/MgO/Co2MnSi magnetic tunnel junctions at low and room temperature, respectively [3]. Large magnetoresistance ratios over 30%, at room temperature, and over 60 %, at low temperatures, have been also reported for current perpendicular-to-plane giant magnetoresistance (CPP-GMR) devices, with Co2MnSi as ferromagnetic electrode [15]. However, the electronic properties and the half-metallicity seem to be very sensitive to the structure and composition of the films [1], which can negatively impact the physical properties and the performance of these films when implemented into GMR or TMR magnetoresistive devices. In this work, we report on the transport properties of Co2MnSi Heusler compounds fabricated by molecular beam epitaxy, and patterned into Hall bars by standard UV-photolithography. The formation of the chemically-ordered L21 phase was verified by X-ray diffraction, reflection high-energy electron diffraction (RHEED) and high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) (see Figure 1). A considerable increase in the resistivity of the films was observed with the decrease of thickness as a result of the increase in the inelastic electron scattering at the film surface. Fitting the film’s resistivity versus thickness using Fuchs and Sondheimer model allows us to estimate the electron mean free path for Co2MnSi equal to 13 ± 5 nm, a key parameter to consider when employing these alloys for current-in-plane (CIP) magnetoresistive devices. Furthermore, by fitting the resistivity of the films versus temperature, we access to the distance between the Fermi energy and the minority-spin conduction band minimum (kB * Δ), as shown in Figure 2. These values in combination with spin-resolved photoemission spectroscopy (SR-PES) measurements, performed to a 20-nm Co2MnSi film, permit to estimate the spin gap of Co2MnSi between 0.55 - 0.7 eV, in good agreement with ab initio calculations [6]. A negative anisotropy magnetoresistance (AMR) ratio was measured for all the samples, which is a signature of the Half-metallicity of the Co2MnSi films. Moreover, AMR values ranging from -0.15 to - 0.24 were obtained, which are in good agreement with the highest values reported in the literature for Co2MnSi. The carrier’s concentration and carrier’s mobility of the films and their dependency with temperature was determined from Hall effect measurements. Finally, the evolution of films resistivity with thickness and temperature provided the ideal scenario to study the scaling of Hall resistivity with longitudinal resistivity. The linear trend observed indicates that screw scattering is the dominant temperature-dependent scattering mechanism taking place in Co2MnSi. The electrical parameter obtained here were measured on high-quality Co2MnSi films, with ultra-low magnetic damping and 100% spin polarization, which can be very useful in views of the implementation of Co2MnSi films in magnetoresistive devices. Moreover, we demonstrate the feasibility of the electrical transport measurements as a mean to verify the half-metallicity of Heusler compounds, and to estimate their spin gap, as a complement to SR-PES measurements.

**References:**

[1] C. Guillemard, S. Petit-Watelot, S. Andrieu et al., J. Appl. Phys., Vol. 128, p.241102 (2020) [2] C. Guillemard, S. Petit-Watelot, S. Andrieu et al., Phys. Rev. Appl., Vol. 11, p.064009 (2019) [3] H. Liu, Y. Honda, T. Taira et al., Appl. Phys. Lett., Vol. 101, p.132418 (2012) [4] Y. Sakuraba, K. Izumi, T. Iwase et al., Phys. Rev. B., Vol. 82, p.094444 (2010) [6] S. Picozzi, A. Continenza, and A.J. Freeman, Phys. Rev. B., Vol. 66, p.094421 (2002)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/e7063f455e3b8802939f7f8fea566be9.jpg)
Fig. 1. Reflection high-energy electron diffraction (RHEED) patterns for a 15-nm Co2MnSi film (noted CMS) along the [110] (left column) and [100] (right column) azimuths (top). High-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) micrograph of the CMS layer along the [110] zone axis (bottom).

![](https://assets.underline.io/uploads/markdown_image/1/image/83bb671dcb7c30a1a9ed3ee3e7bc79dd.jpg)
Fig. 2. Resistivity of the Co2MnSi films versus temperature from 300 to 5 K (top). Distance between the Fermi energy and the bottom of the minority spin band (kb * Δ) versus films thickness (bottom).

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