Tunable perpendicular magnetic anisotropy (PMA) in thin film magnetic devices provides an isotropic in-plane permeability, necessary for integrated microwave and mm-wave devices and an opportunity to break inversion symmetry that allows implementations of non-reciprocal devices like circulators and isolators. In ferrimagnetic alloys like GdxCo1-x, this is usually achieved by changing the composition such that the magnetic properties lie on either side of the composition-dependent magnetic compensation at room temperature, as shown in Fig. 1. Different compositions achieved in this work by changing the sputtering power of the Gd target show that magnetic compensation window lies between x = 28-32, and the effective anisotropy diverges about the compensation point. 

One less explored pathway is the incorporation of oxygen, which until now has been ruled out as a detriment to the ferrimagnetic properties [1]. Here, we show that preferential oxygenation of GdxCo1-x through a reactive sputtering process, such that the cation (Gd and Co) to oxygen anion ratio is 1:1, increases the effective anisotropy energy density by two orders of magnitude compared to the corresponding alloys without oxygen. X-ray photoelectron spectroscopy reveals that strong PMA with an optimal oxygen flow results in a Co-deficient stoichiometry of Gd21Co28O51, which suggests that strong ferrimagnetic order likely arises from a superexchange-like coupling between Gd and Co via the non-magnetic O [2]. This can produce a spontaneous magnetization in the out-of-plane direction due to weaker exchange interactions within the alloy in a heavy-metal/ferrimagnet heterostructure for PMA. Even greater anisotropy fields on the order of 11 kOe are achieved in a super-lattice with 10 repetitions of the GdxCo1-x heterostructure unit-cell, which corresponds to an operating frequency of 30 GHz. Therefore, not only does oxygenation increase PMA and provide tunable anisotropy to amorphous Gd-Co films, but the oxygen incorporation itself also increases the resistivity of the film, making it even more suitable for that frequency range. 
**References:** [1] K. Ueda, A. J. Tan, and G. S. D. Beach, AIP Advances, vol. 8, no. 12, p. 125204, Dec. 2018. 
[2] R. J. Gambino and J. J. Cuomo, Journal of Vacuum Science and Technology, vol. 15, no. 2, pp. 296–301, Mar. 1978. 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/0641d84a745d89c9edb1bbc17e16653a.png) 
Fig. 1. Saturation Magnetization and Effective Anisotropy Energy Density for varying GdxCo1-x compositions for x = 18-39.

Role of Composition and Oxygen in Ferrimagnetic GdxCo1 x Alloys for Microwave/mm

High-performance magneto-dielectrics with high permeability and permittivity, low magnetic and dielectric losses, and high cutoff frequency are promising candidate materials for next-generation communication applications, owing to their significant advantages for antenna miniaturization and bandwidth enhancement. Due to limited resonant frequencies and large natural resonance linewidths, conventional microwave ferrites and their composites, which are usually used over the frequency range from several hundred MHz to several GHz, do not meet the requirements for 5G communications.1-3 A unique type of hexaferrites named Mg-Zn 18H hexaferrite, whose crystal structure can be interpreted as the structure of Y-type hexaferrites with intercalation of a three-layered hexagonal barium titanate block into the middle of the T-block as shown in Fig. 1a, has been synthesized, and its microwave properties have been comprehensively investigated for the first time.4 The Mg-Zn 18H hexaferrite shows an extremely low damping coefficient of 0.1-0.2, indicating concentrated magnetic loss within a narrow frequency band and a narrow ferrimagnetic resonance linewidth of 486-660 Oe. Owing to this remarkably low damping coefficient, the Mg-Zn 18H hexaferrite possesses an excellent magnetic loss tangent as low as 0.06 and a small dielectric loss tangent less than 0.006 over 2-4 GHz, representing superior magneto-dielectric performance among the reported microwave ferrites for the S band applications as shown in Fig. 1b. Moreover, excellent thermal stability for the damping coefficient is observed to be 0.0004 K-1 over the temperature variation of most practical applications. When employed as the substrate of a 3.6-GHz patch antenna, the Mg-Zn 18H hexaferrite shows a miniaturization factor of ~5 and significant bandwidth improvement of ~50-110% over conventional dielectrics. These results imply the great technological potential and commercial value of the 18H hexaferrites for 5G communications. 
**References:** 1V. G. Harris, IEEE Trans. Mag. 48, 1075 (2012). 
2V. G. Harris, A. Geiler, Y. Chen, S. Yoon, M. Wu, A. Yang, Z. Chen, P. He, P. V. Parimi, X. Zuo, C. E. Patton, M. Abe, O. Acher, and C. Vittoria, J. Magn. Magn. Mater. 321, 2035 (2009). 
3Q. Li, Y. Chen, C. Yu, K. Qian, V. G. Harris, J. Am. Ceram. Soc. 103, 5076 (2020). 
4Q. Li, Y. Chen, C. Yu, L, Young, J. Spector, and V. G. Harris, Acta Mater. 231, 117854 (2022). 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/b2b57c67782800adf088a5c437a9d3be.png) 
(a) Schematic illustration of the Mg 18H hexaferrite unit cell with the stacking subunit blocks denoted. (b) Performance of magneto-dielectric materials for microwave applications. The figure of merit (FOM) are indicated by the dashed lines.

Emerging Magneto Dielectric Materials for 5G Antenna Miniaturization: 18H Hexaferrites

The structurally coupled interaction between a piezoelectric and ferromagnetic magnetostrictive material can be exploited to develop magnetoelectric systems which have potential to rival current technologies with reduced power consumption and size. In a magnetoelectric multiferroic system the bilateral control of the magnetic and piezoelectric response is dictated by the material properties, where a soft magnetic material with large magnetostriction facilitates the large voltage-induced strain in the piezo/ferroelectric layer. Thin film deposition techniques utilized for device fabrication often complicate the optimization of the interaction between layers due to inherent stresses occurring during deposition which are often deleterious to the magnetoelectric functionality. While incorporation of metalloid substitutions, such as in (Fe0.5Co0.5)1-xCx, and (Fe0.5Co0.5)1-xBx are able to reduce the inherent coercive field and retain a high magnetostrictive and piezomagnetic properties the as-deposited stress states are rarely discussed [1,2]. To this end we have studied the incorporation of Hafnium in to an Fe50Co50 matrix with a focus on correlation between the film stress and magnetic properties. In these sputter-deposited thin films we find a relationship among the magnetic and stress properties as a function of doping percentage. With increasing Hf composition the system exhibits a minimum coercive field occurring at a crossover from a compressive to tensile stress state. Scanning electron microscopy (SEM) and X-ray diffraction (XRD) of the (Fe0.5Co0.5)1-xHfx system reveal the magnetic softening is also correlated to emergence of an amorphous phase with reduced grain size for these sputter-deposited films. This ternary alloy presents an additional avenue for optimization of artificial magnetoelectric systems and has applications for multiple types of microelectromechanical devices. 
**References:** [1] J. Wang, Phys. Rev. Applied 12, 034011 (2019) 
[2] J. Lou, Appl. Phys. Lett. 91, 182504 (2007)

Development of a Hafnium Iron

Enormous research activities to develop advanced superparamagnetic iron oxide nanoparticles (SPIONPs) enabling to generate higher AC heat induction temperature (TAC) or specific loss power (SLP) at the biologically safe and physiologically tolerable range of AC magnetic field (HAC) (HAC,safe < 1.8 × 109 A m-1 s-1, fappl < 120 kHz, Happl < 190 Oe (12.5 A m-1)) have been intensively made in the past two decades for magnetic hyperthermia application [1-3]. According to the reports made so far, a high magnetic softness (or high magnetic moment m) and a high initial susceptibility (χ0) at the DC magnetic field were revealed to be critical parameters in enhancing the TAC (SLP) due to the correspondingly enhanced Néel relaxation time constant (τN), which is the same as the effective relaxation time constant (τeff), τN ≈ τeff , in solid-state SPIONPs. However, MnFe2O4 SPIONPs with high magnetic moment usually show low TAC (SLP) compared to magnetically semi-hard CoFe2O4 SPIONPs with a relatively low m [4,5]. 
In this work, our research efforts primarily focused on exploring the physical and chemical reasons why MnFe2O4 SPIONPs with high DC magnetic softness show an extremely low TAC (SLP) by systematically investigating the physical role of magnetically semi-hard Co2+ cation addition in enhancing TAC (SLP) of solid (CoxMn1-x)Fe2O4 SPIONPs. According to the experimentally and theoretically analyzed results, it was clearly demonstrated that the enhancement of magnetic anisotropy (Ku)-dependent AC magnetic softness including the Néel relaxation time constant τN (≈ τeff), and its dependent out-of-phase susceptibility (χ″) are the most dominant parameters to enhance the TAC (SLP). This clarified result strongly suggests that the development of new design and synthesis methods enabling to significantly enhance the Ku by improving the crystalline, shape, stress (magnetoelastic), thermally-induced, and exchange anisotropies is the most critical to enhance the TAC (SLP) of SPIONPs at the HAC,safe (particularly at the lower fappl < 120 kHz) for clinically safe magnetic nanoparticle hyperthermia. 
**References:** [1] Joshi et al, J. Phys. Chem. C, 113, 17761-17767 (2009) 
[2] Lee et al, Nat. Nanotechnol., 6, 418-422 (2011) 
[3] Sathya et al, Chem. Mater., 28 1769-1780 (2016) 
[4] Mameli et al, Nanoscale, 8 10124-10137 (2016) 
[5] Albino et al, J. Phys. Chem. C, 123, 6148-6157 (2019)

The Role of Co2+ Cation Addition in Enhancing the AC Heat Induction Power of (CoxMn1 x)Fe2O4 Superparamagnetic Nanoparticles

Rare-earth iron garnets, a ferrimagnetic insulator, have received attention for their many properties including small damping and tunable magnetization and angular momentum compensation temperatures. Most research efforts have been focused on garnet thin films grown on the (111) plane because of their perpendicular magnetic anisotropy (PMA), and the in-plane anisotropy, however neglected, can be important for our understanding of the switching behavior and the energetics of magnetic textures. In-plane anisotropy can be conveniently explored in garnet thin films on (110) planes. Here we combine a theoretical and experimental analysis of the anisotropy landscape for Europium iron garnet (EuIG) epitaxially grown on (110) Gadolinium Gallium garnet (GGG) using pulsed laser deposition. 

The angular dependence of anisotropy is calculated by combining the individual contributions including magnetocrystalline anisotropy, magnetoelastic anisotropy, shape anisotropy and growth-induced anisotropy, which may contribute for non-ideal stoichiometry. This predicts an easy axis out of plane along [110], with hard and intermediate axes in plane along [001] and [1-10] respectively. The anisotropy landscape is probed with vibrating sample magnetometry (VSM) and spin-Hall magnetoresistance (SMR) measurements. The SMR result is simulated and fitted to a Stoner-Wohlfarth model. The experimental measurements yield the expected hard and easy axes but the model requires additional multi-domain consideration to capture the hysteresis behavior when the external field is swept along the intermediate in-plane axis. Understanding the in-plane anisotropy effect, especially the unexpected hysteresis in in-plane direction for a PMA film could have help with the interpretation of the switching behavior. 
**References:** 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/63c6aed2fe471bacc1d3440ce0a33059.png) 
Fig. 1 (a) VSM measurement along the in-plane easy (IP 35, [1-10]), in-plane hard (-55, [001]) and out-of-plane (OP, [110]) axes. (b) Left: Principal anisotropy axis definition in EuIG and setup for Stoner Wohlfarth simulation. Right: 3D polar plot for anisotropy landscape in EuIG. (c) SMR measurement for field swept along the hard anisotropy axis, with fit (red). (d) SMR measurement for field swept along the intermediate anisotropy axis.

Anisotropy Landscape Analysis in (110) Rare earth Iron Garnet Films

Amorphous alloys have excellent low loss characteristics and are suitable for high-performance motor cores [1]. Due to the limitation of the thickness of extremely thin soft magnetic materials, stamping is not suitable for processing. At present, the most commonly used processing method is EDM [2], but this method will generate high temperature at the edge of the material, thereby changing the internal structure of the edge of the material, making iron loss worsens. 
In this paper, a ring-like experiment method was used to explore the effect of EDM on the deterioration of iron loss. The first part of the paper analyzes the research situation of the scholars on the deterioration of the iron loss at the edge of the soft magnetic material core; The second part introduces the basic principles and specific methods of the ring-like experiment（The sample and principle are shown in Fig. 1）, and explores the relationship between the ratio of the area affected by cutting to the total area and the deterioration of iron loss. Taking 0.05mm ultra-thin silicon steel as a control（Some experimental results are shown in Fig. 2）, comparing the degree of iron loss deterioration of the two materials, and analyzing the iron loss deterioration law of ultra-thin soft magnetic materials; The third part analyzes the metallographic diagram of the material, observing the crystallization of amorphous alloys at the edge after EDM cutting and the behavior of 0.05mm ultra-thin silicon steel grains, and explains the reasons for the difference in the degree of deterioration of the two materials from a microscopic point of view; Finally, summarize the relevant conclusions. 
To sum up, this paper compares the iron loss deterioration of amorphous alloys and other ultra-thin soft magnetic materials, and explores the iron loss deterioration law of amorphous alloys with different proportions of the area affected by cutting from the perspective of experimental data and microstructure. In the follow-up work, according to this law, the exact value of the iron loss deterioration at the cutting edge of the material is deduced to provide guidance for the application of amorphous alloys. 
**References:** [1] Li T , Zhang Y , Liang Y , et al. Multiphysics Analysis of an Axial-Flux In-Wheel Motor With an Amorphous Alloy Stator[J]. IEEE Access, 2020, 8:1-1. 
[2] Chai F , Li Z , Chen L , et al. Effect of Cutting and Slot Opening on Amorphous Alloy Core for High-Speed Switched Reluctance Motor[J]. IEEE Transactions on Magnetics, 2020, PP(99):1-1. 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/d02ef63c98d1b3b945fec492fdd4a75a.png) 
Fig. 1 Test ring samples and principle 
![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/696424145d13f052da5f61f4252674b7.png) 
Fig. 2 Part of the experimental data

Study on Deterioration of Iron Loss of Amorphous Alloy by Wire Electrical Discharge Machining

Studies of Giant Magnetoimpedance (GMI) effect have attracted considerable attention considering various technological applications [1,2]. Up to now, most attention has been paid to the achievement of the highest GMI as well as to tailoring of the magnetic field dependence of GMI effect through the modification of the magnetic anisotropy of the magnetic materials. Generally, the magnetic anisotropy of amorphous materials can be controlled by the magnetostriction coefficient (that to great extend is linked to the chemical composition of material) or by special thermal treatment (including magnetic field or stress-annealing) [2,3]. Most of studies of GMI effect are performed in different families of magnetic wires [1-3]. 
Recently, a new approach allowing to tune the magnetic anisotropy of magnetic wires by depositing of magnetic and non-magnetic layers onto the glass-coating [4].
Accordingly, the purpose of this paper is to study the GMI effect in amorphous Co-rich microwires with Co- layers deposited onto glass-coating. 
Studies of magnetic properties and GMI effect of as-prepared amorphous Fe3.6Co69.2Ni1B12.5Si11Mo1.5C1.2 and of the same microwires with deposited Co-layer microwires reveals that both samples present soft magnetic properties and high GMI effect. Low field hysteresis loops of both samples are rather similar, while the contribution of Co-layer is observed in hysteresis loop measured at higher magnetic field (see Figs 1a,b). Such character of hysteresis loop is similar to those observed in microwires with mixed amorphous- crystalline structure [5]. However, the GMI ratio, ΔZ/Z and magnetic field, H, dependences of GMI effect are affected by the Co-layer (see Fig.2). In particularly, higher GMI ratio and sharper peaks on ΔZ/Z (H) dependencies. 
We discussed observed experimental dependences considering both change of the internal stresses originated by the Co-layer as well as the magnetostatic interaction between the amorphous ferromagnetic nucleus and deposited Co Layer. 
**References:** 
[1] T. Uchiyama, K. Mohri, and Sh. Nakayama, IEEE Trans. Magn., 47, No 10 (2011) pp. 3070-3073 
[2] F.Qin, H.-X. Peng, Prog.Mater. Sci,58 (2013) 183–259 
[3] A. Zhukov, et.al. J. Alloys Compound 814 (2020) 152225, 
[4] K.R. Pirota, M. Hernandez-Velez, D. Navas, A. Zhukov and M. Vázquez, Adv. Funct. Mater. 14 No 3 (2004) 266-268. 
[5] V. Zhukova, et.al. , Chemosensors, 9 (2021) 100, doi: https://doi.org/10.3390/ chemosensors9050100 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/fcd16c5915024c52cc375c38ac9ea4a7.png) 
Fig.1 Low field (a) and high field hysteresis loops of studied microwires 
![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/1b1cb1408a5636b26250156f0a2b3a1b.png) 
Fig.2. ΔZ/Z (H) dependencies of microwire without Co-layer (a) and with Co-layer deposited onto glass-coating (b)

Magnetic properties and giant magnetoimpedance effect in multilayered microwires

Recently, multifunctional composite materials with magnetic wire inclusions for non-destructive and non-contact stress and temperature monitoring have been proposed [1]. Therefore, studies of temperature dependence of the Giant magnetoimpedance, GMI, effect become essentially relevant. There are only very few studies on temperature dependence of GMI and most of them were performed in thick amorphous wires without glass coating and in very limited temperature range [2,3,4]. Although usually the highest GMI effect is observed in Co-rich magnetic wires, GMI effect of Fe-rich glass-coated microwires can be substantially improved by stress-annealing induced magnetic anisotropy [5]. 
GMI effect and magnetic properties under temperature influence of as-prepared and stress annealed (annealing temperature Tann= 325 oC, stress applied during the annealing σ= 190MPa) thin amorphous Fe75B9Si12C4 glass-coated microwires produced by the Taylor Ulitovsky technique are analyzed. Remarkable change in the hysteresis loops and GMI effect is observed for both samples upon heating. For as-prepared FeBSiC microwire a beneficial influence of temperature on the GMI ratio is observed and hysteresis loops change of character from almost rectangular shape to inclined one (Fig.1). On the other hand, although GMI ratio improvement after stress-annealing decreases with the temperature increasing (Fig.2), temperature dependence can be tuned by the stress annealing conditions. Additionally, almost complete reversibility of the changes induced by the temperature is observed. 
Temperature dependence of the hysteresis loops and GMI effect of studied microwires is explained considering the heating effect on the internal stresses relaxation, the modification of the thermal expansion coefficients of the metallic nucleus and the glass coating and in terms of the Hopkinson effect. 
**References:** [1] A. Allue et al., Compos. Part A Appl. Sci. and Manuf., Vol. 120, p.12 (2019). 
[2] J. Nabias, A. Asfour and J. Yonnet, IEEE Trans. Magn., Vol. 53(4), p.4001005 (2017). 
[3] J.D. Santos, R. Varga, B. Hernando and A. Zhukov, J. Magn. Magn. Mater. 321, p.3875 (2009). 
[4] M. Kurniawan et al., J. Electron. Mater., Vol. 43, p.4576 (2014). 
[5] V. Zhukova et al., Scr. Mater., Vol. 142, p.10 (2018). 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/4bac301404213f54c4bb4adca5d0984b.png) 
Fig.1. Hysteresis loops (a) and GMI ratio at f= 50 MHz (b) of as-prepared sample, measured at different temperature. 
![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/2cf9acf5640bce6a1403026372c49c55.png) 
Fig.2. Hysteresis loops (a) and GMI ratio at f= 50 MHz (b) of stress annealed sample at 325 oC during 15 min (applied stress σ= 190 MPa), measured at different temperature.

Effect of temperature on magnetic properties and magnetoimpedance effect in Fe rich microwires

Soft magnetic material with high magnetic flux density (B), high permeability (µ), and high resistivity (ρ) is the key for miniaturized high frequency (>10 MHz) passive devices. The popularity of ferrites wane beyond 10 MHz owing to their prohibitively large magnetic losses (Pm), similarly, the spherical ferromagnetic alloys are too lossy due to eddy current losses (Pe). Of late, composites of electrically insulated magnetic particles attracted much attention. However, the trade-offs between µ, ρ, Pm and Pe, etc. demand judicious design of materials to stem eddy-current losses and skin effect by optimizing the thickness and properties of the insulation layer surrounding the magnetic body [1,2]. 
Here we demonstrate magnetically-aligned FeSiB-based soft magnetic flakes (SMFs; 63-106 µm, t:2-5 µm) coated with optimally thick (~10 nm) SiO2 as the potential magnetic core for power inductors operating beyond 10 MHz. The SMFs with such a high aspect ratio was fabricated by combination of mechanical ball milling of ribbons and then electrically insulted by an optimized sol-gel procedure in presence of silane coupling agent (APTES). Milling helped to reduce ribbon thickness below its skin depth to eliminated Pe at high frequencies. The effect of milling (duration, RPM, BPR) and coating conditions on the properties of the SMFs were thoroughly investigated. An optimally-tiny fraction of the milled flakes is allowed to become nanocrystalline (Fig. 1c) that augments B and µ without incurring losses. XPS and magnetization measurement results indicate that the thin but robust insulation layer is preserved through the post-annealing process which is necessary for removal of stress. B-H loop shows post-processing, coercivity is reduced significantly (from ~57 to ~6 Oe), but magnetic flux remains same. 
**References:** [1] T. Suzukia, P. Sharmaa, A. Makino, J. Magn. Magn. Mater. 491 (2019) 165641 
[2] F. Luo, X. Fana, Z. Luoa, W. Hua, J. Wangd, Z. Wu, G. Li, Y. Li and X. Liu, J. Magn. Magn. Mater. 498 (2020) 166084 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/080b991caad833ef058948eeb3dc2146.png) 
Fig 1: (a) Schematic representation of the SMFs core. (b) SEM image of the FeSiB-based as-milled flakes. (c) XRD patterns and (d) hysteresis loops of the as-milled and of SiO2 coated flakes (~63-106 µm) before and after annealing at 425oC in an inert atmosphere.

Fabrication and soft magnetic properties of FeSiB based flakes with insulating surface layer

Spin-orbit torque (SOT) arising from spin-orbit coupling promises efficient magnetization switching in spintronic devices. It is important for device applications that the SOT switches perpendicular magnetizations without an external magnetic field. In addition to field-free switching, reducing SOT switching current is another essential requirement for low energy consumption.
In this talk, we first demonstrate spin currents and associated SOT in ferromagnet/non-magnet/ferromagnet trilayers, in which the torque on the top magnetic layer can be controlled by changing the magnetization of the bottom ferromagnetic layer. In this structure, by aligning the magnetization of the bottom magnetization parallel to the current direction, spin current can carry out-of-plane spin polarization, enabling field-free SOT switching of the top perpendicular magnetization [1]. The out-of-plane SOT is generated by spin current precession at the interface due to the interfacial spin-orbit field. Second, we show that the spin current caused by the spin anomalous Hall effect can be additionally exploited in epitaxial Co-based magnetic trilayers (2). The large in-plane magnetic anisotropy of the epitaxial Co makes it possible to control the magnetic easy axis of the bottom magnetic layer away from the current direction. It is found that the critical current for field-free switching is reduced when the magnetization is at an angle between 30 and 45 degrees from the current direction where the spin anomalous Hall effect is non-negligible.
References (1) S-h. C. Baek, et al, Nat. Mater. 17, 509 (2018)
(2) J. Ryu, et al, Nat. Electron. 5, 217 (2022)

Efficient field free spin

Ultra-rapid annealing (URA) is an effective method to induce nano-crystallization in Fe-B based melt-spun amorphous precursors. The grain size after nano-crystallization depends on the heating rate employed for URA and thus, samples with a range of mean grain sizes can be prepared without altering the chemical composition. Such nanocrystalline samples are ideal for investigating the effect of mean grain size (D) on the core loss. In this study, we prepared a series of nanocrystalline Fe86B13Cu1 samples with grain sizes of 14.5, 21.7, 31.9 and 40.6 nm by varying heating rate between 10 and 104 K s-1. The core loss was measured on an Epstein frame in a frequency range between 10 Hz and 30 kHz. The measured core loss was separated into 3 parts, i.e. the hysteresis loss (Ph), classical eddy current loss (Pc) and the residual part, often referred to as the anomalous loss (Pa). Figure 1(a) shows an example of the relationship between Pa and the product of frequency (f) and the maximum polarization (Jm). The anomalous loss at Jm between 0.6 and 1.0 T is described universally by a simple power dependence with an exponent of about 1.4 over a wide frequency range between 10 Hz to 30 kHz. The grain size dependence of the coercivity (Hc) and the loss per cycle is shown in Fig. 1(b). Hc follows roughly a D3 dependence, suggesting that the samples contain large induced anisotropies. The hysteresis loss per cycle (Ph/f) reflects this steep D dependence while the anomalous loss at low frequencies appears almost independent of the grain size. Thus, the grain size effect on the total loss at low frequencies is attributable to the change in the hysteresis loss which reflects the static coercivity. However, the anomalous loss at 30 kHz shows a clear increase with an increase in D, indicating that the anomalous loss also becomes influential to the grain size dependence of the total core loss at high frequencies. 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/60af3f772649b19f2c862fbc70aeea50.png) 
Fig. 1. (a) Anomalous loss versus Jm*f for a mean grain size (D) = 14.5 nm, and (b) changes in the coercivity and core loss per cycle as a function of D for nanocrystalline Fe86B13Cu1.

Effect of grain size on the core loss of nanocrystalline Fe86B13Cu1 prepared by ultra rapid annealing

The combination of inversion symmetry breaking and spin-orbit coupling (SOC) give rise to spin-orbit torque (SOT), charge pumping, and chiral magnetism. In conventional SOT studies, the inversion symmetry breaking usually comes from the structure or the geometry, e.g. crystal inversion assymmety in the bulk of diluted ferromagnet with zinc-blende structure (Fig. 1a) and space inversion assymmetry in a heavy metal/ferromagnet bilayer (Fig. 1b). It was known that the SOT strength can be controlled by the magnitude of the SOC, therefore, heavy metals with large SOC has been widely used for SOT-based magnetic random-access memory (MRAM).
In our study, we demonstrated that the vertical composition gradient in a single FePt layer acts as a new type of inversion symmetry breaking (Fig. 1c). The SOT efficiencies scale almost linearly with the composition gradient (G), which is defined to be the change of the Co/Pt ratio per 1 nm. We found that by changing G from 0.31 %/nm to 0.71 %, the SOT efficiency increases by 300 %. In experiments, the composition gradient can be easily controlled during sample growth. Therefore, our work provides a powerful tool to tune the SOT strength.
Then we demonstrated the current-induced magnetization switching in a FePt single layer (Fig. 1e). However, this switching requires an in-plane external magnetic field to break the symmetry. For real application, it is pursued to realize magnetic field-free switching. To achieve this goal, we move our attention from L10 FePt (P4/mmm) to fcc CoPt3. Both of them possess good perpendicular magnetic anisotropy (PMA) and hold promise in magnetic storage (media and memory). We found that the CoPt3 has two structural properties, as illustrated in Fig. 2(a). One is the composition gradient along the thickness direction which can break the inversion symmetry and allows for the generation of the in-plane damping-like torque. The other is the formation of the Co platelets in the Pt-rich matrix near the substrate during growth. We can make a symmetry analysis of the Co platelet/Pt structure, and we can easily find that the mirror symmetry is broken relative to the (11-2) plane and preserved relative to the (1-10) plane. Therefore, when the current is applied along the [1-10] direction (low-symmetry axis), the lateral mirror symmetry is broken so that the out-of-plane SOT can be allowed. Then we can achieve the field-free magnetization switching (0 deg in Fig. 2c). In contrast, when the current is applied along the [11-2] direction (high-symmetry axis), the lateral mirror symmetry is preserved and there is no field-free switching (90 deg in Fig. 2c). We also found that the current-induced switching exhibit a three-fold angular dependence on the current angle (θI), which is in perfect agreement with the three-fold rotational symmetry of the crystal structure in Fig. 2b.
To summarize, we observed the field-assisted magnetization switching in FePt single layer by introducing a new type of inversion symmetry breaking: composition gradient. Furthermore, we demonstrated the symmetry-dependent field-free magnetization switching in the CoPt3 single layer. The composition gradient along the film's normal direction gives rise to the in-plane damping-like torque while the low symmetry (3m1) property at the interface of Co platelet/Pt gives rise to the 3m torque in CoPt3. The cooperation of these two effects leads to a three-fold field-free switching in the CoPt3 single layer. Our result of the self-switching in CoPt3 has provided one of the most simplified structures for field-free switching of perpendicular magnetization. The good endurance and high thermal stability make it a good candidate for magnetic memory devices and other spintronic applications.

**References:** 

[1] L. Liu, et.al., Electrical switching of perpendicular magnetization in a single ferromagnetic layer Physical Review B 101 (22), 220402 (2020). 

[2] L.Liu, et.al., Current-induced self-switching of perpendicular magnetization in CoPt single layer Nature Communication 13, 3539 (2022).

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Underline digital video library

Role of Composition and Oxygen in Ferrimagnetic GdxCo1 x Alloys for Microwave/mm

Emerging Magneto Dielectric Materials for 5G Antenna Miniaturization: 18H Hexaferrites

Development of a Hafnium Iron

The Role of Co2+ Cation Addition in Enhancing the AC Heat Induction Power of (CoxMn1 x)Fe2O4 Superparamagnetic Nanoparticles

Anisotropy Landscape Analysis in (110) Rare earth Iron Garnet Films

Study on Deterioration of Iron Loss of Amorphous Alloy by Wire Electrical Discharge Machining

Magnetic properties and giant magnetoimpedance effect in multilayered microwires

Effect of temperature on magnetic properties and magnetoimpedance effect in Fe rich microwires

Fabrication and soft magnetic properties of FeSiB based flakes with insulating surface layer

Efficient field free spin

Effect of grain size on the core loss of nanocrystalline Fe86B13Cu1 prepared by ultra rapid annealing

Spin orbit torque induced magnetization switching in single ferromagnetic layer

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