United States

Hexagonal ferrite materials such as BaFe12O19 and SrFe12O19 have strong anisotropic magnetic field and strong remnant magnetism. These properties enable the working frequency of devices such as phase shifter, isolator and circulator, move up to tens of GHz without a strong external bias field and even achieve self-biasing. Other features such as large saturation magnetization, large anisotropy, and low dielectric loss and most importantly, its potential of achieving self-bias, paves the way to fabrication of planar ferrite device that can play a crucial role in a next generation wireless system. The advantage of ferrite devices are their low insertion loss, high isolation, broad bandwidth and high power handling ability compared to their active counterparts. If the fabrication process of aforementioned devices can be integrated into the mature CMOS process flow as an option, it will gain great competiveness as regards the cost. In this work, thin film ferrite material was deposited by employing spin-casting method [Liu 2013] and patterned with the help of Chemical-Mechanical Polishing (CMP). The spin-casting is a low-temperature process: the nano-sized barium ferrite materials can be processed into composite and spin-casted into thin film layer. This method requires only 120°C baking under external biasing filed. In this research, we present the design, simulation, fabrication and measured results of a self-bias micro-strip line Barium hexagonal Nano-ferrite (BaM) circulator on silicon wafer as Fig. 1. This planar Y-junction circulator is 2mm by 2mm by 0.5mm in size, which is capable of future integration with the top three layers of 180nm CMOS technology. Ferrite thin film is deposited and patterned employing composite spin-casting method. Typical characterization techniques are employed together with free-space quasi-optical spectrometry to study complex permittivity and permeability of deposited film up to 120GHz. S parameters of fabricated circulators are characterized by a set of on wafer probes up to 67GHz as Fig. 2. We observed over 15dB non-reciprocal phenomenon at 55GHz.References: Liu C, Sholiyi O, Afsar M N and Williams J D (2013), “Characterization of micro-structured ferrite materials: course and fine barium, and photoresist composite,” Magnetic, IEEE Transactions on, vol. 49, pp.4319-4322, July 2013.

MMM 2020

Hexagonal Nano-ferrites used on a V-band Self-bias On-chip Circulator for CMOS

The 65th Annual Conference on Magnetism and Magnetic Materials (MMM 2020) was held in a virtual form. The COVID-19 pandemic, with its associated uncertainty about international travel and the ability to gather in large groups, meant that the Steering Committee decided to cancel the face-to-face meeting that had been planned in Palm Beach, Florida November 2-6, 2020.

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technical paper

We investigate the physical origin of nonlinear damping due to mode coupling between several auto-oscillatory modes driven by spin-orbit torque in constricted Py/Pt heterostructures by examining the dependence of auto-oscillation on temperature and applied field angle. We observe a transition in the nonlinear damping of the auto-oscillation modes extracted from the total oscillation power as a function of drive current, which coincides with the onset of power redistribution amongst several modes and the crossover to linewidth broadening of all individual modes, as opposed to linewidth narrowing expected from the larger anti-damping current. This indicates the activation of a new relaxation process by nonlinear magnon-magnon scattering within the modes. We also find that both nonlinear damping and threshold current in the mode interaction damping regime at high drive current after transition are temperature independent, suggesting that the mode coupling occurs dominantly through a non-thermal magnon scattering process via a dipole or exchange interaction rather than thermally excited magnon-mediated scattering.

Origin of Nonlinear Damping due to Mode Coupling in Auto-Oscillatory Modes Strongly Driven by Spin-Orbit Torque

In modern radar and communication systems it is important to determine the frequency composition of complex external signals on the µs time scale and faster [1]. Common swept-tuned spectrum analyzers (SA) are limited to sweep times of 10-100 ms determined by the characteristic times of macroscopic VCOs and YIG-tuned reference oscillators. In contrast, recent progress in spintronics has led to the development of spin-torque nano-oscillators (STNO) generating in the GHz frequency range, and naturally having time constants of the order of several nanoseconds determined by the intrinsic properties of magnetization dynamics at nano-scale [2]. In [3] it was proposed theoretically and in [4] demonstrated experimentally for a vortex-state configuration that STNOs can be used as a central element of an ultra-fast spectrum analyzer. A fastest sweep rate of 0.67us was achieved for spectral analysis in the range of 25MHz around center frequency of 300MHz. Here we demonstrate that an ultra-fast sweep-tuned spectrum analysis can be performed at a central frequency of 3 GHz using uniform-state STNOs. The obtained SA performances sufficiently exceed the results obtained with a vortex-state STNO with a reduced sweep time of T =0.1µs, sweep range of 400 MHz (limited by the STNO power and not by tuning range capabilities) keeping the RBW (resolution bandwidth) close to the theoretical limit (14 MHz). This GHz-frequency technique of spectrum analysis was implemented as shown in Fig.1. The STNO was used as a local oscillator whose frequency was sweep-tuned by injecting a saw-tooth sweep signal. The STNO output (a) is, then, mixed with the input signal (b), digitized (c), and processed with a matched filter, resulting in a narrow output peak (d) whose temporal position corresponds to the input frequency while the width determines the RBW. Financial support is acknowledged from the EC program ERC MAGICAL 669204, from the NSF of the USA (Grants # EFMA-1641989 and “ECCS-1708982), and by the US AFOSR (MURI grant # FA9550-19-1-0307). The EC program GREAT is acknowledged for provision of perpendicular MTJ devices operating at GHz frequencies.References: [1] Chen, V.C. and Miceli, W.J., “Time-varying spectral analysis for radar imaging of manoeuvring targets”, IEEE Proceedings - Radar, Sonar and Navigation 145, 262-268 (1998). [2] Tingsu Chen, et al., “Spin-Torque and Spin-Hall Nano-Oscillators”, IEEE Proceedings, 104, 1919-1945 (2016). [3] Louis, S. et al., “Ultra-fast wide band spectrum analyzer based on a rapidly tuned spin-torque nano-oscillator”, Applied Physics Letters 113, 112401 (2018). [4] A. Litvinenko, et al., “Experimental demonstration of a rapid sweep-tuned spectrum analyzer with temporal resolution based on a spin-torque nano-oscillator,” arXiv preprint arXiv:2004.03508, (2020).

Ultra-fast Spectrum Analysis at GHz frequencies using Spin-Torque Nano-Oscillators

Physical reservoir computing by magnetic devices is becoming an exciting topic in spintronics [1]. Recent studies on physical reservoir computing reveal that high-computation performance is achieved by physical systems at the edge of chaos [2], which is a boundary between chaos and the other dynamical states. An excitation of chaos in spin-torque oscillator (STO) by the delayed feedback was predicted recently [3,4]. Therefore, it becomes of great interest to perform the physical reservoir computing by STOs with the feedback circuit. Although an enhancement of the computation performance of the STO by the feedback was reported in 2019 [5], chaos in the STO was not identified. Since the intensity of the feedback effect in the experiments was weak, only ordered dynamics, such as self-synchronization, had been reported previously [6,7]. In this work, we investigate the edge of chaos in a vortex-type STO by enhancing feedback efficiency. Figure 1 is a schematic view of the STO with the feedback circuit. Spin-transfer torque by direct current excites an autooscillation of the vortex core. The output signal generated from the STO was gained of 40 dB, and was applied to the STO as microwave field with time delay of 150 ns. The magnitude of the feedback signal was toned by an attenuator. Figure 2 summarizes power spectra of the STO with various attenuation rate rAtt. The number of the peaks increases with decreasing the attenuation, as shown in Figs. 2(a) and 2(b), which was typically found in the feedback system [6]. The linewidth of the main peak in Fig. 2(b) is narrow compared with that in Fig. 2(a), indicating the stabilization of the oscillation by the feedback. A further reduction of rAtt , however, results in a broad linewidth with a low power at the main peak shown in Fig. 2(c), which implies an appearance of chaos [8]. The performance of the reservoir computing at this state will be presented at the meeting. This work was supported by NEDO.References: [1] J. Torrejon et al., Nature 547, 428 (2017). [2] J. Nakayama et al., Opt. Exp. 24, 8679 (2016). [3] J. Williame et al., Appl. Phys. Lett. 114, 232405 (2019). [4] T. Taniguchi et al., Phys. Rev. B. 100, 174425 (2019). [5] M. Riou et al., Phys. Rev. Appl. 12, 024049 (2019). [6] S. Tsunegi et al., Sci. Rep. 6, 26849 (2016). [7] D. Kumar et al., Sci. Rep. 6, 30747 (2016). [8] A. Uchida, “Optical communication with chaotic Lasers: Applications of Nonlinear Dynamics and Synchronization”, Wiley (2012).

Physical Reservoir Computing by Spin-Torque Oscillator at the Edge of Chaos

High-frequency ferrite ceramics exhibiting high permeability and low magnetic loss have been recently attracting more and more attention owing to the rapid development of modern communication technologies.1-3 It is known that the magnetic performance of ferrites is strongly associated with the morphology of their polycrystalline structure.4 During the final-stage sintering, densification is typically accompanied by rapid grain growth.5 In this work, we focus on the control of grain growth and densification process for planar Co-Ti doped M-type barium hexaferrites, BaCo1.2Ti1.2Fe9.6O19, by one-step sintering (OSS) and two-step sintering (TSS) techniques. Experimental results in Fig. 1. indicate that the microstructure of the samples prepared by TSS shows visibly finer and more uniformity compared to that of the samples prepared by conventional OSS, evidence in that the grain growth during the second-step sintering of TSS is successfully suppressed while the density continues to increase. More importantly, the TSS technique shifts the resonant frequency to a higher value as shown in Fig. 2. In addition, the uniformity of the microstructure contributes to a narrower resonant peak. The reshaping of the magnetic spectra leads to a significant reduction of magnetic loss below 300 MHz. The ferrites prepared by TSS demonstrate high permeability (μ' = 18-20), low magnetic loss (tan δm = 0.1-0.3), and high Snoek's product (>25 GHz) in the frequency range of 100-400 MHz. By fitting experimental data, we have determined that low magnetic loss is derived from the small damping coefficient of spin rotation in terms of Kittel's theory. Therefore, the TSS technique provides an effective and efficient approach to prepare planar BaM hexaferrite materials for ultra-high frequency (UHF) communication devices requiring low loss and high Snoek's product.References: 1V. G. Harris, Z. Chen, Y. Chen et al., J. Appl. Phys., Vol. 99, p. 08M911 (2006). 2V. G. Harris, A. Geiler, Y. Chen et al., J. Magn. Magn. Mater., Vol. 321, p. 2035 (2009). 3V. G. Harris, IEEE Trans. Magn., Vol. 48, p. 1075 (2012). 4Q. Li, Y. Chen, and V. G. Harris, J. Magn. Magn. Mater., Vol. 453, p. 44 (2018). 5I. W. Chen and X. H. Wang, Nature, Vol. 404, p. 168 (2000).

Permeability Spectra of Planar M-type Barium Hexaferrites with High Snoek’s Product by Two-Step Sintering

With the unprecedented surge in wireless communication systems, microwave (MW) absorbers are becoming increasingly important for civil as well as military applications. When a MW signal is incident on a surface, the signal energy is divided into three parts: (i) reflected, (ii) transmitted and (iii) absorbed energies. For the usual metal-backed MW absorbing coating, transmitted energy=0; thus, minimizing reflection is the key for good absorbers. The reflection of EM energy can be curtailed by two methods: (i) an increase in absorption, and (ii) the quarter wavelength cancellation [1,2]. The loss of EM energy may originate from a number of processes within the absorber such as conduction, resonances, and relaxations etc. MW signal, on passing through an absorber dissipates its energy in the form of heat through interactions with the dielectric and magnetic structures of a material. Hence, in terms of two characteristic material parameters: relative permeability (μ*) and relative permittivity (ε*) in the absorbing medium are to be tailored for attaining a strong and broadband MW absorption. For MW absorbing applications, U-type hexaferrite phase with chemical formula Ba4Me2Fe36O60 (Me2U, Me: divalent transition-metal cation) has most complicated crystal structure and is least studied [3-11]. In present work, we investigate the preparation and MW absorbing properties of the nanoscale U-type hexaferrites (NANO-U) for development of a broadband MW absorber. The nano-powders are prepared using two different methods: (1) mechanical jet-milling of bulk U-type hexaferrite prepared by the standard solid-state reaction route at ∼1250 °C, designated here as (NANO-U)JM and (2) a novel one-pot chemical route, designated here as (NANO-U)C. In the first method, average particle size ∼20–50 nm powders were achieved; whereas, the (NANO-U)C powders of controlled particle sizes (∼65 to ∼170 nm) were prepared by changing the holding time (4, 6, 8 and 10 h) at a constant optimized working temperature of ∼900 °C. Four samples of (NANO-U)C were prepared that are designated as per their holding time as- (NANO-U)C4, (NANO-U)C6, (NANO-U)C8, (NANO-U)C10. A blend of all powders in equi-proportion, is designated as (NANO-U)CMIX, The advantage of one-pot chemical method is attainability of comparable particles sizes of a few tens of nm, at much lower working temperatures. We compare the EM parameters and MW absorbing properties of (NANO-U)JM , (NANO-U)C and bulk U-type hexaferrite powders. It is interesting to note that the (NANO-U)JM demonstrates excellent reflection loss (RL) of ∼ -43.8 dB (99.99% MW absorption) at ∼11.3 GHz frequency with a broad bandwidth of 8.6 GHz (8.9 ≤ f ≤ 17.5 GHz) for 90% or more MW absorption. The values for (NANO-U)C too are comparable, with RL of -44.2 dB (99.99% MW absorption) at 11.6 GHz frequency for (NANO-U)C8 and a broadband MW absorption with an excellent bandwidth of 8.4 GHz (9.3 ≤ f ≤ 17.7 GHz) for (NANO-U)CMIX. Significantly improved MW absorption performance are demonstrated in NANO-U hexaferrites, in comparison to the previously reported nanoscale spinel ferrites (-38.9 dB or 99.8% MW absorption along with a bandwidth of ∼3.7 GHz only). We believe that nanoscale particle sizes in U-type hexaferrites result in synergistic enhancements of the dielectric and magnetic losses. A self-explanatory schematic representation of the various possible loss mechanisms in NANO-U absorbers is shown in Fig. 1. Easy tunability, large magnetic anisotropy, presence of disordered surface spin states, defect polarization centres, greater magnetic and dielectric losses and large hopping conduction are responsible for large and broad-band MW absorption in NANO-U hexaferrites. These economical and easily processed U-type hexaferrite ultrafine particles can be used in the paints and sheets for wide-band and strong MW absorbing coating applications.References: (1) Y. Huang, H. Zhang, G. Zeng, Z. Li, D. Zhang, H. Zhu, R. Xie, L. Zheng, J. Zhu, J. Alloys Compd., 682 (2016) 138-143. (2) L. Wan, J. Zhang, Y. Chen, H. Wang, W. Hu, L. Liu, Y. Deng, J. Phys. D: Appl. Phys., 48 (2015) 355302-355310. (3) D. Lisjak, M. Drofenik, J. Appl. Phys., 93 (2003) 8011-8013. (4) M.N. Afsar, D. Lisjak, A. Bahadoor, Y. Wang, IEEE Trans. Magn., 41 (2005) 3472–3474. (5) D. Lisjak, V.B. Bregar, M. Drofenik, J. Magn. Magn. Mater., 310 (2007) 2558-2560. (6) R.S. Meena, S. Bhattacharya, R. Chatterjee, J. Magn. Magn. Mater., 322 (2010) 2908-2914. (7) R.S. Meena, S. Bhattacharya, R. Chatterjee, Mater. Sci. Eng., B, 171 (2010) 133-138. (8) R.S. Meena, S. Bhattacharya, R. Chatterjee, J. Magn. Magn. Mater., 322 (2010) 1923-1928. (9) R.S. Meena, S. Bhattacharya, R. Chatterjee, Mater. Des., 31 (2010) 3220–3226. (10) S. Padhy, S. Sanyal, R.S. Meena, R. Chatterjee, A. Bose, Journal of Electromagnetic Waves and Applications, 27 (2013) 191-204. (11) S. Padhy, S. Sanyal, R.S. Meena, R. Chatterjee, A. Bose, IET Microw. Antennas Propag., 8 (2014) 165–170.



Nanoscale U-Type Hexaferrites as Microwave Absorbers INVITED

Structural and magnetic properties of a quasi-one-dimensional spin-1/2 compound NaVOPO4 are explored by x-ray diffraction, magnetic susceptibility, high-field magnetization, specific heat, electron spin resonance, and 31P nuclear magnetic resonance measurements, as well as complementary ab initio calculations. Whereas magnetic susceptibility of NaVOPO4 may be compatible with the gapless uniform spin chain model, a detailed examination of the crystal structure reveals a weak alternation of the exchange couplings with the alternation ratio α ~ 0.98 and the ensuing zero-field spin gap Δ0/kB ~ 2.4 K directly probed by field-dependent magnetization measurements. No long-range order is observed down to 50 mK in zero-field. However, applied fields above the critical field Hc1 ~1.6 T give rise to a magnetic ordering transition with the phase boundary TN ∝ (H − Hc1 )1/φ, where φ ~1.8 is close to the value expected for Bose-Einstein condensation of triplons. With its weak alternation of the exchange couplings and small spin gap, NaVOPO4 lies close to the quantum critical point.References: [1] P. K. Mukharjee et. al., Phys. Rev. B 100, 144433 (2019) [2] S. Sachdev, Nat. Phys. 4, 173 (2008) [3] Mukhopadhyay et. al, Phys. Rev. Lett. 109, 177206 (2012) [4] Zapf et. al., Rev. Mod. Phys. 84, (2014)

Bose-Einstein Condensation Of Triplons Close to The Quantum Critical Point in The Quasi-One-Dimensional Spin-1/2 Antiferromagnet NaVOPO4

During the past few years, the Mo3O8 quantum magnets with kagome layers formed by Mo atoms have attracted a great deal of attention as a new candidate to realise quantum spin liquid states. The magnetic susceptibility of LiZn2Mo3O8 has been experimentally shown to follow a Curie-Weiss law with the low- and high-temperature regimes whose Curie constants are related as CL~1/3CH. Originally, the disappearance of 2/3 of the paramagnetic spins at low temperatures in LiZn2Mo3O8 was attributed to valence bond condensation on the trimerized lattice of the Mo3O13 clusters [1], and several possible scenarios have been proposed to describe this unusual behaviour [2,3]. However, their adequacy was questioned by recently synthesized Li2InMo3O8, that shows a conventional Neel 120° magnetic order, and its counterpart Li2ScMo3O8, where no magnetic order has been observed down to 0.5 K [4]. Motivated by these studies, we combine rigorous first-principles calculations and effective low-energy models to study the microscopic origin of magnetism in LiZn2Mo3O8, Li2InMo3O8, and Li2ScMo3O8. Considering the extended Hubbard model constructed in the basis of Wannier functions for the Mo d states on the anisotropic kagome lattice, we argue that the magnetic properties of these systems can be described by two different regimes of electron localization defined by the competition of kinetic energy and intersite Coulomb interactions. Being in the strong interaction limit, LiZn2Mo3O8 will be proposed to reveal a plaquette charge order due to the correlated collective motion of electrons, where the partial spin pairing decoupling 2/3 of the spin originates from the asymmetry of tunneling processes. On the other hand, Li2InMo3O8 and Li2ScMo3O8 will be shown to fall into a cluster Mott insulator regime with the electrons localized at the Mo3O13 clusters, where the former exhibits long-range antiferromagnetic order and the latter is more likely to reveal short-range order with quantum spin liquid-like excitations.References: [1] J. P. Sheckelton, J. R. Neilson, D. G. Soltan, T. M. McQueen, Nat. Mater., Vol. 11, p. 493 (2012). [2] Rebecca Flint and Patric A. Lee, Phys. Rev. Lett., Vol. 111, p. 217201 (2013). [3] Gang Chen, Hae-Young Kee, and Yong Baek Kim, Phys. Rev. B, Vol. 93, p. 245134 (2016). [4] Yuya Haraguchi, Chishiro Michioka, Masaki Imai et. al, Phys. Rev. B, Vol. 92, p. 014409 (2015). 

First-principles studies of quantum magnetism in Mo3O8 cluster systems

Perovskite manganites La1−xSrxMnO3 (LSMO) (0.30 ≤x ≤0.40) exhibits interesting physical properties such as; colossal magnetoresistance, high spin-polarized current (~90%), Curie temperature (~370K) due to coupling between the charge, spin and orbital degrees of freedom, making it potential candidate for research for decades and application [1-3]. Additionally, a material with high magneto-crystalline anisotropy (MCA), which also depends on temperature, is largely influenced by crystal structure and spin-orbital coupling. In this abstract, we present structural, transport, magnetic and magneto-crystalline anisotropy in La1−xSrxMnO3 (x=0.30, 0.33, 0.36, 0.40) synthesized using solid-state reaction method. X-ray diffraction patterns of all the samples were well indexed by a rhombohedral structure with R3c space group. It is observed that lattice parameters and unit cell volume decrease monotonically upon increasing Sr concentration. X-ray photoelectron spectroscopy confirms the presence of Mn4+ and Mn3+, the ratio which from 1.37-1.54 % as increasing Sr2+ concentration. From the ρ(T) and M(T) data analysis we observe that TMI and MS is larger for x=0.33 composition, which suggest weakening of the double-exchange interaction and Jahn-Teller distortion in x=0.30, 0.36 and 0.40 [4]. We have calculated MCA constant (K1) fitting the law of approach [5-6] to saturation magnetisation data at higher magnetic field, well fitted with the equation, M=MS[1-a/H-b/H2]-χ with K12= (105/8)×b . The obtained K1 in order of ~105 erg/cm3 , slightly decreased as Sr2+ increases which is understood due to reduction of crystal volume. In all samples, the value of K1 at 100 K is higher than that at 300 K, suggesting that the samples at 100 K are more magnetically ordered than at 300 K. This work is supported by SERB-DST, New Delhi (EMR/2016/005424), Ames Lab and MRF (MITM)References: 1. J.B. Goodenough, Phys. Rev. 100 564-573 (1955) 2. C.N.R. Rao, J. Phys. Chem. B. 104 (2000) 5877-5889. 3.Ganesha Channagoudra, Ajay Kumar Saw and Vijaylakshmi Dayal, Thin Solid Films, 709, 138132 (2020) 4. A. Urushibara, Y. Moritomo, Y. Tokura, Phys. Rev. B. 51 (1995) 14103-14109. 5. A. D. Souza, P.D. Babu, Mamatha Daivajna, J. Alloys Compd. 797 (2019) 874-882 6. M. Suliga, K. Chwastek, Acta Phys. Pol. A. 135 (2019) 243–245.

Study of Structural, Transport and Magneto-Crystalline Anisotropic Properties in La1-xSrxMnO3 (0.30 ≤ x ≤ 0.40) Perovskite Manganite

The interaction between the 3d-host ferromagnetism and antiferromagnetism and Ce Kondo-type spin fluctuation and are heavy-fermion behavior in 1:2:2 type of Ce compounds is a very interesting topic and currently still unclear. The clarification of this interaction is very valuable for understanding the physics for such class of magnetic materials. In this presentation, experimental results of x-ray diffraction, x-ray absorption, magnetic susceptibility, and electrical resistivity measurements on a re-entrant ferronmagnetic material system, the Sm1-x-yGdxCey Mn2Ge2 (0 ≤ x + y ≤ 1) series, are reported and discussed for the first time. The Ce valence is found to be nearly trivalent in these materials by Ce-L3 edge measurement. The magnetic susceptibility results show that the substitution of Ce for either Sm or Gd atoms in the rare-earth sublattice expands temperature range of the antiferromagnetic phase and shift this range entirely to low temperature side. It is found such effect is stronger in the Ce for Sm substitution process than in the Ce for Gd substitution process. The temperature dependent resistivity results indicate that Ce spin-fluctuation is strongly quenched by the 3d-host magnetic field in these materials and this quenching effect is analyzed in depth.

Effects of Rare-earth Sublattice on 3d Transition-metal-host Magnetism in the Re-entrant Ferromagnetic Sm1-x-yGdxCey Mn2Ge2 Series with 0 ≤ x + y ≤ 1

We report on the effect of varying the Y element on the structural, electronic and magnetic properties of Co2YIn (Y=Nb, Ti) Heusler compounds using Density Functional Theory (DFT). The effect of the lattice parameter and total number of valence electrons on spin polarization and the magnetic properties of the Heusler compounds is revealed by comparing with Co2VIn Heusler compound, which has the same number of valence electrons as Co2NbIn, Nb and V being from the same group in the periodic table, whereas it has almost the same lattice constant as Co2TiIn, but differing in the total number of valence electrons by one, Ti and V being next neighbors in the same period of the periodic table. The optimized lattice parameters for Co2NbIn and Co2TiIn are found to be 6.20 Å and 6.05 Å respectively, while that of Co2VIn has been reported to be 6.00 Å. Co2NbIn is half metallic with an energy band gap of 0.1 eV in the minority states and has total magnetic moments of 2.02 µB/f.u. very close to the 2.00 µB/f.u. predicted by the Slater-Pauling rule, while Co2TiIn is not half metallic but has a highly spin polarized electronic structure having a spin polarization of 89.59% and total magnetic moments of 1.04µB/f.u. While reducing the number of the valence electrons by one in Co2TIIn has a significant effect on the magnetic moments and spin polarization, an increase in the lattice parameter while maintaining the same number of valence electrons in Co2NbIn does not result in the destruction of the half metallic gap.References: [1] T. Graf, C. Felser, and S. S. P. Parkin, “Heusler Compounds: Applications in Spintronics,” in Handbook of Spintronics, Y. Xu, D. D. Awschalom, and J. Nitta, Eds. Springer Netherlands, 2016, pp. 335–364. [2] A. Birsan and P. Palade, “Band structure calculations of Ti2FeSn: A new half-metallic compound,” Intermetallics, vol. 36, pp. 86–89, May 2013. [3] C. Felser, L. Wollmann, S. Chadov, G. H. Fecher, and S. S. P. Parkin, “Basics and prospective of magnetic Heusler compounds,” APL Mater., vol. 3, no. 4, p. 41518, Apr. 2015. [4] J. Ma et al., “Computational investigation of half-Heusler compounds for spintronics applications,” Phys. Rev. B, vol. 95, no. 2, p. 24411, Jan. 2017. [5] S. Mizukami and A. A. Serga, “Advancement in Heusler compounds and other spintronics material designs and applications,” J. Phys. Appl. Phys., vol. 48, no. 16, p. 160301, 2015. [6] X. Xu et al., “Electronic structures of Heusler alloy Co2FeAl1−xSix surface,” Rare Met., vol. 31, no. 2, pp. 107–111, Apr. 2012. [7] T. Graf, C. Felser, and S. S. P. Parkin, “Simple rules for the understanding of Heusler compounds,” Prog. Solid State Chem., vol. 39, no. 1, pp. 1–50, May 2011. [8] T. Graf, S. S. P. Parkin, and C. Felser, “Heusler Compounds—A Material Class With Exceptional Properties,” IEEE Trans. Magn., vol. 47, no. 2, pp. 367–373, Feb. 2011. [9] E. Sasioglu, L. M. Sandratskii, and P. Bruno, “Role of conduction electrons in mediating exchange interactions in Mn-based Heusler alloys,” Quanten-Theorie der Materialien, PreJuSER-754, 2008. [10] I. Galanakis and P. Mavropoulos, “Spin-polarization and electronic properties of half-metallic Heusler alloys calculated from first principles,” J. Phys. Condens. Matter, vol. 19, no. 31, p. 315213, 2007. [11] H. Luo et al., “Prediction of half-metallic properties for the Heusler alloys Mn2CrZ (Z=Al, Ga, Si, Ge, Sb): A first-principles study,” J. Magn. Magn. Mater., vol. 320, no. 3, pp. 421–428, Feb. 2008. [12] I. Galanakis, “Orbital magnetism in the half-metallic Heusler alloys,” Phys Rev B, vol. 71, no. 1, p. 12413, Jan. 2005. [13] I. Galanakis, P. H. Dederichs, and N. Papanikolaou, “Origin and properties of the gap in the half-ferromagnetic Heusler alloys,” Phys. Rev. B, vol. 66, no. 13, p. 134428, Oct. 2002. [14] M. Zipporah, R. Pathak, M. Robinson, J. Mwabora, R. Skomski, and A. Kashyap, “First-principle investigation of structural, electronic and magnetic properties of Co2VIn and CoVIn Heusler compounds,” AIP Adv., vol. 7, no. 5, p. 55705, Jan. 2017. [15] S. Khenchoul, A. Guibadj, B. Lagoun, A. Chadli, and S. Maabed, “First-Principles Prediction of Structural, Magnetic, Electronic, and Elastic Properties of Full-Heusler Compounds Co2YIn (Y = Ti, V),” J. Supercond. Nov. Magn., vol. 29, no. 9, pp. 2225–2233, Sep. 2016. [16] Enamullah et al., “Electronic structure, magnetism, and antisite disorder in CoFeCrGe and CoMnCrAl quaternary Heusler alloys,” Phys Rev B, vol. 92, no. 22, p. 224413, Dec. 2015. [17] I. Galanakis, P. H. Dederichs, and N. Papanikolaou, “Slater-Pauling behavior and origin of the half-metallicity of the full-Heusler alloys,” Phys Rev B, vol. 66, no. 17, p. 174429, Nov. 2002. [18] L. Wollmann, S. Chadov, J. Kübler, and C. Felser, “Magnetism in cubic manganese-rich Heusler compounds,” Phys. Rev. B, vol. 90, no. 214420, Dec. 2014.

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Origin of Nonlinear Damping due to Mode Coupling in Auto-Oscillatory Modes Strongly Driven by Spin-Orbit Torque

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