France



We present our recent realisation of a nanomagnetic Galton board&lt;sup&gt; &lt;/sup&gt;[1], a nanoscale recreation of the paradigmatic experiment in which balls travel through an array of pegs, designed by Sir Francis Galton to demonstrate the emergence of order from randomness. In our nanoscale experiment, balls are substituted by magnetic domain-walls, a honeycomb nanowire lattice recreates the peg array, and an externally applied magnetic field takes the role of gravity (Figure 1).&lt;br/&gt;Using high-resolution immersion Kerr microscopy, we image domain wall propagation through this nanoscale system a very large number of times (Figure 2), and demonstrate that complex domain wall dynamics can be employed to generate high-quality stochasticity suitable for computing applications. By varying the direction of the externally applied field, we were also able to demonstrate the continuous tuneability of the stochastic domain-wall decision process, a critical step to the realisation of functional computing systems.&lt;br/&gt;To conclude, we will discuss the technical advances that enabled this study, in which millions of domain-wall trajectories were imaged and analysed. These will be of great interest to those performing stochasticity studies in spintronics, as being able to acquire and deal with large datasets is an important experimental challenge in the field.&lt;br/&gt;The results demonstrated open promising paths in the design and development of spintronic devices in which the intrinsic stochasticity of domain-wall dynamics is exploited using new computing architectures.

**References:**

[1] Sanz-Hernández, Dédalo, et al. &quot;Tunable Stochasticity in an Artificial Spin Network&quot;, DOI: 10.1002/adma.2020081

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/9e8bc476a41cbcab0159a897cf862dd2.jpg)
Figure 1. Nanoscale magnetic Galton board formed by an elliptical domain-wall injection pad (top) and a bifurcating nanowire network.

![](https://assets.underline.io/uploads/markdown_image/1/image/705a04356594395b96ae40d6c0dfa320.jpg)
Figure 2. Oil-immersion longitudinal Kerr microscopy image of the board presented in Figure 1, after the injection of a domain-wall in the system. The trajectory followed by the wall is observed as a dark trace.

INTERMAG 2021

 Tuneable Stochastic Domain-Wall Trajectories in a Magnetic Galton Board

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We present our recent realisation of a nanomagnetic Galton board [1], a nanoscale recreation of the paradigmatic experiment in which balls travel through an array of pegs, designed by Sir Francis Galton to demonstrate the emergence of order from randomness. In our nanoscale experiment, balls are substituted by magnetic domain-walls, a honeycomb nanowire lattice recreates the peg array, and an externally applied magnetic field takes the role of gravity (Figure 1). Using high-resolution immersion Kerr microscopy, we image domain wall propagation through this nanoscale system a very large number of times (Figure 2), and demonstrate that complex domain wall dynamics can be employed to generate high-quality stochasticity suitable for computing applications. By varying the direction of the externally applied field, we were also able to demonstrate the continuous tuneability of the stochastic domain-wall decision process, a critical step to the realisation of functional computing systems. To conclude, we will discuss the technical advances that enabled this study, in which millions of domain-wall trajectories were imaged and analysed. These will be of great interest to those performing stochasticity studies in spintronics, as being able to acquire and deal with large datasets is an important experimental challenge in the field. The results demonstrated open promising paths in the design and development of spintronic devices in which the intrinsic stochasticity of domain-wall dynamics is exploited using new computing architectures.

**References:**

[1] Sanz-Hernández, Dédalo, et al. "Tunable Stochasticity in an Artificial Spin Network", DOI: 10.1002/adma.2020081

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/9e8bc476a41cbcab0159a897cf862dd2.jpg)
Figure 1. Nanoscale magnetic Galton board formed by an elliptical domain-wall injection pad (top) and a bifurcating nanowire network.

![](https://assets.underline.io/uploads/markdown_image/1/image/705a04356594395b96ae40d6c0dfa320.jpg)
Figure 2. Oil-immersion longitudinal Kerr microscopy image of the board presented in Figure 1, after the injection of a domain-wall in the system. The trajectory followed by the wall is observed as a dark trace.

technical paper

Among nanomaterials, metal nanowires (NWs), consisting of alternating layers of various compositions (layered NWs), are of particular interest. Such structures can be obtained by the method of matrix synthesis - filling of nanosized pores in a special matrix. Layered NWs can have various applications, for example, as optically active surfaces (SERS). Another practically important property is giant magnetoresistance (GMR). According to preliminary estimates, NWs consisting of alternating layers of various magnetic metals can also be used to generate electromagnetic radiation. It is known that when current passes through the magnetic layer, its spin polarization occurs. When this current flows through subsequent layers, a change in the energy state of the electrons is possible. Relaxation of this state can lead to the generation of electromagnetic radiation, in particular, terahertz frequency. In this work, NWs arrays consists of several (three) layers (for example- Ni/Co/Ni ) were grown from aqueous solutions of corresponding metal salts, using “two-bath” electrochemical approach. A track membrane with a pore diameter of 100 nm was used as a matrix. Particular attention was paid to the method of bringing contacts to the resulting array of layered NWs. When passing a current through such arrays, a signal with a frequency of 15-25 THz was detected. The measurements were carried out on a Golay cell and a Bruker spectrometer. It was found that with the standard method of making the contacts (a thin flat layer over the entire surface), the generated signal is not stable. Local burnout of a thin conductive layer occurs. To solve this problem, a method was proposed for forming contacts in the form of discontinuous periodic stripes. This method also made it possible to change the total effective electrical resistance of the array. An example of the obtained sample with contact strips is shown in Fig. 1. An SEM image of an array of layered NW is also shown. Fig. 1. SEM image of the sample surface with separate strips-current leads (left); SEM image of an array of layered NW between two contact layers (right). Figure 2 shows the generation signal and its dependence on time (for the NWs array and the GLOBAR (heat source)). Fig. 2. Left- Signal intensity versus time: 1- NWs array, 2- heat source-GLOBAR; On the right, the figure shows the nature of the angular distribution of the signal intensity. Comparison of the dependence of the signal intensity on time for the NWs array and for the heat source shows a sharp increase of the signal in the first case. This proves the nonthermal nature of the signal that arises when current flows through an array of NWs with magnetic transitions. The paper also provides a theoretical assessment of the possibility of using such an NWs array to solve the inverse problem, namely, to obtain a THz radiation detector.

**References:**



**Images:**

 Magnetic nanowires as a source of irradiation of THz frequency

Spin-torque oscillators (STOs) have been extensively studied due to their potential applications in hardware neural networks [1]. For future practical STO devices, multiple magnetic tunnel junctions in series are demanded. Because it will involve a complicated stack structure, there are very limited experimental attempts so far. In this work, the spin-torque oscillation modes of a composite synthetic antiferromagnetic free layer in dual magnetic tunnel junctions with MgO barriers are studied experimentally by analyzing its field- and current-dependent power spectra. Two oscillation modes are observed under different magnetic fields and bias currents due to the unique layer structure as follows: seed layer/PtMn/Co70Fe30/Ru/Co60Fe20B20/MgO/Co20Fe60B20/Ru/Co20Fe60B20/MgO/Co60Fe20B20/Ru/Co70Fe30/PtMn/capping layer. With increasing field, the first mode shows a frequency reduction at low magnetic fields followed by an increasing frequency at high magnetic fields, while the second mode reveals a frequency increase at both low and high magnetic fields (Fig. 1(b)). The current-dependent power spectra of these two modes are also different. With increasing current, the frequency of the first mode drops at low magnetic fields (Fig. 2(a)) and rises at high magnetic fields (Fig. 2(c)), while the other decreases at low and high magnetic fields. These two modes could be tentatively understood by considering the coupling, the bias asymmetry of the spin torque, and the different thicknesses of Co20Fe60B20 in the composite synthetic antiferromagnetic free layer.

**References:**

[1] M. Romera, P. Talatchian, S. Tsunegi et al., Nature, Vol. 563, p. 230, (2018).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/5e2f10db377ec008ba72f706161f7df6.jpg)
Fig. 1 (a) The power spectral density of the free layer measured at the current of 0.3 mA and the bias fields of 400, 800, and 1000 Oe. The hollow signs are experimental results. The solid curves are Lorentzian fittings. (b) The power spectral density of the free layer as a function of magnetic field from 0 to 1100 Oe. The triangles and the crosses correspond to the frequencies of the two modes.

![](https://assets.underline.io/uploads/markdown_image/1/image/ec7159002dc17d22c71088883f41636f.jpg)
Fig. 2 The current-dependent power spectral density of the two modes measured at the magnetic fields of (a) 400 Oe, (b) 800 Oe, and (c) 1000 Oe. The triangles are the frequencies of the first mode, and the crosses are the frequencies of the second mode.

 Spin-Torque Oscillation Modes of a Composite Synthetic Antiferromagnetic Free Layer in Dual Magnetic Tunnel Junctions

Up-to-date technologies require modern information devices to process large amounts of data at high rates. Methods of the ultrafast magnetism are very promising in this respect since they allow controlling the magnetization of a magnetic material by the femtosecond laser pulses at a picosecond time scales. Ferrimagnetic alloy of gadolinium-iron-cobalt (GdFeCo) is one of the most promising materials for further development of the information storage devices, since it allows to perform a single-shot all-optical magnetization switching during a few picoseconds in the area of pulse action on the GdFeCo film. A mechanism of all-optical switching originates from the ultrafast spin dynamics of the exchange-coupled Gd and FeCo sublattices which are thrown out of balance due to the light-induced thermal heating of the spin sublattices. If the delivered energy exceeds the threshold, the magnetizations of the two sublattices are reversed at the picosecond timescales due to the difference of the relaxation times for these sublattices. Thus, ultrafast all-optical magnetization switching depends on the amount of energy delivered by the optical pulse and is characterized by a threshold femtosecond pulse intensity required for the magnetization switching. Nowadays many efforts are put to study how to control the process of all-optical switching via tailoring the properties of the femtosecond pulse and via the additional patterning of the magnetic structure. In this work we propose a design of photonic nanostructure where the parameters of the dielectric layers determine the spatial light distribution and the resonances of the absorption in the GdFeCo layers. We propose to use the magnetophotonic crystal (MPC) structures, that were shown to perform tunable localization of light at the resonant frequencies enabling the enhancement of the optomagnetic interaction in a magnetic material. The proposed magnetophotonic crystal with thin smooth or patterned layers of GdFeCo ferrimagnetic alloy provides the local magnetization control and targeted remagnetization of the single layers of the multilayer structure. By the frequency tuning of the input femtosecond laser pulses one can select the magnetic layer of GdFeCo in which the energy of the laser pulse is mostly concentrated and exceeds the magnetization reversal threshold, while in others it is 1.5-2 times lower. In other words, the proposed MPC allows to ‘turn on’ one certain magnetic layer of the structure and leave all other layers ‘turned off’. As GdFeCo material is perspective for data storage applications allowing a significant increase of the writing speed, the proposed structure can be implemented for the purposes of the record density increase in such a device. Usually, the magnetic bit cells are arranged in the plane of a single magnetic layer. Using the proposed MPC, bit cells can be arranged in several magnetic layers separated by the submicron dielectric spacers and addressed individually. This configuration is quite simple for fabrication and doesn’t require a precise positioning of the laser pulse. Besides that, another configuration of the chirped MPC structure with the patterned GdFeCo layers is addressed. For the higher density of the information recording the magnetic layer can be nanostructured to separate bit cells in the lateral direction. The patterning of the magnetic layer can be implemented along both axes in the plane of the structure layers. In our work we limited ourselves by one-dimensional patterning for the sake of the modelling simplicity. It should be stressed that the patterned chirped MPC allows combining two approaches instantaneously, the bit cells arranged in plane and the bit cells arranged in different layers. It opens up the ample opportunities for the significant increase of the information recording density. We also provide the method of an all-optical single-wavelength information reading in this multilayered structure. Thus, the designed MPC with GdFeCo layers could serve as a basis of 3D information storage devices. To sum up, a design of the MPC structure providing a selective magnetization switching in the different magnetic layers at different frequencies is proposed. The MPC contains the thin layers of GdFeCo as magnetic counterparts. By illuminating the MPC by femtosecond laser pulses at the certain frequencies we create the conditions for the highest concentration of the electromagnetic field in the necessary layer of the structure while in the other GdFeCo layers the intensity is at least 1.5 times smaller. Thus, one can achieve selective all-optical magnetization reversal in a single layer of the multilayered stack determined by the laser frequency without any impact on the other layers. The magnetic layers of the MPC are separated from each other by the non-magnetic layers, and can be patterned, so, they can serve as the unit cells for information storage. We also provide a mechanism of single-wavelength reading of the information stored in such a multilayered stack. The approach was demonstrated for the 4 layers of SiO2, TiO2 and GdFeCo for the sake of simplicity, however it could be extended to the larger number of layers by the proper design of the chirped photonic crystal. The work was supported by Russian Science Foundation, grant No. 19-72-10139.

**References:**

A. Kirilyuk, A.V. Kimel, T. Rasing. Rev. Mod. Phys. Vol. 82, p. 2731 (2010). A.V. Kimel, A. Kirilyuk, P.A. Usachev, et al. Nature Vol. 435, p. 655 (2005). J.Y. Bigot, M. Vomir, E. Beaurepaire. Nature Physics Vol. 5, p. 515 (2009). A.I. Chernov, M.A. Kozhaev, D.O. Ignatyeva, et al. Nano Letters Vol. 20, p. 5259 (2020). U. Atxitia, T.A. Ostler. Appl. Phys. Lett. Vol. 113, p. 062402 2018). M. Inoue, et al. J. Phys. D. Appl. Phys. Vol. 39, p. R151 (2006).

**Images:**

 Chirped Photonic Crystals with GdFeCo for Layer-Selective Magnetization Control

The recent development of techniques (various methods of deposition have been used),enabling the elaboration of very thin epitaxial YIG films has brought a renewed interest for exploiting the resonance properties of such films. When the thin YIG film is coated with a heavy metal (such as Pt), a non local extra damping of the microwave magnetization is observed [associated to the (YIG/Pt) interfacial coupling].Different techniques [1,2] of microwave absorption measurements have been used to characterize the resonance properties of such films. We highlight here basic results we have obtained in our cavity-FMR studies at X-band (9.725 GHz) on the 5 films whose characteristics are given below. These films correspond to (111) oriented YIG layers deposited by LPE [3] on GGG substrates. We have: F1 [YIG58], F2 [YIG44], F3 [YIG15], with thicknesses in nm, corresponding to the virgin YIG layers. Films F4 [YIG15/Pt3] and F5 [YIG58/Pt3] refer, respectively, to films F3 and F4 which have been coated by a Pt (3nm) over layer deposited by evaporation. We performed a detailed study of the angular variation of the resonance spectrum (angle θH of the dc field with the film normal) and we exploit the main characteristics of the observed resonance lines. A basic observation in these YIG films is that the resonance spectrum corresponds indeed to the superposition of individual resonances (arising from different parts of the film, weakly coupled by the dipolar interactions). We summarize below the results obtained for the main characteristics (Hres , linewidth ΔH) of the principal resonance. Angular variation of Hres : results and analysis In perpendicular (PER) geometry, the resonance condition reads [4, 5]: (ω/γ) = HPER – Heff (Eq.1), where Heff = 4πM - HA – 2/3 Han , with HA = 2K/M a uniaxial perpendicular anisotropy (spin-orbit origin) and Han = 2K1 /M the YIG cubic anisotropy. Taking the measured value for 4πM and the bulk value for Han (- 87 Oe), we get for the 3 virgin YIG films: F1: (- HA) = 37 Oe (easy plane); F2: HA = 48 Oe (easy axis); F3: HA = 130 Oe (easy axis). One observes thus that the uniaxial perpendicular anisotropy changes sign versus the YIG thickness. Linewidth ΔH of the principal resonance : angular variation and analysis The linewidth ΔH of the principal resonance is the sum of two different contributions: ΔH = Δ+ ΔHinh . The first one (Δ) corresponds to the relaxation rate of the magnetization vector (proportional to the intrinsic damping parameter α). The second one is an inhomogeneous width corresponding to a distribution ΔHres .The basic observation for the virgin YIG layers is that ΔH displays a sharp minimum at a specific field orientation θH where it reduces to the intrinsic width Δ .This behavior is well accounted for theoretically [ref 4], where the inhomogeneous contribution induced by a distribution P(Hi) has been discussed (where Hi = 4πM - HA). Thus for F2 we find Δ= 0.8 Oe [leading to α= 2 x 10-4 ] . Intrinsic width for the films F4 and F5 coated by a Pt(3nm) overlayer : Δ may be decomposed as: Δ= Δ0 + ΔS, where the second term corresponds to the increment of the damping induced by the (YIG/Pt) interfacial coupling .We find ΔS(F5) = 1.57 Oe and ΔS(F4) = 5.25 Oe varying approximately as (1/t) with the YIG thickness t . Characteristics of the resonance spectra : remarkable phenomena observed A) For the virgin thick (58nm)YIG layer (filmF1),in a broad range of field orientations, the FMR spectrum displays a fine structure: on superposition of the principal resonance, a series of regularly spaced narrow (0.8 Oe) resonance lines are observed. We ascribe them to standing elastic waves, excited in the YIG layer through the magneto-elastic coupling [6], which develop across the whole sample [500µm thick GGG substrate +YIG layer].Taking into account the transverse sound velocity in such a medium, the estimated frequency splitting (3.5 MHz) between two successive waves is well consistent with the observed field splitting (~1.2 Oe) between the individual resonance lines. B) For the two thin (15 nm) YIG layers (films F3 and F4),besides the principal resonance, two standing spin waves (we label SW1 and SW2) are observed in the resonance spectrum. These spin waves are collective modes associated to the non-uniform exchange in the YIG films. Such standing spin waves are here observed since the YIG layer thickness is comparable to the YIG exchange length (18nm).The resolved spin wave spectrum is observed continuously from the PAR to the PER geometry, except for a specific orientation (31 deg for F2) where it collapses to the uniform mode.

**References:**

[1] Y. Sun et al, Phys.Rev.Lett.111, 106601 (2013). [2] C. Du et al, Phys.Rev. Applied. 1, 044004 (2014). [3] N. Beaulieu et al, IEEE Magn. Letter.9, 3706005 (2018). [4] H. Hurdequint, J.Magn.Magn.Mater. 242-245 , 521 (2002). [5] H. Makino and Y.Hidaka, Mat.Res.Bull. Vol16 , pp 957-966 (1981). [6] A.Gurevich and G. Melkov,Magnetization oscillations and Waves, CRC Press (1996).

**Images:**

 Cavity-FMR studies of LPE epitaxial YIG films

Spin control in magnetic materials is a fundamental basis of the most current energy efficient devices, such as magnetic memory, Boolean and quantum logical elements [1]. In the last few decades, femtosecond laser systems opened up opportunities for ultrafast spin control in various magnetic materials such as ferromagnetic metals, iron garnets, and even antiferromagnetic dielectric oxides [2]. Special attention is paid to nonthermal spin wave control via inverse magnetooptical effects, such as inverse Faraday, inverse transverse magnetooptical Kerr, or inverse Voigt effects. Moreover, recent advances in fabrication techniques provide capabilities for light localization at the nanoscale regions together with optical modes excitation in the nanostructures [3,4]. The aforementioned advances of the nanostructures increase the efficiency of light-matter interaction and bring new horizons to all-optical spin control in magnetic materials. Here we report on spin wave amplitude enhancement in all-dielectric iron garnet nanostructure based on one-dimensional iron garnet grating. The grating consists of solitary strips of 400 nm width on gadolinium gallium garnet substrate placed with subwavelength period (600 nm). The height of the nanostructure was 225 nm. For spin wave launch pump-probe technique is utilized in Voigt configuration [2]. For pumping a circularly polarized pulse of ~200 fs duration at 600 nm and normal incidence was used. Probe pulse of 200 fs duration at 820 nm (transparency region of the structure) was linearly polarized. The probe angle of incidence was ~30 deg. The external magnetic field was equal to 100 mT. The nanostructure support propagation of waveguiding modes that are well defined in transmittance spectra at ~600 nm (Figure 1). The electromagnetic field localization and enhancement inside the nanostrips due to waveguiding mode excitation result in spin wave amplitude enhancement (up to 2 times). Moreover, as can be noted from figure 2 there is a shift in spin wave frequency between pure film and nanostructure. The effect can be associated with the existence of additional boundaries between magnetic strips and external media. This work was financially supported by the Russian Ministry of Education and Science, Megagrant project N 075-15-2019-1934

**References:**

1. A. V. Chumak et. al. Nature Physics, Vol. 11(6), p. 453, (2015) 2. A. Kirilyuk et. al. Reviews of Modern Physics, Vol. 82(3), p. 2731, (2010). 3. A. I. Chernov et. al. Nano Letters, Vol. 20(7), p. 5259, (2020). 4. A. L. Chekhov et. al. Nano letters, Vol. 18(5), p. 2970, (2018).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/ff4ec02eadaa48a1da002f1ada82a1fc.jpg)
Figure 1 Transmission of the nanostructure as a function of incident angle and wavelength

![](https://assets.underline.io/uploads/markdown_image/1/image/0f50b3bfdc75944256271a9c07bf3f25.jpg)
Figure 2 Spin wave precession for a pristine garnet film of 225 nm thickness (black) and nanostructure (red)

 Optically induced spin wave excitation in one-dimensional iron-garnet nanostripes

A phenomenon of Y3Fe5O12 (YIG)-ferromagnetic-resonance (FMR) linewidth broadening in magnetically coupled YIG-Co films is reported. The broadened linewidth cannot be attributed to previous effects [1-3] which only depend on the crystalline quality of YIG. Through micromagnetic simulation, the origin of this broadened linewidth was found to be a new type of inhomogeneity effect induced by the inhomogeneous dipolar field of Co layer. Furthermore, it shows that the extent of the linewidth broadening depends on the magnetization state of Co. The broadening is remarkable when the Co domains are random. The influence of Co on YIG-FMR linewidth still exists when the spacer between YIG and Co is 315 nm, indicating it is a long-range effect due to the dipolar origin. Our experiment results reveal that the influence of the dipolar interaction on FMR is remarkable in magnetically coupled heterostructures. Researchers should pay more attention to the dipolar interaction while investigating these systems.

**References:**

[1] L. Chen and C. H. Back* et al., Nature Physics 14, 490–494 (2018). [2] Kh. Zakeri* and J. Lindner et al., Phys. Rev. B 76, 104416 (2007). [3] Hiroto Sakimura and Kazuya Ando* et al. Phys. Rev. Research 1, 013013 (2019).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/8acabddae0340ae8430a23c27c3fe07a.jpg)
Figure 1 YIG-FMR properties of Sample 1 and Sample 2. The structures of Sample 1 and 2 are YIG (100 nm) and YIG(100)/MgO(15)/Co(3)/IrMn(10)/Ru(2 nm). (a)-(c) and (e)-(g) are H dependence of resonance frequency fr, intensity I and full width at half maximum (FWHM) Δf of Sample 1 and 2, respectively. (d) and (h) are fr dependence of ΔH converted from (c) and (g). Black (red) curves represent the sweep direction is decreasing (increasing) in (a)-(h). The left (right) black dashed lines in (e)-(g) represent the field where Mco=0 as H decreases (increases). In (b) and (f), all the intensity I has been normalized to IINC(100 Oe). In (f), the blue curves represent M/Ms-H loop of Sample 2.

 Ferromagnetic resonance linewidth broadening induced by a tunable inhomogeneity effect

I. Introduction Tunable magnetization dynamic properties having frequencies in the GHz range have great potential in a variety of reprogrammable microwave technologies [1]. Magnetic nanostructures and their arrays are found to be promising for microwave devices that operate in sub-20 GHz frequency regime [2]. Microwave properties can be tuned by controlling the magnetization orientations and magnetic interactions in nanostructures or multilayers. In general, tunable microwave properties are driven by an external bias field which hinders device integration. Therefore, a bias-field-free operation is of great interest. Previously, we have shown such operations based on rhomboid-shaped nanomagnet [3-5]. Here, we have proposed a new zigzag magnetic nanowire for reprogrammable magnetic and microwave properties in the absence of any external bias field using micromagnetic simulations [6]. II. Initialization of remanent magnetic states: We have designed zigzag nanowire based on number of crests (Zn), example Z5 having the five crests as shown in fig. 1(a). Figure 1(a) indicates schematic of the zigzag nanowire have the dimensions are width (w) = 100 nm, arm length (L) = 300 nm, thickness (t) = 20 nm, slanted edge angle (phi) = 45 degree and zigzag angle (theta) = 90 degree. We have obtained two different remanent magnetic states in zigzag nanowire by using a simple field initialization process. When the field initialized from 2000 to 0 Oe along y, we have observed tail to tail or head to head magnetic configuration in a remanent magnetic state and it is referred as Y-state. On the other hand, such kind of domain walls are not exist when the field initialized along x and which is known as X-state. The magnetic configuration of X- and Y-states as shown in figure 1(b). Shape anisotropy of the zigzag nanowire is a major role to get two distinct remanent magnetic states. These two distinct remanent states having two different magnetic dynamic responses. III. Ferromagnetic resonance: The dynamics responses of the remanent magnetic states obtained by applying the Sinc pulse along the x axis. The sinc pulse is denoted by HS and it is defined as, where HS0 = amplitude (50 Oe), fc = cut-off frequency which is less than the Nyquist frequency (fN), i.e. (fc &lt; fN) and = simulation time. The time dependent magnetization recorded up to 4 ns in step of 10 ps. The Fourier transforms are performed on time dependent magnetization to obtain the ferromagnetic resonance (FMR) spectra in frequency domain. Figure 1(c) shows the FMR spectra for X and Y-states of the zigzag magnetic nanowire (Z5) at Hex = 0. The frequency responses are found in 3-15 GHz range. The FMR modes observed at 7.8 and 9.6 GHz for the X-state. On the other hand, the frequency absorption appeared at 4.5, 6.4 and 8.4 GHz for the Y-state. IV. 2D spatial profiles: The location of the FMR modes are identify based on detail investigation of the 2D spatial profiles of X- and Y –states as shown in figure 2 (a & b). We have observed 7.8 GHz mode at near the bend and 9.6 GHz mode at the central of the zigzag nanowire for the X-state. We have labelled the modes are e-type (7.8 GHz) at near bend and c0 type (9.6 GHz) at the center. On the other hand, two e modes (e1 and e2) and c0 mode observed for the Y-state. We have investigated the frequency shift of these two distinct modes between the X-state and Y-state. The frequency shift found Δf=1.2 GHz for the c-type mode and Δf = 1.4 GHz for the e type mode (e1). The large frequency shift can be clearly distinguishing the distinct states. The frequency responses are in GHz range and have good potential to use in microwave device operation. Also, Zigzag magnetic nanowire applicable for flexible microwave devices.

**References:**

 1. A. V. Chumak, V. I. Vasyuchka, A. A. Serga, and B. Hillebrands, Nat. Phys. 11, 453 (2015). 2. M. Krawczyk and D. Grundler, J. Phys.: Condens. Matter 26, 123202 (2014). 3. A. Haldar and A. O. Adeyeye, ACS Nano 10, 1690 (2016). 4. A. Haldar and A. O. Adeyeye, Appl. Phys. Lett. 108, 022405 (2016). 5. K. Begari and A. Haldar, J. Phys. D: Appl. Phys. 51, 275004 (2018). 6. M. J. Donahue and D. G. Porter, Interagency Report No. NISTIR 6376, National Institute of Standards and Technology, Gaithersburg, MD, 1999.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/0d9e75b45505572be8981d892f119e2f.jpg)
Figure 1 : (a) Schematic diagram of zigzag nanowire (b) remanent states and (c) ferromagnetic resonance spectra at Hex = 0.

![](https://assets.underline.io/uploads/markdown_image/1/image/5ca6d13d04e472860ec897281f2b4030.jpg)
Figure 2: 2D spatial profiles for the (a) X-State and (b) Y-State.

 Tunable Microwave Properties of Zigzag Nanowires

I. INTRODUCTION Ferromagnetic resonance (FMR) measurement technique is well known to be one of the important methods to evaluate the dynamic magnetic properties such as the effective saturation magnetization, damping constant, and so on, of magnetic thin film materials [1]. Recently, a broadband FMR (B-FMR) measurement technique with a coplanar waveguide (CPW) and a vector network analyzer (VNA) has been widely used to investigate them [2]-[4]. The reason for this is that the films are excited in a very wide range of RF frequency changing external magnetic field intensity and its high sensitivity allows for downsizing of the samples to the micro-scale, which provide detailed information on very thin films subjected to practical use under a variety of circumstances. In general, for FMR measurement technique, it is pointed out that the non-uniform magnetization precession mode occurs by the applied direction of external magnetic field. However, for the B-FMR measurement technique, this problem still remains an open question. Herein, we chose Fe-M binary alloys as magnetic thin film materials, investigated the in-plane and out-of-plane dynamic magnetic properties of Fe-M binary alloy thin films using the B-FMR measurement technique, and further discussed the difference between these properties in their films by the applied direction of external magnetic field in detail. II. EXPERIMENTAL PROCEDURES 10-nm thick Fe-M (M=Ni, Si, Co, and Ga) binary alloy thin films were fabricated by DC magnetron sputtering onto glass substrates. These film compositions were determined by energy dispersive x-ray spectroscopy (EDX), while the crystallographic structure of these films was performed using the high-angle XRD analysis and TEM observation, indicating that all film structures are polycrystalline and bcc phase. As for the dynamic magnetic properties of these films, the in-plane and out-of-plane effective saturation magnetization (4πMs,eff, //, 4πMs,eff,⊥) and the in-plane and out-of-plane effective damping constants (α//, α⊥) were evaluated by the B-FMR measurement technique. The external magnetic field was applied parallel to the CPW plane and swept between -0.01–0.3 T at various resonance frequencies. On the other hand, 4πMs,eff,⊥ and α⊥ of the films were determined in an external magnetic field applied perpendicular to the CPW plane swept between 1.4–3.3 T at various resonance frequencies. These measurements were performed at room temperature. The other magnetic properties of these films were already described in [4], [5] in detail. III. RESULTS AND DISCUSSION 4πMs,eff, //, 4πMs,eff,⊥, α//, and α⊥ of 10-nm thick Fe-M (M=Ni, Si, Co, and Ga) thin films are summarized in Table 1 and 2. As be noticed in Table 1, 4πMs,eff, // values of these films became higher or lower than those of saturation magnetization (4pMs) evaluated by VSM, which might be attributed to the appearance of negative or positive surface anisotropy. On the other hand, 4pMs,eff,⊥ of these films almost agreed with those of 4πMs evaluated by VSM, meaning that the easy magnetization direction of every film is in the film plane. As for the effective damping constant (Table 2), in case of M=Ni, α// value was almost equal to that of α⊥, indicating that the intrinsic damping can be obtained regardless of the external magnetic field direction. On the other hand, in case of M=Si, Co, and Ga, these damping depend on the external field direction, and these α// values were higher than those of α⊥. The reason for these differences might be that the non-uniform magnetization precession mode appears by magnetic inhomogeneities such as the two-magnon scattering, the anisotropy dispersion, and so on when the external magnetic field is applied in the film plane. On the basis of these results, it is suggested that the external magnetic field direction must be seriously selected by the kind of magnetic materials as their effective damping constants are evaluated by the B-FMR measurement technique. ACKNOWLEDGEMENT The authors thank Prof. Satoshi Okamoto, and Associate Prof. Nobuaki Kikuchi at Tohoku University for performing the photo lithography and measuring XRD diffraction patterns. This work was supported in part by KAKENHI (JP17H03226) from MEXT, Japan. This work was supported in part by CSIS, CSRN, and CIES, Tohoku University. This work was also supported in part by the ASRC in Japan.

**References:**

[1] J. H. E. Griffiths, Nature 148, 670 (1946)., [2] G. Counil et al., J. Appl. Phys. 95, 5646 (2004). [3] M. Toda et al., J. Magn. Soc. Jpn. 31, 435 (2007). [4] Y. Endo et al., J. Appl. Phys. 109, 07D336 (2011). [5] Y. Kawabe et al., Trans. Magn. Soc. Jpn. 3, 34 (2019).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/4fc57e3b82465a0fe4857ce200b27537.jpg)
Table 1. Comparison between the in-plane and out-of-plane effective saturation magnetization (4πMs,eff, //, 4πMs,eff,⊥) for Fe-M binary alloy thin films.

![](https://assets.underline.io/uploads/markdown_image/1/image/b17d7443a35e49fed8dce0227d6c370d.jpg)
Table 2. Comparison between the in-plane and out-of-plane effective damping constants (α// and α⊥) for Fe-M binary alloy thin films.

 Study on comparison between in-plane and out-of-plane dynamic magnetic properties for Fe-M binary alloy thin films

Compensated ferrimagnets show both ferromagnetic and antiferromagnetic dynamics, i.e., fast magnetization dynamics [1-5] and vanishing Skyrmion Hall effect [6] with finite magnetization. As the dynamics of ferrimagnets can be driven with current-induced spin torques [7, 8], it is important to find a way of quantifying spin torques in ferrimagnetic materials. One of the main methods to quantify the spin torque in ferromagnets is the spin torque ferromagnetic resonance (ST-FMR) technique [9, 10]. For ferromagnets, the damping-like (DL) and field-like (FL) torque components are separately determined through ST-FMR line-shape analysis. However, it is unclear if this line-shape analysis is valid even for ferrimagnets. In this work, we report a theory of spin torque ferrimagnetic resonance (ST-FiMR) in ferrimagnet/heavy metal bilayer structures. We investigated ST-FiMR for two cases. (i) Identical DL and FL torque efficiencies of two sublattices in a ferrimagnet, and (ii) Different DL and FL torque efficiencies of two sublattices, considering different spin polarization between rare-earth and transition metal elements [11]. For both cases, the mixing voltage originating from the DL torque is linearly proportional to the effective net spin density of the system, resulting in sign reversal at the angular momentum compensation condition. In addition, at the compensation condition, the line-shape can be anti-symmetric, in contrast to entirely symmetric signals for ferromagnets. Our result suggests that the line-shape analysis established for ferromagnets is invalid for ferrimagnets especially near the compensation condition so that the proposed theory must be implemented to analyze the spin torque ferrimagnetic resonance.

**References:**

[1] K.-J. Kim et al., Nat. Mater. 16, 1187 (2017). [2] S.-H. Oh et al., Phys. Rev. B 96, 100407(R) (2017). [3] L. Caretta et al., Nat. Nanotechnol. 13, 1154 (2018). [4] S. A. Siddiqui et al., Phys. Rev. Lett. 121, 057701 (2018). [5] S.-H. Oh and K.-J. Lee, J. Magn. 23, 196 (2018). [6] Y. Hirata et al., Nat. Nanotechnol. 14, 232 (2019). [7] J. Yu et al., Nat. Mater. 18, 29 (2019). [8] T. Okuno et al., Nat. Electron. 2, 389 (2019). [9] A. A. Tulapurkar et al., Nature 438, 339 (2005). [10] J. C. Sankey et al., Phys. Rev. Lett. 96, 227601 (2006). [11] C. Kaiser et al., Phys. Rev. Lett. 95, 047202 (2005).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/f8bb2c0202f39a1849a2dd00cdb94a4f.jpg)
Fig. 1. Spin torque ferrimagnetic resonance signal only with damping-like torque (DLT).

![](https://assets.underline.io/uploads/markdown_image/1/image/293aa0f64f1b4c6580837ff6a06e31d7.jpg)
Fig. 2. Sign reversal of spin torque ferrimagnetic resonance near angular momentum compensation condition.

 Theory of Spin-Torque Ferrimagnetic Resonance

The orthogonal magnetization multilayer has the in-plane and perpendicular anisotropy magnetic layers, which has been proposed for the fast magnetization switching by spin transfer torque [1]. On the other hand, it is difficult to obtain the stable spin transfer torque oscillation (STO) in the orthogonal magnetization since the switching occurs too easily. In this study, we introduced the 90 degree magnetic coupling to obtain the STO in the orthogonal configuration. In typical, the 90 degree coupling between two magnetic layers is described by the bilinear coefficient A12 and biquadratic coefficient B12, and obtained under the conditions of A12&lt;|B12| and B12&lt;0 by using suitable layer as a spacer. [2] In our model, the multilayer consists of three layers with thickness of 2 nm; a top layer with the in-plane magnetic anisotropy, a nonmagnetic spacer, and a bottom layer with the perpendicular magnetic anisotropy sequentially. Figure 1 shows the calculated magnetization map in the top layer (a) and the side views of the magnetization configuration of the top and bottom layers (b) when the top layer is CoFe with Ms of 1450 emu/cc, Hk of 35 Oe, and a damping constant of 0.01, and the bottom layer is Fe/Pt with Ms of 800 emu/cc and Hk of 15000 Oe. The top and bottom layer has the vortex magnetization and the perpendicular magnetization, respectively, when a current density is zero. By increasing the current density, the magnetization of the top layer oscillates with frequency 35 GHz while the bottom layer maintains the perpendicular magnetization. This stable STO is due to the 90 degree coupling. Figure 2 shows the STO frequency as a function of the current density for various conditions. First, let us focus on the relation between the STO frequency and magnitude of 90 degree coupling. The STO frequency of the CoFe top layer was increased by decreasing B12 from −0.3 to −0.6, that is, increasing the 90 degree coupling. Next, we compared the STO performances by changing the top layer material from CoFe to NiFe and Ni with small Ms and small damping constant. As a result, the frequency achieved 45 GHz and the necessary current density was reduced to 6x107 A/cm2. In summary, it was found that the STO was stably realized in the orthogonal configuration by introducing 90 degree magnetic coupling, and the STO frequency was increased by enhancement of 90 degree coupling. Additionally, our calculation indicates that it is possible to increase the frequency and necessary current density by material selection.

**References:**

[1] H. Liu et al., Appl. Phys. Lett. 97, 242510 (2010). [2] G. Nagashima., et al, J. Appl. Phys. 126, 093901 (2019)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/0ab8e84ec749f770d055d306dfad3181.jpg)
Fig. 1 (a) Magnetization configuration in the top layer. (b) Side views of magnetization configuration in the top and bottom layers. The shown magnetization corresponds to the enclosed area in (a).

![](https://assets.underline.io/uploads/markdown_image/1/image/0d156a12ee9515515270d71c3b90fa7a.jpg)
Fig. 2 STO frequency as a function of the current density for various conditions; B12=−0.3 and B12=−0.6 for CoFe top layer, and B12=−0.6 for CoFe, NiFe, and Ni top layers.

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