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The rare earth nitride (REN) series is a promising candidate for spintronics applications. It is the only epitaxy-compatible series of intrinsic ferromagnetic semiconductors, with members possessing complementary and contrasting magnetic properties.1 It is established that REN properties display high sensitivity to native defects, mainly the nitrogen vacancies (VN). VN form at the level of a few percent or less during thin film growth even in the most nearly stoichiometric films. The vacancies act as dopants and introduce n-type conductivity. The literature reports on more VN-induced effects in the REN such as the enhanced Curie temperature in GdN (from 50K to 70K) due to the formation of magnetic polarons at VN sites, and superconductivity below 4K in heavily VN-doped ferromagnetic semiconducting SmN thin films 2,3 Here, we show that the rate of N2 flow during growth and thin film properties are intimately linked, suggesting that the growth stoichiometry is key for understanding the structural, transport, and magnetic properties of the REN. X-ray diffraction, magnetic, Hall-effect, and transport measurements are carried out on a series of polycrystalline REN (GdN, SmN, and DyN) thin films. We show remarkable changes to the properties of the films: SmN film resistivity can be controlled over six orders of magnitude by less than one order of magnitude change of the N2/RE growth ratio. Hall-effect measurements correlate this increase in resistivity to a drop in the VN concentration. We also observe the signature of a secondary structural phase of GdN associated with N-deficient regions that develops as the N2 pressure decreases during the growth and has a smaller lattice parameter than stoichiometric GdN. We also observe an enhanced TC (up to 90 K) for the films grown with the lowest N2/Gd ratio.References: 1F. Natali et al, Prog. Mater. Sci. 58, 1316 (2013). 2F. Natali, et al, Phys. Rev. B 87, 035202 (2013). 3E. M. Anton et al, Phys. Rev. B 94, 024106 (2016).

MMM 2020

Effect of the N2/RE Ratio During Growth on the Properties of Rare Earth Nitrides

The 65th Annual Conference on Magnetism and Magnetic Materials (MMM 2020) was held in a virtual form. The COVID-19 pandemic, with its associated uncertainty about international travel and the ability to gather in large groups, meant that the Steering Committee decided to cancel the face-to-face meeting that had been planned in Palm Beach, Florida November 2-6, 2020.

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technical paper

Magnetic skyrmions are topologically stable configuration with particle-like properties. Due to their efficient current-induced manipulation, they could act as carrier of information in futur devices. They where initially observed at low temperature and by applying an intense magnetic field in bulk materials exhibiting broken inversion symmetry[1-2] and in epitaxial ultrathin films with interfacial Dzyaloshinskii-Moriya interaction[3-4]. An intense research effort during the past few years has led to their stabilization at room temperature[5] but still by applying an external magnetic field. A promising strategy to overcome this last obstacle is to exploit the interlayer exchange coupling in magnetic heterostructure to produce an internal effective magnetic field Bint[6-7]. Here, we demonstrate that magnetic skyrmions with a mean diameter around 60 nm can be stabilized at room temperature and zero external magnetic field in an exchange-biased Pt/Co/Ni80Fe20/Ir20Mn80 multilayerstack[8]. This is achieved through an advanced optimization of the multilayer-stack composition in order to balance the different magnetic energies controlling the skyrmion size and stability. Magnetic imaging is performed both with magnetic force microscopy and scanning nitrogen-vacancy magnetometry, the latter providing unambiguous measurements at zero external magnetic field. Simulation of the PL quenching image are also achieved and the results, in agreement with experimental data, allows us to extract informations such as skyrmion's size. These results establish exchange-biased multilayer stacks as a promising platform toward the effective realization of memory and logic devices based on magnetic skyrmions.References: [1] S. Mühlbauer et al., Science323, 915 (2009) [2] X. Z. Yu et al., Nature (London) 465, 901 (2010) [3] S. Heinze et al., Nature Phys.7, 713 (2011) [4] N. Romming et al., Science341, 636 (2013) [5] W. Jiang et al., Science349, 283 (2015) [6] G. Chen et al., Appl. Phys. Lett.106, 242404 (2015) [7] Y. Guang et al., Nat. Commun.11, 949 (2020) [8] K. Gaurav Rana et al., Phys. Rev. Applied 13, 044079 (2020)

Room-Temperature Skyrmions at Zero Field in Exchange-Biased Ultrathin Films

Skyrmions induced by the Dzyaloshinskii–Moriya (DM) interaction have the great potential for spintronic applications, owing to emergent electromagnetic phenomena, and ultra-low current driven motion. Although near room temperature skyrmions were reported for B20-type FeGe (ferromagnetic Curie temperature TC = 278 K)1, β-Mn type CoxZnyMnz (TC = 420 K)2 and tetragonal Heusler Mn1.4Pt1-yRhySn (TC = 390 K)3, their skyrmion size were found to be relatively large around 100 nm. It is of particular importance to develop new materials that exhibited skyrmions with small skyrmion sizes at and above room temperature. In this study, we focused on β-Mn type nitride A2Mo3N, because skyrmion phase was observed at 100 K by Lorenz transmission electron microscopy (LTEM) in FexCo1.5-xRh0.5Mo3N (x = 0.3 and 0.5)4. We prepared the epitaxial A2Mo3N films and investigated the effects of multi doping of A site on magnetic properties as well as the appearance of skyrmion phases. A series of A2Mo3N (A = Fe, Pd, Ni, Pt,) epitaxial thin films was fabricated on c-plane sapphire substrates with the (110) orientation by reactive magnetron sputtering. The skyrmion phase in a 50 nm thick film with Fe1.68Pd0.32Mo3N was determined by topological Hall effect (THE) and LTEM imaging. Topological Hall resistivity ρTH induced by skyrmions at 4 K and 300 K are shown in Fig. 1 as a function of applied magnetic field. Enormous ρTH at 4 K indicates the dense skyrmion phase, and reduced ρTH at 300 K indicates the isolated skyrmion phase with sign reversal, which is considered to be induced by the temperature-dependent electronic state. LTEM images of single skyrmion at 90 K and 300 K are shown in Fig. 2. Small size skyrmion (ca. 60 nm) was observed unaffected by the temperature. These results indicate that β-Mn-type A2Mo3N has a great potential and is a candidate as a host of new kind of skyrmion, which may help us to understand the fundamental mechanisms of DM interaction in the skyrmion.References: [1] P. Upadhyaya et al., Phys. Rev. B 92, 134411 (2015). [2] Y. Tokunaga et al., Nat. Commun. 6, 7638 (2015). [3] V. Kumar et al., Phys. Rev. B 101, 014424 (2020). [4] W. Li et al. Phys. Rev. B 93, 060409(R) (2016).

Magnetic skyrmions in epitaxial thin films of A2Mo3N with the filled β-Mn-type structure

Magnetic skyrmions are localized magnetic textures in magnetic films, behaving as particles and topologically different from the uniform ferromagnetic state, which have been identified to be extremely promising for applications, as well as of fundamental interest [1]. The magnetism community has provided a great effort in the last years to stabilize them at room temperature, most often by designing magnetic and heavy-metal multilayers combining perpendicular magnetic anisotropy and Dzyaloshinskii-Moriya interaction (DMI) [2]. The DMI promotes a unique chirality of the skyrmionic spin textures and, combined with spin-orbit torques generated in the heavy-metal layer(s), allows efficient current-induced motion of skyrmions [3]. However, recent observations have revealed that multilayered skyrmions are prone to present a hybrid chirality, due to the competition between dipolar interaction and DMI, which can negatively influence their current-induced motion [4] and also their size and stability [6]. We will discuss how those effects can be reduce thanks to synthetic antiferromagnets (SAF) based systems that allow the stabilisation of smaller antiferromagnetic skyrmions, due to the cancellation of the long range dipolar effects [7]. We will mainly focus on Pt/Co/Ru and Pt/CoFeB/Ru based systems and present the optimization process that has been done on the thicknesses of the different layer in order to maximize the antiferromagnetic RKKY coupling without cancelling the perpendicular magnetic anisotropy, needed to stabilize skyrmions. Those optimizations enabled for example the observation at room temperature of spin spiral, predicted by micromagnetic simulations, by reaching an effective anisotropy close to zero. We will then describe how, combined to a bias layer structure, multi-repeats SAF can host antiferromagnetic skyrmions and present their observation by MFM techniques without needs to go under vacuum. Those observations will also be completed by NV center microscopy images. The ANR grant TOPSky TOPSKY (ANR-17-CE24-0025), the SESAME Ile de France IMAGeSPIN (EX039175), the DARPA TEE program grant (MIPR#HR0011831554) and EU grant SKYTOP (H2020 FET Proactive 824123) are acknowledged for their financial support.References: [1] A. Fert, N. Reyren, V. Cros, Nat. Rev. Mat. 2 (2017), 17031. [2] C. Moreau-Luchaire et al, Nat. Nanotech, 11 (2016), 444 ; S. Woo et al, Nat. Mater. 15 (2016), 501 ; A. Soumyanarayanan et al, Nat. Mater. 16 (2017), 898 ; A. Hrabec et al, Nat. Comm. 8 (2017), 15765. [3] K. Litzius et al, Nat. Phys. 13 (2017), 170 ; S. Woo et al, Nat. Comm. 8 (2017), 15573. [4] W. Legrand et al, Sci. Adv. 4 (2018), eaat0415 ; Y. Dovzhenko et al, Nat. Comm. 9 (2018), 2712. [5] F. Büttner et al, Sci. Rep., 8 (2018), 4464 ; A. Bernand-Mantel et al, SciPost Phys. 4 (2018), 027. [6] W. Legrand et al, Phys. Rev. Applied 10 (2018), 064042. [7] W. Legrand et al, Nat. Mater. 19 (2019), 34–42.

Room-temperature magnetic imaging of antiferromagnetic skyrmions in multi-repeats synthetic antiferromagnets

Magnetic skyrmions [1] are promising candidates for next-generation spintronic devices. Their solitonic and chiral nature allows an efficient current-induced motion up to high velocities [2]. A fine tuning of their chirality would enable highly-manipulable magnetic skyrmions, which paves the way for new functionalities in spintronic memory, logic and neuromorphic devices [3,4]. This gives great importance to the control of the interfacial Dzyaloshinskii-Moriya interaction (iDMI) [5,6] strength and sign, at the origin of magnetic skyrmions and their chirality. In this study, we directly demonstrate magnetic skyrmion’s chirality switching in a Ta/FeCoB/TaOx trilayer. In fact, by varying the thickness of FeCoB and the oxidation state at the FeCoB/TaOx interface, we are able to obtain different regions in which magnetic skyrmions are right-handed (iDMI>0) or left-handed (iDMI<0) (resp. regions #4 and #2 on Fig.1). This material-dependent chirality switching brings a new degree of freedom to the exciting physics of magnetic skyrmions. For the first time, we show that the iDMI sign crossover in the different regions, as measured by Brillouin-Light-Scattering (BLS), is accompanied by a change of skyrmion chirality, as confirmed by the opposite direction of current-induced motion of magnetic skyrmions (See Fig. 2). Notably, between the two regions of opposite iDMI sign we have found, as expected, a region where iDMI∼0. In this region, the control of the iDMI with an electric field [7] may lead to a voltage-induced chirality switching, which hasn’t been observed yet. This all-electrical control of magnetic skyrmions represents a cornerstone towards power efficient spintronic devices and multidirectional logic functionnalities.References: [1] A. N. Bogdanov and D. A. Yablonskii, J. Exp. Theor. Phys., Vol. 95, p101−103 (1989) [2] W. Jiang, P. Upadhyaya and W. Zhang et al., Science, Vol. 349 (2015) [3] X. Zhang, Y. Zhou and K. M. Song et al., J. Phys.: Condens. Matter, Vol. 32 (2020) [4] A. Fert, N. Reyren and V. Cros et al., Nat. Rev. Mater., Vol. 2 (2017) [5] I. E. Dzyaloshinskii, Sov. Phys. JETP, Vol. 5 (1957) [6] T. Moriya, Phys. Rev., Vol. 120 (1960) [7] T. Srivastava, M. Schott and R. Juge et al., Nano. Lett, Vol. 18 (2018)

Chirality Switch of Magnetic Skyrmion in Ta/FeCoB/TaOx Trilayers

Praseodymium Iron Boron (PrFeB) thin film has recently attracted considerable attention for the potential magnetic property, which can alternate for currently NdFeB magnetic materials. The super low spin-reorientation temperature (about 4.2 K), huge uniaxial magnetocrystalline anisotropy (Ku), large coercivity (Hc), high saturation magnetization (Ms), and large energy products (BHmax) are the great properties that make PrFeB become a promising candidate in application of magnetic recording media nowadays. It is known that there is the body-centered tetragonal (BCT) structure of Pr2Fe14B phase mainly existing in PrFeB thin films to strengthen perpendicular magnetic anisotropy (PMA). The small lattice mismatch (δ) between Pr2Fe14B (00l) texture with [100] direction and BCC(110) texture underlayer with [110] and [001] directions makes the easy axis [001] perpendicular to the film plane. In this study, the Pr-Fe-B films with PMA were fabricated without underlayer on biased substrate by Pr25Fe65B10 alloy target. The substrate temperature was kept at 650oC and the bias was adjusted from -150 V to +100 V during sputtering hard magnetic Pr-Fe-B films. Then, Si3N4 cover layer was deposited at room temperature (RT). The deposited films were characterized for structural and magnetic properties by employing appropriate techniques. Effect of the substrate bias voltage on physical properties of thin film was systematically investigated. From our results, the squareness of the Pr-Fe-B film was enhanced significantly, because an epitaxial growth was initiated from applying substrate bias continuously through the Pr-Fe-B magnetic layer with the range of voltage from -50 to +50 V. Applying positive substrate bias changed atomic mobility, the Pr, Fe, and B atoms may diffuse chaotically in the magnetic layer. Consequently, an epitaxial barrier of the Pr-Fe-B alloy was broken among the elements in the magnetic layer, affected the deposition rates, improved the magnetic performance, and epitaxial growth of Pr-Fe-B thin films.

Strengthen the Magnetic Properties of Pr-Fe-B Thin Films by Biased Substrate

We report on magnetoresistance studies in La0.67Sr0.33MnO3 (LSMO) thin film on LaAlO3 by strain engineering at the interface. For this we investigate the magnetization and transport properties of compressively strained ferromagnetic LSMO films. We patterned Hall bars of the LSMO films and measure the longitudinal resistance in a 4-probe configuration applying a dc current bias. We systematically characterize the magnetic anisotropy of the thin films by varying temperature, applied magnetic field and the angle between current and field. The temperature and angular dependence of the longitudinal magnetoresistance for an in plane magnetic configuration explicitly shows three distinctly different magnetic phases. We observe a fourfold symmetry in the angular dependence of the magnetoresistance, for the temperature range between 10 to 125 K, indicating a biaxial anisotropy in the plane parallel to the (110) and (1-10) directions of thin film. Increasing the temperature further shows the presence of a second magnetic phase between 125 K to 250 K characterized by a twofold in-plane angle dependent magnetoresistance signal. We postulate that the fourfold symmetry is driven by magneto crystalline anisotropy whereas the twofold symmetry arises due to conventional anisotropic magnetoresistance. On increasing the temperature further, the thin film transit to a paramagnetic insulating phase. We show that the temperature variation of the angular dependence of the magnetoresistance is an important approach to study the different anisotropy induced in such strained thin oxide films and can complement torque based magnetometry studies.

Temperature dependence of the anisotropic magnetoresistance of compressively strained thin films of La2/3Sr1/3MnO3 on LaAlO3

The effect of high tensile strain and low dimensionality on the magnetic and electronic properties of CaMnO3 ultrathin films, epitaxially grown on SrTiO3 substrates, are theoretically analyzed (Fig. 1). By means of ab initio calculations, we find that, both, the high strain produced by the substrate and the presence of the free surface contribute to the stabilization of an in-plane ferromagnetic coupling, giving rise to a non-zero net magnetic moment in the ultrathin films. Remarkably, the FM component of the magnetic structure is stabilized, not as a consequence of a direct electron doping, as it happens when substituting the divalent Ca by trivalent elements or in the presence of O vacancies, as reported in the past, but rather because of a self-doping charge redistribution due to, both, the strain and the absence of apical oxygens. A deeper analysis of this charge redistribution can be obtained from the partial densities of states (pDOS) depicted in Fig. 2, where we separate the contributions of different MnO2 planes. From the total density of states projected onto each layer, we can see that the oxygens located at the surface are the ones which loose part of their charge, and this charge is redistributed in the Mn atoms located in inner layers, and begin to occupy the dx2-y2 orbitals. The self-doping electrons of this eg states, allow the presence of the FM double exchange and the AAF magnetic structure with more FM pairs becomes more stable. As it can also be seen from Fig.2, coupled with this change in the magnetic order we find an insulator-metal transition triggered by the quantum confinement and the tensile epitaxial strain.

Strain induced magnetic transition in CaMnO3 ultrathin films

Soft magnetic materials have been studied extensively in the recent years due to their applications in micro-transformers, micro-inductors, spin dependent memories etc. The unique features of these materials are the high frequency operability and high magnetic anisotropy. High uniaxial anisotropy is one of the most important properties for these materials. There are many methods to achieve high anisotropy field (Hk) which include sputtering with presence of magnetic field, exchange bias and oblique angle sputtering without the presence of the magnetic field, etc. There are multiple ways to increase the ferromagnetic resonance frequency which is proportional to coercivity Hk and magnetic saturation Ms. The ferromagnetic resonance depends on softness of the magnetic material to the applied field. With a highly soft magnetic material, one can operate the devices made out of these films at giga hertz regions without loss of efficiency. of the magnetic films is also highly desirable for many applications, such as power conversion and radio frequency (RF) devices operating at high frequencies. This work focuses on analyzing different growth conditions of thin films of CoZrTaB and the resulting magnetic and electrical properties of the films. Thin films are grown by oblique-angle sputtering method, where the sputtering gun forms an angle with respect to the sample substrate normal, ranging from 0 to 75 degrees. External magnetic field normally applied in order to form magnetic anisotropy is not used during film sputtering process. Using vibrating sample magnetometer, it was observed that films resulting from small oblique angles have no clear magnetic anisotropy developed; whereas in samples deposited at large angles close to 60 degree, there is clear magnetic anisotropy observed. Scanning electron microscopy imaging of the cross-section views of such film suggests the formation of tilted columns, which is likely to be the reason for magnetic anisotropy. Resistivity of the films was measured systematically and found to increase as the magnitude of oblique angle during sputtering increased.References: 1. M. Yamaguchi, K. H. Kim and S. Ikedaa, J. Magn. Magn. Mater. 304 (2), 208-213 (2006). 2. H. Wu, D. S. Gardner, W. Xu and H. B. Yu, IEEE Trans. Magn. 48 (11), 4123-4126 (2012). 3. H. Wu, D. S. Gardner, S. R. Zhao, H. Huang and H. B. Yu, J. Appl. Phys. 115 (17) (2014).

Magnetic Anisotropy and Electrical Property Of CoZrTaB Thin Films Deposited by Oblique Sputtering

Epitaxial films of Mn5Ge3/Ge<111> are interesting as a potential source of highly spin polarized electrons directly into Ge. Moreover, the high out-of-plane anisotropy of Mn5Ge3 opens up prospect for combining spintronics with data storage. The ferromagnetic Mn5Ge3 compound crystallizes in the hexagonal D88 structure; Mn atoms occupy two magnetically and structurally nonequivalent positions: 4d (MnI) and 6g (MnII). The Curie temperature of 296 K can be increased up to 445 K by doping with carbon [1]. Recent 55Mn NMR studies have shown that the magnetocrystalline anisotropy in Mn5Ge3 originates from the unquenched orbital moment of Mn in both crystallographic positions [2]. Furthermore, the 55Mn NMR study in Mn5Ge3C0.2/Ge(111) film has shown that carbon enters interstitially occupying the 2(b) octahedral voids and reduces the magnetic moment of the MnII atoms in the corners of a host octahedron [3]. To achieve further understanding of the role that carbon plays in this system, we carried out a systematic FMR and 55Mn NMR study on a series of epitaxial 30 nm thick Mn5Ge3Cx/Ge(111) films with the nominal carbon content x varying between 0 and 0.8. The FMR experiment shows that the uniaxial anisotropy constant Ku measured at 4.2 K systematically drops from 5,69x106 erg/cm3 to 8,06x105 erg/cm3 for the nominal concentration of x ≈ 0.6. The 55Mn NMR shows that in the concentration range up to x=0.5 the MnII atoms are found in two distinctly different magnetic states, identified as MnII (no carbon nearest neighbor) and MnII_C (one carbon nn). With increasing carbon concentration the NMR signal intensity is systematically transferred from MnII to MnII_C, and at x=0.5 no MnII NMR signal is observed anymore. On the other hand, no second satellite line is observed in the vicinity of the MnII signal in the entire concentration range, even though there are two available 2(b) positions around the MnII atoms. These two observations implicate that carbon does not enter statistically in the 2(b) voids, but shows a strong preference towards ordering, occupying every second 2(b) void along the hexagonal c-direction. This sets the limit for the uptake of the carbon atoms in the Mn5Ge3 lattice to x=0.5.References: [1] M. Gajdzik et al., J. Magn. Magn. Mater., Vol. 221 p. 248 (2000) [2] R. Kalvig et al., Phys. Rev. B, Vol. 97 p. 174428 (2018) [3] R. Kalvig et al., Phys. Rev. B, Vol. 101 p. 094401 (2020)

Ordered occupancy of interstitial voids in Mn5Ge3 lattice by the carbon dopant

TiO2 crystallizes in three different structures such as anatase, brookite and rutile [1-3]. In addition, Magneli phase is a titanium sub oxide (TinO2n-1, 4 ≤ n ≤ 10) have been explored as a promising candidate because of their high electrical conductivity, chemical inertness and corrosion resistance [4]. Among the Magneli phase compounds, Ti4O7 is important for its high electrical conductivity. In general, Ti4O7 is synthesised by thermal reduction of TiO2 [5]. These Magneli phases can easily accommodate oxygen deficiency through anionic vacancies, which leads to the partial reduction of Ti4+ to Ti3+. This Ti3+ gives local ferromagnetism in the material through hopping of the single 3d electron [6]. In this work, ion irradiation is used as a unique tool for the material modification depending upon the projectile ion, energy and the nature of the target. Ion irradiation has been found to amorphize, recrystallise and induce crystalline to crystalline phase transition or defects in various materials. In our earlier studies, we have used 500 keV Ar2+ ions to irradiate on the TiO2 thin films grown on Si substrate by e-beam evaporation technique and subsequently annealed under O2 environment at 500 C [7-8]. However, we have observed phase transformation from anatase to brookite through amorphisation and room temperature ferromagnetism (RTFM) in the films attribute to oxygen vacancies [7-8]. Hence, in the present study we have explored the role of 500 keV Ar2+ ion irradiation on the structural and magnetic properties of TiO2 thin films annealed under Ar at 900 C. The annealed films show Ti4O7 phase which transform to anatase phase upon irradiation with fluence 1 × 1014 ions.cm-2 as observed from the glancing angle x-ray diffraction (GAXRD). Further, irradiation with fluence 5 × 1016 ions.cm-2 recrystallizes to Ti4O7 phase. Raman spectroscopic studies also support the changes in phase. AFM show small change of surface morphology upon ion irradiation with roughness, 0.060, 0.062, 0.079 nm and grain size, 28, 28, 29 nm for the pristine film, films irradiated with ion fluenece 1 × 1014 and 5 × 1016 ions.cm-2, respectively. The origin of RTFM is coined with the oxygen vacancies concentration in the films.References: [1] C. Rath, P. Mohanty, A.C. Pandey, N. C. Mishra, J. Phys, D: Appl. Phys 47 315001 (2009). [2] P. Mohanty, V. P. Singh, N. C. Mishra, S. Ojha, D. Kanjilal, C. Rath, J. Phys, D: Appl. Phys 47 315001 (2014). [3] B. Bharati, N. C. Mishra, A. S. K. Sinha, C. Rath, Materials Research Bulletin 123 110710 (2020). [4] P. Geng, J. Su, C. Miles, C. Comninellis, G. Chen, Electrochimica Acta 153 316–324. (2015) [5] G. Wang, Y. Liu, J. Ye, W. Qiu, Journal of Alloys and Compounds 704 18 (2017). [6] M. Parras, A. Varela, R. C. Gil, K. Boulahya, A Hernando, J. M. G. Calbet, J. Phys. Chem. Lett. 4 2171 (2013). [7] B. Bharati, N. C. Mishra, D. Kanjilal, C. Rath, Applied Surface Science 428 723 (2018). [8] B. Bharati, N. C. Mishra, C. Rath, Applied Surface Science 455 717 (2018).

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Effect of the N2/RE Ratio During Growth on the Properties of Rare Earth Nitrides

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Room-Temperature Skyrmions at Zero Field in Exchange-Biased Ultrathin Films

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