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Skyrmions typically appear in systems with perpendicular magnetic anisotropy (PMA) and Dzyaloshinskii-Moriya interactions (DMI). Bloch skyrmion states can be stabilized in magnetic dots with no need of DMI [1]. However, PMA is typically considered to be necessary. Nanoparticle geometry is an additional important factor for the skyrmion stabilization due to the influence of magnetostatic energy. Therefore, the sample shape (e.g. spherical) can result in stabilization of the skyrmions [2]. Recently, stabilization of the half-hedgehog skyrmions in soft magnetic (Permalloy) hemispherical dots by the MFM tip was demonstrated [3].&lt;br/&gt;Here we conduct micromagnetic simulations in 3D soft magnetic dots with planar (cylindrical) or curved (spherical cap) geometry with neither PMA nor DMI. The geometries of both magnetic elements correspond to the base radius 60-120 nm and the aspect ratio thickness/ radius ranged from 0.4 to 2 and magnetic parameters of permalloy. In a wide range of the dot sizes, we observed the co-existence of multiple magnetic states. Particularly, in the spherical caps we stabilized for the same geometry, the in-plane, the out-of-plane (flower-like), the 3D vortex-like (Bloch skyrmion), the 3D Néel skyrmion –like (see Fig.1) and the Bloch point-like states. The Bloch skyrmion is characterized by a vortex configuration in the basal plane while the Neel-like skyrmon – by the radial vortex configuration and is similar to the half hedgehog structure.&lt;br/&gt;The existence of magnetic skyrmions without DMI or PMA in cylindrical nanodots was demonstrated by analytical calculations using the Belavin-Polyakov ansatz [4]. Both Néel and Bloch (vortex-like) skyrmions structures have been proven to be metastable or stable states in some range of dot sizes. The Néel skyrmion always has larger energy than the Bloch skyrmion. Direct micromagnetic simulations confirm the co-existence of both types of skyrmions, although in a smaller range of geometrical parameters than predicted by analytical calculations. In spherical caps, the curved geometry provides an additional factor for the Néel skyrmion stabilization which was obtained for a wide range of geometrical parameters. Typically, the Néel skyrmion has the largest energy of all structures, however its energy decreases as a function of the cap basal diameter and aspect ratio. Consequently, for some geometrical parameters we found a Néel skyrmion having smaller energy than that of the Bloch skyrmion. The spherical geometry also leads to a coupling between the skyrmion polarization and radial magnetization components, so that only the skyrmions with positive Polarity (P) and outward chirality (Q) or negative polarity and inward chirality are possible, see Fig. 1&lt;br/&gt;Finally, we present the state diagram for skyrmions in soft magnetic caps and nanopillars. We have also calculated 2D topological charges and the gyrovector values, both depending on the geometrical parameters.

**References:**

[1] K. Guslienko, K. Y. IEEE Magn. Lett. Vol. 6, p,4000104 (2015)&lt;br/&gt;[2] V.P. Kravchuk et al Phys. Rev. B, Vol. 85, p.144433 (2012).&lt;br/&gt;[3] E.Berganza et al, Nanoscale, Vol.12, p.18646 (2020)&lt;br/&gt;[4] A. A. Belavin and A. M. Polyakov, Pis’ma Zh. Eksp. Teor. Fiz. Vol. 22, p. 503 (1975) .

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/c0723cd91b5db4d72e227b49f23c8980.jpg)
Figure.1 (a-b) Chiral (Neel-like) skyrmion magnetic configurations in permalloy caps with diameter 60 nm and height 30 nm colored by the axial-component mz. Left and right figures are cross sections in the XZ plane and in the XY basis plane respectively. P and Q stand for the polarity and the chirality of the skyrmion respectively.



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 Skyrmions in 3D soft magnetic nanodots with no Dzyaloshinskii-Moriya interactions

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Skyrmions typically appear in systems with perpendicular magnetic anisotropy (PMA) and Dzyaloshinskii-Moriya interactions (DMI). Bloch skyrmion states can be stabilized in magnetic dots with no need of DMI [1]. However, PMA is typically considered to be necessary. Nanoparticle geometry is an additional important factor for the skyrmion stabilization due to the influence of magnetostatic energy. Therefore, the sample shape (e.g. spherical) can result in stabilization of the skyrmions [2]. Recently, stabilization of the half-hedgehog skyrmions in soft magnetic (Permalloy) hemispherical dots by the MFM tip was demonstrated [3]. Here we conduct micromagnetic simulations in 3D soft magnetic dots with planar (cylindrical) or curved (spherical cap) geometry with neither PMA nor DMI. The geometries of both magnetic elements correspond to the base radius 60-120 nm and the aspect ratio thickness/ radius ranged from 0.4 to 2 and magnetic parameters of permalloy. In a wide range of the dot sizes, we observed the co-existence of multiple magnetic states. Particularly, in the spherical caps we stabilized for the same geometry, the in-plane, the out-of-plane (flower-like), the 3D vortex-like (Bloch skyrmion), the 3D Néel skyrmion –like (see Fig.1) and the Bloch point-like states. The Bloch skyrmion is characterized by a vortex configuration in the basal plane while the Neel-like skyrmon – by the radial vortex configuration and is similar to the half hedgehog structure. The existence of magnetic skyrmions without DMI or PMA in cylindrical nanodots was demonstrated by analytical calculations using the Belavin-Polyakov ansatz [4]. Both Néel and Bloch (vortex-like) skyrmions structures have been proven to be metastable or stable states in some range of dot sizes. The Néel skyrmion always has larger energy than the Bloch skyrmion. Direct micromagnetic simulations confirm the co-existence of both types of skyrmions, although in a smaller range of geometrical parameters than predicted by analytical calculations. In spherical caps, the curved geometry provides an additional factor for the Néel skyrmion stabilization which was obtained for a wide range of geometrical parameters. Typically, the Néel skyrmion has the largest energy of all structures, however its energy decreases as a function of the cap basal diameter and aspect ratio. Consequently, for some geometrical parameters we found a Néel skyrmion having smaller energy than that of the Bloch skyrmion. The spherical geometry also leads to a coupling between the skyrmion polarization and radial magnetization components, so that only the skyrmions with positive Polarity (P) and outward chirality (Q) or negative polarity and inward chirality are possible, see Fig. 1 Finally, we present the state diagram for skyrmions in soft magnetic caps and nanopillars. We have also calculated 2D topological charges and the gyrovector values, both depending on the geometrical parameters.

**References:**

[1] K. Guslienko, K. Y. IEEE Magn. Lett. Vol. 6, p,4000104 (2015) [2] V.P. Kravchuk et al Phys. Rev. B, Vol. 85, p.144433 (2012). [3] E.Berganza et al, Nanoscale, Vol.12, p.18646 (2020) [4] A. A. Belavin and A. M. Polyakov, Pis’ma Zh. Eksp. Teor. Fiz. Vol. 22, p. 503 (1975) .

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/c0723cd91b5db4d72e227b49f23c8980.jpg)
Figure.1 (a-b) Chiral (Neel-like) skyrmion magnetic configurations in permalloy caps with diameter 60 nm and height 30 nm colored by the axial-component mz. Left and right figures are cross sections in the XZ plane and in the XY basis plane respectively. P and Q stand for the polarity and the chirality of the skyrmion respectively.

technical paper

Spin-orbitronics, which takes advantage of spin-orbit coupling (SOC), has expanded the research objects of spintronics to nonmagnetic materials. Here, we report the emerging nonlinear spintronic phenomena in the inversion-asymmetric nonmagnetic quantum materials with SOC. For instance, the surface state of three-dimensional topological insulator (TI) owns helical spin textures with the spin and momentum perpendicularly locked. We show the observation of a nonlinear magnetoresistance (called bilinear magneto-electric resistance, BMER) [1] and nonlinear Hall effect [2] in a prototypical TI Bi2Se3, which scale linearly with both the applied electric and magnetic fields. We further reveal that these effects are originated from the conversion of a nonlinear spin current to charge current under the application of an external magnetic field. A close link between the BMER and the spin texture was established in TI surface states, which enables a novel transport probe of spin textures. We further extended the observation of BMER effect to the d-orbital two-dimensional electron gas (2DEG) at a SrTiO3 (STO) (111) surface [3]. The BMER probes a three-fold out-of-plane spin texture, in addition to an in-plane one at the STO (111) surface 2DEG. This novel spin texture is in contrast to the conventional one induced by the Rashba effect. By performing tight-binding supercell calculations, we find that this 3D spin texture is fully described by the confinement effects of the STO t2g conduction band in the (111) plane. We recently reported the observation a sign reversal of nonlinear magnetoresistance with temperature in a semimetal WTe2 [4]. Theoretical calculations revealed the critical role of Fermi surface topology and convexity on the nonlinear magneto-response. These findings open a new branch in spintronics, which discusses the nonlinear transport effects in spin-polarized quantum materials, and is therefore referred as nonlinear spintronics.

**References:**

[1] Pan He, et al. Nature Physics 14, 495 (2018) [2] Pan He, et al. Phys. Rev. Lett. 123, 016801 (2019) [3] Pan He, et al. Phys. Rev. Lett. 120, 266802 (2018) [4] Pan He, et al. Nature commun., 10, 1290 (2019)

**Images:**

 Nonlinear spintronics in quantum materials with inversion symmetry breaking INVITED

Various types of Anomalous Hall effects have been widely investigated in recent years [1, 2]. In most of the cases, the predicted or measured Hall signal has been attributed to spontaneous magnetic moment arisen from the dynamics of the current flow [1]. In this work, we aim to investigate the role of anisotropic band dispersion of chiral Weyl fermions in generating a transverse current resulting in a Hall signal. For this purpose, the simplest Weyl semimetal phase consisting of two Weyl nodes with opposite chirality is adopted and the angular dependence of conductance is calculated [3, 4]. Multi-terminal devices with circular geometry as illustrated in Fig. 1 are commonly used to probe the dependence of the signal on transport direction in experiments [1, 3]. Therefore, in the proposed model, we adopt the circular channel geometry and calculate the conductance for arbitrary transport directions. The Hamiltonian of the simplest Weyl system is as follows, H = V0 + Σi hki τ (viσi+wi), where σ’s are Pauli matrixes, v’s are velocities and their sign (τ = ±) carry the chirality of Weyl nodes. We assume symmetric velocities equal to vF = 106 m/s. The dispersion of Weyl fermion can be tilted along all three directions, and the strength of the tilt is denoted by wi. In the current work, two Weyl nodes having opposite chirality are also tilted along opposite directions. The tilt direction is chosen to lie along the high anisotropy axis, which is close to one of the crystal axes in most of the Weyl semimetals reported up to date [e.g., Refs. 3, 5]. The angular dependence of the conductance [3, 4, 5] can be calculated based on transmission probability along an arbitrary direction and integrated over all transverse wave vectors based on the following equation, Gβ = G0 ∫ -(∂f/∂E)dE ∬ dSFS Tφ,γ cosφ cosγ. In the above equation, γ is the angle between Fermi wave vector k and the x-y plane, φ is the azimuthal angle with respect to the x-axis, G0 is the quantum conductance, dSFS is the infinitesimal element of the elliptical Fermi surface per unit variation of the coordinates φ and γ. The anisotropy in crystal symmetry and the bandstructure make the conductance dependent on the angle between the transport direction and the crystal axis. Based on the conductance profile, the voltage difference between the transverse electrodes can be found as follows, Vt = Vt1-Vt2 ∝ (S/ρ)[(Gt1-Gt2)/(L/√2)], where Gt1 = Gβ+(π/4) and Gt2 = Gβ-(π/4). The longitudinal potential difference can be calculated similarly by replacing the respective conductance value and distance between the voltage probes. As shown in Fig. 2 and predicted by the above equation, transverse voltage emerges at some angles which are related to the imbalance of Gt1 and Gt2. The highest Vt occurs at the maximum imbalance, where Gt1 and Gt2 coincide with the lowest and highest conductance points in the conductance profile shown in Fig. 1 (right). On the other hand, the conductance between source and drain is minimum in this direction as seen in Fig. 2. Our predicted results are quite consistent with the experimental results presented recently in literature [1] thus revealing a possible origin of the measured Hall signals in Weyl semimetals in the absence of a magnetic field.

**References:**

[1] Kang, K., Li, T., Sohn, E. et al. Nonlinear anomalous Hall effect in few-layer WTe2. Nat. Mater. 18, 324–328 (2019). [2] Ma, Q., Xu, SY., Shen, H. et al. Observation of the nonlinear Hall effect under time-reversal-symmetric conditions. Nature 565, 337–342 (2019). [3] Qisheng Wang, Can Yesilyurt, Fucai Liu, Zhuo Bin Siu, Kaiming Cai, Dushyant Kumar, Zheng Liu, Mansoor B. A. Jalil, and Hyunsoo Yang Nano Letters 2019 19 (4), 2647-2652 [4] Yesilyurt, C., Siu, Z.B., Tan, S.G. et al. Electrically tunable valley polarization in Weyl semimetals with tilted energy dispersion. Sci Rep 9, 4480 (2019). [5] Soluyanov, A., Gresch, D., Wang, Z. et al. Type-II Weyl semimetals. Nature 527, 495–498 (2015).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/6d703c64fb6f07d5598af24065e4402f.jpg)
Illustration of the adopted model, i.e., circular multi-terminal circuit (left). Terminal A and B denote source and drain electrodes respectively, and the Hall signal is calculated as the voltage difference at two transverse points t1 and t2. Normalized anisotropic conductance profile of the Weyl system with two opposite chirality Weyl nodes (right). Blue (Red) arrow(s) indicates the conductance between the source and drain (transverse electrodes).

![](https://assets.underline.io/uploads/markdown_image/1/image/d819182570aba9d154a697f1728aa977.jpg)
Angular dependence of anomalous Hall effect, where the Hall voltage Vt is calculated as the voltage difference between the points t1 and t2 (i.e., shown in Fig. 1). The longitudinal voltage VSD is calculated as the voltage difference between points A and B (i.e., shown in Fig. 1)

 Anomalous Hall Effect in Anisotropic Weyl Semimetals

Magnetotransport properties of magnetic materials receive considerable interests, because of they make an important role in basic science and technological applications[1]. Anomalous Hall Effect (AHE), as an important topic in condensed matter, contains extensive physics for their many different mechanisms, such as intrinsic mechanism associated with the Berry curvature in entangled Bloch electronic bands, extrinsic mechanism including skew scattering and side jump scattering[2]. In this study, the magnetotransport properties in antiferromagnetic half-Heusler single crystals of TbPtBi, a magnetic-field-induced topological semimetal with simple band structure, were investigated. We found a non-monotonic dependence of the anomalous Hall resistivity on the magnetic field in a strong magnetic field (B&gt;7T), which comes from the change of band structure caused by the Zeeman-like splitting when an external magnetic field is applied. The experimental results show that credible anomalous Hall resistivity and conductivity reach up to 0.68mΩcm and 125Ω-1cm-1, respectively. A large anomalous Hall angle (AHA) up to 33% is achieved in TbPtBi, which is comparable to a typical ferromagnetic Weyl semimetal Co3Sn2S2[3]. The analysis of the results shows that this should be attributed to topological band around EF and low carrier density.

**References:**

[1] Science advances 4 : eaar7880 (2018). [2] Rev. Mod. Phys. 82 (2), 1539 (2010); Physical Review 95 (5), 1154 (1954); Physica 24, 39 (1958); Physica 21, 877 (1955); Phys. Rev. B 2 (11), 4559 (1970). [3] Nat. Phys. 14, 1125 (2018); Adv. Funct. Mater., 2000830 (2020); Nano Lett. 7476–7481, (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/72c83298ed580c527c76631a5810d453.jpg)
Figure 1. Dependence of the longitudinal resistivityρxx(a) and Hall resistivity ρxy (b) on magnetic field B at temperatures from 1.8K to 50K. (c) Separation progress of normal Hall resistivity ρxyN and anomalous Hall resistivity ρxyA at 1.8K. The inset shows the normal Hall resistivity obtained by linear fitting for low magnetic field curves at corresponding T. (d) The anomalous Hall resistivity ρxyA after subtracting the fitting normal Hall resistivity ρxyN. The inset is the maximum value of ρxyA at different temperatures.

 Large Anomalous Hall Angle in a Topological Semimetal Candidate TbPtBi

The thermoelectric generation based on the anomalous Nernst effect (ANE) has become one of the promising approaches to realize efficient energy harvesting from waste heat and heat flux sensor due to its several advantages over conventional devices based on the Seebeck effect (SE) 1,2. However, till date, the observed ANE thermopower is very small and a systematic material investigation to realize large anomalous Nernst coefficient is necessary. Recent theoretical and experimental investigations identified a Weyl semimetal as a potential material having giant ANE which can be achieved by a little tuning of Fermi level (EF) near Weyl points3,4,5. However, systematic tuning of EF and investigation of thermoelectric properties based on many films with different compositions are time-consuming. Furthermore, in this process, one losses many intermediate compositions due to the limitation of number of films that can be prepared. In this regard, we introduce an efficient approach to tune EF for Weyl semimetals and demonstrate the approach through a layer-by-layer combinatorial deposition of a Co2MnAl1-xSix (CMAS) thin film with x varied from 0 to 1 on a single substrate. The fabrication procedure is represented schematically in Fig.1 (a). The structural characterization reveals the formation of single-phase CMAS alloys throughout the composition range. Hard X-ray photoemission spectroscopy (HAXPES) directly confirmed a continuous shifting of EF from Co2MnAl to Co2MnSi with a maximum shift of 0.4 eV (see Fig.1. (b)), which is consistent with the theoretical prediction. We also measured the anomalous Ettingshausen effect (AEE), the reciprocal of ANE, for the all x range using a single strip along the composition gradient (see Fig.1. (c)) by means of the lock-in thermography technique6,7. Only one LIT image tells us that large AEE is obtained between x = 0.06 to 0.12, which well agrees with the composition dependence of the ANE signals (see Fig.1. (d)), measured by making many parallelly aligned Hall bars elongated to the orthogonal direction to the composition gradient (see Fig.1. (c)). The findings clearly demonstrate that the AEE measurement using the composition spread film is an effective approach to investigate the composition dependence of ANE and find the highest performance without fabricating many films and performing systematic measurements. These demonstrations will enable the optimization of the composition in Weyl semimetals and exploration of new materials to obtain giant ANE/AEE, which is essential to realize applications based on the transverse thermoelectric effects.

**References:**

[1] Y. Sakuraba et al., Appl. Phys. Express 6, 033003 (2013) [2] W. Zhou et al., Appl. Phys. Express 13, 043001 (2020) [3] K. Sumida et al., Commun. Mater. 1, 89 (2020) [4] J. Noky et al., NPJ Comput. Mater. 6, 77 (2020) [5] Y. Sakuraba et al., Phys. Rev. B 101, 134407 (2020) [6] S. Daimon et al., Nat. Commun. 7, 13754 (2016) [7] T. Seki et al., Appl. Phys. Lett. 112, 152403 (2018)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/58d6615be315220821aa1a7a138fb225.jpg)
Fig.1 (a) Schematic representation of composition-spread CMAS combinatorial film deposited with wedge shaped layer by layer deposition (b) Valance band HAXPES spectra for CMAS composition-spread film at Co2MnAl (CMA) and Co2MnSi (CMS) side (c) Schematic measurement configuration used for ANE and AEE (d) AAEE/jc and SANE as a function of x. Where AAEE is the amplitude of temperature modulation due to AEE, jc is the charge current density and SANE is anomalous Nernst coefficient. The inset shows observed AAEE image in LIT.

 Efficient tuning of electronic, transport, and thermoelectric properties of Weyl semimetal Co2MnAl1-xSix composition-spread thin film

Lately, Magnetic Random-Access Memory (MRAM) has stimulated significant interests compared to traditional semiconductor memory devices due to its non-volatility combined with expeditious read and write endurance. In the preceding studies, conventional methods that had been investigated widely include spin-orbit torque (SOT)1, spin-transfer torque (STT)2 and current-driven switching. However, magnetization switching in MRAM utilizing such techniques fall short to observe the desired switching and inevitably supplemented by thermal issues, leading to inefficient functionality. Recently, considerable endeavour towards a new paradigm of straintronic devices (STR)3 for efficient magnetization switching is explored. A magnetoelectric STR constitutes of ferromagnetic and piezoelectric order parameters, in which an applied electric field across the piezoelectric order parameter instigate mechanical strain at the heterostructure interface giving rise to the magnetization switching due to the Villari effect. Though both out-of-plane and in-plane magnetization switching are examined in the aforementioned studies to explore the STR devices, magnetization switching in the in-plane direction is obscured on account of thermal instability in smaller element size and multi-domain formation in larger element size. Also, the self-biased STR-MRAM device that extinguishes the external bias magnetic field is still undiscovered. In this work, we investigated the size-dependent in-plane magnetization switching of FeGaB/PMN-PT (ferromagnetic/piezoelectric) heterostructure (Fig. 1(a)) using micromagnetic finite element method (FEM) coupled with electrodynamic and elastic analysis. Three elliptical nanodiscs of FeGaB magnetoelastic material having cross-sectional areas 100×90.9 nm2, 100×66.67 nm2, and 100×50 nm2 are investigated by varying the thickness from 2 nm to 28 nm on a 10×10×0.5 mm3 single-crystal PMN-PT (011) piezoelectric substrate. Initially, minimum thickness (dmin) at pre-stress condition for three elliptical nanodiscs are investigated (Fig. 1(b)) using in-plane induced energy well (△E) scaled by kbT (where kb is Boltzmann constant and T is the temperature in Kelvin). △E/kbT≤70 is an assumed condition for thermal instability to ensure dmin for STR-MRAM devices. To explore the maximum thickness related to self-biasing (dsb), pre-stress equilibrium exchange and demagnetization energies associated with the three elliptical nanodiscs are analyzed against thickness. The larger size magnets make an effort to minimize the energy by aligning the magnetization with the elliptical nanodisc boundary and gives rise to vortex state. On contrary, smaller size magnets minimize the energy by aligning the magnetization along the easy axis (0° or 180°) of the elliptical FeGaB nanomagnets without applying the external magnetic bias field (Fig. 2). This result is pivotal as such self-biasing would give primacy to future STR-MRAM devices by omitting the necessity for an extrinsic magnetic bias field. Although the above analysis is performed to obtain optimum size where STR-MRAM device is stable and self-biased, the maximum thickness (dmax) for in-plane 180° magnetization switching is limited by the critical stress requirement. It is observed that dsb is not necessarily the same as dmax for in-plane 180° magnetization switching. When compressive strain equal or greater than the critical compressive strain is applied from the pre-stress state, where magnetization is along the easy axis, in-plane 90° magnetization switching (along 90° or 270°) is observed. This happens as exchange and stress anisotropy energies are almost negligible and the demagnetization energy rises as the magnetization is switched from the easy to the hard axis. Magnetic precession is used to obtain in-plane 180o switching. When the magnetization component along the x-axis is negative during the precession, removal of external strain causes another 90o switching because the ferromagnet tries to reduce its total energy by gravitating to its nearest easy axis. In-plane fastest 180o magnetization switching time and associated external strain are investigated also. For fixed thickness, compressive strain requirement rises with increasing cross-sectional area. As the thickness is increased, tradeoff between fastest switching time and associated switching energy is observed for the same cross-sectional area. Whereas faster switching time and lesser switching energy are required for larger cross-sectional nanodiscs having the same thickness. This work can be potentially useful in the future STR-MRAM devices that eliminates the necessity of extrinsic magnetic field bias and completes in-plane 180o magnetization switching.

**References:**

1C. Zhang, S. Fukami, H. Sato, F. Matsukura, H. Ohno, Appl. Phys. Lett., 107, 012401 (2015). 2C.F. Pai, L. Liu, Y. Li, H. W. Tseng, D. C. Ralph, R. A. Buhrman, Appl. Phys. Lett., 101, 122404 (2012). 3K. Roy, S. Bandyopadhyay, J. Atulasimha, Appl. Phys. Lett., 99, 063108 (2011).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/f80b0892f94f3338bf712e9f149fd36a.jpg)
FIG 1: (a) Proposed structure consists of FeGaB/PMN-PT (ferromagnetic/piezoelectric) heterostructure and corresponding magnetization components. (b) △E/kbT vs thickness curve to examine the minimum thickness (dmin) requirement for thermal stability.

![](https://assets.underline.io/uploads/markdown_image/1/image/58c037c03f736d7b2641a003318c63ad.jpg)
FIG 2: (a) Simulated in-plane 90o magnetization switching from initial random magnetization state after applying critical stress. (b) Simulated in-plane 180o magnetization switching after magnetization switches to in-plane easy axis for 100×90.9×9.5 nm3 nanodisc.

 Micromagnetic study of strain-induced magnetization switching in FeGaB nanomagnets for self-biased MRAM applications

In this study, we report room temperature negative magneto capacitance due to 60% Fe doping and positive magneto capacitance due to 60% Ti doping at Mn site in La0.7Pb0.3MnO3. We have studied the structural, mixed valence studies using synchrotron X-ray absorption spectroscopy (XAS), magnetic and magneto capacitance properties of La0.7Pb0.3Mn0.4Fe0.6O3-δ and La0.7Pb0.3Mn0.4Ti0.6O3-δ. La0.7Pb0.3Mn0.4Fe0.6O3-δ and La0.7Pb0.3Mn0.4Ti0.6O3-δ were synthesized by solid state method. The x-ray diffraction (XRD) patterns show (i) successful substitution of Fe and Ti at Mn site and (ii) change in lattice parameters of La0.7Pb0.3Mn0.4Fe0.6O3-δ and La0.7Pb0.3Mn0.4Ti0.6O3-δ. L edge absorption studies using synchrotron XAS show the presence of mixed valence states in these compositions. La0.7Pb0.3Mn0.4Fe0.6O3-δ show maximum ~64 % negative magneto capacitance at 500 gauss(G) magnetic field, ~60 % at 5kG magnetic field and -56 % at 10 kG magnetic field at 300 K. La0.7Pb0.3Mn0.4Fe0.6O3-δ show ~51% negative magneto capacitance at 15 kG magnetic field while La0.7Pb0.3Mn0.4Ti0.6O3-δ show ~ 12 % positive magneto capacitance at 15 kG magnetic field. Magneto capacitance values in these compositions at room temperature in accordance with the Maxwell Wagner effect, which was explained by Catalan et al. Interaction between Mn+3 and Mn+4 via oxygen atom in the lattice originates the local magnetic region in the middle of non magnetic regions which originated negative magneto capacitance while Ti doped samples show positive magneto capacitance due to the presence quantum interference and coulombic interaction effects. Presence of unpaired electrons in the d orbitals of Fe, Mn and Ti dictates the magneto capacitance properties of these materials.

**References:**

1. G. Catalan Appl Phys Lett 88, 102902 (2006) 2. P. Chen , D. Y. Xing and Y. W. Du Phys. Rev. B 64, 104402 (2001) 3. S. S. Manoharan, B. Singh, R.K. Sahu, et al. J. Phys.: Condens. Matter 20, 235205 (2008) 4. B. Singh Mater. Let. 156, 76 (2015)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/d8756a16e22f94e3a35f045e93a84cc9.png)
Fig. 1 Magneto capacitance vs frequency plots at different applied Magnetic field for La0.7Pb0.3Mn0.4Fe0.6O3-δ polycrystalline sample.

![](https://assets.underline.io/uploads/markdown_image/1/image/60a94b74ab5d40cb913da542d67977db.png)
Fig. 2 Magneto capacitance vs frequency plots at different applied Magnetic field for La0.7Pb0.3Mn0.4Ti0.6O3-δ polycrystalline sample.

 Huge room temperature negative magneto capacitance in La0.7Pb0.3Mn0.4Fe0.6O3-δ and positive magneto capacitance in La0.7Pb0.3Mn0.4Ti0.6O3-δ

Coupling lattice and spin degrees of freedom without the use of external magnetic fields allows for energy-efficient spintronic devices. In this context, hybrid materials composed of an oxide layer undergoing a first-order, structural phase transition (SPT), such as V2O3, and a ferromagnetic layer, such as Ni, constitute a very promising paradigm for the development of such applications. In the case of a Ni/V2O3 heterostructure, the structural domains inherent to the first-order phase transition in the V2O3 cause a differential strain pattern in the Ni layer. By virtue of the inverse magnetorestrictive effect, this strain pattern is converted into a magnetic anisotropy distribution in the Ni. This offers a promising alternative to voltage-controlled magnetism or other switching mechanisms without a magnetic field [1,2]. Here we show by direct imaging of the thermal evolution of the Ni spin structure that the magnetic domains can be tuned in both size and orientation upon crossing the structural phase transition (SPT) of the proximal V2O3 layer [3]. We find a drastic temperature-driven reorientation of the Ni magnetic domains across the SPT which is responsible for an abrupt increase in the coercive field (up to 500%). By synchrotron-based X-ray microscopy we show a reconfiguration of the ferromagnetic domain pattern in the Ni layer across the V2O3 SPT together with changes in magnitude and direction of the magnetic anisotropy. These observations are in good agreement with both angular dependent ferromagnetic resonance measurements and micromagnetic simulations. Our simulations successfully replicate the change in the coercivity as well as the reorientation of the magnetization of the Ni domains after the implementation of a simple model of strain-dependent magnetic anisotropies. Furthermore, simulations also exhibit a phase coexistence of different magnetic domains across the SPT in the V2O3. Direct observations of the lateral correlation length of the Ni domains show an increase of almost an order of magnitude at the SPT compared to room temperature as well as a broad spatial distribution of the local transition temperatures. This corroborates the phase coexistence of Ni anisotropies due to the V2O3 structural domains coexistence across the SPT. Our data reveal that the reorientation of Ni domains is controlled by the reconfiguration of the structural domains of the oxide layer across the SPT [4,5], due to strain induced proximity. Our findings reveal a novel pathway to control magnetic domains without a magnetic field through proximity to a material undergoing a first-order structural phase transition, which allows for engineering of coercive fields for novel data storage architectures and novel device concepts based on “straintronics”. Acknowledgements: This work was supported by the Spanish MINECO projects MAT2015-68772-P and PGC2018-097789-B-I00 and European Union FEDER funds. A.F.R. and M.G.M acknowledge financial support from the EU CALIPSO Transnational Access programme. J.G.R. acknowledges support from Colciencias under grant 120471250659. The work by I.V., C.W. and I.K.S. at UCSD were supported by the Office of Basic Energy Science, U.S. Department of Energy, BES-DMS funded by the Department of Energy’s Office of Basic Energy Science, DMR under grant DE FG02 87ER-45332.

**References:**

[1] de la Venta, J., Wang, S., Ramirez, J. G., et al., Appl. Phys. Lett. 102, 1 (2013); [2] de la Venta, J., Wang, S., Saerbeck, T., et al., Appl. Phys. Lett. 104, 062410 (2014). [3] Valmianski, I., Fraile Rodríguez. A., Rodriguez-Alvarez, J., et al., (in review). [4] McLeod, A. S., Van Heumen, E., Ramirez, J. G., et al. Nat. Phys. 13, 80 (2017). [5] Gilbert, D. A., Ramírez, J. G., Saerbeck, T., et al., Sci. Rep. 7 13471 (2017).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/609df7dde4c22e1de9b043b18a9dd651.jpg)
Fig. 1. Top row panels show representative XMCD-PEEM images recorded at temperatures below (150 K), across (170 K) and above (200 K) the SPT of V2O3. The insets show their Fourier transforms. The initial state (blue contrast) at low temperature (LT) splits into a pattern of small domains (yellow) which progressively rotate and grow across the V2O3 SPT as the high-temperature (HT) phase is reached. Bottom row panels show histograms of the absolute value of the average rotation angle of the Ni magnetization, Df, at selected temperatures (calculated from the images in the top row). Sharp Df distributions are found for the LT (150 K) and HT (200 K) phases in contrast to broader distributions in the middle of the V2O3 SPT (170 K).

![](https://assets.underline.io/uploads/markdown_image/1/image/0691162ae0a39dfe6b44c065dd312054.jpg)
Fig. 2. Coercivity as a function of temperature of Ni(10 nm)/V2O3(100 nm) across the V2O3 SPT recorded while cooling the sample from 300 K to 120 K (only data from 200 K are shown). A sharp rise in the coercive field, Hc, of about a factor of four, is found as the temperature goes below the V2O3 SPT. The garnet circles represent the coercivity values obtained from the experimental loops while the green triangles correspond to those obtained from micromagnetic simulations.

 Nanoscale manipulation of magnetic domains by interfacial strain-induced proximity

Systematic studies of magnetic properties observed in epitaxial W/Co/Pt layered structures grown by molecular beam epitaxy are discussed. In this system contributions to interfacial Dzyaloshinskii-Moriya interaction (DMI) from the asymmetric interfaces between ferromagnet (Co) and non-magnetic heavy metals with high spin-orbit coupling (W or Pt) are of additive nature. DMI can stabilize the chiral magnetic texture, vortex and skyrmions, being promising in future data storage technology. Presented progressive investigations encompass layered structures containing: a single Co layer (magnetic anisotropy), two Co layers (interlayer coupling) and multilayers (dipolar interactions, complex domain structure). Layered structures containing a single Co layer exhibit spin reorientation transition (SRT) with increasing thickness, dCo,from perpendicular (perpendicular magnetic anisotropy, PMA) to in-plane aligned magnetisation. The range of dCo with PMA and the critical thickness dSRT depend on the type and sequence of adjacent covers. In the Pt/W/Co/Pt system dCo range with PMA shifts towards higher values (from 0.6-0.9 nm to 2.1-2.4 nm) with increasing bottom W layer thickness, dW, from 2.4 nm to 8.0 nm. This behaviour differs from the similar system with Mo component leyer, studied earlier [1]. Hysteresis loops measured by polar magnetooptical Kerr effect (PMOKE) magnetometry exhibit shapes typical of fine domain structure with perpendicular magnetisation. In the W/Co(1.0 nm)/Pt(dPt)/W(dW)/Co(1.0 nm)/Pt interlayer antiferromagnetic coupling of perpendicular magnetization with the strength as high as 0.6 kOe is very distinct for the component spacers of equal thickness, dPt = dW, in the range between 0.7 and 1.1 nm. For dW ≠ dPt (keeping the same total thickness dW + dPt) the coupling strength decreases. Particularly, the single spacer systems (Pt or W; dPt or dW kept in the corresponding range from 1.4 nm to 2.0 nm) do not exhibit such feature, indicating a crucial role of the complex spacer structure affecting both coupling and PMA (Figure 1). The multilayer structures W/Co(0.6 &lt; dCo &lt; 1.0 nm)/Pt (10-20 repetitions) are magnetised in perpendicular direction to the film plane and display at the remanent state typical labyrinth domain structure with tendency towards bubble domains formation with diameter of around 75 nm (Figure 2). DMI strength determined form (aligned) domain structure reaches the value of D = 2.49 mJ/m2 [2]. Such high value of D is a result of high quality crystalline structure characteristic for epitaxial systems and additive contribution to DMI from asymmetric well-defined interfaces. The above discussed structures are compared to those with different component layer thickness and opposite sequence (i.e. Pt/Co/W). This work is supported by IEEE educational seed funding 2020 (beneficiary:-Sukanta Kumar Jena), Foundation for Polish Science (FNP) under the European Regional Development Fund – Program REINTEGRATION 2017 OPIE 14-20 and by the National Science Centre in Poland, projects no: 2016/23/G/ST3/04196 and 2020/37/B/ST5/02299.

**References:**

[1] A Wawro et al. J. Phys. D: Appl. Phys. 50 215004 (2017). [2] S.K. Jena et al. to be submitted (2021).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/f62fbee3caf0455305aedeea9ea695c0.jpg)
“Fig.1” Hysteresis PMOKE loop from W/Co/Pt/W/Co/Pt layered structures composed of two Co (1nm) layers separated by the Pt/W spacer with total thickness of 1.4 nm showing distinct antiferromagnetic coupling (red). Corresponding structures with a single spacer: W (black) or Pt (green) 1.4 nm thick do not exhibit such coupling.

![](https://assets.underline.io/uploads/markdown_image/1/image/5285c84da6791eb5744546eceba7f522.jpg)
"Fig.2" Magnetic force microscopy image from as grown W/Co/Pt multilayer with basic trilayer repetition number equal to 20.

 Magnetic anisotropy, interlayer coupling and Dzyaloshinskii-Moriya interaction in epitaxial W/Co/Pt multilayers

The interfacial Dzyaloshinskii-Moriya Interaction has had profound consequences on the possible magnetic configurations that can be stabilized in multi-layer thin films, most notably chiral Neel skyrmions and domain walls.[1] More recently, there have been theoretical calculations and experimental work confirming the existence of an appreciable anisotropic DMI in epitaxial thin films with further reduced symmetry – namely the C2v (or mm2) point group.[2] However, so far the systems under consideration have been based on cubic crystals where the magnetocrystalline anisotropy is nearly isotropic. Here, we identify a new epitaxial relationship with C2v symmetry based on HCP Co(10.0)/FCC Pt(110). Although it is quite common to grow FCC Co(111)/Pt(111), for the case of a Pt(110) underlayer, the lattice mismatch is actually smaller for the HCP Co(10.0) orientation [as opposed to FCC Co(110)] where the c-axis lies along a single direction in the plane of the film (figure 1). Such an orientation is expected to offer some degree of anisotropic DMI based on the heavy metal Pt and reduced symmetry as well as the added feature of significant uniaxial in-plane magnetocrystalline anisotropy. Samples were prepared by DC magnetron sputtering on HF-etched Si(110) single crystal substrates. Following the work of Yang et al., we use a Ag (10nm) buffer layer, which is known to grow with (110) orientation on Si(110) at room temperature, thereby avoiding further unwanted interface diffusion.[3] This is followed by deposition of the Pt (10nm) /Co (10-50nm) bilayers, which are the focus of this work. All depositions were done in an Ar atmosphere with the working pressure fixed at 2.5 mTorr. The films were characterized structurally by standard θ/2θ x-ray diffraction (XRD) measurements and phi-scans to characterize the epitaxial relationship. The XRD scan shows primarily Ag(220), Pt(220), and Co(10.0) peaks with no identifiable Co(220) peak suggesting the film is predominantly HCP. Phi scans (figure 2) on Pt(111), Ag(111), and Co(10.1) confirm the epitaxial relationship shown in figure 1. Moreover, reciprocal space q-scans on the HCP Co spots were leveraged to characterize directional peak broadening due to stacking faults. As it is known that stacking faults cause broadening only of certain peaks (h-k ≠ 3m) along the c* direction (with breadth also determined by the parity of l), it is possible to extract the density of growth and deformation faults in the Co layer, which are found to be approximately 10% and 3% respectively in 50nm Co films. Details on how these stacking fault densities are calculated will presented in detail. Alternating gradient field magnetometry was used to measure M-H loops along different crystallographic directions in the plane of the film. A clear in-plane easy axis is identified along Si[001] (parallel to Co[0001]). The hard axis saturation field of 1.5 kOe suggests a notably smaller magnetocrystalline anisotropy than would be expected for bulk cobalt, likely due to the aforementioned stacking faults. Although the relatively thick Co layer in these films makes any interface induced DMI unlikely, the epitaxial relationship is expected to be preserved in thinner samples along with the reported uniaxial anisotropy. Together with the expected interfacial anisotropic DMI, this in-plane anisotropy makes the proposed material system an interesting playground for exploring new chiral magnetic ground states.

**References:**

[1] Thiaville, A., Rohart, S., Jué, É., Cros, V. and Fert, A., 2012. Dynamics of Dzyaloshinskii domain walls in ultrathin magnetic films. EPL (Europhysics Letters), 100(5), p.57002. [2] Hoffmann, M., Zimmermann, B., Müller, G.P., Schürhoff, D., Kiselev, N.S., Melcher, C. and Blügel, S., 2017. Antiskyrmions stabilized at interfaces by anisotropic Dzyaloshinskii-Moriya interactions. Nature communications, 8(1), pp.1-9. [3] Yang, W., Lambeth, D.N. and Laughlin, D.E., 1999. Unicrystal Co–alloy media on Si (110). Journal of applied physics, 85(8), pp.4723-4725.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/cf10786ba9d1e164cc2eadffc57f6d46.jpg)
Fig 1. Schematic of the lattice matching for Ag(110)/Pt(110) with bottom left) FCC Co(110) or bottom right) HCP Co(10.0). The HCP (10.0) orientation has a better match along the Pt [001] direction.

![](https://assets.underline.io/uploads/markdown_image/1/image/78b7907db3cc501cd82fd177111f404e.jpg)
Fig 2. Phi scans for Pt (111), Ag (111), and Co (10.1) confirming the epitaxial relationship shown in figure 1.

 Structural and Magnetic Characterization of Epitaxial Co(10.0)/Pt(110) Multi-layers for Future Anisotropic DMI Systems Based on C2v Symmetry

Exchange-spring nanomagnets [1–3] are composed of the interaction of the magnetic exchange coupling between magnetically hard and soft phases. Such frameworks are promising for cutting edge perpetual magnetic applications, as they have a high energy product - the mix of permanent magnetic field and magnetization - contrasted with the conventional, single-phase magnetic materials. Hence, for the last three decades, these exchange spring nanomagnets have taken the keen attention of the scientific community. However, the necessary condition that both the hard and soft phases are controlled at the nanometer scale, to ensure effective exchange coupling, has posed significant preparation challenges. In pursuit of preparing multi-nanolayered-structured nanomagnetic material, sputtering, electron beam lithography/ evaporation (EBL/EBE) have inspired a wealth of experimental results. However, to date, there is a very limited experimental understanding of preparing in situ multilayered nanomagnetic material using electrodeposition technique and the elucidation of their magnetic behavior. Towards this end, using electrodeposition technique with a modified and stable acidic bath chemistry at room temperature, we have prepared in situ multilayered nanomagnetic cobalt phosphorus (CoP) thin film and investigated its characteristics structurally and magnetically combined with micromagnetic simulation utilizing MuMax3. Despite the availability of various techniques, the electrodeposition technique [4–7] has been chosen for the preparation of the nanomagnetic cobalt phosphorous thin films at room temperature using acidic bath chemistry due to its relatively higher deposition rate and low cost. Here, the crossover from the exchange spring structure to exchange coupled structures by the manipulation of thickness in nanometer level in a single amorphous system of cobalt phosphorus nanomagnetic thin film has been demonstrated. We have characterized the developed smooth, stress-free, and shiny electroplated samples structurally by XRD (shown in FIG. 1), SEM, and magnetically by the hysteresis loop tracer (ShB Instruments, USA). The SEM micrographs confirm the fine grain surface morphology of the cobalt phosphorous nanomagnetic thin films. The XRD analysis further ensures the amorphousness of the thin film, as in the XRD pattern, the three dominating peaks only appears from the substrate, i.e., the largest peak near 2θ = 69.22° is due to the Si-wafer and the rest of the two peaks near 2θ = 38° and 83° are from the top conducting seed layer of gold (Au). The elemental analysis by energy dispersive X-Ray (EDX) yields the stoichiometry of the electrodeposited cobalt phosphorous. An optimum exchange coupling can be obtained by tuning the spin configuration with respect to the multi-nano layer thicknesses. The static in-plane magnetic measurement by the hysteresis loop tracer shown in FIG. 2 reveals different hysteresis loops of electrodeposited CoP thin film. FIG. 2(a) confirms the exchange spring amorphous cobalt phosphorus films with a relatively higher coercivity of ~197 Oe for 0.68 µm CoP thin film while the FIG. 2(b) affirms the flat hysteresis loop with a coercivity of 162 Oe for the 11.54 µm thick CoP thin film which signifies the exchange coupled structure. Utilizing the finite difference method-based freely available GPU-accelerated micromagnetic simulator, MuMax3 [8], we have also verified the experimentally obtained results further by doing a micromagnetic simulation. Considering the typical magnetic material parameters (i.e., Saturation Magnetization (MS) as obtained from the static measurement, Exchange Stiffness Constant (AEx), Anisotropy Constant (Ku1)), MuMax3 solves the well-known Landau-Lifshitz-Gilbert (LLG) equations, and so forth gives the static micromagnetic evolution of the nanomagnetic thin films. To proceed with the simulation, we have discretized the overall amorphous cobalt phosphorous thin film into the cells of dimension 5 x 5 x 5 nm3. To include all the exchange interactions in the static magnetization of nanoscale thin film, this cell size in each direction is considered lower than the exchange length (lex = 5.1 nm) of the system, as well as to precisely reproduce the nanomagnetic impression of the thin film under study. The dimensions of the whole atlas we used for the simulation are (l x w x t = 8000 x 6000 x 5400 nm3), where l, w, and t are the length, width, and thickness of the atlas, respectively. Finally, we report the micromagnetic spin configuration at every coordinate point within the nanomagnetic thin film at every instant of field determined by the simulator, which confirms the formation of a multidomain state from a single domain state (shown in FIG. 2(e))

**References:**

[1] E. F. Kneller and R. Hawig, IEEE Trans. Magn. 27, 3560 (1991). [2] E. E. Fullerton, J. S. Jiang, M. Grimsditch, Phys. Rev. B 58, 12193 (1998). [3] H. Zeng, J. Li, J. P. Liu, Z. L. Wang, Nature 420, 395 (2002). [4] P. McCloskey, B. Jamieson, T. O’Donnell, J. Magn. Magn. Mater. 320, 2509 (2008). [5] P. McCloskey, B. Jamieson, T. O’Donnell, J. Magn. Magn. Mater. 322, 1536 (2010). [6] P. McCloskey, T. O’Donnell, B. Jamieson, in Handb. Nanoelectrochem. Electrochem. Synth. Methods, Prop. Charact. Tech.,2016, pp. 1–27. [7] S. Roy, A. Connell, M. Ludwig, J. Magn. Magn. Mater. 290–291, 1524 (2005). [8] A. Vansteenkiste, J. Leliaert, M. Dvornik, AIP Adv. 4, 107133 (2014).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/ab0568662cd1fd8eb2bea9c14dc8237e.jpg)
FIG. 1. XRD of 0.68 µm, 5.06 µm thick electrodeposited thin films having only the substrate peaks (i.e., Au and Si) confirms the amorphousness of the samples.

![](https://assets.underline.io/uploads/markdown_image/1/image/af142b7a2e9ace085c438741e63feae8.png)
FIG. 2. Hysteresis loop of the electrodeposited CoP thin films measured in XY plane, and here, dir-1+ 90° = dir-2. The thickness of the films is (a) 0.68 µm, (b) 11.54 µm. (c)-(d) The differential of the magnetization of the (a) 0.68 µm, (b) 11.54 µm thick CoP thin films, respectively. (e) Simulated Hysteresis Loop and different micromagnetic spin configurations at different coordinates of the hysteresis loop.

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