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One of the main goals of quantum computing is to find stable quantum bit realizations. Magnetic chains on superconducting surfaces manifest topologically protected Majorana quasiparticles as zero-energy modes located at the ends of the chain makeing them possible candidates for such fault-tolerant quantum computing.&lt;br/&gt;The rapid development of scanning tunneling microscopy measurements in the past decade provided an effective way to study these system in experiments with a high energy resolution turning not only the experimental but the theoretical interest to this way.&lt;br/&gt;In the present work we introduce an ab initio approach employing multiple scattering theory and Green&#39;s function embedding for the calculation of the spectral properties of magnetic impurities embedded onto the surface of a superconducting host.&lt;br/&gt;We consider different Fe clusters separated by a single Au overlayer on Nb(110) which is highly motivated by experiments. We perform systematic calculations for dimers and chains along different crystallographic directions, with different distances of the Fe atoms and in different magnetic configurations. Based on the local density of states (LDOS) we study the conditions under which Majorana zero modes might appear.

![](https://assets.underline.io/uploads/markdown_image/1/image/95e695f41378765994be56999251c555.jpg)

Fig.1 The spatial distribution of a YSR state for an Fe dimer on Au/Nb(110)

2022 Joint MMM-INTERMAG

Theoretical study of Yu-Shiba-Rusinov states and Shiba bands for Fe dimers and chains on Au/Nb(110)

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INTERMAG 2021

One of the main goals of quantum computing is to find stable quantum bit realizations. Magnetic chains on superconducting surfaces manifest topologically protected Majorana quasiparticles as zero-energy modes located at the ends of the chain makeing them possible candidates for such fault-tolerant quantum computing. The rapid development of scanning tunneling microscopy measurements in the past decade provided an effective way to study these system in experiments with a high energy resolution turning not only the experimental but the theoretical interest to this way. In the present work we introduce an ab initio approach employing multiple scattering theory and Green's function embedding for the calculation of the spectral properties of magnetic impurities embedded onto the surface of a superconducting host. We consider different Fe clusters separated by a single Au overlayer on Nb(110) which is highly motivated by experiments. We perform systematic calculations for dimers and chains along different crystallographic directions, with different distances of the Fe atoms and in different magnetic configurations. Based on the local density of states (LDOS) we study the conditions under which Majorana zero modes might appear.

![](https://assets.underline.io/uploads/markdown_image/1/image/95e695f41378765994be56999251c555.jpg)

Fig.1 The spatial distribution of a YSR state for an Fe dimer on Au/Nb(110)

technical paper

The 15th Joint MMM-INTERMAG Conference (2022 Joint) is sponsored jointly by AIP Publishing and the IEEE Magnetics Society. Members of the international scientific and engineering communities interested in recent developments in fundamental and applied magnetism are invited to attend and contribute to the technical sessions. The technical program will include invited and contributed papers in oral and poster sessions, invited symposia, a plenary session, and an evening session, with about 1500 presentations overall. This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

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The meta-magnetic phase transition of equiatomic FeRh allows the 3 temperature model of phase transitions to be probed as it undergoes: (i) a lattice expansion, (ii) an antiferromagnetic (AF) to ferromagnetic (FM) transition [1], and (iii) a change in electronic structure. A spin canting model has been used to describe a spin re-orientation pathway [2], where a feedback loop with induced Rh moments promotes FM order. To investigate such behaviour, a probe of the AF spins is required [3]. In general, the zero-stray field of anti-ferromagnetic materials means that it is hard to detect and perform such measurements. Here, we demonstrate a probe of long-range AF order using non-resonant x-ray scattering. The G2-type order of FeRh in the AF state provides a probe of AF order using ‘magnetic’ Bragg peaks [4]. We demonstrate that these peaks can be measured using x-rays at energies below the Fe K edge. Due to the low efficiency of the magnetic scattering in this material, we describe a grazing incidence geometry to optimise the intensity (see Fig. 1). Based on Scherrer analysis we estimate a coherence length of 40-80 nm, smaller than previous reports in XMLD experiments [5], indicating we are limited by structural defects. The temperature dependent behaviour of the AF order shows an inverse correlation to the emergence of FM moment as seen in Fig. 2. The AF-FM transition as determined by the ordering appears later indicating a mixed phase [6]. Long-range AF order appears to persist when FM moment is already established. Time resolved experiments based on this technique may determine the existence of a meta-stable AF state on time scales where the FM band structure has already formed [7]. It has been shown that the lattice expansion occurs in ≈ 30 ps [8], but it is not known how the long range AF order evolves on such timescales. X-ray diffraction can therefore be used to ascertain if how and if the AF structure is related to lattice expansion occurring at the phase transition.

![](https://assets.underline.io/uploads/markdown_image/1/image/a76ec58a6231ba98b20b00b66541e5c6.jpg)

Dependence of the (3/2,1/2,1/2) peak intensity upon grazing incidence angle (E=4.95 keV)

![](https://assets.underline.io/uploads/markdown_image/1/image/7d4ef6a766865d9d74ecbbf6cb3bfec2.jpg)

The inverse correlation between the intensity of the FeRh (1/2, 3/2, 1/2) magnetic peak, and the saturation moment of the FeRh film

X-ray investigation of long-range antiferromagnetic ordering in FeRh

Flexibility for interface engineering, and access to all-optical switching of the magnetization, make synthetic ferrimagnets (SFiMs) an interesting candidate for advanced spintronic devices like racetrack memory [1,2]. However, the absence of compensation at room temperature (RT) in Co/Gd bilayers has hampered the efficiency with which their magnetic order can be manipulated, as the highest efficiency of spin-orbit torques and current induced domain wall motion (CIDWM) are generally achieved under compensation [3,4]. In order to combine the favourable properties of SFiMs with compensation at RT, Co/Gd/Co/Gd quadlayer structures are investigated. We present a systematic study of the conditions for magnetization compensation and perpendicular magnetic anisotropy (PMA) in Co/Gd/Co/Gd quadlayers. These conditions were investigated on a sample with the middle Co and Gd films wedged orthogonally with respect to each other, as shown in Fig. 1a. By scanning the polar magneto-optical Kerr effect (MOKE), a magnetostatic phase diagram like in Fig. 1b can be obtained. Three regimes are distinguished: In-plane magnetization (teal), and out-of-plane (OOP) Co (red) and Gd (blue) dominated. The boundaries between these regimes provide valuable insight into the balance between shape anisotropy and PMA, and the conditions for compensation. A simple model based on partial intermixing at Co/Gd interfaces has been developed which explains the experiments well, and provides a tool to qualitatively and quantitatively understand these phase diagrams. This work provides a simple framework to experimentally characterise, and describe basic magnetostatic properties in these promising heterostructures. The compensated SFiMs investigated in this research, carry the promise of breaking the elusive 1000 m/s barrier for CIDWM, and exhibiting ultrafast exchange-driven dynamics, both relevant properties for future spintronic devices.

![](https://assets.underline.io/uploads/markdown_image/1/image/97d2d2073b964b56a371f90f9d4c02dc.jpg)

Characterization of double wedge Co(0.65)/Gd(0-3)/Co(0-2)/Gd(1.5) SFiMs. a): Schematic of wedge orientations in the multilayer. b): Magnetostatic phase diagram measured with polar MOKE. Yellow dashed line indicates compensation at RT. Green lines indicate a toy model fit to the boundaries between the three regimes.

Tuning Room Temperature Compensation in Synthetic Co/Gd Ferrimagnetic Quadlayers for Advanced Spintronics Devices

Metallic ferrimagnets consisting of rare earth (RE) / transition metal (TM) alloys exhibit an intriguing magnetic compensation of the RE/TM magnetic sublattices as a function of composition and temperature. We are developing compositionally modulated RE/TM alloy films that exploit the large change in TMagComp as the RE content is varied. We grow Fe1-xGdx films where the Gd content x is modulated throughout the depth of the film and key question in such structures is the interface length between two Fe1-xGdx layers with different Gd content; this will establish the minimum modulation length of RE/TM structures with varying composition. We examine a series of bilayer structures [Si/ SiO2(3nm)/Ta(10nm)/Fe1-xGdx(50nm)/ Fe1-yGdy(50nm)/ Ta(8nm)] where the Gd content (x or y) is varied. To investigate the magnetic profile of these films, we utilize polarized neutron reflectometry (PNR) as a function of temperature. PNR is an ideal technique to examine these structures as it probes the magnetization parallel to the field as a function of depth and the magnetic scattering length density (mSLD) is modified significantly as the temperature is tuned through TMagComp of a particular layer. We examine samples where TMagComp of a particular layer is &gt; 300 K, ~100 K and ~50 K. A sample that has TMagComp &gt;300K and ~100K for the bottom and top layers respectively exhibits strong modifications to the spin asymmetry [SA: (↑↑- ↓↓)/(↑↑+↓↓)] of the PNR. The SA develops a pronounced dip at Q~0.045 Å-1 and reduced broadening of the peak at Q~0.28 Å-1 as the temperature decreases (Fig 1). Similar variations to the SA are observed in samples with different compensation temperatures. To extract the magnetic behavior of the samples while emphasizing the interfacial region, we fit the mSLD for each temperature while keeping the structural properties the same. The fitting suggests that the evolution of the magnetic interface is nontrivial.

![](https://assets.underline.io/uploads/markdown_image/1/image/44fb4812d3585f892c0995ff14de1a9a.jpg)

1-A: High field (1 T) magnetometry vs. temperature for a magnetic bilayer. PNR measurements performed at selected temperatures, denoted by stars, across the complicated temperature profile. 1-B: Spin Asymmetry for the bi-layer samples performed at the 5 temperatures from 1-a.

Modified Magnetic Interface in Compositionally Modulated Ferrimagnetic Fe1-xGdx Multilayers

Exchange springs are versatile systems in which domain walls can be tailored by the different magnetic properties of exchange coupled layers such as in ferrimagnetic GdCo/GdCo’ multilayers [1]. We present here an experimental study by soft X-ray magnetic vector tomography [2] of Gd12Co88/Nd17Co83/Gd24Co76 multilayers with weak stripe domains (induced by NdCo) and in which the competition between exchange and magnetostatic coupling can be tuned by the composition of the ferrimagnetic GdCo layers (as sketched in Fig. 1) [3]. The 3D analysis of the vector magnetic configuration of the Gd sublattice m(Gd) in a demagnetized state shows a complex configuration that includes stripe domains with a distorted closure domain structure across the thickness, exchange spring walls with out-of-plane magnetization reversal and modulated ripple patterns (Fig. 2). An analytical model, proposed to describe global coupling across the exchange spring boundary between NdCo and GdCo layers, shows that the strength of effective interlayer coupling can be finely tuned playing with the averaging of lateral and in-depth competing interactions so that it can be externally adjusted by magnetic history. Work supported by Spanish MICINN under grant PID2019-104604RB/AEI/10.13039/501100011033.

![](https://assets.underline.io/uploads/markdown_image/1/image/6887055ecf6e425f078f1db90e0ff8e4.jpg)

Fig. 1 Sketch of GdCo/NdCo/GdCo' ferrimagnetic multilayer with competing interactions. Exchange at the interface favors parallel alignment of M(Co) in all the layers. However, at top layer Gd24Co76 layer, net magnetization is aligned with M(Gd) and antiparallel with M(Co). Magnetostatic interactions, represented by an effective stray field εHd, favor an antiparallel alignment of M(Co) at both sides of the interface. These competing interactions create an exchange spring near the top of the multilayer.

![](https://assets.underline.io/uploads/markdown_image/1/image/ee173d4a2dd2f9bc12ca1560245e6d9e.jpg)

Fig 2. Tomographic reconstruction of m(Gd) (my contrast): At top Gd24Co76, there is a ripple pattern around easy anisotropy axis; At bottom Gd12Co88, there is a distorted closure domain structure. Across the thickness, closure vortex cores are arranged in a zig-zag. Sketch shows the exchange spring between stripe domains at NdCo/GdCo layers and in-plane domain with ripple at top Gd24Co76 layer.

Adjustable exchange springs in ferrimagnetic multilayers with stripe domain patterns visualized by X-ray vector tomography

Interfacial phenomena in magnetic thin film systems are key to future spintronic applications. For materials close to the Stoner criterion, such as Pt, electronic hybridisation at the interface with a magnetic material results in a proximity induced moment (PIM), with debate ongoing regarding the role of the induced moment with regards to interfacial spin transport [1,2]. Recently, rare-earth:transition metal (RE:TM) ferrimagnetic alloys have shown promise in spintronic applications, due to the net zero magnetisation at the compensation point of the two competing magnetic sub-lattices. This compensation, which occurs as a function of both temperature and alloy composition, enhances domain wall motion [3], thermal switching [4] and leads to vanishing skyrmion Hall angles [5]. However, in multilayered systems, it has not been experimentally shown whether the induced moment in a Pt at the interface with a RE:TM ferrimagnet will align with the net moment, or one of the magnetic sublattices. Here we present the results of a recently published study [6] investigating the magnetic moments in ferrimagnetic / Pt systems, using Co77Gd23 and (Co50Fe50)77Gd23 ferrimagnetic alloys to vary the dominant magnetic sublattice. Temperature dependent SQUID measurements, combined with element specific resonant x-ray measurements at the APS, Argonne Lab on the Pt and Gd L3 edges, allowed for the determination of the alignment of the Gd moments and induced Pt moments on either side of the compensation transition. In both cases, the PIM was found to be parallel to the TM sublattice rather than the RE or the net moment. Our results highlight the prominence of the d−d mediated interactions between the Pt and the constituents of the ferrimagnetic RE:TM alloys over the net macroscopic moment.

![](https://assets.underline.io/uploads/markdown_image/1/image/4ff3a1ca1079ff9c262e75f9fde1108a.jpg)

Fig 1: Element specific hysteresis loops taken at the Pt and Gd L3 edges for CoGd/Pt (Gd dominated) and CoFeGd/Pt (CoFe dominated)

Proximity induced magnetism in Pt layered with rare-earth:transition metal ferrimagnetic alloys

Combining perpendicular magnetic anisotropy (PMA) with half-metallicity (HM) in thin-film geometry may provide additional functionalities for spintronic devices. However, such combination may be a challenging task, since HM is usually destroyed in thin-film geometry (e.g., due to the emergence of surface states), while PMA is most pronounced in reduced geometry, because of the contribution from surface anisotropy. Here, we explore the nature of PMA in thin-film full Heusler alloy Co2MnSi. This material is one of the first compounds for which half-metallic electronic structure was experimentally confirmed. In addition, it has been reported that this alloy may exhibit PMA in thin-film geometry. Here, by analyzing site-projected magnetocrystalline anisotropy energy (MAE), we confirm that both PMA and surface half-metallicity are very sensitive to the termination surface and mechanical strain. In particular, while MnSi-termination under compressive strain may retain both 100% spin-polarization and out-of-plane magnetization orientation, Co-termination has a detrimental impact on both. These results may serve as a guide for practical nano-device applications in the field of spintronics. This research is supported by the National Science Foundation (NSF) under Grant Numbers 2003828 and 2003856 via DMR and EPSCoR.

First principles study of perpendicular magnetic anisotropy in thin-film Co2MnSi

In the race for the miniaturization of electronic devices, modern science reached the ultimate level of monoatomic layers. Whereas, magnetic tunnel junctions with perpendicular magnetic anisotropy reached the limit of about twenty atomic monolayers [1]. In our work, we systematically study the magnetic anisotropy of Fe and FeCo thin films of size from one to twenty atomic monolayers. Theoretical studies are based on calculations using the full-potential local-orbital electronic structure code FPLO [2] and generalized gradient approximation (GGA). The chemical disorder in FeCo layers was modeled using virtual crystal approximation (VCA). A set of layers with different thicknesses formed based on the bcc structure was subjected to full geometry optimization. The set of equilibrium structures was then recalculated using a fully relativistic approach for two orthogonal magnetization directions (in-plane and out-of-plane). The results of calculations allow the interpretation of parallel experimental studies in which FeCo layers on Au substrate are analyzed. The result of ab-initio calculations is a series of dependences of structural and magnetic parameters on layer thickness. Fig. 1 shows an example of the dependence of the optimized lattice constant on the Fe layer thickness. For few-atom-thick Fe layers there is a large reduction of the lattice parameter with respect to the value for bulk bcc Fe, to which the parameters determined for thicker layers converge. Fig. 2 presents the dependence of the magnetocrystalline anisotropy energy (MAE) on the Fe layer thickness. Positive values denote perpendicular magnetic anisotropy, negative values denote anisotropy in-plane. The calculated value of MAE for Fe monolayer equal to 0.58 meV/atom is in good agreement with the previous GGA result equal to 0.50 meV/atom [3]. These results were compared with measurements of the ratio of orbital to spin magnetic moment using VNA-FMR. We found that the contribution of surface anisotropy to the effective anisotropy is strong enough to overcome the shape anisotropy in Au/CoFe/Au systems.

![](https://assets.underline.io/uploads/markdown_image/1/image/0cc0613d2960ba04eae25216e4150cf3.jpg)

Fig.1 Dependence of the lattice parameter on the Fe layer thickness.


![](https://assets.underline.io/uploads/markdown_image/1/image/05159cf1c9b8516a3e45b8cc11e76092.jpg)

Fig.2 Dependence of MAE on Fe layer thickness.

Magnetocrystalline Anisotropy of Fe and FeCo Thin Films

Motivated by immense scientific interest in Co-based Heusler compounds [1 - 3] Co2FeSi and Co2TiSi as promising candidates for spintronics applications, 100 nm thick Co2Fe0.5Ti0.5Si (CFTS) thin films were grown on Si(100) substrates at substrate temperatures (TS) ranging from 200°C to 550°C by ultra-high vacuum magnetron sputtering. The deposited films were annealed in-situ at TS for 30 min. Energy-dispersive X-ray absorption spectroscopy yielded the actual alloy composition as Co2.01Fe0.51Ti0.24Si1.24. X-ray diffraction (XRD) patterns, shown in figure 1, reveal no Bragg peaks for TS200 film, broad fundamental peak (220) for TS350 film, and three sharp peaks (111), (220), and (422) for the remaining films. Thus, the crystalline structure gradually evolves from amorphous to ordered L21 structure as the TS increases; the TS500 film has the highest L21 order. Ferromagnetic resonance (FMR) spectra were recorded at various polar (‘out-of-plane’, OP) field angles, θH, at a fixed frequency of 9.45 GHz. A typical FMR spectrum, taken at θH = 0 for the TS500 film, shown in figure 2(a), demonstrates that besides the uniform precession q = 0 spin wave (SW) mode, the SW modes with q ≠ 0 exist. A detailed analysis [4 - 6] of the resonance field, Hres, versus θH plots (see Fig.2(a) inset) reveals a dominant OP uniaxial anisotropy. Fig.2(b) bears out that the frequency (f) vs. Hres plots, obtained using the broad-band (3–17 GHz) FMR setup, are well described by the Kittel resonance condition [7] (the curves through the data points):f=γ/2π[(Hr+Hk)×(Hr+HK+4πMeff)]1/2, where γ=(2πgµB)/h is the gyromagnetic ratio, Meff, effective magnetization while HK, g, and µB are the in-plane (IP) anisotropy field, Lande g-factor and Bohr magneton. We find that the IP anisotropy is very weak, and g has the minimum value of 2.02 for the TS500 film with the highest L21 order. The Gilbert damping constant (α) is determined from the linear fits (straight lines) to the frequency-dependent `peak-to-peak’ FMR linewidth (ΔH) data (symbols), shown in Fig.2(b) inset, based on the relation [8] ΔH=ΔHinhomo+(2/√3)2παf/γ. The TS500 film has the lowest value of α = 0.0032.

![](https://assets.underline.io/uploads/markdown_image/1/image/9533bfba1a7a0a2925e327fb6b2a7807.jpg)

Fig.1:XRD patterns.

![](https://assets.underline.io/uploads/markdown_image/1/image/def68b16a566ae375f2c4e18bf05d2ba.jpg)

Fig.2(a) FMR spectrum; inset: Hres(θH). (b) f(Hres); inset: ΔH(f).

Effect of site disorder on the resonant microwave absorption in Co2Fe0.5Ti0.5Si Heusler alloy thin films

Buckminsterfullerene (C60) can exhibit ferromagnetism at the interface (called as a spinterface) when it is placed next to a ferromagnet (FM). The formation of spinterface can influence the domain size and dynamics of the organic/ferromagnetic heterostructure [1-3]. Perpendicular magnetic anisotropic (PMA) systems are the most suitable candidates for data storage devices due to their high intrinsic anisotropy [4]. It has been demonstrated that with increasing thickness of the OSC layer on a Co ultrathin film one can tune the anisotropy of the system from in-plane to out-of-plane geometry [5]. However, FM-OSC systems with PMA have not been studied extensively. In this context, we have studied the tunability of magnetization relaxation and domain structure for Pt/Co/C60/Pt system with perpendicular anisotropy. We have prepared thin films of Pt/Co/Pt [sample 1] and Pt/Co/C60/Pt [sample 2]. Fig.1 show the hysteresis loops and domain images measured using polar MOKE for both the samples. It has been observed that the size of the bubbles shrinks for sample 2 in comparison to sample 1. The possible explanation may be the formation of spinterface at Co-C60 interface, which increases the overall anisotropy of the system and decreases the domain size. However, the overall shape of the bubble domains remains same to its parent Pt/Co/Pt thin film. To calculate the relaxation time of a system we have performed magnetic relaxation measurements at different sub-coercive fields (0.93, 0.95, 097 Hc). For both the samples relaxation time decrease with increasing the applied magnetic field, which is expected. However, for Pt/Co/C60/Pt (sample 2) the relaxation time is reduced by ~ 50% as compared to Pt/Co/Pt (sample 1). Therefore, it is inferred that by introducing a C60 layer the switching speed of a system can be tuned which is a promising way to build device applications. Further, we have performed DFT calculation to understand the underneath mechanism of the Co/C60 spinterface.

![](https://assets.underline.io/uploads/markdown_image/1/image/aa68447e1fc66264cd907063616e005f.jpg)

Figure 1: (A) Hysteresis loops for sample 1(red) and 2 (blue). (a–c) and (d–f) are the domain images at different field marked in (A) for samples 1 and 2, respectively.

Effect of Fullerence on magnetization relaxation and domain wall dynamics in a perpendicularly magnetized Pt/Co/C60/Pt system

Though nano-hetero-structured (NHS) magnetic materials preparation using sputtering, electron beam lithography/ evaporation (EBL/EBE) have inspired a wealth of experimental results, to date, there is a very limited experimental understanding of preparing in situ NHS magnetic material using electrodeposition technique and the elucidation of their magnetic behavior. Towards this end, using pulse reverse [1] electrodeposition technique with a modified and stable acidic bath chemistry at room temperature, we have prepared in situ NHS magnetic cobalt phosphorus (CoP) thin film and investigated its characteristics structurally and magnetically combined with micromagnetic simulation utilizing MuMax3 [2]. Despite the availability of various techniques, the electrodeposition technique [1,3–5] has been chosen due to its relatively higher deposition rate and low cost. Here, CoP thin films with ultralow coercivity to moderate coercivity have been prepared from a single starting material from the same bath. The crossover from the ultralow coercivity to a comparatively higher coercivity has been demonstrated by the manipulation of the time width of the current (shown in FIG. 1) in a single amorphous system of CoP nanomagnetic thin film. We have characterized the developed smooth, stress-free, and shiny electroplated samples structurally by SEM, TEM, and magnetically by the hysteresis loop tracer (ShB Instruments, USA). The SEM micrographs confirm the fine-grain surface morphology of the cobalt phosphorous nanomagnetic thin films. The elemental analysis by energy dispersive X-Ray (EDX) yields the stoichiometry of the electrodeposited cobalt phosphorous. This pulse reverse plating technique could be an ideal option to tune the spin configuration with respect to the multi-nano layer thicknesses to obtain an optimum exchange coupling. The static in-plane magnetic measurement by the hysteresis loop tracer is shown in FIG. 2(c)-(d) reveals different hysteresis loops of electrodeposited CoP thin film.

![](https://assets.underline.io/uploads/markdown_image/1/image/354a83ea035e65fd21569e8d324cea3e.jpg)

Waveform and timing diagram for PR electroplating to develop nanomaterials from a single bath.

![](https://assets.underline.io/uploads/markdown_image/1/image/2597ecc569fa0fdcb4c80560a976b20e.jpg)

(a) An SEM and (b) a cross-sectional TEM image of CoP thin film. Hysteresis loop of (c) ultralow CoP, and (d) comparatively higher CoP

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