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Complex dielectric and magnetic properties of micro- and nano-size hexagonal ferrites have been studied. Two different measurement techniques as shown in Fig. 1 have been applied to characterize the samples in the broad frequency range from 1.7 GHz to 120 GHz. It was observed that the constitutive material properties, namely permittivity and permeability, as well as the ferromagnetic resonance frequency of the samples vary with the change in particle dimensions. Based on the results of these measurements, a model for calculating the ferromagnetic resonance frequency of ferrite powders has been derived, which takes into account the size and shape of the particles in the sample. Since the properties have been found to be size dependent, it is important that the measurement set-up is accurate enough to detect these differences. In the past, the powder samples have been diluted with conductive materials or epoxy to fabricate a solid sample for measurements. The procedure followed in this study does not use any such additive. Therefore, the properties of the samples can be determined precisely. The results presented in Fig. 2 reveal that the ferromagnetic resonance frequency of the ferrite samples varies with the particle size. Therefore, the material can be tuned to resonate at different frequencies by changing the size of the particles. The resonance observed in the case of nanoparticles is much sharper than that observed for bulk samples or samples containing micro-sized particles. Absolutely no resonance was observed in case of samples that did not contain the proper phase of barium hexaferrite. The techniques developed in this study can be used for non-destructive testing to check if the desired phase has been achieved or not. Accurate characterization would allow scientists to utilize nanomaterials to their full potential and achieve high performance in diverse applications.

MMM 2020

Study of Ferromagnetic Resonance of Micro and Nano Size Barium Ferrite Powders

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The magnetodynamic properties of a square thin-film micromagnet (2μm×2μm×16nm) with a flux-closure magnetic ground state were investigated by micromagnetic simulations. The system was excited with an applied magnetic field, displacing the vortex core sufficiently far from its equilibrium position to result in a nonlinear relaxation upon removal of the field. We focus on the edge defects that are created in the process of the vortex core displacement, and carry a half-integer winding number. The edge topological defects are seen to perform quasi-periodic exchange explosions and a resulting emission of short-wavelength spin waves upon travelling back to the equilibrium position. The exchange explosions of the edge topological defects are investigated and explained in terms of vortex/antivortex creation and the formation of a Bloch point. This finding could prove useful to the development of nanoscale devices for periodic generation of high-frequency microwave radiation.References: 1. S. D. Slöetjes, E. Folven, and J. K. Grepstad, Physical Review B Vol. 101, p. 014450 (2020) 2. R. Hertel, and C. M. Schneider, Physical Review Letters Vol. 97, p. 177202 (2006) 3. M. Noske et al., Physical Review B Vol. 91, p. 014414 (2015) 4. S. D. Slöetjes et al., Applied Physics Letters Vol. 112, p. 042401 (2018)

Exchange Explosions of Topological Edge Defects in a Square Micromagnet

Recently, noncollinear antiferromagnets (AFMs) have become one of the most fascinating classes among AFMs, because they exhibit various peculiar magnetotransport properties include the anomalous Hall effect (AHE).[1] The theoretical study shows that the noncollinear AFM Néel vector can be manipulated by spin current with a realistic current density of 107 A/cm2[2]. The antiperovskite manganese nitride Mn3GaN (MGN) is a good platform to investigate the electrical current manipulation of noncollinear AFMs. In MGN, the Mn atoms form a kagome lattice in the (111) plane. The Neel temperature is reported to be above 380 K[3], which are relatively high for this class of materials. In this presentation, we show the spin-torque switching of noncollinear AFM MGN/Pt bilayers at room temperature[4] as well as AHE. MGN (001) films were prepared on MgO (001) substrates by reactive magnetron sputtering. The AHE versus magnetic field curve for MGN films are shown in Fig. 1. The AHE loop is observed with the same coercive field as the out of plane magnetization curves for MGN films. Therefore, the AHE loops shows the electrical detection of the magnetization for MGN films. The change in the Hall resistivity as a function of current density for MGN(20 nm)/Pt(3 nm) bilayers is shown in Fig. 2. Hall resistivity changes sharply and a clear hysteresis loop is observed at 300 K without an external magnetic field. The change of Hall resistivity is the same as AHE loop shown in Fig. 1, indicating the electrical write–read operation of noncollinear AFM Néel vector. The critical current density is estimated to be 3.6×106 A/cm2, which is one to two orders of magnitude smaller than that for typical FM/HM bilayers[5] and the threshold current for collinear AFMs NiO/Pt spin-torque switching.[6] These results open the pathway to the efficient control of the noncollinear AFM order.References: [1] S. Nakatsuji, N. Kiyohara, and T.Higo, Nature 527, 212-215(2015). [2] Y. Yamane, O. Gomonay, and J. Sinova, Phys. Rev. B 100, 054415 (2019). [3] W. J. Feng, D. Li, Y. F. Dend, and Q. Zhang et al., J. Mater. Sci. 45, 2770 (2010). [4] T. Hajiri, S. Ishino, and K. Matsuura et al., Appl. Phys. Lett. 115, 052403 (2019). [5] L. Liu, O. J. Lee, and T. J. Gudmundsen et al., Phys. Rev. Lett. 109, 096602 (2012). [6] X. Z. Chen, R. Zarzuela, and J. Zhang et al., Phys. Rev. Lett. 120, 207204 (2018).

Electrical switching of Hall resistance in noncollinear antiferromagnetic antiperovskite nitrides

Antiferromagnets (AFMs) are promising spintronic materials compared to ferromagnets, since they potentially enable faster operation, enhanced stability with respect to interfering magnetic fields and higher bit packing density due to the absence of stray fields [1]. However, the use of AFMs in applications requires efficient electrical reading and writing of information. While current-induced switching in NiO/Pt thin film systems has been shown, with various mechanisms proposed [2-4], key information such as the absolute torque strength is missing. Studying MgO//CoO(001)/Pt entails a number of advantages: due to the compressive strain by the substrate, a fourfold in-plane magnetic anisotropy of the CoO layer with two easy axes in the (001) plane is favored and the spin flop field is accessible [5]. Such anisotropy is ideal for applications where the orientation of the Néel order n is read by spin Hall magnetoresistance (SMR) [6,7]. To study current-induced switching, we used 8-arms Hall stars devices with the pulsing arms oriented along the [110] and [-110] easy axes directions (Fig. 1a). Initially n is aligned along [110]. When current pulses are applied along the contacts 3-2 (initial state n ‖ jpulse), the transverse resistance drops after the first pulse, indicating a current-induced 90° n rotation (Fig. 1b). Performing a MR scan with field along 4-1 afterwards (Fig. 1c) yields a field-induced spin flop transition of n back to the initial state (Fig. 1d). By applying current pulses and magnetic fields, we can quantify the current field equivalence of the current-induced torques on the reorientation of n in the CoO, showing that, for the switching of AFMS, currents are much more efficient than magnetic fields.References: [1] V. Baltz et al., Rev. Mod. Phys., 90, 015005 (2018). [2] X. Z. Chen et al., PRL, 120, 207204 (2018). [3] L. Baldrati et al., PRL, 123, 177201 (2019). [4] P. Zhang et al., PRL 123, 247206 (2019). [5] L. Baldrati et al., ArXiv:2003.05923 (2020). [6] H. Nakayama et al., PRL, 110, 206601 (2013). [7] L. Baldrati et al., PRB, 98, 024422 (2018).

Quantifying current-induced torques leading to Néel vector switching in CoO/Pt bilayers

We predict staggered-field-stabilized collinear, spiral, cone, skrymion crystal (SkX), and square crystal (SC) of vortices and antivortices phases in antiferromagnets (see figure). In SkX and SC phases, magnons experience emergent gauge fields, which leads to magnon-mediated topological spin responses. The underlying physics can be qualitatively understood by considering magnon Landau levels induced by the fictitious magnetic flux. In the long wavelength limit, the unevenly spaced energy bands can be described by the relativistic Klein-Gordon equation. As we propose, these Landau levels can be also realized in antiferromagnetic magnonic topological insulator where the fictitious flux is induced by inhomogeneous DMI. A smoking gun experiment observing the Hofstadter's butterfly of magnons in AFM could establish the connection between emergent electromagnetism and topological properties of antiferromagnetic magnons.

Magnon Landau Levels and Topological Spin Responses in Antiferromagnets

We present a spin-transfer torque oscillator (STO) based on composite (hard-soft) synthetic antiferromagnets (CSAFs) with perpendicular uniaxial magnetic anisotropy energy density. The CSAF STO can operate with and without an applied field and generates strong oscillations in a broad frequency range from tens to hundreds GHz with precessions mostly generated by the soft layer. The STO is comprises of a cylindrical cross – section stack of diameter D (Fig.1), including a reference layer and a free layer composed of SAF layers (FLsoft and FLhard). FLhard is much harder than FLsoft and the sub-layers are exchange coupled with surface exchange energy density JAF. The results are obtained via micromagnetic simulations with the FastMag1 simulator. Fig.1 shows the precession frequency of the FLsoft as a function of the applied current density J for weak and strong JAF. The precession frequency of FLsoft is proportional to JAF and J and it can be tuned in a broad range of frequencies up to 200 GHz. Fig.2 shows the time dependence of the magnetization components for FLsoft and FLhard. Both z-components are in the same direction while the in-plane components are opposite. The precession direction sense is clockwise for both layers, but the precession is dominated by the soft layer, i.e. the device generates a strong oscillating magnetic field. The operation mechanism is based on the exchange field due to the AF coupling, which is similar to AF STO2. However, CSAF STO offers a great flexibility in tuning the parameters and practicality in the material choice. It can be used to generate electric signal or for microwave assisted magnetic recording, This work was supported by the Quantum-Materials for Energy Efficient Neuromorphic-Computing(Q-MEEN-C), an Energy Frontier Research Center funded by the U.S. DOE, under Award No. DE-SC0019273.References: [1] R. Chang, S. Li, M. V. Lubarda, B. Livshitz, and V. Lomakin, J Appl Phys 109 (3), 07D358 (2011). [2] V. Puliafito, R. Khymyn, M. Carpentieri, B. Azzerboni,1 V. Tiberkevich, A. Slavin, and G. Finocchio, PRB 99, 024405 (2019).

Spin-transfer torque oscillator based on composite synthetic antiferromagnets

Bayesian optimization (BO) is a well-developed machine learning algorithm for black box optimization. In BO a predictive model, here a Gaussian process regression, is implemented to predict the black box function and the uncertainty of the predictive model is evaluated as predicted variance, then an acquisition function defined by the surrogate predictive model decides where to sample next. In this study we applied this technique to known ferroic materials such as ferromagnetic (Fe100−y Gay)1−xBx (x=0–21 & y=9–17) and ferromagnetic (Co0.5Fe0.5)1-xCx (x=0–16) to provide proof of concept of how BO can be used to optimize properties such as magnetostriction and ferromagnetic resonance (FMR) linewidth with fewer samples required than traditional experimental approaches.1,2 Additionally, we applied this technique to optimize thin films of ferromagnetic (Fe100−y Gay)1−xCx (x=1–26 and y=2–18) and ferroelectric (HfO2)1-xYx (x=0–15). For each of these systems, we applied BO through building a predictive model with the GPy library (https://sheffieldml.github.io/GPy/) and evaluating the next experiment to sample with the GPyOpt library (https://github.com/SheffieldML/GPyOpt), both in python.References: [1] J. Lou et al. Appl. Phys. Lett. 91, 182504 (2007). [2] J. Wang et al. Phys. Rev. Applied 12, 034011 (2019)

Application of Bayesian Optimization to Ferroic Materials Development

The BaTiO3 (BTO)/CoFe multiferroic material interface is an example of an interface which displays voltage-controlled magnetic anisotropy (VCMA), a valuable property in the operation of multiferroic tunnel junctions in an STT-MRAM device. Through first principles calculations, it is possible to predict trends in film magnetic anisotropy energy (MAE) and enumerate the individual physical mechanisms contributing to ferroelectric control of MAE in the CoFe film. For CoFe of up to 2 atomic layers on BTO, MAE can be modulated by ferroelectric switching through Fe-O orbital interations in BaO-terminated interfaces, and Ti-Fe orbital interactions in TiO2-terminated interfaces. A difference in interface termination produces a difference of MAE in CoFe films of up to 9 atomic layers. The inclusion of a 5d transition metal capping layer (Hf, Ta, W, Re, Os, Ir, Pt, or Au) on top of the CoFe layer exerts a significant effect on both MAE and the ferroelectric switching effect, in particular inducing a discernible ferroelectric switching control even in thicker CoFe films. This points to the additional, if counterintuitive, contribution of CoFe 3d top interface (or surface) states and their interactions with partially filled 5d orbitals of the capping layer atoms.References: A. P. Chen and Y. P. Feng, ACS Appl. Mater. Interfaces., Vol. 12, p25383-25389 (2020) A. P. Chen, W. Lin, J.-S. Chen, and Y. P. Feng, in preparation.

Free Layer Magnetic Anisotropy Control in the Multiferroic Tunnel Junction: a Computational Study on Materials Interfaces

The coupling between ferroelectric and magnetic orders is an enduring experimental challenge with fundamental importance to elucidate the nature of magnetoelectric (ME) effects in multiferroic materials. In this work, we have studied the response of magnetization to ferroelectric switching in thin-film hexagonal YbFeO3, an improper multiferroic which is a fruitful platform for investigating the ME coupling in single-phase materials. The bulk ME decoupling and potential domain-wall ME coupling were revealed using X-ray magnetic circular dichroism (XMCD) measurements with in-situ ferroelectric polarization switching. Our Landau theory analysis suggests that the bulk ME-coupled ferroelectric switching path has an higher energy barrier than that of the ME-decoupled path; this extra barrier energy is also too high to reduce by the magneto-static energy in the process of breaking single magnetic domains into multi-domains. In addition, the reduction of magnetization around the ferroelectric domain walls predicted by the Landau theory, may induce the domain-wall ME coupling in which he magnetization is correlated with the density of ferroelectric domain walls. These results provide important experimental evidences and theoretical insights to the rich possibilities of ME couplings in hexagonal ferrites.References: 1] J.F. Scott, Room-temperature multiferroic magnetoelectrics, NPG Asia Materials, 5 (2013) e72-e72. [2] S. Fusil, V. Garcia, A. Barthelemy, M. Bibes, Magnetoelectric Devices for Spintronics, Annual Review of Materials Research, 44 (2014) 91-116. [3] P. Mandal, M.J. Pitcher, J. Alaria, H. Niu, P. Borisov, P. Stamenov, J.B. Claridge, M.J. Rosseinsky, Designing switchable polarization and magnetization at room temperature in an oxide, Nature, 525 (2015) 363-366. [4] N.A. Spaldin, R. Ramesh, Advances in magnetoelectric multiferroics, Nat. Mater., 18 (2019) 203-212. [5] S.-W. Cheong, Topological domains/domain walls and broken symmetries in multiferroics, National Science Review, 6 (2015) 624-626. [6] S. Dong, J.M. Liu, S.W. Cheong, Z.F. Ren, Multiferroic materials and magnetoelectric physics: symmetry, entanglement, excitation, and topology, Adv Phys, 64 (2015) 519-626. [7] M. Fiebig, T. Lottermoser, D. Meier, M. Trassin, The evolution of multiferroics, Nature Reviews Materials, 1 (2016). [8] H. Das, A.L. Wysocki, Y. Geng, W. Wu, C.J. Fennie, Bulk magnetoelectricity in the hexagonal manganites and ferrites, Nature communications, 5 (2014) 2998. [9] S. Artyukhin, K.T. Delaney, N.A. Spaldin, M. Mostovoy, Landau theory of topological defects in multiferroic hexagonal manganites, Nat. Mater., 13 (2014) 42-49. [10] W. Wang, J. Zhao, W. Wang, Z. Gai, N. Balke, M. Chi, H.N. Lee, W. Tian, L. Zhu, X. Cheng, D.J. Keavney, J. Yi, T.Z. Ward, P.C. Snijders, H.M. Christen, W. Wu, J. Shen, X. Xu, Room-temperature multiferroic hexagonal LuFeO3 films, Phys Rev Lett, 110 (2013) 237601. [11] X. Xu, W. Wang, Multiferroic hexagonal ferrites (h-RFeO3, R = Y, Dy-Lu): a brief experimental review, Modern Physics Letters B, 28 (2014) 1430008. [12] S. Cao, K. Sinha, X. Zhang, X. Zhang, X. Wang, Y. Yin, A.T. N'Diaye, J. Wang, D.J. Keavney, T.R. Paudel, Y. Liu, X. Cheng, E.Y. Tsymbal, P.A. Dowben, X. Xu, Electronic structure and direct observation of ferrimagnetism in multiferroic hexagonal YbFeO3, Physical Review B, 95 (2017). [13] W. Wang, J.A. Mundy, C.M. Brooks, J.A. Moyer, M.E. Holtz, D.A. Muller, D.G. Schlom, W. Wu, Visualizing weak ferromagnetic domains in multiferroic hexagonal ferrite thin film, Physical Review B, 95 (2017). [14] K. Sinha, H.H. Wang, X. Wang, L.Y. Zhou, Y.W. Yin, W.B. Wang, X.M. Cheng, D.J. Keavney, H.B. Cao, Y.H. Liu, X.F. Wu, X.S. Xu, Tuning the Neel Temperature of Hexagonal Ferrites by Structural Distortion, Phys Rev Lett, 121 (2018). [15] K. Du, B. Gao, Y.Z. Wang, X.H. Xu, J. Kim, R.W. Hu, F.T. Huang, S.W. Cheong, Vortex ferroelectric domains, large-loop weak ferromagnetic domains, and their decoupling in hexagonal (Lu, Sc)FeO3, Npj Quantum Mater, 3 (2018). [16] Y. Geng, N. Lee, Y.J. Choi, S.W. Cheong, W. Wu, Collective magnetism at multiferroic vortex domain walls, Nano Lett, 12 (2012) 6055-6059. [17] J.A. Moyer, R. Misra, J.A. Mundy, C.M. Brooks, J.T. Heron, D.A. Muller, D.G. Schlom, P. Schiffer, Intrinsic magnetic properties of hexagonal LuFeO3 and the effects of nonstoichiometry, APL Materials, 2 (2014) 012106. [18] M.E. Holtz, K. Shayovalov, J.A. Mundy, C.S. Chang, Z.W. Yan, E. Bourret, D.A. Muller, D. Meier, A. Cano, Topological Defects in Hexagonal Manganites: Inner Structure and Emergent Electrostatics, Nano Lett, 17 (2017) 5883-5890. [19] T. Matsumoto, R. Ishikawa, T. Tohei, H. Kimura, Q. Yao, H. Zhao, X. Wang, D. Chen, Z. Cheng, N. Shibata, Y. Ikuhara, Multivariate statistical characterization of charged and uncharged domain walls in multiferroic hexagonal YMnO3 single crystal visualized by a spherical aberration-corrected STEM, Nano Lett, 13 (2013) 4594-4601. [20] Y.K. Jeong, J.H. Lee, S.J. Ahn, S.W. Song, H.M. Jang, H. Choi, J.F. Scott, Structurally tailored hexagonal ferroelectricity and multiferroism in epitaxial YbFeO3 thin-film heterostructures, J Am Chem Soc, 134 (2012) 1450-1453. [21] Y.N. Geng, H. Das, A.L. Wysocki, X.Y. Wang, S.W. Cheong, M. Mostovoy, C.J. Fennie, W.D. Wu, Direct visualization of magnetoelectric domains, Nature materials, 13 (2014) 163-167.

Magnetoelectric coupling and decoupling in multiferroic hexagonal YbFeO3 thin films

Being studied mostly in nonpolar chiral structures, skyrmions in polar crystals are of great interest owing to their interplay with electric polarization, giving rise to fascinating multiferroic properties. Recently, skyrmion lattices have been reported in lacunar spinel GaV4S8 [1], where a complex phase diagram comprising paramagnetic, ferromagnetic, skyrmion, and cycloidal states has been demonstrated, and the spin-driven excess polarization was assigned in each magnetic phase with a total value of ~100 μC/m2 [2]. The existence of multiple ferroelectric phases in GaV4S8 indicates an intricate interplay between charge, spin, and lattice degrees of freedom, making their theoretical description extremely important. In our studies, we present the microscopic theory of spin-driven electric polarization P in GaV4S8 and GaMo4S8 [3,4]. To this end, we extend the theory of superexchange for magnetic interactions to deal with the change of electric polarization depending on the relative direction of spins in each bond. Based on realistic Hubbard-type models derived for the magnetically active molecular orbitals formed in the V4 and Mo4 tetrahedra, we show that (i) although a skyrmion layer in these materials is mainly formed by the in-plane magnetic interactions, the spin-excess polarization perpendicular to the rhombohedral z axis is given by the interlayer electron transfer and originates from strongly competing isotropic and antisymmetric contributions; (ii) P arises from the stacking misalignment of such layers in the perpendicular direction, which is inherent to the lacunar spinel structure; (iii) while the interorbital Hund’s coupling is small, it is one of the key parameter responsible for P in lacunar spinels; (iv) an importnat aspect of multiferroicity in GaMo4S8, which can also potentially host skyrmionic states, is strong exchange anisotropy; and (v) the direction of rhombohedral distortions leads to opposite signs of P in GaV4S8 and GaMo4S8.References: [1] I. Kézsmárki, S. Bordács, P. Milde et. al, Nat. Mater., Vol. 14, 1116 (2015). [2] E. Ruff, S. Widmann, P. Lunkenheimer et. al, Sci. Adv., Vol. 10, e1500916 (2015). [3] S. A. Nikolaev and I. V. Solovyev, Phys. Rev. B, Vol. 99, 100401(R) (2019). [4] S. A. Nikolaev and I. V. Solovyev, Phys. Rev. B 102 014414 (2020).

Microscopic theory of spin driven electric polarization in lacunar spinels GaV4S8 and GaMo4S8

Magnetoelectric materials with exceptional properties emerging from the coupling between the magnetic and electric ferroic orders bring about functionalities that can be exploited in fields such as sensors, energy harvesters, MERAM, antenna, and biomedical 1,2. Multi-phase ME composites that are composed of a ferromagnetic/piezoelectric junction can be fabricated in versatile connectivity configurations with a wide choice of materials and microstructure 3,4. The extrinsic ME effect in these composites occurs due to the generation of magnetostriction in the ferromagnetic phase and its transfer via the interface to the piezoelectric one, which induces a voltage. Cobalt ferrite as a ferrimagnet and barium titanate as a piezoelectric are promising candidates for the preparation of nanostructured ME materials due to their outstanding magnetic and electric properties, respectively 5. We report synthesis, characterization, and optimization of CoFe2O4-BaTiO3 composite using commercial nanoparticle precursors. The dry ball milling followed by high-temperature annealing of pressed powder was used as a low cost and highly reproducible synthesis method. We have investigated the structural, electric, magnetic, and magnetoelectrical properties of CFO-BTO composites prepared and electrically poled with two different types of BTO nanoparticles: 50 nm (cubic) and 200 nm (tetragonal) in conjunction with CFO nanoparticles of about 30 nm. The transformation of non-piezoelectric cubic BTO to piezoelectric tetragonal one after sintering at temperatures higher than Curie point was confirmed utilizing XRD. The maximum obtained ME coefficient (3.7 mV/Oe.cm for 50 nm BTO) is higher than the reported values for core-shell structures 6. The hypothesis is that the smaller BTO nanoparticles can form shell-like structures around CFO nanoparticles and enhance the interface and resistivity of the samples. This enhancement results in a more efficient poling process and an improved ME coupling. The ME analysis has confirmed the dependence of the coupling coefficient on the size and fraction of BTO nanoparticles in the composite.References: 1. Cheng, Y., Peng, B. and Hu, Z., Physics Letters A vol. 382 3018–3025 (2018). 2. Spaldin, N. A., Cheong, S.-W. & Ramesh, R, Physics Today vol. 63 38–43 (2010). 3. Andrew, J. S., Starr, J. D. & Budi, M. A. K, Scripta Materialia vol. 74 38–43 (2014). 4. Ortega, N., Kumar, A., Scott, J. F. & Katiyar, R. S, Journal of Physics: Condensed Matter vol. 27 504002 (2015). 5. Baji, A., Mai, Y.-W., Yimnirun, R. & Unruan, S, RSC Adv. vol. 4 55217–55223 (2014). 6. Duong, G. V., Groessinger, R. & Turtelli, R. S, IEEE Transactions on Magnetics vol. 42 3611–3613 (2006).

Materials characterization and multiferroic properties optimization of magnetoelectric composites based on sintered cobalt ferrite/barium titanate nanoparticles

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Study of Ferromagnetic Resonance of Micro and Nano Size Barium Ferrite Powders

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