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The unidirectional spin Hall magnetoresistance (USMR) is initially discovered in ferromagnetic (FM) and normal metal (NM) structures[1] and magnetic semiconductor structures[2]. It is a phenomenon observed in bilayer structures and is related to interfacial spin generation and scattering processes at the interface. The similar unidirectional spin Hall and Rashba-Edelstein magnetoresistance (USRMR) is observed in FM-topological insulator (TI) bilayers being much larger than that in FM-NM bilayers in bilayer structures[3]. They are of particular interest due to its potential of 180-degree sensitive electrical readout of magnetization in bilayer structures for spin-orbit torque switching devices.
Here, we report large unidirectional spin Hall and Rashba−Edelstein magnetoresistance in a new material family - magnetic insulator (MI)/TI Y3Fe5O12 (YIG)/Bi2Se3 bilayers. Such heterostructures exhibit a USRMR that is about an order of magnitude larger than the highest values reported in all-metal Ta/Co bilayers[1]. The polarized neutron reflectometry (PNR) reveals a unique temperature-dependent magnetic intermediary layer at the MI-substrate interface and a proximity layer at the MI-TI interface. These PNR findings echo the magnetoresistance results in a comprehensive physics picture. Finally, we demonstrate a prototype memory device based on a MI/TI bilayer, using USRMR for electrical read out of current-induced magnetization switching aided by a small Oersted field[4].
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**References** [1] C. O. Avci, K. Garello, A. Ghosh et al., Nat. Phys., vol. 11, no. 7, p. 570–575 (2015)
[2] K. Olejník, V. Novák, J. Wunderlich et al., Phys. Rev. B - Condens. Matter Mater. Phys., vol. 91, no. 18, p. 180402 (2015)
[3] Y. Lv et al., Nat. Commun., vol. 9, no. 1, p. 111 (2018)
[4] Y. Lv et al., Appl. Phys. Rev., vol. 9, no. 1, p. 011406, (2022)&lt;br&gt;&lt;br&gt;
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MMM 2022

Large unidirectional spin Hall and Rashba−Edelstein magnetoresistance in topological insulator/magnetic insulator heterostructures

The unidirectional spin Hall magnetoresistance (USMR) is initially discovered in ferromagnetic (FM) and normal metal (NM) structures[1] and magnetic semiconductor structures[2]. It is a phenomenon observed in bilayer structures and is related to interfacial spin generation and scattering processes at the interface. The similar unidirectional spin Hall and Rashba-Edelstein magnetoresistance (USRMR) is observed in FM-topological insulator (TI) bilayers being much larger than that in FM-NM bilayers in bilayer structures[3]. They are of particular interest due to its potential of 180-degree sensitive electrical readout of magnetization in bilayer structures for spin-orbit torque switching devices.
Here, we report large unidirectional spin Hall and Rashba−Edelstein magnetoresistance in a new material family - magnetic insulator (MI)/TI Y3Fe5O12 (YIG)/Bi2Se3 bilayers. Such heterostructures exhibit a USRMR that is about an order of magnitude larger than the highest values reported in all-metal Ta/Co bilayers[1]. The polarized neutron reflectometry (PNR) reveals a unique temperature-dependent magnetic intermediary layer at the MI-substrate interface and a proximity layer at the MI-TI interface. These PNR findings echo the magnetoresistance results in a comprehensive physics picture. Finally, we demonstrate a prototype memory device based on a MI/TI bilayer, using USRMR for electrical read out of current-induced magnetization switching aided by a small Oersted field[4].
 
**References** [1] C. O. Avci, K. Garello, A. Ghosh et al., Nat. Phys., vol. 11, no. 7, p. 570–575 (2015)
[2] K. Olejník, V. Novák, J. Wunderlich et al., Phys. Rev. B - Condens. Matter Mater. Phys., vol. 91, no. 18, p. 180402 (2015)
[3] Y. Lv et al., Nat. Commun., vol. 9, no. 1, p. 111 (2018)
[4] Y. Lv et al., Appl. Phys. Rev., vol. 9, no. 1, p. 011406, (2022) 
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technical paper

#### Welcome to the 67th Annual Conference on Magnetism and Magnetic Materials, MMM 2022!

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The discovery of two-dimensional van der Waals ferromagnets [1,2] has been long anticipated since the effects of spatial dimensionality on criticality were recorded [3,4]. The potential applications of this new class of materials seem vast within the field of spintronics. Fe3GeTe2 has already proved highly efficient for spin-orbit torque switching [5], yet rich skyrmionic textures [6,7] and semi-metallicity [8] are also found within its roster of ever-growing phenomena. Fe5GeTe2, a related compound with a higher Tc [9], presents its own unique set of magnetic order that can be tuned with doping [10] and gate voltage [11]. In a recent collaboration [12] we found spin-orbit torques within bulk Fe3GeTe2 due to a site preference that breaks the crystal’s centrosymmetry [13]. Meanwhile, in Fe5GeTe2, we found skyrmionic textures present even up to room temperature [14]. To understand the origins of these effects one must delve into the underlying electronic structure to provide a comprehensive understanding of the associated spin dynamics.

Using a variety of first-principles methods [12,14,15] we evaluate the exotic phenomena observed in both Fe3GeTe2 and Fe5GeTe2. In Fe3GeTe2 strong ‘hidden’ current-induced torques are harvested by each of the two-dimensional Fe3GeTe2 layers separately. Analysis of the electronic structure elucidates an interplay of spin and orbital degrees of freedom which have a profound impact on spin-orbit torques. A drastic difference in the behavior of the individual components of the torque results in non-trivial switching. In Fe5GeTe2 we use first principles methods in combination with atomistic spin-dynamics simulations to characterize the domain wall and subsequent spin textures. These distinct features from both compounds present an opportunity to tailor the spin and orbital dynamics with Fe concentration, opening a new era of van der Waals spin orbitronics. 
**References** [1] C. Gong et al., Nature 546, 265 (2017).
[2] B. Huang et al., Nature 546, 270 (2017).
[3] R. B. Griffiths, Physical Review 136, 437 (1964).
[4] N. D. Mermin et al., Physical Review Letters 17, 1133 (1966).
[5] M. Alghamdi et al., Nano Letters 19, 4400 (2019).
[6] B. Ding et al., Nano Letters 20, 868 (2020).
[7] H.-H. Yang et al., 2D Materials 9, 025022 (2022).
[8] K. Kim et al., Nature Materials 17, 794 (2018).
[9] A. F. May et al., ACS Nano 13, 4436 (2019).
[10] A. F. May et al., Physical Review Materials 4, 074008 (2020).
[11] C. Tan et al., Nano Letters 21, 5599 (2021).
[12] F. Martin et al., arXiv:2107.09420.
[13] A. Chakraborty et al., Advanced Materials 34, 2108637 (2022).
[14] M. Schmitt et al., arXiv:2204.11348.
[15] T. G. Saunderson at al., arXiv:2204.13052.

Harnessing the spin and orbital dynamics of iron based 2D van der Waals ferromagnets

Recent studies revealed that spin diffusion length (λs) and spin lifetime (τs) of electrons in Ge are governed by spin-flip scattering among conduction band valleys (intervalley spin-flip scattering) [1]. To reduce the intervalley spin-flip scattering frequency, Tang et al. have theoretically predicted that lifting the degenerate four valleys through a lattice strain is effective [2]. In this study, we experimentally study the effect of strain on spin transport in strained Si0.1Ge0.9, which exhibits a Ge-like electronic band structure.
A strained n-Si0.1Ge0.9 spin transport layer (~70 nm) with a carrier concentration (n) of ~1×1018 cm-3 was grown on Ge/Si(111) substrates by molecular beam epitaxy (MBE), where the in-plane tensile strain of ~0.66% was confirmed by reciprocal space map. Then, we fabricated lateral spin-valve (LSV) devices with a Co-based Heusler alloy spin injector/detector [3,4]. A representative four-terminal nonlocal spin signal (|ΔRNL|) at room temperature is shown in the inset of Fig. 1. Figure 1 shows contact distance (d)-dependent |ΔRNL| at room temperature for LSV devices with the strained n-Si0.1Ge0.9 and an n-Ge. The dashed lines are fits to the data using |ΔRNL| ∝ exp(-d/λs) and the estimated value of λs for the strained n-Si0.1Ge0.9 (n-Ge) is estimated to be ~0.93 µm (~0.50 µm). Notably, an approximately twofold increase in λs is attributed to the enhanced electron mobility and spin lifetime, induced by lifting the valley degeneracy and by obtaining relatively low carrier concentration [5]. We also demonstrate long-distance spin-drift transport under the electric field (E) and clearly observe pronounced Hanle oscillations with d = 7 µm at T = 50 K in a three-terminal measurement with a drift current of ID = -0.5 mA, as shown in Fig. 2. 
**References** [1] K. Hamaya et al., J. Phys. D: Appl. Phys., Vol. 51, p.393001 (2018)
[2] J. -M. Tang et al., Phys. Rev. B, Vol. 85, p.045202 (2012)
[3] M. Yamada et al., NPG Asia Mater., Vol. 12, p.47 (2020)
[4] K. Kudo et al., Appl. Phys. Lett., Vol. 118, p.162404 (2021)
[5] T. Naito et al., Phys. Rev. Applied (accepted)
 
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Long distance spin transport in strained SiGe

Substantial gaps remain in the understanding of spin transport in low-Z nonmagnetic (N) metals, despite their use in spintronic technology. While Elliot-Yafet spin relaxation is known to prevail in such metals, the βi constants that relate spin relaxation times to momentum relaxation times are only known for certain defect types (i), primarily in simple metals like Cu [1] and Al [2]. Other low-Z metals with potentially long spin diffusion lengths have been barely explored [3], and their βi remain unknown. In this work we thus explore spin transport in Mg, using nonlocal spin valves (NLSVs). Mg-based NLSVs were deposited by UHV evaporation on Si/SiNx using Al and Ti seed layers. As shown by specular wide-angle X-ray diffraction (Fig. 1(a)) and (0002) pole figures (Fig. 1(b)), strong out-of-plane (0001) texture arises, while in-plane texture (Fig. 1(c)) is negligible. Significantly, the (0001) texture of HCP Mg is significantly stronger with HCP Ti vs. FCC Al seeds (right and left of Figs. 1(b,c)). These Mg films exhibit the lowest residual resistivities (0.99 μΩ cm) and highest residual resistivity ratios (>6) reported for polycrystalline Mg films and nanowires. In NLSVs, the low-temperature spin diffusion length, βphonon, and βdefect reach 550 nm, 28000, and 5300 in Ni80Fe20/Al(5 nm)/Mg(100 nm) NLSVs, compared to 370 nm, 16000, and 1200 in Ni80Fe20/Ti(4 nm)/Mg(100 nm) NLSVs (Fig. 2). We hypothesize that these improvements in spin transport parameters in the Al-seed case arise due to weaker (0001) texture. Specifically, recent spin-hot-spot-based [4] theoretical predictions for HCP Mg predict 2200% higher β for spins injected along the Mg c-axis vs. in the basal plane [5]; our results may constitute the first experimental evidence for this highly anisotropic spin relaxation. This work was supported by the NSF. 
**References** [1] J. D. Watts, L. O’Brien, J. S. Jeong et al., Phys. Rev. Mater., Vol. 3, p.124409 (2019). [2] J. D. Watts, J. T. Batley, N. A. Rabideau et al., Phys. Rev. Lett., Vol. 128, p.207201 (2022). [3] H. Idzuchi, Y. Fukuma, L. Wang et al., Appl. Phys. Exp., Vol. 3, p.049202 (2010). [4] J. Fabian and S. Das Sarma, Phys. Rev. Lett., Vol. 81, p.5624 (1998). [5] B. Zimmermann, P. Mavropoulos, N. Long et al., Phys. Rev. B, Vol. 93, p.144403 (2016) 
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Spin Transport in Mg based Nonlocal Spin Valves

Magnetic nanoparticles (NPs) provide an ideal support for developing a wide range of nanotechnologies and biomedical applications, such as drug-delivery, gene delivery,
hyperthermia, or contrast agents for MRI.[1] Magnetite (Fe3O4
) NPs are good candidates for these applications due to their non-toxicity and long-life in the bloodstream. To optimize these
applications, it is crucial to well control the magnetic response of individual NP when manipulating a collection of them via a magnetic field. In particular, it is useful to identify any
interparticle magnetic correlations that may cause the magnetic response to deviate from superparamagnetism, induce superferromagnetism and magnetic hysteresis, and affect the
dynamics of fluctuations. To that end, we have studied the magnetic response of 5 – 100 nm Fe3O4 NPs and its dependence on NP size, using magnetometry [2] and spin muon resonance
[3]. However, this information remains macroscopic or spatially averaged. Here we show how nanoscale spatial information on inter-particle magnetic correlations can be obtained via xray resonant magnetic scattering (XRMS) [4] as illustrated in Figure 1. By tuning the energy of the x-rays to resonant edges of Fe and comparing opposite polarization helicities, we have
extracted information about the local inter-particle magnetic orders within NP assemblies of various sizes.[5] We fitted the XRMS data using a model based on chains of NPs.[6] The data
fitting shows ferromagnetic ordering when an external magnetic field is applied, and the emergence of antiferromagnetic ordering, competing with magnetic randomness, when the field is
brought back near the coercive point (zero net magnetization). We studied how these correlations depend on particle size and found an enhancement of magnetic couplings and
antiferromagnetic orders for bigger particles. [7] Additionally we will show preliminary studies of the dynamics of magnetic fluctuations via x-ray photon correlation spectroscopy (XPCS). 
**References** 
1. Frey et al., Chem. Soc. Rev. 2009, 38, 2532-2542 (2009) 
2. Klomp et al., IEEE Trans. Mag. 56, 2300109 (2020) 
3. Frandsen et al., Phys. Rev. Matter 5, 054411 (2021) 
4. Kortright et al., Phys. Rev. B 71, 012402 (2005) 
5. Chesnel et al., Magnetochemistry 4, 42-58 (2018) 
6. Rackham et al., AIP Advances 9, 035033 (2019) 
7. Rackham et al., to be submitted (2022) 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/7896aef6336626e4350d501b0e78c9d3.png) 
Figure 1: Layout of the x-ray resonant magnetic scattering (XRMS) measurement of a nanoparticle assembly.

Interparticle magnetic correlations and dynamics of fluctuations in assemblies of Fe3O4 nanoparticles

Magnetic skyrmions are vortex-like spin textures. They are topologically protected from external perturbation and can be driven with extremely low currents. Therefore, they have been paid much attention and they are expected to be applied to the spintronic devices such as the magnetic memories and the logic devices. They can be discovered in so-called chiral magnets which are lacking in the inversion symmetry. The one of the characteristics of the chiral magnets is non-vanishing Dzyaloshinskii-Moriya interaction (DMI). The DMI, which tilts the neighboring spins, is an essential interaction to stabilize the magnetic skyrmions. The characteristics of the DMI are determined by the symmetry of the system. The Neel-type skyrmions are generally observed in Cnv symmetric thin film materials. Recently, the elliptical skyrmions have been observed and they are stabilized in the C2v symmetric systems. This is because the different values of the DMI constants of the x-axis and y-axis can be allowed in the C2v symmetric systems. The elliptical skyrmions have several advantages in comparison with circular skyrmions when applied to the spintronic devices. For example, the skyrmion Hall angles of the elliptical skyrmions can be controlled by changing the shapes of them [1]. In this study, we investigate both the dynamics and the phase diagram of elliptical ferromagnetic skyrmions. We consider Co thin films on W as ferromagnetic materials [2]. We drive the elliptical skyrmions by applying the spin current in the x-direction. Figures 1 and 2 show the dependences of the velocity (|v|) and the skyrmion Hall angle (θSkHE) on the elliptical ration (b/a), respectively. Here, a (b) is the length of major (minor) axis of the elliptical skyrmions. We find that |v| increases with the decreasing the value of b/a and θSkHE decreases with the decreasing the value of b/a Therefore, the elongated skyrmions along the current direction are useful in comparison with the circular skyrmions when applied to the spintronic devices. At the conference, we are going to show the phase diagrams and discuss the regions where the elliptical skyrmions appear. 
**References** 
J. Xia, X. Zhang, M. Ezawa, Q. Shao, X. Liu, and Y. Zhou, Appl. Phys. Lett., Vol. 116, p.022407 (2020) 
L. Camosi, J. PeñaGarcia, and J. Vogel et al, New J. Phys., Vol. 23, p.013020 (2021) 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/8e967bd96ed03513ee0b331aacc4912e.png) 
Fig. 1 The dependence of |v| on b/a. 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/edf45e69357d05e62f0bbe4ab1c3ca6b.png) 
Fig. 2 The dependence of θSkHE on b/a.

Elliptical Ferromagnetic Skyrmions

The high cost of CoFe alloys has prevented their widespread use regardless of their promising properties: high magnetisation, high Curie temperature, as soft magnetic materials for high temperature applications. Our research has shown that the additional of AlMn can be used to create CoFeMnAl alloys, which have reduced Co content but similar saturation magnetisation as CoFe alloys, therefore providing a more economical alternative to pure CoFe soft magnets. The research studied how the addition of Al to CoFeMn0.5 changed the alloy phases and hence the magnetic properties. The CoFeMn0.5Alx alloys (0 < x <0.75) were fabricated using arc-melting, and characterised using X-ray diffraction (phases present), scanning electron microscope (composition) and SQUID magnetometry (magnetic properties as a function of magnetic field and temperature). It was found that for Al content of x < 0.2, there existed mixed FCC and BCC phases, while with further addition of Al, the BCC phase was stabilised (Figure 1a.). This lead to an increase in the saturation magnetisation and a decrease in the coercive field (Figure 1b). The alloy CoFeMn0.5Al0.25 was determined to have a competitive saturation magnetisation compared to CoFe, but with the reduction of Co concentration in the alloy should also be cheaper to produce. 
**References:** 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/e63d51817e925cf4cb35b336e4ed1f51.png) 
Figure 1a. XRD of the CoFeMn0.5Alx alloys. 1b Saturation magnetisation and coercive field as a function of Al concentration.

CoFeMn0.5Alx: High magnetization CoFe based soft alloys with reduced Co content

In magnonic and spintronic devices, a low magnitude magnetic damping is desired for efficient operation via the long-range propagation of spin waves [1]. However, thin magnetic ferrite films (low damping but insulating) may not suffice if a charge current is needed [2]. Thin films of the conducting binary alloy of cobalt and iron (Co25Fe75) have exhibited low damping (~10-3) [3]. To further decrease the damping of this system, a multilayer film consisting of ten 10 nm layers of Co25Fe75 alternated with 2 nm layers of hafnium (Hf) is proposed. This structure would decrease the damping by preventing eddy current losses and decrease coercivity and magnetic saturation via smaller crystallite sizes [4,5]. These single and multilayer films were deposited via sputtering, with thicknesses (t) of 10, 50, and 100 nm. The ferromagnetic resonance (FMR) of the films showed as the t increases, at a constant frequency (17 GHz shown), the FMR field decreases and linewidth increases, but the 100 nm multilayered film maintains the linewidth and FMR field of the 10 nm film (Fig. 1). The linewidth and FMR for each film (at 14-17 GHz) in addition to the saturation magnetization were used to calculate the damping parameter (α) of each film. This showed that as t increases up to 100 nm, the damping increases from ~1x10-2 (10 and 50 nm) to ~8x10-2 (100 nm) (Fig. 2). The damping of the multilayered film (~5x10-3) is below that of the 10 nm film, an order of magnitude improvement. This work shows that increasing t for single layered Co25Fe75 decreases FMR field, increases linewidth, and increases damping. The multilayer structure shows the ability to tune the FMR and damping. This provides avenues for other heterostructures, including the use of an insulating interlayer or other magnetic materials. 
**References:** [1] H. Glowinski, F. Lisiecki, P. Kuswik, J. Alloys Compd., 785, 891-896 (2019). 
[2] E. Edwards, H. Nembach, and J. Shaw, Phys. Rev. Appl., 11, 054036 (2019). 
[3] R. Weber, D. Han, I. Boventer, J. Phys. D: Appl. Phys., 52, 325001 (2019) 
[4] S. Balaji and M. Kostylev, J. Appl. Phys., 121, 123906 (2017). 
[5] L. Garten, M. Staruch, K. Bussmann, ACS Appl. Mater. Interfaces, 14, 25701-25709 (2022). 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/bf9f3851b4e267d6a47336d9f874f7b2.png) 
Fig. 1. FMR measurements of the CoFe films at 17 GHz, showing a decrease in FMR field and increase in linewidth as thickness increases, and the multilayer sample returns to the FMR and linewidth of the 10 nm film. 
![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/275607c48d5ec3ed3b02592fd99e8110.png) 
Fig. 2. Calculated damping parameters of the CoFe films, showing that the multilayered film damping (0.0055) is comparable to a typical low damping value of CoFe (0.005) [3].

Fabrication of Co25Fe75/Hf multilayer thin films to decrease the magnetic damping coefficient

Heat capacity is a basic physical quantity most important for studying magnetocaloric materials. Not only it reflects how much heat can be stored in the material, but it also allows to quantify the two main performance parameters: the isothermal entropy change Î”S and the adiabatic temperature change Î”Tad. On top of that, being sensitive to structural, electronic and magnetic degrees of freedom, heat capacity also provides fundamental insights. In Fe2P materials, at the exception of the binary parent, heat capacity studies were so far limited to indirect determinations of the magnetocaloric effect. Here, we will present an extensive heat capacity study of a prototypical MnFe(P,Si,B) compound. Semi-adiabatic relaxation calorimetry, commercial heat flow and home-made Peltier cells differential scanning calorimeters were used to record the heat capacity both around first-order ferromagnetic transition and at low temperatures. This systematic investigation fills several knowledge gaps on the promising MnFe(P,Si,B) magnetocaloric materials. First, we will describe the development of a Peltier cell differential scanning calorimeter designed â€œas an optionâ€ for commonplace commercial cryostat equipped with high magnetic field. This system can be used to measure directly the isothermal entropy change Î”S induced by a magnetic field and it even allows targeting the cyclic (reversible) effect due to successive magnetization/demagnetization. In MnFe0.95P0.585Si0.34B0.075, an exceptionally large cyclic entropy change at intermediate field (Î”Scyclic = 13.2 J kg-1 K-1 for Âµ0Î”H = 1 T) is observed. Then, the heat capacity is analyzed over a broad temperature range to provide an estimate of several important parameters, such as the electronic density of states (N(EF)â‰ˆ 7.2 states eV-1f.u.-1) or an estimate of the Debye temperature Î¸D â‰ˆ 455 K. Different methods (non-magnetic reference, Debye function, phonons calculations) were used to model the lattice contribution to the heat capacity. Our study highlights the difficulty to disentangle lattice, electronic and magnetic contributions in Fe2P-type materials. It nonetheless reveals that the magnetic entropy plus latent heat is considerably larger in MnFe(P,Si,B) than in the parent Fe2P.

Heat Capacity and Giant Magnetocaloric Effect of a MnFe(P,Si,B) Compound investigated by semi adiabatic and Peltier Cell Calorimetry Techniques

Magnetometer with diamond nitrogen-vacancy (NV) centers [1] is a highly-sensitive magnetic sensor under the application of a highly uniform (99.9%) bias magnetic field
[2]. The integration of magnetometer with diamond NV magnetic sensors is required for various applications. However, there is a problem about the design of small magnet generating
uniform magnetic field in the conventional methods. Therefore, in the study, we propose innovative method based on inverse problem approach for optimizing the shape of magnet.
To optimize the shape of magnet, we estimate the shape of the magnet from the perfectly uniform magnetic field we set up. The magnet is groups of magnetic moment m as shown in Fig.
1(a). Figure 1(b) shows the optimized shape of magnet from the model of vertical rectangle. In Figure 1(c), we depicted cross-section of each z-stage of optimized the magnet vertical
rectangle. Figure 1(d) shows the magnetic field Bz on the diamond surface. The uniformity was 98.5% before optimization and improved to 99.9% after optimization on the diamond
surface. However, the uniformity on the entire diamond was low at 89.0%. To achieve the target magnetic field uniformity, we changed the thickness of the diamond NV center from 2mm
to 0.1 mm and model from vertical rectangle to horizontal rectangle. Figure 2(a)(b) show the model of horizontal rectangle and the optimized shape of magnet. In Fig. 2(c), we depicted
cross-section of each z-stage of optimized the magnet of horizontal rectangle. The magnetic field on the diamond surface was 99.6% and the uniformity of the entire diamond improved to
97.5%. We developed a method to determine the shape of a magnet from a highly uniform magnetic field. As the next step, we fabricate the optimized small magnet for diamond NV center
and evaluate the improvement in magnetic sensitivity. 

**Acknowledgement:** 

This work was supported by the Uehara Memorial Foundation and Hitachi Global Foundation. 

**References:** 

[1] A. Kuwahata et al., Scientific Reports 10 (1), 1-9,(2020). 
[2] Alexander P. Nizovtsev et al., nanomaterials 11 (5), 1-13 (2021). 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/7eac9ecc88866d3a7bbced5499772007.png)

Development of a compact magnet for applying a highly uniform magnetic field to a diamond magnetic sensor by inverse problem analysis

Interest in superconducting computing is being driven by two concerns. On the one hand, large-scale computing facilities and data centers are using electrical power at an ever-increasing rate. Projections suggest that a fully superconducting computer would consume considerably less power than conventional semiconductor-based computers [1]. On the other hand, a quantum computer based on superconducting qubits would benefit from having a classical superconducting processor nearby in the cold space, to avoid a plethora of control and readout lines between room temperature and the cold space [2]. Building a large-scale memory for a superconducting computer is a challenge. One approach is to use Josephson junctions containing ferromagnetic materials as the basic memory element for such a memory [3]. In that approach, the information storage device is a Josephson junction containing a pseudo spin valve. Depending on the relative orientation of the two magnetizations in the spin valve, and with suitably chosen thicknesses of both magnetic layers, the ground-state phase difference across the junction can be either zero or π. We have demonstrated two different types of junctions that can be controllably switched between the 0-phase state and the π-phase state [4,5]. While such junctions are promising components for a scalable superconducting memory [6], much more work needs to be done to enable scaling of this approach to a large-scale memory array.
Work supported by the US DOE under grant DE-FG02-06ER46341, by Northrop Grumman Corporation, and by IARPA via U.S. Army Research Office contract W911NF-14-C-0115. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the ODNI, IARPA, or the U.S. Government. 
**References** [1] D.S. Holmes, A.L. Ripple, & M.A. Manheimer, IEEE Trans. Appl. Supercond. 23, 1701610 (2013). 
[2] E. Leonard et al., Phys. Rev. Applied 11, 014009 (2019). 
[3] A.Y. Herr & Q.P. Herr, US Patent 8,270,209 (2012). 
[4] E. C. Gingrich, B. M. Niedzielski, J. A. Glick, Y. Wang, D. L. Miller, R. Loloee, W. P. Pratt Jr., and N. O. Birge, Nature Phys. 12, 564 (2016). 
[5] J.A. Glick, V. Aguilar, A. Gougam, B.M. Niedzielski, E.C. Gingrich, R. Loloee, W.P. Pratt, Jr., and N.O. Birge, Science Advances 4, eaat9457 (2018). 
[6] I. M. Dayton et al., IEEE Magnetics Lett. 9, 3301905 (2018).

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