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Atomistic spin models [1] provide a natural bridge between electronic and micromagnetic length scales, where the magnetic properties are described by localised atomic spins within the Heisenberg model. The model parameters can be calculated ab-initio but the macroscopic magnetization dynamics and properties can also be simulated. While powerful, atomistic models are computationally expensive. A particular difficulty is the calculation of long-range dipole-dipole interactions, arising from the stray magnetic fields of localised atomic moments and causes complex magnetisation structures, such as magnetic vortices or Skyrmions. The dipole -dipole interactions are typically solved using a Fast-Fourier-Transform (FFT) [2] or the Fast Multipole Method (FMM) [3]. However, for atomistic simulations the continuum approximation does not accurately reflect the local dipole-dipole interactions at the atomic level and leads to systematic errors in the calculation of the dipole field. A brute force atomistic dipole-dipole approach is infeasible for the time (nanosecond+) and length (100 nm+) scales needed to extract useful data. Here we present modifications to the VAMPIRE software package [1] to include accurate and scalable calculations of dipole-dipole interactions for improved performance and scalability on ARCHER, the UK national supercomputer. We have developed a space-time hierarchical calculation of the dipole field calculation with order NlogN scalability with problem size, a comparison to the brute force tensor approach [4] is shown in Fig. 1. Our novel approach combines exact near-field computation of the dipole field with an M-Level hierarchical representation of the far-field dipole field [5]. The method is hierarchical in time and space, since the far-field time-evolution of the magnetization is much slower than the near-field which changes on the femtosecond timescale. Our improved algorithm enables the inclusion of accurate dipole-dipole interactions in atomistic simulations for large system sizes in the micrometre range for the first time.References: [1] R. F. L. Evans et al, J. Phys.: Condens. Matter 26, 103202 (2014) [2] S. Yuan and H. Bertram, IEEE Trans. Mag. 28, 2031 (1992) [3] G. Brown et al, IEEE Trans. Mag. 40 2146 (2004) [4] G.J. Bowden et al., J. Phys. Condens. Matter 28, 066001 (2016) [5] J.J. Miles and B.K. Middleton, J. Magn. Magn. Mater. 95, 99 (1991)

MMM 2020

Scalable space and time hierarchical dipole-dipole interactions in the VAMPIRE code

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MMM 2022

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Non-equilibrium phenomena of quasiparticles (QPs) in a spin-split superconductor (SC) rely on the mutual coupling between different non-equilibrium imbalances of spin, charge, heat, and spin-heat [1]. Although recent experiments and theories have shown a variety of exotic transport properties in SC-based devices with either Zeeman or exchange spin splitting [1], how QP interplays with magnon spin currents [2] remains elusive. Here, using non-local magnon spin-transport devices [3] where a singlet SC (Nb) on top of a ferrimagnetic insulator (Y3Fe5O12) serves as a magnon spin detector, we demonstrate that the conversion efficiency of magnon spin to QP charge via inverse spin-Hall effect (iSHE) in such an exchange-spin-split SC [4] can be greatly enhanced by up to 3 orders of magnitude compared with that in the normal state, particularly when its interface superconducting gap matches the magnon spin accumulation. Through systematic measurements with varying the current density and SC thickness, we identify that superconducting coherence peaks and exchange spin-splitting of the QP density-of-states, yielding a larger spin excitation while retaining a modest QP charge-imbalance relaxation, are responsible for the giant QP iSHE. Our results provide a new device concept in which the non-local voltage created from long-rage magnon-carried spin is orders of magnitude controllable by turning the superconductivity on and off [5].References: [1] F. S. Bergeret, M. Silaev, P. Virtanen, and T. T. Heikkilä, Rev. Mod. Phys. 90, 041001 (2018). [2] L. J. Cornelissen, J. Liu, R. A. Duine, J. Ben Youssef, and B. J. van Wees, Nat. Phys. 11, 1022 (2015). [3] A. V. Chumak, V. I. Vasyuchka, A. A. Serga, and B. Hillebrands, Nat. Phys. 11, 453 (2015). [4] M. Silaev, P. Virtanen, F. S. Bergeret, and T. T. Heikkilä, Phys. Rev. Lett. 114, 167002 (2015) [5] K.-R. Jeon, J.-C. Jeon, X. Zhou, A. Migliorini, J. Yoon and S. S. P. Parkin, arXiv:2004.09467 (2020).

Giant transition-state enhancement of quasiparticle spin-Hall effect in an exchange-spin-split superconductor detected by non-local magnon spin-transport

Spin-dependent scattering transport at heavy metal (HM)/magnetic insulator (MI) interface can be described in terms of three parameters: the spin-sink conductance Gs and the real and imaginary part of the spin-mixing conductance, G↑↓=Gr+iGi [1,2]. Each parameter is relevant for different spin-dependent phenomena. For instance, Gs originates from spin-flip processes and therefore is the leading parameter in electrical biasing of magnons [3], whereas Gr accounts for the spin-transfer (Slonczewski) torque to the magnetization and plays a fundamental role in spin-pumping experiments [4]. On the other hand, Gi quantifies the interfacial exchange field, which induces a field-like torque in the conduction electrons of the HM and is important for example in spin-splitting field experiments in superconductivity [5]. These conductances are broadly studied in ferrimagnetic insulators, where usually the contribution of Gr is much larger than that of Gi [6], leading to only a few reports on the exchange field at HM/MI interfaces [7]. In this work [8], we study the three spin conductance terms by spin Hall magnetoresistance (SMR) in a new system: a ferromagnetic insulator (FMI) such as EuS. By SMR measurements as a function of the temperature, and taking advantage of the newly developed microscopic theory for SMR [2], we can extract relevant microscopic parameters such as the exchange interaction between the 1s electrons in Pt and the localized magnetic moments in EuS (Jint~18 meV) [8]. An interfacial exchange field of the order of 1 meV (~15 T) acting upon the conduction electrons of Pt can be estimated from Gi, which is at least three times larger than Gr below the Curie temperature [8]. Our work provides an easy method to quantify this interfacial spin-splitting field, which is of interest in different areas of Condensed Matter Physics, such as proximity effects in superconducting hybrid systems.References: [1] T.-Y. Chen et al., Phys Rev. B 87, 144411 (2013) [2] X.-P. Zhang et al., Nano Lett. 19, 6330 (2019) [3] L. J. Cornelissen et al., Nat. Phys. 11, 1022 (2015). [4] M. Weiler et. al., Phys. Rev. Lett., 111, 176601 (2013) [5] B. Li et al., Phys. Rev. Lett. 110, 097001 (2013). [6] X. Jia et al., Europhysics Lett. 96, 17005 (2011). [7] N. Vlietstra et al., Appl. Phys. Lett. 103, 032401 (2013); T. Kosub et al., Appl. Phys. Lett. 113, 222409 (2018). [8] J. M. Gomez-Perez et al., arXiv:2004.12009 (2020)

Strong Interfacial Exchange Field in a Heavy Metal/Ferromagnetic Insulator System Determined by Spin Hall Magnetoresistance

Relatively little work has been done to date to understand the transport of spin waves generated via ferromagnetic resonance (FMR) in anisotropic high-temperature superconductors. To this end, we have fabricated bilayers of yttrium barium copper oxide (YBCO) with the half-metallic ferromagnet lanthanum strontium manganite (LSMO) via pulsed laser deposition on (LaAlO3)0.3(Sr2TaAlO6)0.7 (LSAT) (001) substrates. We fix the LSMO thickness at 30 nm and vary the YBCO thickness from 2-17 nm. We have verified that the YBCO superconducts with Tc varying from 55-88 K depending on YBCO thickness (with a minimum thickness of 5 nm required for superconductivity). Since the variation in Tc with thickness is not as strong in single YBCO layers grown on LSAT substrates we believe that the magnetic exchange field from the LSMO, rather than a epitaxial strain effect, is the governing factor for Tc. To characterize spin wave transport, we performed FMR measurements on the bilayers as a function of temperature and YBCO thickness. We find that the resonance linewidth of bare LSMO increases with decreasing temperature, which is attributed to an increased contribution from two-magnon scattering at lower temperatures. Additionally, with the addition of 17 nm of YBCO, we see a near doubling of the FMR linewidth at all temperatures. Although more work needs to be done to fully characterize the system, these results possibly point to spin wave dissipation in the YBCO layer, which has not previously been observed.

Spin transport in La0.67Sr0.33MnO3/YBa2Cu3O7-δ bilayers

Spin orbit torques (SOTs) are being actively considered for use in the next generation memory devices for magnetization switching, spin oscillators and racetrack memories, including those using magnetic skyrmions. SOTs are fundamentally based on charge-to-spin conversion by the spin-Hall or Rashba effect. Taking advantage of the spin current, the torques can be used to switch magnetic insulators or the free layer of magnetic tunnel junctions with high energy efficiency. Therefore, it is important to accurately measure the charge-to-spin conversion efficiency. SOTs are principally of interest in nanostructured samples, samples with minimum dimension less than a micron. However, the magnitude and form of the torques are most often characterized in micron scale samples, using spin torque ferromagnetic resonance (ST-FMR), a technique that involves analyzing the resonance linewidth [1] or lineshape [2]. On microstructures, these two analysis methods are quite consistent. Here we present ST-FMR results on permalloy Ni80Fe20 nanowires --- with widths varying from 150 to 800 nm --- that show that the standard model used to analyze the resonance linewidth and lineshape give different results [3]. Fig. 1 a-c show examples of ST-FMR spectra. Fig. 1d shows the efficiency of nanowires with different width, which shows greatly enhanced efficiency when the lineshape method is used. We present a ST-FMR model that properly accounts for the sample shape. It shows a much better consistency between the two methods, as illustrated in Fig. 2. Micromagnetic simulations are used to verify the model. These results and the more accurate nanowire model presented are of importance for characterizing and optimizing charge-to-spin conversion efficiencies in nanostructures.References: [1] S. Petit et al., Physical Review Letters 98, 077203 (2007) [2] L. Liu et al., Physics Review Letters 106, 036601 (2011). [3] J.-W. Xu et al., arXiv:2004.03784(2020). [to appear in Physical Review Applied]

Charge-to-spin conversion efficiency in ferromagnetic nanowires by spin torque ferromagnetic resonance: Reconciling lineshape and linewidth analysis methods

Generation and manipulation of pure spin current play an important role in fabrication of power efficient spintronics devices1. Spin pumping is very efficient way of creation of pure spin current in ferromagnetic (FM)/nonmagnetic (NM) system by microwave excitation which can be converted into a voltage by inverse spin Hall effect (ISHE) Various materials possessing high spin orbit coupling (SOC) like Pt, Ta, W, Bi2Se3 etc., have been utilized for efficient spin to charge conversion2,3. However, these are limited by very small spin diffusion length (λsd ~10 nm). In this context organic semiconductors (OSC) e.g. C60 are emerging as a potential candidate due to large value of λsd. The low value of SOC in OSC limits them for efficient spin to charge conversion. However, when the OSC is deposited on a substrate the structural distortion may exhibit enhancement of SOC. Here we report simultaneous observation of spin pumping and ISHE measurements in the CoFeB/C60 bilayers by ferromagnetic resonance (FMR) in the frequency range 6 – 17 GHz. During the measurement the sample was kept on the wide coplanar waveguide (CPW) in the flip-chip manner. Angle dependent ISHE measurements have been performed at fixed frequency of 7 GHz and 11 mW power by using a nanovoltmeter at the two edges of the sample. Figure1 shows dc voltage (Vmeas) and FMR signal versus applied magnetic field (H) plot. At 180-degree ISHE signal is reversed as the magnetic field direction is reversed, which indicates that signal is not coming from any artefacts and it is due to spin pumping. Also, we have calculated the spin Hall angle for CoFeB/C60 bilayer system is 0.04 which is higher than the reported value.References: 1. Y. Tserkovnyak, A. Brataas, et al., Rev. Mod. Phys. 77, 13751421 (2005) 2. B. B. Singh et al., physica status solidi (RRL) Rapid Research Letters 13, 1800492 (2019) 3. B. B. Singh et. al., Phys. Rev. Appl. 13, 044020 (2020)

Observation of inverse spin hall effect at CoFeB/C60 interface

2D-transition metal dichalcogenides (TMD) are known to have high spin-orbit coupling, an essential property for spintronic applications [1,2]. TMD materials with this property can replace the heavy metals for next generation spintronic devices. In this context MoS2 has been of great interest in recent years due to its unique electrical and optoelectronics properties. It can be fabricated in very thin layers due to weak Van der waals forces, which makes it suitable to investigate interface dominated Rashba and Edelstein effects. However, fabrication of MoS2 by chemical or exfoliation methods makes it difficult for spintronics applications. In this work, we demonstrate inverse spin Hall effect in MoS2(t)/CoFeB(10nm)/MgO(2nm) heterostructures where ‘t’ varies from 7 to 30nm.The heterostructure was fabricated by RF and DC sputtering of MoS2 and CoFeB, respectively, on thermally oxidized Si substrate. MgO capping layer was deposited by thermal evaporation. Here the spin current was generated from CoFeB and injected into MoS2 layer via spin pumping using ferromagnetic resonance (FMR). The resulting spin to charge conversion at interface was measured using nanovoltmeter. Various spin rectification effects were separated by performing angle dependent measurements [3]. For the sample with MoS2(30nm), a spin pumping voltage of -1.6 mV was measured which was dominant over the rectification effects. The spin mixing conductance value was found to be ~ 3.72×1018 m-2 which is comparable to that of MoS2 and Pt obtained from literature. Figure 1 shows the measured voltage signal for the sample Si/SiO2/MoS2(30nm)/CoFeB(10nm)/MgO(2nm). In order to understand the origin of this voltage, power and frequency dependent measurements were also performed. The linear increase in the symmetric component of dc voltage with the microwave power further indicated spin pumping [4].References: [1] Qing Hua , Kourosh Kalantar-Zadeh, Andras Kis, Jonathan N. Coleman and Michael S. Strano Nature Nanotechnology, 7, 699–712 (2012) [2] Zehua Hu, Zhangting Wu, Cheng Han, Jun He, Zhenhua Ni and Wei Chen, Chemical Society Reviews, 47, 3100-3128, (2018) [3] Braj B. Singh, Sukanta K. Jena, Manisha Samanta, Kanishka Biswas, Biswarup Satpati and Subhankar Bedanta, Phys. Status Solidi RRL,Volume 13, Issue 3,1800492 (2019) [4] K. Ando, S. Takahashi, J. Ieda, Y. Kajiwara, H. Nakayama, T. Yoshino, K. Harii, Y. Fujikawa, S. Maekawa and E. Saitoh, J. Appl. Phys.109, 103913 (2011).

Inverse Spin Hall Effect in Sputtered MoS2/CoFeB Bilayers

Pure spin currents have been ubiquitous in contemporary spintronics research. Despite its pro- found physical and technological significance, the detection of pure spin current has largely remained indirect, which is usually achieved by probing spin-transfer torque effects or spin-to-charge conversions. By using scanning transmission X-ray microscopy, we report the direct detection and spatial mapping of spin accumulation in a nonmagnetic Cu layer without any direct charge current injection. Such a pure spin current is induced by spin pumping from a NiFe layer and is not accompanied by concomitant charge motion. The observed frequency dependence indicates that the signal is dominated by a coherent, pure spin current, but the magnitude of the spin accumulation suggests also possible additional thermal contributions. Our technique takes advantage of the X-ray magnetic circular dichroism and the synchronization of microwave with X-ray pulses, which together provide a high sensitivity for probing transient magnetic moment. From the detected X-ray signals, we observe two distinct resonance modes induced by spin pumping, which, based on micromagnetic simulations, we attribute to non-linear microwave excitations. Our result provides a new pathway for detecting pure spin currents that originate from many spintronics phenomena, such as spin Hall and spin Seebeck effects, and which can be applied to both metal and insulator spin current sources [1]. Work at Argonne, including experimental design and measurement, sample fabrication, data analysis, and manuscript preparation, was supported by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences, Materials Science and Engineering Division under Contract No. DE-AC02-06CH11357. Use of the Stanford Synchrotron Radiation Light source, SLAC National Accelerator Laboratory, is supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Contract No. DE-AC02-76SF00515. W.Z. acknowledges the DOE visiting Faculty Program.References: 1.) “Direct Observation of spin accumulation in Cu induced by spin pumping” J. Ding, W. Zhang, B. Jungfleisch, J.E. Pearson, H. Ohldag, V. Novosad, A. Hoffmann, Phys. Rev. Res vol 2(1), p. 013262 (2020)

Direct Observation of Spin Accumulation in Cu Induced by Spin Pumping

This paper presents engineering of magnetic domains and perpendicular magnetic anisotropy (PMA) in magnetic thin films and multilayer (ML) employing ion-beam irradiation [1]. Two model systems have been selected for this study namely, amorphous Tb-Fe-Co (200 nm) film and ultrathin Co/Pd ML (Si (substrate) / Ta (30) / Pd (30) / [Co (3) / Pd (8)] ×50 / Pd (12) Å) which show strong PMA in the pristine state, however, the origin of PMA is different for both the systems. The pristine Tb-Fe-Co film depicts a rectangular hysteresis loop and elongated, inter-connected maze-like magnetic domains with strong out-of-plane contrast. Irradiation at higher fluences (≥1015 ions/cm2) of Ar+ ions at an energy of 200 keV results in transformation of magnetization reversal mechanism from rapid domain wall motion to nucleation and propagation of reverse domains due to the pinning of domain walls. The elongated magnetic domains get fragmented with reduced contrast and interestingly inhomogeneous flux closure patterns are observed at higher fluences, indicating a spin reorientation transition, as shown in Fig. 1 (a). The modifications in magnetic properties are correlated with the structural investigations which reveal the crystallization of Fe-Co phase in the amorphous Tb-Fe-Co matrix at higher energy and fluences of the projectile ions. On the contrary, ion-induced intermixing at the interfaces for perpendicularly magnetized ultrathin Co/Pd ML causes amorphization for the pristine poly-crystalline films. In this case, low energy ion-irradiation (50 keV) does not have significant role in modifying the microstructure, however, control of pinning sites can be achieved through variable fluences which play an important role in the modification of magnetic domains, as depicted in Fig. 1 (b). Micromagnetic simulations on domain modification complement the experimental results.References: 1. J. Fassbender, D. Ravelosona and Y. Samson, Journal of Physics D: Applied Physics 2004, 37 (16), R179-R196.

Engineering Magnetic Domains in Perpendicularly Magnetized Thin Films and Multilayers Using Ion-beam Irradiation

The Dzyaloshinskii-Moriya interaction (DMI) plays a crucial role in the stabilization of chiral spin textures [1]. Interfacial DMI (iDMI) induced by a lack of inversion symmetry and strong spin orbit coupling at the interface of Ferromagnet/Heavy Metal (FM/HM) heterostructures provides various opportunities for future spintronic devices. Recently, iDMI in a thin film of NiFe/Graphene (NiFe/Gr) heterostructures has been detected using Brillouin light scattering [2] and using spin-polarized electron microscopy [3]. In this study, we propose a simple method of measuring DMI by using the Bragg magneto-optical Kerr effect (MOKE). We observe an asymmetric shift in the hysteresis loop, which is proportional to the strength of iDMI [4]. Here, we utilize Bragg-MOKE in longitudinal mode to which occurs when a broad polarized beam is incident on a periodic array of the magnetic features with size comparable to the wavelength of laser. We have investigated the hysteresis loop shift for 1st and 2nd order of diffraction in off-specular geometry for both patterned graphene (Gr/NiFe(10nm)/Ta) and reference (NiFe(10nm)/Ta). We used triangular pattern (Fig. 1) as proposed in Ref [4]. We found a shift in hysteresis loop for the Gr/NiFe/Ta sample (Fig. 2), which likely due to the presence of iDMI that was previously measured using BLS [2]. Hence, the Bragg-MOKE technique can be a potential technique for rapid quantification of iDMI in magnetic heterostructures. We will also present variable field magnetic force microscopy (MFM) and micromagnetic simulations to support these results.References: 1. M. Bode, et al., Nature 447, 190 (2007). 2. A. Kumar, et al. Phys. Rev. B 99.3,035402 (2019). 3. H. Yang, et al. Nat. Mater. 17, 605 (2018). 4. D-S Han, et al. Nano Lett. 16, 4438 (2016).

Evidence of the interfacial Dzyaloshinskii-Moriya interaction in Ni80Fe20/graphene using Bragg-MOKE

The perpendicular magnetic media has the potential to improve data storage beyond 1 Tb/in2. Improving data density is a major challenge in data recording industries due to its sustainability and performance issues [1]. In the present study, by employing Ti as under-layer (UL) and spacer-layer (SL) the bulk perpendicular magnetic anisotropy (PMA) of Tb-Fe thin films is found to be improved considerably. 100 nm thick Tb-Fe film devoid of UL exhibited a maze-like domain pattern with strong out-of-plane (OOP) contrast. With 10 nm thin Ti UL, the domain width, and the OOP contrast of Tb-Fe (100 nm) film were found to improve considerably (fig. 1). Accordingly, the coercive field for Tb-Fe film with Ti UL was doubled when compared with the bare Tb-Fe film. The possible reason for the enhancement in OOP properties could be due to the lateral extent of d-d hybridization that exists at the interface. Similarly, PMA and domain areal density also increased by placing a 2 nm thin Ti SL: Tb-Fe (100 nm) / Ti (2 nm) / Tb-Fe (100 nm) (fig. 1). Here, we observed a large dipolar coupling that exists between the top and bottom Tb-Fe layers. The Hc of about 0.5 T observed for bare Tb-Fe (200 nm), was found to increase to about 1 T for the Tb-Fe films with Ti SL. Interestingly, Tb-Fe film with SL exhibited a hybrid domain pattern probably due to the bottom Tb-Fe layer. Thus, Ti when used either as UL or SL improved the OOP magnetic properties of Tb-Fe thin films considerably. The fundamental observation and understanding will have a significant impact on perpendicular media which may also useful in other areas of spintronic applications.References: 1. K. Tang, et. al, IEEE transactions on magnetics, Vol. 45 p. 786-792 (2009).

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