United States

First-order reversal-curves (FORCs) are a powerful tool, which is increasingly used in material science and nano-magnetism as well as ferroelectricity, geology, archeology, and for spin-transition materials [1-4]. Ideally, it can access microscopic distributions of interaction and coercive fields without the need for lateral resolution [5]. Unfortunately, the reliable data analysis and interpretation poses a major challenge. This is why FORC is often seen as a magnetic fingerprint instead of a measurement method yielding quantitative information. To push past these limitations, we present a fast and user-independent analysis algorithm and possibilities to interpret the resulting FORC diagrams beyond the Preisach model. We present a new evaluation approach which exploits the diversity of Fourier space to not only speed up the calculation by a factor of 1000 but also move away from the conventional smoothing factor towards real field resolution. By comparing the baseline resolution of the new and the old algorithm we are able to deduce an analytical equation which converts the smoothing factor into field resolution making the old and new algorithm comparable. We find excellent agreement not only for various systems of increasing complexity but also over a large range of smoothing factors. The achieved speed up enables us to calculate a large number of first-order reversal-curve diagrams with increasing smoothing factor allowing for an autocorrelation approach to find a hard criterion for the optimum smoothing factor. This previously computational prohibitive evaluation of first-order reversal-curves solves the problem of over- and undersmoothing by increasing general readability and preventing information destruction. However, these measured FORC densities are not always straightforward to interpret, especially if the system is interaction dominated and the Preisach-like interpretation of the FORC density breaks down. To understand additional features arising from the interactions in the system, we purposely designed permalloy microstructures which violate the Mayergoyz criteria [7]. These artificial systems allow us to isolate the origin of an additional interaction peak in the FORC density. Modeling the system as a superposition of dipoles allows us to extract interaction strength parameters from this static simulation. Additionally, we suggest a linear relation between integrated interaction peak volume and interaction strength within the system. The presented correlation could be used to investigate the interaction behavior of samples as a function of structural parameters within a series of FORC measurements. This is an important step towards a more quantitative understanding of FORCs which violate the Mayergoyz criteria and away from a fingerprint interpretation.References: [1] J. Gräfe, Phys. Rev. B, 93 (2016) 014406 [2] F. Groß, Phys. Rev. B, 99 (2019) 064401 [3] C.-I. Dobrota, J. Appl. Phys., 113 (2013) 043928 [4] C. R. Pike, Phys. Rev. B, 71 (2005) 134407 [5] J. Gräfe, Rev. Sci. Instr., 85 (2014) 023901 [6] D. Cimpoesu, J. Appl. Phys., 125 (2019) 023906 [7] I. D. Mayergoyz, Phys. Rev. Lett., 56 (1986) 1518

MMM 2020

Modern FORC data analysis and interpretation approaches INVITED

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

The volatility in price and uncertainty in supply of the rare earth elements makes it highly desirable to find alternatives to rare-earth based magnets, in order to meet the increasing global demand for permanent magnets. One interesting candidate in this quest is the chemically-ordered L10 phase of Fe50Ni50 (tetrataenite) found in iron meteorites. While the laboratory synthesis of the ordered phase is very difficult due to the slow diffusion of atoms at the rather low order-disorder transition temperature, several attempts have been made to achieve samples with a high degree of chemical order. Nevertheless, synthesis of a fully ordered system remains challenging. Using first-principles-based density-functional theory calculations in combination with Monte Carlo (MC) simulations, we investigate the interplay between the degree of chemical order and the magnetic properties of L10 FeNi [1]. Our calculations demonstrate a strong effect of the magnetic order on the chemical order-disorder transition temperature, and a strong effect of the chemical order on the magnetic transition temperature, in agreement with previous studies. Furthermore, we investigate the dependence of the magneto-crystalline anisotropy on the chemical long range order. Our results indicate that the anisotropy does not decrease significantly as long as the deviations from perfect order are not too large. Moreover, we also find that a slight disorder in the alloy can in principle result in an even higher anisotropy than for the fully ordered structure. We further analyze the correlation between the magneto-crystalline anisotropy and the orbital magnetic moment anisotropy. This allows us to study the effect of the local chemical environment on both quantities, potentially enabling further optimization of the magneto-crystalline anisotropy with respect to both long-range order and stoichiometric composition.References: 1. A. Izardar, C. Ederer, Phys. Rev. Materials, Vol. 4, p.054418 (2020)

First-principles investigation of the impact of chemical order on the magneto-crystalline anisotropy in L10 FeNi (tetrataenite)

In the present investigation, the magnetic and electromagnetic character of cobalt substituted M-type barium hexaferrite with composition BaCoxFe12-xO19 (x = 0.0 to1.0 in the steps of 0.2) by co-precipitation method has been studied. After the appropriate heat treatments, the structural, magnetic and electromagnetic properties at X band ranging from 8-12 GHz are thoroughly examined. XRD confirmed the formation of M phase and revealed that with an increase in the content of cobalt ions the average crystallite size is found to be increased from 28 to 45 nm whereas the morphology examined from FESEM and TEM confirmed the formation of high quality and densely packed nano ferrites. From all the six samples the composition BaCo0.8Fe11.2O19 exhibit remarkable magnetic and electromagnetic properties and found to be one of the best compositions. For this particular composition very higher value of coercivity of the order of 3789 Oe along with good saturation magnetisation value of 65 emu/g is observed. Similar kinds of results are observed form electromagnetic properties of the same composition. Again the composition BaCo0.8Fe11.2O19 showed some excellent and sustainable values of complex permittivity and tangent losses i.e 11, 0.024 and 0.035. So based on the magnetic and electromagnetic performances, the composition BaCo0.8Fe11.2O19 may emerge as an ideal candidate for high-speed recording, permanent magnet applications, microwave absorption at high-frequency applications ranges from 8-12 GHz and many more.References: Robert C Puller, Progress in Material Science., 57, 1191-1334 (2012). K. Kumar and D. Pandey, Physical Review B., 96, 024102 (2017). H. Lou, S. Sun, X. Lu, C. He, Y. Pan, Q. Song, W. Xuejin, W. Jianjiang, J Mater Sci: Mater Electron., 27, 11231–11240 (2016). A. Baykal, I. A. Auwal, S. Guner, H. Sozeri,J. Magn. Magn Mater. 430, 29-35 (2017). S Kumar, M K Manglam, S Supriya and H Kumar et.al., J Magn. Magn. Mater., 473, 312-319 (2019).

Investigation of Magnetic and Electromagnetic Properties of Cobalt Substituted M-type Barium Hexaferrite in X-band.

The increasing demand of permanent magnets (PM) based technology going along with the limitation of global supply of rare-earths (RE) elements drives the development of RE-free PM [1]. Based on the material requirements regarding magnetic properties, costs and criticality, Mn-Al(-C) alloys have been pointed as candidates for PM applications. The hard magnetic properties originate from the metastable τ-phase which is usually formed during annealing from the parent high temperature ε-phase [2,3]. However, the annealing parameters have to be optimized in order to avoid the decomposition of the ferromagnetic phase into the nonmagnetic stable phases in the Mn-Al system. In this context, the Spark Plasma Sintering (SPS) can be a useful technique to optimize this process by combining uniaxial pressure and fast heating/cooling rates due to efficient Joule heating, caused by direct current pulses, and possible side effects related to electric field/current [4]. In this study, we investigate the transformation from ε- to τ-Mn54Al44C2 using the SPS and compared the results with conventional annealing. The ε- to τ-phase transformation has been done by SPS at different temperatures (400, 450, 500 and 550°C) and different times (5 and 15 min). A pure τ-MnAlC is obtained at 500°C/5min (Figure 1 (a)). Below this temperature there is still presence of ε-MnAlC and above we observe the formation of undesired β-phase. On the other hand, conventional heat treatment shows a full transformation at 500°C only after 30 min. Magnetic properties are dependent on the phase formation (Figure 1 (b)), but similar coercivity and saturation magnetization are obtained for the pure τ-MnAlC formed either by SPS or by conventional annealing. However, the SPS method allows to significantly shorter the time necessary to complete the transformation and limits the grain growth.References: [1] K.P. Skokov, O. Gutfleisch, Scripta Mater., 154 289 (2018) [2] V. Øygarden et al., J. Alloys Compd. 779 776 (2019) [3] H. Jian et al., J. Alloys Compd. 622 524 (2015) [4] O. Guillon et al., Adv. Eng. Mater., 16 830 (2014)

Formation and Magnetic Properties of τ-MnAlC Synthesized by Spark Plasma Sintering Process

Hard magnetic ferrites have broad applications ranging from permanent magnets and data storage media to high-frequency devices. The only known ferrite material exhibiting giant coercivity over 20 kOe at room temperatures is epsilon-iron oxide (ε-Fe2O3). In addition, it displays sub-THz natural ferromagnetic resonance (NFMR) frequency of 182 GHz. The Rh-doping of the material leads to an increase in both the NFMR up to 209 GHz and the coercivity up to 27 kOe [1]. However, since ε-Fe2O3 is a metastable polymorph and its production as a pure phase is quite complex, it still has not been applied in industry. Recently we have reported [2] an effective method for production of single-domain M-type hexaferrite particles with composition of Sr0.67Ca0.33Fe8Al4O19, which demonstrated coercivity of 21.3 kOe and saturation magnetization of 15 emu/g, which is close to ε-Fe2O3. The proposed preparation technique is based on citrate-nitrate auto-combustion method; therefore, it is simple, economical, and readily scalable, and it can be efficiently integrated into modern ferrite technology. Herein, we show that further increase of Al substitution degree leads to significant improvement of coercivity (up to 36 kOe) and NFMR frequency (up to 250 GHz), which are record-high values for ferrites to date [3]. Furthermore, we discuss temperature dependence of the magnetic and microwave properties, crystal and magnetic structures of the ultra-hard magnetic hexaferrites Sr1−x/12Cax/12Fe12−xAlxO19 (x = 3 – 5.5) in a range of 4.2 – 700 K. Temperature dependencies of both NFMR and coercivity have a maximum shifted to low temperatures with increase of aluminium content. For x = 5.5 the compound coercivity is raised from 36 kOe at 300 K up to 41 kOe at 180 K. Furthermore, we developed a technique for preparation of dense ceramics with single-domain grains and studied their room temperature magnetic properties and NFMR. The obtained ceramic materials possess coercivity higher than 18 kOe at specific density of 67 - 95%. NFMR frequency of the ceramics is 200 GHz, which is 20% blue-shifted compared to that of a powder sample. The ferrite ceramics with a coercivity of more than 10 kOe and sub-terahertz absorption were obtained for the first time. The work was supported by RFBR grant No. 20-02-00887.References: [1] A. Namai, et al, Nature Communications, Vol. 3, p. 1035, (2012). [2] L.A. Trusov, E.A. Gorbachev, et al, Chemical Communications, Vol. 54, p. 479-482 (2018). [3] E.A. Gorbachev, L.A. Trusov, et al, Materials Today, Vol. 32, p. 13-18 (2020).

Novel ferrite materials possessing record magnetic hardness

There exists a wide array of uses for ferromagnetic materials with easy-axis magnetic anisotropy, including motors, magnetic imaging devices, and acoustic devices. As most of the highest quality permanent magnets are financially and environmentally costly, the search for alternative magnetic materials is ongoing and paramount. Magnetic elements are rare, and the best way to predict novel magnetic materials is to constrain a search to analyzing the magnetic properties of compounds containing iron, cobalt, and manganese. However, while many databases exist for the purposes of analyzing structural properties of compounds, any such database of magnetic materials that exists is either outdated or incomplete. The magnetic properties of 10,760 compounds containing the element cobalt are being gathered through a literature search, with the goal to eventually complete the entire list, as well as those of iron and manganese compounds. As of now, a total of 1,282 ferromagnetic compounds have been found and catalogued. Structure types, lattice parameters, cobalt percentage, and lattice angles of each compound were also collected; the shortest cobalt-cobalt bond lengths within the crystal lattice were calculated; and data trends were analyzed to predict novel ferromagnetic and anisotropic compounds. From this data, a previously unstudied member of the Cu2MnAl family was confirmed to be ferromagnetic with a Curie temperature above room temperature. Currently, compounds in the MgZn2, La6Co11Ga3, and Mg3Cd families are being studied to check for ferromagnetism and uniaxial anisotropy. The research was supported by the Critical Materials Institute, an Energy Innovation Hub funded by the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, Advanced Manufacturing Office.

Novel Database Driven Method for Discovering New Co-based Ferromagnets INVITED

We report large field-like torques with non-negligible damping-like torques in sputtered, amorphous Ru2Sn3 thin films. We confirm the amorphous structure of the films with high resolution tunneling electron microscopy and the 2:3 composition with Rutherford backscattering techniques. Through the second harmonic Hall measurement we can extract and characterize the damping-like (DL) and field-like (FL) SOTs originating in the Ru2Sn3 films. We find room temperature a DL torque efficiency of 0.14 ± 0.008 and 0.07 ± 0.012 and a FL torque efficiency of -0.03 ± 0.006 and -0.20 ± 0.009 for 4 and 10 nm Ru2Sn3 films respectively. By analyzing the resistivity dependence of the spin torque efficiencies, we extracted the contributions from the intrinsic and extrinsic spin Hall effects. The FL torques show dominant contributions from the intrinsic spin Hall effect with intrinsic spin conductivity up to -240 ± 19 (Ωcm)-1 while the DL torques show dominate contributions from the extrinsic spin hall effects with sum of the skew scattering and side jump up to -175 ± 19 μΩcm. We performed macro-spin calculations of the LLGS equation to simulate switching a perpendicular magnetic layer including both the DL and FL torques generated from our Ru2Sn3 SOT channel. We find the inclusion of FL toques three times greater than the DL can reduce the critical current required for switching and the switching time by almost 50% compared to the DL torque only case.

Large field like torque in amorphous Ru2Sn3 originated from intrinsic spin Hall effect

Spin-orbit coupling (SOC) and symmetry breaking, which may be due to the interface between a thin film of a ferromagnet and a heavy metals aid to the development of Dzyaloshinskii-Moriya interaction (DMI) 1,2, favoring the formation of a chiral arrangement of spin configurations. Electrical detection and manipulation are the key requirements for any potential exploitation of these materials and that demands proper understanding of the transport behavior of charge carriers in these materials. Different feature such as topological Hall effect3,4, narrow band noise5 unusual magneto resistance6 in electronic transport measurements are observed owing to interactions between conduction electrons and different magnetic states and their dynamics, revealing intriguing underlying physics. In this work, we have performed electronic transport (Hall, magnetoresistance, noise fluctuation spectroscopy) measurements for CoFe/Pt-based thin film sample. A characteristic peak in Hall resistance is reproducibly observed during up and down sweep of the magnetic field as shown in Fig.1. Temperature dependent Hall effect measurements reveal that such peak shifts towards higher value with decreasing temperature as shown in the inset of Fig.1. The dynamics of charge carriers as measured using noise fluctuation spectroscopy technique at varying field as shown in Fig.2 shows systematic and reproducible variations across Hpeak. Particularly, electronic fluctuations are found to increase at around these fields. The results demonstrate an interesting correlation between the interface induced magnetic states and the carrier dynamics.References: 1 I. Dzyaloshinsky, J. Phys. Chem. Solids 4, 241 (1958). 2 T. Moriya, Phys. Rev. 120, 91 (1960). 3 A. Neubauer, et al., Phys. Rev. Lett. 102, (2009). 4 D. Liang, et al., Nat. Commun. 6, 8217 (2015). 5 T. Sato, et al., Phys. Rev. B 100, (2019). 6 K. Meng, et al., Sci. Rep. 6, 20522 (2016).

Unusual Electronic Transport Properties of Sputter-deposited Co25Fe75 /Pt Based Heterostructured Thin Film Sample

We measured the Hall effect (HE) in a ferromagnetic nanomagnet with a strong perpendicular magnetic anisotropy (PMA), in which the local magnetic moments are very stable and well- aligned along the easy axis of the nanomagnet. The adopted mechanisms of HE predict linear plus a constant dependence on the external field originating from the ordinary and anomalous Hall effects, respectively. Our measurement revealed an extra non- linear contribution indicating an additional contribution to HE, which was suggested to be the Inverse Spin Hall effect (ISHE). The ISHE describes the fact that an electrical current is created perpendicularly to the flow of the spin- polarized current. The ISHE requires existence of the spin-polarized electrons. In a ferromagnetic metal the electron gas is spin- polarized even in equilibrium and any electrical current in a ferromagnetic metal is spin- polarized. As a result, any electrical current in a ferromagnetic metal must always experience the ISHE and there must be a flow of the Hall current perpendicularly to the bias current. There are several methods to change the number of spin- polarized electron in a ferromagnetic metal and therefore the magnitude of the ISHE. E.g. the spin polarization can arise due to the influence of an external magnetic field, the mechanism considered by Landau and Lifshitz a long time ago[1]. The Hall angle αHE can be presented as αHE = αOHE H+ αAHE + αISHE PS(H) where the non-linear dependence of spin polarization PS on magnetic field is calculated as[2] PS(H)=(PS,0+H/HS)/(1+H/HS) where PS,0 is the spin polarization at H=0. HS is the scaling magnetic field. Figure 1 shows that the fit of the experimental data with the above relation is excellent proving the importance of the ISHE contribution to the HE in a ferromagnetic metal.References: [1] L. D. Landau and E. M. Lifshitz, Phys. Z. Sowjetunion. Vol. 8, p.153 (1935). [2] V. Zayets, J. Magn. Magn. Mater. Vol. 356, p. 52 (2014).

Study of magnetic field dependence of Hall effect in FeB and FeCoB nanomagnets. An evidence of contribution of Inverse Spin Hall effect

A spin-thermoelectric generator is composed of a thin paramagnetic metal (PM) layer, ferrimagnetic insulator (FMI) and PM/FMI bilayer interface. To raise the spin thermoelectric voltage VSTE, studies for improving the characteristics of each part have been done.1-3 We took notice of the bismuth-substitution for yttrium to increase the spin pumping at the PM/FMI interface,2,4 and tested the Bi-substituted YIG films grown by liquid phase epitaxy (LPE). LPE Bi-substituted YIG films exhibit a large growth-induced magnetic anisotropy perpendicular to the film surface,5 and the in-plane M-H properties vary due to this anisotropy. Figure 1 shows the normalized M-H and VSTE-H curves concerning Y3-xBixFe5O12 films. It is confirmed that the VSTE-H curve agrees well with the M-H curve indicating VSTE strongly depends on the magnetic properties of FMI’s. Figure 2 shows the dependence of the spin Seebeck coefficient SSSE on the Bi-concentration x. SSSE increases very clearly with increasing x, and the SSSE value for x=1.3 is about 1.5 times that of x=0 in our measurements. It has been suggested that the mixing of the 6p orbitals of Bi ions with the O 2p orbitals increases the effective spin-orbit coupling of Fe3+ ions.6 We presume that this physical situation increases the damping constant αBi:YIG and, as a result, the spin mixing conductance gr at the PM/FMI interface becomes large. We have obtained the high VSTE value of 80μV (SSSE=3.2μV/K) with a generator comprising the Y2.35Bi0.65Fe5O12 film in the condition of ld=5mm, tPt=4nm and ΔT=25K. To obtain higher VSTE values, the issue of a heat-flow in the STE generator is important from its structural viewpoint. [The ref. paper #3 (3M. Imamura et al., Electr Eng Japan, Vol. 208, No. 3-4 (Wiley Online Library 2019)) can be referred by putting the paper title “Spin-thermoelectric voltage in longitudinal SSE elements incorporating LPE YIG films and polycrystalline YIG slabs with an ultrathin Pt layer” into Google’s search window.]References: 1K. Uchida, H. Adachi and T. Kikkawa, Proc. IEEE, Vol. 104, p.1946 (2016) 2M. Ishida, JJAP, Vol. 87, p.11 (2018) in Japanese 3M. Imamura, H. Asada and D. Tashima, Electr Eng Japan, Vol. 208, No. 3-4, p.10 (Wiley Online 2019) 4H. Asada, A. Kuwahara and N. Sakata, JAP, Vol. 117, p.17C724 (2015) 5P. Hansen, K. Witter and W. Tolksdorf, Phys. Rev. B, Vol. 27, p.6608 (1983) 6P. Hansen and J. P. Krumme, Thin Solid Films, Vol. 114, p.69 (1984)

Enhancements of the Spin Seebeck Effect owing to the Bismuth-substitution in Thermoelectric Generators Comprising an LPE Bi-substituted YIG Film

Current-induced spin-orbit torque (SOT) originating from the spin-Hall effect (SHE) in heavy metal/ferromagnet (HM/FM) systems has attracted attention due to their potential application in the efficient manipulation of magnetization of nano magnets in SOT-MRAM [1], skyrmion and domain wall devices. For the application to a large-scale integration, the efficient SOT operation (high spin Hall angle |θSH|) in low resistivity (ρxx) HM is necessary [2-4]. Due to the extensive efforts, the |θSH| becomes larger day by day, however, almost all HMs with large magnitude of |θSH| have a very high ρxx. The magnitude of |θSH| for both intrinsic and extrinsic (side jump mechanism) terms is proportional to the magnitude of ρxx value (|θSH|～σSH ρxx) [5, 6], where σSH is spin Hall conductivity. Therefore, increase in the magnitude of σSH would be important from the application point of view. Recently, we observed large magnitude of σSH and enhancement of perpendicular magnetic anisotropy in MgO/CoFeB/(W/Hf)-multilayer system compared to MgO/CoFeB/β-W system [4]. In this paper, we prepared MgO/CoFeB/(W/Hf)-multilayer systems with various W/Hf thickness ratios and investigated the W/Hf thickness ratio dependence of θSH, σSH, ρxx, and (100) texture of MgO tunnel barrier in the MgO/CoFeB/(W/Hf)-multilayer systems. These systems were patterned into the microscale Hall bar by photolithography and Ar ion milling, and annealed at 573 K. SHE in MgO/CoFeB/(W/Hf)-multilayer systems by means of spin Hall magnetoresistance (SMR) was studied. The analysis based on the drift diffusion model reveals that the magnitude of σSH monotonically increases with increasing W/Hf thickness ratio (Fig. 1). Spin diffusion length (λ) for (W/Hf)-multilayer is shorter than the estimated value of β-W (Fig. 1), which would be related to the increase in the interfacial scattering of multilayer system. In this presentation, we will report the details of SMR, θSH, λ and the film structure including the (100) texture of MgO tunnel barrier. This work was supported by the JST OPERA (JPMJOP1611) and JSPS KAKENHI (19H00844).References: [1] H. Honjo et al., IEDM Tech. Dig. 28.5 (2019). [2] Y. Saito et al., Appl. Phys. Exp. 12, 053008 (2019). [3] Y. Saito et al., AIP Advances, 9, 125312 (2019). [4] Y. Saito et al., Appl. Phys. Lett. 116, 132401/1-5 (2020). [5] C. Zhang et al., Appl. Phys. Lett. 109, 192405 (2016). [6] L. Wang et al., Phys. Rev. Lett. 116, 196602 (2016).

Flat and highly (100) texture of MgO tunnel barrier and W/Hf thickness ratio dependence in MgO/CoFeB/(W/Hf)-multilayer large spin Hall effect electrode system

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First-principles investigation of the impact of chemical order on the magneto-crystalline anisotropy in L10 FeNi (tetrataenite)

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First-principles investigation of the impact of chemical order on the magneto-crystalline anisotropy in L10 FeNi (tetrataenite)

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