United States

The development of dual phase soft magnetic laminate for advanced electric machines at General Electric is summarized, including alloy development, properties, manufacturing trials, prototype experience, potential applications, and future material development. Dual phase soft magnetic laminates provide the flexibility to tune magnetic/non-magnetic state at the desired locations, using solution nitriding treatment with protective mask/coating. This enabling material technology benefits electric machine performance by reducing flux leakage in the laminates. It also decouples electromagnetic and mechanical design, which opens up the design space for advanced electric machines. Magnetic and mechanical properties of dual phase laminates were compared to commercial FeSi and FeCo soft magnetic laminates. Driven by the market needs for high power density and high-speed electric machines, a synchronous reluctance (SynRel) machine without permanent magnets and an interior permanent magnet machine using dual phase soft magnetic laminates were assessed in machine electromagnetic performance as well as rotor stress analysis by finite element simulation. Successful prototype build and testing further retired manufacturing risks and advanced the technology maturity level. Future material development with higher mechanical strength, higher saturation magnetization, higher permeability, and lower loss are highly desired for ground and air transportation electrification.&lt;br&gt;
**References:**&lt;br&gt;

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/46e620f4bd7ba04d15e62e86fe52c5db.png)&lt;br&gt;
Figure 1. Dual phase laminate processing route for motor prototype.&lt;br&gt;

MMM 2022

Development of Dual Phase Soft Magnetic Laminate for Advanced Electric Machines

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INTERMAG 2021

The development of dual phase soft magnetic laminate for advanced electric machines at General Electric is summarized, including alloy development, properties, manufacturing trials, prototype experience, potential applications, and future material development. Dual phase soft magnetic laminates provide the flexibility to tune magnetic/non-magnetic state at the desired locations, using solution nitriding treatment with protective mask/coating. This enabling material technology benefits electric machine performance by reducing flux leakage in the laminates. It also decouples electromagnetic and mechanical design, which opens up the design space for advanced electric machines. Magnetic and mechanical properties of dual phase laminates were compared to commercial FeSi and FeCo soft magnetic laminates. Driven by the market needs for high power density and high-speed electric machines, a synchronous reluctance (SynRel) machine without permanent magnets and an interior permanent magnet machine using dual phase soft magnetic laminates were assessed in machine electromagnetic performance as well as rotor stress analysis by finite element simulation. Successful prototype build and testing further retired manufacturing risks and advanced the technology maturity level. Future material development with higher mechanical strength, higher saturation magnetization, higher permeability, and lower loss are highly desired for ground and air transportation electrification. 
**References:** 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/46e620f4bd7ba04d15e62e86fe52c5db.png) 
Figure 1. Dual phase laminate processing route for motor prototype.

technical paper

#### Welcome to the 67th Annual Conference on Magnetism and Magnetic Materials, MMM 2022!

The Conference was held from October 31 to November 4 and offers both in-person and on-demand content.

MMM 2022 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 tutorial, and several special sessions. 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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Cobalt oxides have long been understood to display spin-state crossovers. A very different situation was recently uncovered in Pr-containing cobalt oxides, where a first-order spin-state/structural/metal-insulator transition occurs, driven by a remarkable Pr valence transition. Such valence transitions offer appealing functionality, but have thus far been confined to cryogenic temperatures in bulk materials (e.g., 90 K in Pr1-xCaxCoO3). In this work we combine epitaxy with synchrotron diffraction, scanning transmission electron microscopy with electron energy loss spectroscopy, electronic and magnetic measurements, polarized neutron reflectometry, and density-functional calculations to make the first full study of strained films of the perovskite (Pr1-yYy)1-xCaxCoO3-Î´. Remarkably, heteroepitaxial strain tuning enables stabilization of valence-driven spin-state/structural/metal-insulator transitions to at least 291 K, i.e., around room temperature (Fig. 1). The technological implications of this result are accompanied by fundamental prospects, as complete strain control of the electronic ground state is demonstrated, from ferromagnetic metal under tension to nonmagnetic insulator under compression (Fig. 2), exposing a potential novel spin-state quantum critical point [1]. Work supported by DOE through the Center for Quantum Materials.

Strain Stabilized Room

The angle dependence of field-induced switching was investigated in magnetic tunnel junctions (MTJ) with in-plane magnetization and a pinned synthetic antiferromagnet reference layer. 60 nm x 90 nm elliptical nanopillars were patterned from a film stack of SiOx/Ta (5)/CoFeB (2.5)/MgO (1)/CoFeB (2.5)/Ru (0.85)/CoFe (2.5)/IrMn (8)/Ru (10), (units in nm).

The tunnel magnetoresistance (TMR) was measured while the external field was applied at an angle θ, varying from 0° to 180° relative to the major axis of the ellipse (MAE), as shown in the inset of Fig.1. The relative angle between the free layer magnetization and the MAE, φ, was calculated from the TMR using an empirical cosine relation. Single sharp switches are seen when the field was applied along the MAE, but even with small deviations, reversal occurred through an intermediate state. Fig.1 shows a representative hysteresis loop measured at θ = 20°.

To determine the magnetization direction at different points in the hysteresis loop, the energy landscape was modeled in terms of the effective shape anisotropy field, the external magnetic field, and the SAF stray field. Using an 8 Oe shape anisotropy effective field and the 26 Oe SAF stray field strength estimated from the loop shift, the magnetization direction as a function of the external field magnitude and direction was reconstructed. Fig.2 shows the energy diagrams of the device at the critical fields. Near 26 Oe the barrier between the two lowest energy states is low, consistent with the telegraphing observed in Fig. 1. Intentional misalignment of the SAF and shape anisotropy fields has potential for development of faster probabilistic spintronic devices [1]. 
**References** 1. H. Chen, et al., Appl. Phys. Lett. 120, 212401 (2022).
 
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Angle Dependent Switching in a Magnetic Tunnel Junction Containing a Synthetic Antiferromagnet

We study the current-induced spin-orbit torque (SOT) switching and out-of-plane (OOP) effective field in a CuPt/CoPt heterostructure with interface oxidation. By introducing the oxidized copper at the interface, we found their switching abilities show remarkable improvement which is attributed to an unconventional OOP effective field. The OOP effective field is three times stronger than that without oxide treatment. Our observation identified the important role of the interface oxidation in the SOT process of CuPt/CoPt heterostructure.
The spin current can trigger a torque in ferromagnetic (FM) layer to electrically manipulate the magnetization. It is promise for an Magnetoresistive random-access memory (MRAM) device due to its endurance and speed [1-3]. To efficiently manipulate the magnetism in MRAM, the key point is to increase the spin accumulation in ferromagnetism (FM). In additiona, for traditional SOT devices, the external magnetic field is required to break the symmetry. Thus, the field-free switching has attracted attention.
We believe there could be a different path to enhance the field-free magnetization switching from material perspective. Previously, we studied the symmetry dependent field-free SOT switching in a CuPt/CoPt heterostructure [4]. The intrinsic broken mirror symmetry related SOT process is also reported in WTe2 [5]. The L11 CuPt deposited on SrTiO3 (111) substrate possesses a 3-fold symmetry, as shown in figure 1. The field-free switching emerges when the current is injected along the low symmetry axes ([1-10] and the other two equivalent axes).
In this work, we show the 3-fold symmetry unconventional out-of-plane torque is from the CuPt and it can be manipulated by the oxidation at the surface. Comparing to unoxidized sample, the oxidized sample approve a much larger switching ratio, since the large out-of-plane torque as the figure 2 shown. Regarding the oxidation degree of the copper is controllable by the time of oxidation treatment, thus a tuneable and efficient MRAM based on SOT induced magnetization switching is promised. 
**References** [1] K. Garello et al., 2018 IEEE Symposium on VLSI Circuits., p.81-82 (2018).
[2] F. Oboril, R. Bishnoi, M. Ebrahimi and M. B. Tahoori, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems., Vol. 34.3, p.367-380 (2015).
[3] G. Prenat et al., IEEE Transactions on Multi-Scale Computing Systems., Vol. 2.1, p.49-60 (2016).
[4] L. Liu et al., Nat. Nanotechnol., Vol. 16.3, p.277-282 (2021).
[5] MacNeill, D., Stiehl, G., Guimaraes, M. et al., Nature Phys., Vol. 13, p.300–305 (2017).
 
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Unconventional spin orbital torque enhanced magnetization switching by interface oxidation in CuPt/CoPt bilayer

We present spin transport studies on a low-field, room-temperature magnetoelectric multiferroic polycrystalline Sr3Co2Fe24O41|Pt heterostructure wherein a highly tunable transverse conical magnetic phase is responsible for static and dynamic magnetoelectric coupling [1, 2]. We measured angular dependence of spin Hall magnetoresistance (SMR) at constant magnetic fields (H) in the range of 50 to 100 kOe. Application of field below the critical value (Hc1 ≈ 2.5 kOe), yielded negative SMR and the H-evolution of normalized SMR (△R/R0 × 100 %) exhibited a negative gradient. Further, an increase in the H resulted in the positive slope of △R/R0 × 100 % Vs. H and later at higher H around 14 kOe, a crossover from negative to positive SMR was observed. We employed a simple model for estimating the equilibrium magnetic configuration and computed the SMR modulation at various values of H. We argue that the tilting of the cone is dominant and in turn responsible for the observed nature of SMR below 2.5 kOe (Fig.1) while, the closing of the cone-angle is pronounced at higher fields causing a reversal in sign of the SMR from negative to positive (Fig.2). Importantly, SMR experiments revealed that a change in the helicity with a reversal of the magnetic field has no influence on the observed SMR. Longitudinal spin Seebeck effect (LSSE) signal was measured to be ≈ 500 nV at 280 K, under application of thermal gradient, △T = 23 K and field, 60 kOe. The observed LSSE signal, originating from pure magnon spin current, showed a similar H-dependent behavior as that of the magnetization of Sr3Co2Fe24O41. Our detailed spin transport studies on polycrystalline Sr3Co2Fe24O41|Pt heterostructure demonstrate high tunability of the amplitude and the sign of the SMR, highlighting its potential for novel spintronic devices such as SMR-based spin valves [3] and voltage-controlled spin transport devices. 
**References** [1] Y. Kitagawa, Y. Hiraoka, T. Honda, Nat. Mater., Vol. 9, p. 797 (2010)
[2] H. Ueda, Y. Tanaka, Y. Wakabayash, Phys. Rev. B, Vol. 100, p. 094444 (2019)
[3] Y.-T. Chen, S. Takahashi, H. Nakayama, Phys. Rev. B, Vol. 87, p. 144411 (2013) 
![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/7d8322f485f892adf4eb37ce29746a02.png)

Highly tunable spin Hall magnetoresistance in room temperature magnetoelectric multiferroic, Sr3Co2Fe24O41|Pt hybrids

Magnetic skyrmions are a topic of extensive research due to their unique magnetic properties and spintronic applications. The primary way to achieve skyrmion dynamics is through electric currents, via STT effects [1]. The current can displace a skyrmion, but it usually also imparts an unwanted perpendicular velocity component known as skyrmion Hall effect (SkHE) [2]. Finding a way to counter SkHE has recently become a topic of intense research [3, 4]. In this work, we show that geometric variations can be used to achieve confinement of skyrmions in both static and dynamic cases. We have analyzed skyrmions in FeGe structures using finite-element and finite-difference micromagnetic simulations. For the static case, we find that by locally lowering the film thickness in dot-shaped regions (Fig. 1), skyrmions can be "captured" at geometrically defined sites [5]. In this way, skyrmions can be stabilized at positions such as square lattices, which otherwise do not occur in usual non-centrosymmetric ferromagnets. For the dynamic case, we consider a novel "H"-shaped racetrack geometry (Fig. 2). In the presence of a current along the track length, the simulations confirm that the barrier counters the SkHE while allowing skyrmion propagation along the geometrically defined path. We further analyze its trajectories and velocities as a function of current density and compare the numerical results with Thiele's equation [6]. Our study confirms that the numerically obtained skyrmion velocities are in accordance with Thiele's equation. In summary, we present a way to confine three-dimensional skyrmions by exploiting the dependence of skyrmion energy on the film thickness. This can prove valuable in the study of exotic configurations such as a rectangular skyrmion lattice. It may also prove relevant to countering the SkHE in skyrmion-based racetrack devices. This work was financially supported by initiative of excellence IDEX-Unistra (ANR-10-IDEX-0002-02) and the EPSRC Program grant on Skyrmionics (EP/N032128/1). 
**References** 
[1] J. Sampaio et al., Nat. Nanotechnol., 8, 839 (2013).
[2] I. Purnama et al., Sci. Rep., 5, 10620 (2015).
[3] W. Legrand et al., Nat. Mater., 19, 34 (2020).
[4] B. Göbel et al., Phys. Rev. B, 99, 020405 (2019).
[5] S. A. Pathak & R. Hertel, Magnetochemistry, 7, 26 (2021).
[6] J. Iwasaki et al., Nat. Nanotechnol., 8, 742 (2013). 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/6ac4bf556e621ea9fb648f35b3add524.png) 

Fig. 1 Geometrically constrained skyrmions in FeGe platelets with circular pockets. 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/c005717dbed00534585cb985131760a3.png) 

Fig. 2 Snapshots of the skyrmion dynamics in an H-shaped racetrack geometry.

Three dimensional Skyrmion Confinement Through Thickness Modulation

The share of electric vehicles (EVs) on the road has seen a dramatic upward trend in the last decade as maximum range per charge has increased and the necessary infrastructure has grown to increase competitiveness with conventional gasoline-powered vehicles. However, maximal efficiency, achieved by minimizing the losses experienced by the motor stator and rotor, is limited by a tradeoff between low coercivity and high mechanical strength, which is necessary to withstand the significant torques experienced during operation [1–3]. Radiofrequency (RF) transverse induction annealing (T-IA) is suggested as a novel pathway for imposing a continuous spatial variation in microstructure of bulk crystalline soft magnetic alloys [4,5]. Via local control of grain size, magnetic and mechanical properties may be separately prioritized as functions of position, enabling fabrication of optimized motor laminations with reduced losses while still possessing requisite mechanical strength. Here we demonstrate through FEA modeling the dependence of achievable temperature profile on lamination and coil geometry, and we confirm feasibility of spatially optimized microstructure through experiments. We find that certain combinations of coil/lamination geometry may allow for simultaneous stamping of spatially optimized laminations, due to enhanced heating and higher temperature distributions in the region of the laminations where the magnetic flux density is greatest. We also present a basic feasibility modeling study examining performance of a motor containing motor laminations with radial variation in coercivity to motivate future work in this area. 
**References:** [1] T. Sourmail, Prog. Mater. Sci., Vol 50, p.816–880 (2005) 
[2] P. Ramesh and N.C. Lenin, IEEE Trans. Magn., Vol. 55, 0900121 (2019) 
[3] T. Sourmail, Scr. Mater., Vol. 51, p.589–591 (2004) 
[4] A. Talaat, D.W. Greve, and S. Tan, Adv. Energy Mater., Vol. 2022, 2200208 (2022) 
[5] A. Talaat, D.W. Greve, and M. V. Suraj, J. Alloys Compd., Vol. 854, 156480 (2021) 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/22a24c959fc2dde91f2bd9577aee7567.png) 
Fig. 1: (a) Schematic of temperature/property profile achievable with a cylindrical coil as simulated in COMSOL Multiphysics (b) Experimental temperature profile observed with a cylindrical coil and square Hiperco lamination.

Fabrication and Feasibility Study of Motor Laminations with Radially Varying Coercivity via Transverse Induction Annealing

Ferrimagnets composed of two or multi antiferromagnetically coupled magnetic sublattices have attracted much attention recently due to the easily controlled and detected net magnetization and a fast magnetic dynamic behavior [1]. Especially, ferrimagnetic thin films with perpendicular magnetic anisotropy (PMA) show great potential for high-density spintronics devices [2]. Currently, most of work focus on the rare earth-transition metal ferrimagnetic alloys, such as GdFeCo and TbCo. However, the magnetization of these materials is sensitive to the temperature and composition [3]. The antiperovskite Mn4N compound is a rare-earth-free ferrimagnet showing a PMA, high thermal stability, high spin polarization and low saturation magnetization which make it promising for practical spintronics devices [4]. 
For the crystalline structure of Mn4N compound, Mn atoms occupy the corners (MnA) and face-centers (MnB) of the cubic unit cell, respectively, while N atom is located at the body center, as shown in Fig. 1(a). The magnetic moment of MnA and MnB are antiferromagnetically coupled with a high Curie temperature, 740 K. PMA in Mn4N thin films had been observed by epitaxially depositing it on the MgO substrate. However, the large lattice mismatch between Mn4N and MgO, −6%, induces a misfit dislocation of Mn4N resulting in a poor PMA. In this work, by inserting a thin Pd buffer layer with a very close lattice constant of Mn4N, we prepared the stacks MgO(substrate)/Pd(t = 0, 2 and 8 nm)/Mn4N(80 nm)/Ta(3 nm). We systematically studied the effect of Pd buffer layer on the crystalline structure and magnetization of Mn4N thin films. With inserting a Pd buffer layer, a good quality of crystalline structure can be formed which significantly improves the PMA, as shown in Fig. 1(b). 
**References:** [1] S. K. Kim et al., Nat. Mater. 21, 24–34 (2022) 
[2] B. Dieny and M. Chshiev, Rev. Mod. Phys. 89, 025008 (2017) 
[3] H. Bai et al., Adv. Electron. Mater. 8, 2100772 (2022) 
[4] Z. Zhang and W. Mi, J. Phys. D: Appl. Phys. 55 013001 (2022) 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/8c0e2564383234f67714a1850714808a.png) 
Fig. 1: (a) Crystalline structure of Mn4N. (b) Pd thickness dependence of magnetization of Mn4N under an external out-of-plane magnetic field.

Perpendicular Magnetic Anisotropy of Ferrimagnetic Mn4N Thin Film Improved by the Pd Buffer Layer

Graphene has unique electronic properties which make it a promising material for next-generation electronics. It has high electron mobility at room temperature and a long spin-diffusion length. The latter is due to its weak intrinsic hyperfine interactions and small spin-orbit coupling. Therefore manipulating spins directly in a layer of pristine graphene is not easy. However, this can be overcome by an induced proximity effect using an exchange-coupled interface between the graphene and a ferromagnetic layer. Several studies predicted that the conduction band of graphene will spin split at the interface with a ferromagnetic substrate [1-4]. 

We report the magnitude of the induced magnetic moment in graphene as a result of the proximity effect in the vicinity of a Ni layer using polarised neutron reflectivity (PNR) and X-ray magnetic circular dichroism (XMCD). The Ni film was grown by sputtering upon which the graphene was grown by chemical vapour deposition. The growth parameters were tuned to produce epitaxial and rotated graphene domains (Fig. 1). The XMCD results at the C K-edge confirm the presence of magnetic polarisation in rotated graphene. Intensive quantitative analysis of the PNR fits, ascertained based on Bayesian analysis, indicate that at 10 K 0.53 and 0.38 μB/C atom is induced in rotated and epitaxial graphene grown on Ni(111), respectively. These values are three times higher than those predicted in other studies [4,5]. Two possible mechanisms were elaborated for the observed induced magnetic moment [4,6,7]. To clarify the origin of the measured moment, further PNR measurements were carried out on graphene grown on a non-magnetic substrate (Ni9Mo1) [8]. 

We will present the different models used to fit the data and discuss the challenges of fitting the PNR of a 2D material which is within the resolution limit of the technique. We will also show the results of other techniques used to characterise the samples. 
**References:** [1] H. Haugen et al., Phys. Rev. B 77, 115406 (2008). 
[2] Q. Zhang et al., Appl. Phys. Lett. 98, 032106 (2011). 
[3] H.X. Yang et al., Phys. Rev. Lett. 110, 046603 (2013). 
[4] M. Weser, Y. Rehder et al., Appl. Phys. Lett. 96, 012504 (2010). 
[5] H. -Ch. Mertins et al., Phys. Rev. B 98, 064408 (2018). 
[6] V. Karpan, P. Khomyakov et al., Phys. Rev. B 78, 195419 (2008). 
[7] F. Ma’Mari, T. Moorsom et al., Nature 524, 69 (2015). 
[8] R. O. M. Aboljadayel et al., arXiv:2101.09946v2 (2022). 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/26e01e1a2ae11689057c5c16ffd68ca2.png) 
SEM images at 1 kV showing the graphene domains for (a) epitaxial graphene/Ni and (b) rotated graphene/Ni and (c) The LEED diffraction pattern of epitaxial graphene on a Ni(111) substrate at 300 eV. The red circle in (b) highlights a single graphene domain with a diameter of ∼ 0.25 μm.

Determining Quantitatively the Induced Magnetic Moment in Graphene by Polarised Neutron Reflectivity and X ray Magnetic Circular Dichroism

Low dimensional molecular magnets are considered to be one of the best materials for cryogenic magnetocaloric effect (MCE) [1,2]. The magnitudes of magnetic entropy change for the most efficient molecular materials are comparable to that of the famous gadolinium gallium garnet (Gd3Ga5O12). Although much research effort is focused on searching high efficient compounds for conventional MCE, a new type of magnetocaloric effect, namely rotating magnetocaloric effect (RMCE), has been introduced. In RMCE, the applied magnetic field is constant and the aligned material (often in single crystal form) with significant magnetic anisotropy is being rotated. Cooling with rotation has several advantages compared to the conventional MCE cooling setups: high efficiency (high frequency cooling cycles), simple construction and low power consumption ( possibility of using permanent magnets). In our research we have investigated the RMCE in 2D compounds (based on MnII-NbIV [3] and CuII-WV [4] ions) and clusters (based on TbIII and DyIII [5]). We have noticed that the inverse magnetocaloric effect can be used to enhance RMCE (in our case up to 51 % for the 2D compounds). In the case of the Tb cluster, with large uniaxial anisotropy, the magnetic entropy change for conventional and rotating MCE is comparable, showing significant values (Î”Smax â‰ˆ 4 J K-1 kg-1) at 2.0 K in low field (Î¼0H â‰ˆ 1.2 T), which can be achieved with permanent magnets.

Rotating Magnetocaloric Effect in Low Dimensional Molecular Compounds

The family of 2D compounds has grown almost exponentially since the discovery of graphene and so too the rapid exploration of their vast range of electronic properties. Some family members include superconductors, Mott insulators with charge-density waves, semimetals with topological properties, and transition metal dichalcogenides with spin-valley coupling1. Among several compounds, the realization of long-range ferromagnetic order in van der Waals (vdW) layered materials has been elusive till very recently. Long searched but only now discovered 2D magnets are one of the select group of materials that retain or impart strongly spin correlated properties at the limit of atomic layer thickness. In this presentation I will discuss how different layered compounds (e.g., CrX3 (X=F, Cl, Br, I), VI3, MnPS3, Fe3GeTe2, FePS3, CrGeTe3) can provide new playgrounds for exploration of spin correlations involving quantum-effects, topological spin-excitations and higher-order exchange interactions. I will show that this new generation of vdW magnets can help to revolutionize several technological domain wall applications from sensing to data storage, which can lead to new magnetic, magnetoelectric and magneto-optic applications in industry2,3,4,5. Moreover, I will discuss some challenges at the forefront of 2D vdW magnets and new opportunities to understand fundamental problems. 

**References:** 
1. Q. Wang et al. ACS Nano 16, 6960 (2022). 
2. D. Wahab et al. Adv. Mater. 33, 2004138 (2021). 
3. D. Wahab et al. Appl. Phys. Rev. 8, 041411 (2021). 
4. M. Alliati et al. npj Comput. Mater. 8, 3 (2022). 
5. J. Macy et al., Appl. Phys. Rev. 8, 041401 (2021). 

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