France



Despite attempts to design correlated systems to influence the properties of a physical system, it is often those inspired by nature that yield the best results. Artificial spin ice (ASI) are lithographically defined 2D projections of geometrically frustrated materials that are often used for experimentally model more complex atomistic systems [1-2]. In addition, ASI exhibit interesting physics, including collective dynamics [3-4] and emergent monopole stabilisation [5], that can be applied to probabilistic computing, signal propagation, and logic devices [6-7]. The capacity to design an almost infinite number of topologies to induce novel effects, and the ability to probe these characteristics optically, electrically and by scanning probe techniques have made ASI an exciting candidate for probabilistic computing [8].&lt;br/&gt;&lt;br/&gt;Here, two custom ASI systems are shown to exhibit interesting defect behaviours from the inherent array design. The first design models the influence of a ferromagnetic defect in the centre of the structured array. Defects in crystal systems can have bountiful effects on the local physical properties. These effects in-turn can often be exploited for novel applications. For example, defects in transition-metal dichalcogenides have applications in quantum information processing as single photon point-sources due to highly localised excitons bound to the defect-site [9]. Alternatively, nitrogen vacancies in diamond exhibit spin-dependent fluorescent rates required for high resolution magnetometry [10].&lt;br/&gt;&lt;br/&gt;The magnetic defect in the ASI system acts as a source of emergent monopoles at lower energy-barriers than a pristine lattice. Recent results of the delicate interplay between defect and lattice states are studied in the context of signal propagation applications by magnetic imaging techniques, including magnetic force microscopy (MFM); Lorentz TEM; and electron holography. We reveal how the magnetic defect affects the surrounding structure compared to those formed independently from the defect, e.g., from discontinuous lattice-edges.&lt;br/&gt;&lt;br/&gt;The second presented system is a quasi-hexagonal ASI lattice, which is arranged to encompass competing interactions from both ferromagnetic/antiferromagnetic coupling between parallel islands and geometric frustration (Fig. 1a) [11]. By including parallel islands along just one axis, the lattice exhibits an additional shape anisotropy under field directions (Fig 1b-c). We demonstrate that the inclusion of these coupled islands promotes the non-uniform break-down of Ising &quot;macro-spins&quot; in the islands under a specified field protocol (Fig. 1d). Through MFM and micromagnetic modelling, we investigate the disrupted periodicity of the energy states across the lattice and the predictability of non-Ising state formation. Control over the local coupling effects have application in programmable logic, e.g. non-Boolean or probabilistic computing [12].

**References:**

[1] R. F. Wang &lt;i&gt;et al.&lt;/i&gt;, &lt;i&gt;Nature&lt;/i&gt;, vol. 439, no. 7074, pp. 303–306, Jan. 2006.&lt;br/&gt;[2] M. Tanaka &lt;i&gt;et al.&lt;/i&gt;, &lt;i&gt;Phys. Rev. B - Condens. Matter Mater. Phys.&lt;/i&gt;, vol. 73, no. 5, pp. 3–6, 2006.&lt;br/&gt;[3] M. B. Jungfleisch &lt;i&gt;et al.,&lt;/i&gt; &lt;i&gt;Phys. Rev. Appl.&lt;/i&gt;, vol. 8, no. 6, pp. 1–7, 2017.&lt;br/&gt;[4] A. Farhan &lt;i&gt;et al.&lt;/i&gt;, &lt;i&gt;Phys. Rev. B&lt;/i&gt;, vol. 96, no. 6, p. 064409, Aug. 2017.&lt;br/&gt;[5] S. Ladak &lt;i&gt;et al.&lt;/i&gt;, &lt;i&gt;Nat. Phys.&lt;/i&gt;, vol. 6, no. 5, pp. 359–363, May 2010.&lt;br/&gt;[6] S. H. Skjærvø &lt;i&gt;et al.,&lt;/i&gt; &lt;i&gt;Nat. Rev. Phys.&lt;/i&gt;, vol. 2, no. 1, pp. 13–28, Jan. 2020.&lt;br/&gt;[7] S. Gliga, E. Iacocca, and O. G. Heinonen, &lt;i&gt;APL Mater.&lt;/i&gt;, vol. 8, no. 4, p. 040911, Apr. 2020.&lt;br/&gt;[8] H. Arava &lt;i&gt;et al.&lt;/i&gt;, &lt;i&gt;Nanotechnology&lt;/i&gt;, vol. 29, no. 26, 2018.&lt;br/&gt;[9] A. Srivastava &lt;i&gt;et al.,&lt;/i&gt; &lt;i&gt;Nat. Nanotechnol.&lt;/i&gt;, vol. 10, no. 6, pp. 491–496, Jun. 2015.&lt;br/&gt;[10] G. Balasubramanian &lt;i&gt;et al.&lt;/i&gt;, &lt;i&gt;Nature&lt;/i&gt;, vol. 455, no. 7213, pp. 648–651, 2008.&lt;br/&gt;[11] R. Puttock &lt;i&gt;et al.&lt;/i&gt;, &lt;i&gt;Small&lt;/i&gt;, vol. 2003141, pp. 1–8, Sep. 2020.&lt;br/&gt;[12] Project supported by the UK government department for Business, Energy and Industrial Strategy through NMS funding (Low Loss Electronics). LTEM and EH was available through funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 823717 – ESTEEM3.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/80e75899528a7a4590fb6f72ac0d7385.jpg)
Figure 1. (a) AFM image of four primitive cells of the quasi-hexagonal ASI lattice where three vertex-shapes are outlined. MFM images of unimodal (b) and bimodal (c) configurations favourable when the field is aligned along y- and x-axes, respectively. (d) Four possible magnetic configurations in parallel islands upon application of a critical field.



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 Magnetic defect-driven dynamics in artificial spin ice

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Despite attempts to design correlated systems to influence the properties of a physical system, it is often those inspired by nature that yield the best results. Artificial spin ice (ASI) are lithographically defined 2D projections of geometrically frustrated materials that are often used for experimentally model more complex atomistic systems [1-2]. In addition, ASI exhibit interesting physics, including collective dynamics [3-4] and emergent monopole stabilisation [5], that can be applied to probabilistic computing, signal propagation, and logic devices [6-7]. The capacity to design an almost infinite number of topologies to induce novel effects, and the ability to probe these characteristics optically, electrically and by scanning probe techniques have made ASI an exciting candidate for probabilistic computing [8]. Here, two custom ASI systems are shown to exhibit interesting defect behaviours from the inherent array design. The first design models the influence of a ferromagnetic defect in the centre of the structured array. Defects in crystal systems can have bountiful effects on the local physical properties. These effects in-turn can often be exploited for novel applications. For example, defects in transition-metal dichalcogenides have applications in quantum information processing as single photon point-sources due to highly localised excitons bound to the defect-site [9]. Alternatively, nitrogen vacancies in diamond exhibit spin-dependent fluorescent rates required for high resolution magnetometry [10]. The magnetic defect in the ASI system acts as a source of emergent monopoles at lower energy-barriers than a pristine lattice. Recent results of the delicate interplay between defect and lattice states are studied in the context of signal propagation applications by magnetic imaging techniques, including magnetic force microscopy (MFM); Lorentz TEM; and electron holography. We reveal how the magnetic defect affects the surrounding structure compared to those formed independently from the defect, e.g., from discontinuous lattice-edges. The second presented system is a quasi-hexagonal ASI lattice, which is arranged to encompass competing interactions from both ferromagnetic/antiferromagnetic coupling between parallel islands and geometric frustration (Fig. 1a) [11]. By including parallel islands along just one axis, the lattice exhibits an additional shape anisotropy under field directions (Fig 1b-c). We demonstrate that the inclusion of these coupled islands promotes the non-uniform break-down of Ising "macro-spins" in the islands under a specified field protocol (Fig. 1d). Through MFM and micromagnetic modelling, we investigate the disrupted periodicity of the energy states across the lattice and the predictability of non-Ising state formation. Control over the local coupling effects have application in programmable logic, e.g. non-Boolean or probabilistic computing [12].

**References:**

[1] R. F. Wang et al., Nature, vol. 439, no. 7074, pp. 303–306, Jan. 2006. [2] M. Tanaka et al., Phys. Rev. B - Condens. Matter Mater. Phys., vol. 73, no. 5, pp. 3–6, 2006. [3] M. B. Jungfleisch et al., Phys. Rev. Appl., vol. 8, no. 6, pp. 1–7, 2017. [4] A. Farhan et al., Phys. Rev. B, vol. 96, no. 6, p. 064409, Aug. 2017. [5] S. Ladak et al., Nat. Phys., vol. 6, no. 5, pp. 359–363, May 2010. [6] S. H. Skjærvø et al., Nat. Rev. Phys., vol. 2, no. 1, pp. 13–28, Jan. 2020. [7] S. Gliga, E. Iacocca, and O. G. Heinonen, APL Mater., vol. 8, no. 4, p. 040911, Apr. 2020. [8] H. Arava et al., Nanotechnology, vol. 29, no. 26, 2018. [9] A. Srivastava et al., Nat. Nanotechnol., vol. 10, no. 6, pp. 491–496, Jun. 2015. [10] G. Balasubramanian et al., Nature, vol. 455, no. 7213, pp. 648–651, 2008. [11] R. Puttock et al., Small, vol. 2003141, pp. 1–8, Sep. 2020. [12] Project supported by the UK government department for Business, Energy and Industrial Strategy through NMS funding (Low Loss Electronics). LTEM and EH was available through funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 823717 – ESTEEM3.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/80e75899528a7a4590fb6f72ac0d7385.jpg)
Figure 1. (a) AFM image of four primitive cells of the quasi-hexagonal ASI lattice where three vertex-shapes are outlined. MFM images of unimodal (b) and bimodal (c) configurations favourable when the field is aligned along y- and x-axes, respectively. (d) Four possible magnetic configurations in parallel islands upon application of a critical field.

technical paper

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

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.

 Spin Transfer Torque Oscillation in Orthogonal Magnetization Disks

Spin-torque diode is one of the emerging novel technology in spintronics. Based on the spin-torque diode effect, it could be used for effective RF detection and harvesting, as its sensitivity significantly overcomes the sensitivity of commonly used Schottky diodes. Usage of perpendicular magnetic anisotropy (PMA) in the free layer appears to be one of the most promising designs for spin-torque diodes. We report an efficient design rule to develop spin-torque diodes with PMA with record microwave sensitivity. We study the impact of the free layer magnetization tilt on the sensitivity of the spin-torque diode. This magnetization tilt can be effectively engineered by choosing the ratio of the shape and surface anisotropy and interlayer magnetostatic interactions. With the help of micromagnetic modeling over a broad range of input powers and free layer thicknesses, we demonstrate a significant role of non-linearity and inhomogeneous magnetization dynamics in achieving high sensitivity levels (see Fig.1). Our modeling for typical state-of-the-art parameters of magnetic tunneling junction demonstrates a possibility to reach a record-breaking unbiased microwave sensitivity of 3500 mV/mW (see Fig.2), which is far beyond the parameters of commercial Schottky diodes. We also analyze the impact of direct current bias on sensitivity both in case of current is lower than the critical one and in case of current is higher than the critical one and injection locking occurs. These results can be very important for the development of efficient spintronic ambient energy harvesters. Financial support by the Russian Science Foundation (Project No. 19-12-00432) is gratefully acknowledged.

**References:**



**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/7698082bae26856f7ff2cb3d64de7fa5.jpg)
Unbiased spin-torque diode sensitivity as a function of free layer thickness derived from micromagnetic modeling. Color refer to input power: red – 2 nW, blue – 20 nW, green – 100 nW, brown – 1000 nW.

![](https://assets.underline.io/uploads/markdown_image/1/image/f2f39922dd26de7259c1364e356d5aef.jpg)
Unbiased diode sensitivity dependences on the thickness for Rp = 600Ω, Rap = 1200Ω (red) and Rp = 100Ω, Rap = 200Ω (blue) in case of 20 nW incident power.

 Sensitivity optimization of spin-torque diode with perpendicular anisotropy through free layer thickness tuning

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.

 Tuneable Stochastic Domain-Wall Trajectories in a Magnetic Galton Board

Domain walls (DWs) in magnetic nanowires are a topic of intense interest due to proposals to use them as data carriers in non-volatile logic and memory devices. However, despite their apparent technological potential such devices are challenging to realise, in part because DWs pinning and propagation is highly stochastic, making digital devices unreliable [1]. While materials engineering approaches can be used to supress stochasticity [2], it is also interesting to consider whether alternative computer paradigms could prove more resistant to, or even benefit from, stochasticity. In this talk we will present three examples of how embracing DW stochasticity as a functional, rather than technologically inhibiting feature can facilitate novel computational devices. Figure 1(a) presents results that illustrate typical stochastic DW behaviours in a 400 nm wide Ni80Fe20 nanowire device, as characterised by focused magneto-optic Kerr effect (FMOKE) magnetometry. DWs were injected from the pad to a patterned defect in the nanowire’s middle and the distributions of magnetic fields required to propagate them through the defect characterised. The depinning field histogram shows both fractional pinning probabilities and multimode depinning field distributions, both characteristic features of stochasticity induced by complex DW dynamics [3]. However, while individual reversals of such a device are highly stochastic, average properties are well-defined, and more importantly, highly tuneable. Figure 1(b) illustrates how applying modest magnetic fields orthogonal to a similar nanowire/defect combination allows DWs pinning probabilities to be tuned between 0 and 1. Thus, stochastic pinning can be used to create random bit-streams with tuneable average values. In our first example of the utility of these effects we use stochastic DW pinning to realise the stochastic computing paradigm in DW logic networks. In stochastic computing, floating point numbers are encoded in the average value of random binary bit-streams, and single conventional logic gates perform complex mathematical operations that would usually require extended logic networks to perform. For example, an AND gate performs a multiplication operation. Figure 2(a) presents the results of FMOKE magnetometry, illustrating how the output of a DW AND gate with stochastic input produces output bitstreams consistent with those expected. In our second example we use the stochastic pinning of DWs to facilitate two neuromorphic computing approaches: a feed-forward neural network and a Boltzman machine. In the feed-forward network, nanowires act as binary stochastic synapses, with the probability of DW propagation taking the role of a synaptic weight. Simulations of network behaviour allow us to demonstrate that such a device can perform machine learning tasks including written digit recognition. In the Boltzman machine, where stochasticity is used to sample a defined, or trained, probability distribution, the nanowires take the role of stochastic neurons. We apply this approach to an integer factorisation problem where network is defined so that the binary representation of the integer factors are the most probable states for the neurons. In our final example, we show how DWs driven by rotating magnetic fields within an interconnected nanoring array, can be used to perform reservoir computing [4]. We characterise a ring array’s behaviour using a combination of MOKE, polarised neutron reflectivity and photoemission electron microscopy, and show how emergent behaviour arises from stochastic interactions between DWs at the array’s junctions (Figure 2(b)). Using the magnitude of the rotating applied field as an input we then demonstrate how this allows the array to be used as a reservoir and perform a range of time series analysis tasks including speech recognition and chaotic series prediction.

**References:**

[1] T.J. Hayward and K.A. Omari, Beyond the quasi-particle: stochastic domain wall dynamics in soft ferromagnetic nanowires, Journal of Physics D: Applied Physics 50, 8, 084006 (2017). [2] T.J. Broomhall, A.W. Rushforth, M.C. Rosamond, E.H. Linfield, and T.J. Hayward, Physical Review Applied 13, 024039 (2020). [3] T.J. Hayward, Scientific Reports 5, 13279 (2015). [4] R. W. Dawidek, T. J. Hayward, I. T. Vidamour, T. J. Broomhall, M. Al Mamoori, A. Mullen, S. J. Kyle, P. W. Fry, N. J. Steinke, J. F. K. Cooper, F. Maccherozzi, S. S.Dhesi, L. Aballe, M. Foerster, J. Prat, E. Vasilaki, M. O. A. Ellis, D. A. Allwood, submitted to Advanced Functional Materials (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/158b0ac6376b52704edb84a394fcac23.jpg)
Figure 1: (a) Characterisation of stochastic DW pinning at a dN = 80 nm notch in in a 400 nm wide, 25 nm thick Ni80Fe20 nanowire. The experimental geometry is shown at the top of the figure with green circles representing where injection and depinning field histograms were measured. (b) Illustration of how the pinning probability of DWs in similar system were tuned by applying magnetic fields (Hy) orthogonal to the nanowire.

![](https://assets.underline.io/uploads/markdown_image/1/image/c816108946b00cb61778bad36bbb92b6.jpg)
Figure 2: (a) Stochastic computing with a DW AND gate. An SEM of the measured device is shown at the top of the figure, with green circles indicating where FMOKE measurements were made to measure the probability of DWs passing through the input nanowires (PA and PB) and output nanowire (Pout). The plot shows PA x PB and Pout as a function of applied field; the close tracking of these curves shows that AND gate performed a multiplication operation on the input bit-streams. (b) Behaviour of an interconnected nanoring array as a function of rotating applied field amplitude. The number of rings with propagating DWs, pinned DWs and in vortex states are shown at each applied field value.

 From Stochasticity to Functionality: Harnessing Magnetic Domain Walls for Probabilistic and Neuromorphic Computing

Magnetic Skyrmion is a particle-like magnetic excitation in ferromagnetic material similar to the Dirac-monopole in the spin-ice systems. Since the magnetic Skyrmion is topologically protected [1], it can survive under thermal agitation and shows Brownian motion. The skyrmion system can be an ideal platform to design stochastic computer [2] and/or in Brownian computer [3], since magnetic Skyrmion is a special particle that may show Brownian motion in all-solid-state devices. Therefore, investigation of the Brownian motion of the magnetic Skyrmion is now the subject of scientific and technical interest. The dynamics of the Skyrmions in a two-dimensionally extended film at finite temperature is described by the Thiele equation [4]. According to the equation, the Skyrmion may pose a velocity perpendicular to the force's direction and tend to turn right or left depending on its chirality determined by the Skyrmion number. This gyro-motion reduces the (diagonal element of the) diffusion constant [5]. Naïvely thinking, we may suppose that the diffusion flow may pose a component perpendicular to the gradient of the skyrmion density because of the gyro-motion. The component should be proportional to the gradient of the Skyrmion density and newly defined “gyro-diffusion constant” (off-diagonal element of the diffusion constant) [6]. However, such flow is divergence-less and does not appear in the equation of diffusion. According to this context, we mention the gyro-diffusion constant as “the hidden diffusion constant”. In this talk, we show evidence of gyro-motion in diffusion and discuss the observation of the gyro-diffusion constant. Then, we mention recent progress to implement “Brownian computer” by use of Skyrmions. In our experiments, the magnetic Skyrmions are bubble-shaped magnetic domains generated in a ferromagnetic thin film having spontaneous magnetization perpendicular to the film surface. The Skyrmions have their diameter adjusted to 1 μm to allow the observation by an optical microscope with polarization analysis (MOKE microscope). To create the Skyrmions, Ta/CoFeB /Ta sandwiched films [7] possessing perpendicular magnetic anisotropy and the interfacial- Dzyaloshinskii-Moriya interaction (i-DMI) were fabricated. Changing the upper and lower Ta film thicknesses independently, the ratio of the i-DMI energy to the magnetic anisotropy energy was adjusted. Besides, by eliminating the annealing process, the generation of grain boundaries was suppressed. The annealing free process enhanced the diffusion coefficient of skyrmions by a factor of more than 10 compared to the previous study [2] and comparable to the recent observations [7,8]. Firstly, we have developed the Skyrmion channel by a slight modification of the SiO2 passivation layer thickness. By this method we could make degradation and dipole-field free channels. With this method the Skyrmions show free Brownian motion even in a complicated Skyrmion circuit like Hub (Y-cross) [7]. Secondly, we put a Skyrmion in one-dimensional channels to interfere with its gyro-motion. As a result, a significant increase in the diagonal diffusion constant was observed. This is clear evidence of the role of gyro-motion in the diffusion process. Thirdly, we have observed the diffusion of a Skyrmion in uniformly extended ferromagnetic films. In the uniform film, Skyrmions show free diffusion as it is shown in Fig. 1. The analysis of the simultaneous position-position correlation function &lt;X(t)*X(t)&gt;, which is a half of the mean square displacement (MSD), results that &lt;X(t)*X(t)&gt; is proportional to the elapsed time providing the diagonal diffusion constant as its slope. On the other hand &lt;X(t)*Y(t)&gt; is zero as it is expected form the symmetry. While, we have found that simultaneous velocity-position correlation functions (&lt;Vx(t)*X(t)&gt; and &lt;Vx(t)*Y(t)&gt;) are non-zero. From the theory, &lt;Vx(t)*Y(t)&gt; corresponds to the gyro-diffusion constant. The size of the observed gyro-diffusion constant is about 1/10 of the diagonal diffusion constant, and non-negligible. However, the sign of the observed gyro-diffusion constant is opposite to that expected from a sense of gyro-motion. Since the sense of the gyro-motion is determined by the sign of the Skyrmion number, it should not be changed easily. The change of the sign in the gyro-diffusion constant will be discussed in terms of the diffusion in a potential. Finally, essential devices to construct a Brownian computing circuit, i.e. hub, ratchet, and c-join [3], were tested. By now, ratchet and c-join need a control using MOKE observation and manual feedback. To overcome this difficulty, we are now developing autonomous devices using voltage control [9, 10] of the Skyrmion (Fig. 2). Acknowledgments The authors acknowledge Mr. Y. Jibiki of Osaka University, Dr. S. Auffret, Dr. C. Baraduc, and Dr. Hélèn Béa of Spintech, France for their initial contributions. The authors also acknowledge Dr. M. Oogane for his FMR measurements. This research and development work was supported by the ULVAC, Inc., the Ministry of Internal Affairs and Communications, Basic research S (20H05666) of JSPS, and CREST (Non-classical Spin project) of JST.

**References:**

[1] N. Nagaosa et al., Nat. Nanotech. 8, 899-911 (2013). [2] J. Zazvorka et al., Nat. Nanotech. 14, 658 (2019). [3] F. Peper et al., ACM J. Emerg. Technol. Comput. Syst, 9, 1, Article 3 (2013). [4] A. Thiele et al., Phys. Rev. Lett. 30, 230 (1973). [5] C. Schuette et al., Phys. Rev. B 90, 174434 (2014) [6] E. Tamura et al. https://arxiv.org/abs/2005.04860. [7] Y. Jibiki et al., Appl. Phys. Lett. 117, 082402 (2020). [8] L. Zhao et al., Phys. Rev. Lett. 125, 027206 (2020). [9] T. Nozaki et al., Appl. Phys. Lett. 114, 012402 (2019). [10] M. Scott et al., Nano Lett. 17, 3006 (2017).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/6533c8637225b7f1b2cad390443cbfe3.jpg)
Fig. 1 Trajectories of magnetic skyrmions observed at 316 K using a MOKE microscope.

![](https://assets.underline.io/uploads/markdown_image/1/image/4c8fd416dc80b83ea49919378f59a037.jpg)
Fig. 2 Voltage/current controlled Skyrmion ratchet (test device).

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