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Magnetoelectrics (ME), materials which possess a coupling between their magnetic and electric orders, are the most studied type of multiferroic (MF) materials due to their obvious potential in technological applications such as: ultralow power logic-memory devices, magnetic sensors, energy harvesting/conversion devices, spintronic devices, among others [1-4].&lt;br/&gt;&lt;br/&gt;Still, the ME effect presents an inherent obstacle which is related to the apparent necessity of empty d orbitals (d&lt;sup&gt;0&lt;/sup&gt;) for Ferroelectrics against semi-filled d orbitals (d&lt;sup&gt;n&lt;/sup&gt;) for magnetic order [4-5].&lt;br/&gt;&lt;br/&gt;Therefore, the search for magnetoelectric materials typically revolves around the struggle to simultaneously coexist magnetic and ferroelectric orders in the same material, either using an intrinsic or extrinsic/composite approach. In fact, due this paradoxical limitation when having an electric and magnetic order in a single phase, extrinsic MF have been showing the most promising results, managing to achieve substantial ME couplings even at temperatures close to room temperature [4,6-8].&lt;br/&gt;&lt;br/&gt;Via &lt;i&gt;ab initio &lt;/i&gt;calculations of a prototypical Fe/BaTiO&lt;sub&gt;3&lt;/sub&gt; interface, we predict that it is possible to tune the magnitude of the individual magnetic moments, even for non-polar BaTiO&lt;sub&gt;3&lt;/sub&gt; (BTO), through a uniaxial strain in cubic and tetragonal Fe/BTO heterostructures.&lt;br/&gt;&lt;br/&gt;By comparing polar and non-polar Fe/BTO heterostructures, we show that the Fe, Ti and equatorial O atomic magnetic moments are induced and enhanced as a result of their local crystal field. The crystal field may be controlled solely by the manipulation of the inter-atomic distances of their neighboring atoms (which will affect their electrostatic fields and orbital hybridizations), or by the BTO electric dipole moments, working as a local polarization.&lt;br/&gt;&lt;br/&gt;Contrary to conventional assumptions, a Fe/BTO interface does not require electrical polarization to be able to tune its magnetic moment. In fact, by applying strain, the sensitivity of the non-polar region is higher than that of its polar equivalent. Additionally, comparing the tensile region of the cubic and tetragonal supercells, it is clear that the non-polar cubic supercell reaches higher total magnetizations than its polar tetragonal counterpart. When the polarization is present, it dominates the crystal field contributions, thus constraining the effects of other perturbations such as strain.&lt;br/&gt;&lt;br/&gt;The results of our work reiterate the extrinsic magnetoelectric potentialities and reduces the requirements for an electric control of magnetism. Therefore, we should rethink the conventional search and optimization of ME materials, without the limitations which come with magnetic ferroelectrics.

**References:**

[1] Dong, S.; Liu, J.-M.; Cheong, S.-W.; Ren, Z. Multiferroic materials and magnetoelectric&lt;br/&gt;physics: symmetry, entanglement, excitation, and topology. Advances in Physics 2015,&lt;br/&gt;64, 519–626.&lt;br/&gt;[2] Fiebig, M. &lt;i&gt;et al, &lt;/i&gt;The evolution of multiferroics. Nature Reviews Materials 2016, 1, 16046.&lt;br/&gt;[3] Song, C.; Cui, B.; Li, F.; Zhou, X.; Pan, F. Recent progress in voltage control of magnetism: Materials, mechanisms, and performance. Progress in Materials Science&lt;br/&gt;2017, 87, 33–82.&lt;br/&gt;[4] Spaldin, N. A.; Ramesh, R. Advances in magnetoelectric multiferroics. Nature materials&lt;br/&gt;2019, 18, 203.&lt;br/&gt;[5] Hill, N. A. Why are there so few magnetic ferroelectrics? J. Phys. Chem. B 2000, 104,&lt;br/&gt;6694–6709.&lt;br/&gt;[6] Vaz, C. A.; Hoffman, J.; Ahn, C. H.; Ramesh, R. Magnetoelectric coupling effects in&lt;br/&gt;multiferroic complex oxide composite structures. Advanced Materials 2010, 22, 2900–&lt;br/&gt;2918.&lt;br/&gt;[7] Cherifi, R. O. &lt;i&gt;et al&lt;/i&gt;, M. Electric-Field Control of Magnetic Order Above Room Temperature. Nat. Mater. 2014, 13, 345–351.&lt;br/&gt;[8] Mundy, J. A. &lt;i&gt;et al, &lt;/i&gt;Atomically engineered ferroic layers yield a room-temperature magnetoelectric multiferroic. Nature 2016, 537, 523–527.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/ba3c379438319f04c388e1912d26dcba.jpg)
Fe&lt;sub&gt;2&lt;/sub&gt;/BaTiO3 supercell composed of a Fe monolayer on top of a BaTiO&lt;sub&gt;3&lt;/sub&gt; unit cell.

![](https://assets.underline.io/uploads/markdown_image/1/image/247f5d1b42c5962cf8c4bc17c094a531.jpg)
Total magnetization of the Fe&lt;sub&gt;2&lt;/sub&gt;/BaTiO&lt;sub&gt;3&lt;/sub&gt; heterostructure as a function of D (the supercell total heigh), for the supercells containing the cubic and tetragonal BTO unit cells. The inset shows the binding energy in the same range of D.

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 Enhanced strain-induced magnetoelectric coupling in polarization-free Fe/BaTiO3 heterostructures

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Magnetoelectrics (ME), materials which possess a coupling between their magnetic and electric orders, are the most studied type of multiferroic (MF) materials due to their obvious potential in technological applications such as: ultralow power logic-memory devices, magnetic sensors, energy harvesting/conversion devices, spintronic devices, among others [1-4]. Still, the ME effect presents an inherent obstacle which is related to the apparent necessity of empty d orbitals (d0) for Ferroelectrics against semi-filled d orbitals (dn) for magnetic order [4-5]. Therefore, the search for magnetoelectric materials typically revolves around the struggle to simultaneously coexist magnetic and ferroelectric orders in the same material, either using an intrinsic or extrinsic/composite approach. In fact, due this paradoxical limitation when having an electric and magnetic order in a single phase, extrinsic MF have been showing the most promising results, managing to achieve substantial ME couplings even at temperatures close to room temperature [4,6-8]. Via ab initio calculations of a prototypical Fe/BaTiO3 interface, we predict that it is possible to tune the magnitude of the individual magnetic moments, even for non-polar BaTiO3 (BTO), through a uniaxial strain in cubic and tetragonal Fe/BTO heterostructures. By comparing polar and non-polar Fe/BTO heterostructures, we show that the Fe, Ti and equatorial O atomic magnetic moments are induced and enhanced as a result of their local crystal field. The crystal field may be controlled solely by the manipulation of the inter-atomic distances of their neighboring atoms (which will affect their electrostatic fields and orbital hybridizations), or by the BTO electric dipole moments, working as a local polarization. Contrary to conventional assumptions, a Fe/BTO interface does not require electrical polarization to be able to tune its magnetic moment. In fact, by applying strain, the sensitivity of the non-polar region is higher than that of its polar equivalent. Additionally, comparing the tensile region of the cubic and tetragonal supercells, it is clear that the non-polar cubic supercell reaches higher total magnetizations than its polar tetragonal counterpart. When the polarization is present, it dominates the crystal field contributions, thus constraining the effects of other perturbations such as strain. The results of our work reiterate the extrinsic magnetoelectric potentialities and reduces the requirements for an electric control of magnetism. Therefore, we should rethink the conventional search and optimization of ME materials, without the limitations which come with magnetic ferroelectrics.

**References:**

[1] Dong, S.; Liu, J.-M.; Cheong, S.-W.; Ren, Z. Multiferroic materials and magnetoelectric physics: symmetry, entanglement, excitation, and topology. Advances in Physics 2015, 64, 519–626. [2] Fiebig, M. et al, The evolution of multiferroics. Nature Reviews Materials 2016, 1, 16046. [3] Song, C.; Cui, B.; Li, F.; Zhou, X.; Pan, F. Recent progress in voltage control of magnetism: Materials, mechanisms, and performance. Progress in Materials Science 2017, 87, 33–82. [4] Spaldin, N. A.; Ramesh, R. Advances in magnetoelectric multiferroics. Nature materials 2019, 18, 203. [5] Hill, N. A. Why are there so few magnetic ferroelectrics? J. Phys. Chem. B 2000, 104, 6694–6709. [6] Vaz, C. A.; Hoffman, J.; Ahn, C. H.; Ramesh, R. Magnetoelectric coupling effects in multiferroic complex oxide composite structures. Advanced Materials 2010, 22, 2900– 2918. [7] Cherifi, R. O. et al, M. Electric-Field Control of Magnetic Order Above Room Temperature. Nat. Mater. 2014, 13, 345–351. [8] Mundy, J. A. et al, Atomically engineered ferroic layers yield a room-temperature magnetoelectric multiferroic. Nature 2016, 537, 523–527.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/ba3c379438319f04c388e1912d26dcba.jpg)
Fe2/BaTiO3 supercell composed of a Fe monolayer on top of a BaTiO3 unit cell.

![](https://assets.underline.io/uploads/markdown_image/1/image/247f5d1b42c5962cf8c4bc17c094a531.jpg)
Total magnetization of the Fe2/BaTiO3 heterostructure as a function of D (the supercell total heigh), for the supercells containing the cubic and tetragonal BTO unit cells. The inset shows the binding energy in the same range of D.

technical paper

Room temperature magnetoelectric (ME) compounds are rare and high-quality artificially multilayered ones are in general difficult and costly to produce. In this respect, magnetic Naturally Layered Perovskite structures (NLP) with improper ferroelectricity [1, 2], such as the Ruddlesden-Popper (RP) calcium manganite compound Ca3Mn2O7 [2], offer an alternative route to achieve non-expensive and high-performance room temperature MEs for information storage, sensors, and actuators or low power energy-efficient electronics. They allow exploring oxygen octahedra nonpolar rotations and cation site displacement to attain non-centrosymmetry. Additionally, due to their high sensitivity to lattice-distortions, their preparation in thin film form over crystalline substrates allows the manipulation of acentricity and enables the tuning of lattice, electric and magnetic interactions. However, crystallizing the desired layer with RP structure is challenging. Thus, the preparation conditions to obtain the envisaged Can+1MnnO3n+1 phases, with different n, need to be optimized. The objective of this study is to identify the deposition conditions that lead to different phases of (CaO)(CaMnO3)n with n = 2 (improper ferroelectric Ca3Mn2O7) and/or with n = ∞ (CaMnO3). Here we adopted the Laser ablation deposition method for developing (CaO)(CaMnO3)n thin films. As such, thin films of calcium manganate have been prepared over SrTiO3 substrates using Ca3Mn2O7 target by laser ablation. Polycrystalline Ca3Mn2O7 was synthesized using a conventional high-temperature ceramic route. The phase purity of the target was checked using XRD. The deposition parameters were studied, specifically oxygen partial pressures (from 10-3 to 10-1 mbar), laser fluences (10-5 J/cm2), substrate temperatures (from room temperature to 730 oC) and post-annealing influence. Further, a detailed structural study using X-ray diffraction (XRD), microstructural analysis by scanning electron microscopy (SEM), quantification of composition with energy-dispersive X-ray spectroscopy (EDS), magnetic property using SQUID magnetometer, and dielectric analysis by impedance analyzer were carried out. The XRD results show that for oxygen pressures in the range 10-2 - 10-1 mbar, deposition temperatures of 600 oC to 730 oC and laser fluences from 1.7 J/cm2 to 2.9 J/cm2, the films are polycrystalline, stabilizing in the CaMnO3 orthorhombic Pnma phase. The SEM measurements show dense films with smooth surfaces (Fig.1). The corresponding EDS measurements indicate a 1:1 atomic proportion in these samples. On the other hand, by decreasing the oxygen pressure, increasing the temperature and increasing the laser fluence, the Ca/Mn proportion increases, so that for films prepared on SrTiO3, at 730 oC, with 4 J/cm2 laser fluence, ~10-3 mbar oxygen pressure and with a post-annealing process, the Ca2Mn3O7 (n = 2) phase is stabilized, as confirmed by XRD (Fig.2). The corresponding EDS analysis further gives a Ca/Mn atomic ratio of ~1.5:1, consistent with the presence of this phase. The corresponding magnetic properties of the films, that are correlated with the stabilized phases and preparation conditions, will be present as well as the dielectric properties that were characterized by impedance spectroscopy.

**References:**

[1] Ghosez, P., Triscone, J.-M., Coupling of three lattice instabilities: Multiferroics, Nature Materials, vol. 10, n. 4, 2011, 269–270. [2] Rocha-Rodrigues, P., Santos, S. S. M., Miranda, I. P., Oliveira, G. N. P, Correia, J. G., Assali, L. V. C., Petrilli, H. M., Araújo, J. P., Lopes, A. M. L., Ca3Mn2O7 structural path unraveled by atomic-scale properties: A combined experimental and ab initio study, Physical Review B, 101, 064103, 2020.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/0bee090bfd5ee13876d09318b47cab4d.jpg)
The cross-section image from SEM shows a dense film with a thickness of about 300 nm.

![](https://assets.underline.io/uploads/markdown_image/1/image/ff9a5f8b7a402acdcaca185e32eb98fb.jpg)
The XRD diffractogram confirms the stabilization of the Ca2Mn3O7 phase (n = 2).

 Growth of Ruddlesden–Popper (CaO)(CaMnO3)n Thin Films by Laser Ablation Deposition

Complex oxide thin films have highly tunable magnetic properties, not only due to the correlated degrees of freedom within these materials, but also due to the constraints imposed by choice of substrate material. For example, the magnetic properties of manganite materials depend heavily on the bond lengths and angles, resulting in a dead layer at the substrate/film interface [1,2,3]. Recently, techniques have been developed to separate oxide thin films from the substrate after growth, decoupling structural and chemical degrees of freedom at the interface [4]. This technique therefore may allow us to reduce dead layers at the interface of manganite thin films. Thin films of (001)-oriented LaMnO3+δ (LMO) were grown using pulsed laser deposition on a water-soluble Sr3Al2O6 (SAO) film on top of a (001) SrTiO3 substrate. After coating the film with a 1μm thick support layer of PMMA polymer, the SAO was dissolved in water, allowing the film to be separated from the substrate; this freestanding film could then be transferred to a different substrate, in this case, oxidized Si or LSAT. X-ray diffraction measurements show that freestanding films remain highly crystalline and oriented, but are no longer strained to the substrate. Magnetometry measurements indicate very similar TC, magnetic anisotropy, and saturation magnetization for both freestanding and epitaxial films, and cannot discern any difference in dead layer. Therefore, polarized neutron reflectometry (PNR) was performed at multiple temperatures to understand the depth profile of both the nuclear and magnetic structure of these freestanding films. As shown in Fig. 1, the film transferred onto the LSAT substrate is very smooth and has an expected structure. Between the substrate and freestanding film is a region with slightly lower nuclear scattering length density (SLD); from STEM and EELS, we find that this region is caused by intermixing with or residue from the water-soluble layer. In contrast, the film transferred onto silicon has a much more complicated structure, as shown in Fig. 2. The PNR data can only be explained with a long-range corrugation or rumpling of the film when placed on the Si substrate, with water incorporated into the interfacial region. After chemical removal of the PMMA support, this corrugation remains. Regardless of the substrate material, the magnetic profile within the freestanding manganite film is uniform, and there is no evidence of the magnetically dead layers at the substrate/film interface seen in epitaxial films. Thus, although choice of substrate can still affect freestanding films through chemical effects – which may have implications for the integration of these freestanding films with silicon-based devices – removing the structural constraints imposed by epitaxial growth is a promising avenue to reduce the dead layer in manganites.

**References:**

[1] Zhai, X., Cheng, L., Liu, Y., et al. Nat. Commun. 5, 4283 (2014). [2] Moon, E. J., Balachandran, P. V., et al. Nano Lett. 14, 2509-2514 (2014). [3] Liao, Z., Zhang, J. Appl. Sci. 9, 144 (2019). [4] Lu, D., Baek, D. J., Hong, S. S., et al. Nat. Mater. 15, 1255–1260 (2016).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/bd954455d1393d7baa1acecb08ea8393.jpg)
(a) PNR data and (b) spin asymmetry of a 20 nm LMO freestanding film transferred onto an LSAT substrate, taken at 50K in an in-plane magnetic field of 3T. (c) The nuclear and magnetic depth-profile used to generate the best-fit model.

![](https://assets.underline.io/uploads/markdown_image/1/image/f23f5b70115419a383466b864d2fe667.jpg)
(a) PNR data and (b) spin asymmetry of a 40 nm LMO freestanding film transferred onto a Si/SiOx substrate, taken at 7K in an in-plane magnetic field of 1.5T. (c) The nuclear and magnetic depth-profile used to generate the best-fit model.

 Interfacial Corrugation and Magnetism of Freestanding LaMnO3+δ Thin Films

Energy gap parameters can vary significantly in X2YZ Heusler alloys [1], where Y-elements are 3d-transition metals and Z-components are s- and p-elements. Therefore, changes in different physical properties, especially, in electronic and optical characteristics are observed. Some features may indicate conditions close to half-metallic ferromagnets (HMFs) [2] and spin gapless semiconductors (SGSs) [3]. Such compounds are promising materials for spintronics because they can possess almost 100% spin polarization of charge carriers. HMFs hold an energy gap near the Fermi level for the current carriers with spin down, while its absence for current carriers with spin up. In turn, SGSs are like HMFs for the spin projection down, however, for the opposite spin direction, the gap is being zero [2, 3]. Thus, the aim of the work is to follow the changes in the electronic transport, optical properties of the Co2YSi (Y = Ti, V, Cr, Mn, Fe, Co, Ni) Heusler alloys system experimentally, and to compare the results obtained with the electronic band structure calculation, to establish their interconnection and suggest possible proximity to HMF- and/or SGS-states in the Co2YSi system. According to the data of X-ray structural analysis, all compounds are found to be ordered in the L21 structure. The electrical resistivity was measured in a wide temperature range using a PPMS setup. The field and the temperature dependences of the magnetic properties being studied too on the SQUID magnetometer. The coefficients of the normal and anomalous Hall Effect were found. The values of current carrier concentration and their mobility were estimated. Results of optical measurements showed good agreement with electronic band structure calculation. Besides, the correlation between the changes in these electronic, optical characteristics, and the coefficient of the current carrier spin polarization depending on the number of valence electrons are observed, which may point to the possible states of the HMF or SGS in this system of Heusler alloys. The work was performed within the framework of the state assignment of the Ministry of Science and High Education of Russia (the themes “Spin”, No. AAAA-A18-118020290104-2-2 and “Electron” No. AAAA-A18-118020190098-5) with partial support from the RFBR (project No. 20-32-90065), and the Government of the Russian Federation (Decree No. 211, Contract No. 02.A03.21.0006).

**References:**

[1] T. Graf, C. Felser, and S.S.P. Parkin, Prog. Solid State Chem., Vol. 39, p. 1 (2011) [2] M.I. Katsnelson, V.Yu. Irkhin, L. Chioncel et al., Rev. Mod. Phys., Vol. 80, p. 315 (2008). [3] X.L. Wang, Phys. Rev. Lett. Vol. 100, p. 156404 (2008).

**Images:**

 Electronic properties and electronic structure of Co2YSi (Y = Ti, V, Cr, Mn, Fe, Co, Ni) Heusler alloys

Antiferromagnets (AFMs) have regained strong attention from the magnetism community especially with the advent of antiferromagnetic spintronics [1]. The key operational element of spintronic devices is represented by information carriers, such as domain walls (DWs) and skyrmions. The simplest AFM DW separates two regions with the opposite orientation of the Neel order parameter. Although highly relevant, the experimental studies of AFM DWs (visualization, dynamics, mechanics) are challenging because of strict requirements on measurement techniques to access their properties. Here, we overcome these limitations and conduct detailed, quantitative studies of the mechanics and the nanoscale properties of individual, antiferromagnetic DWs in a single crystal Cr2O3 – a room-temperature, magnetoelectric, insulating AFM [2]. Our results reveal a remarkably pristine DW behaviour, which is governed by DW energy minimization and boundary conditions, but largely unaffected by pinning or disorder – a “textbook example” of antiferromagnetic DW physics. In our experiment, the crystal’s (0001) surface is patterned by a grid of mesas with mean thickness and width t=166 nm and w=2400 nm, respectively. The DW is nucleated by means of magnetoelectric field cooling by inverting the electric bias field over opposite halves of the sample. The DW may also be dragged through the mesa pattern by a focused laser spot. The magnetic texture is imaged using Nitrogen Vacancy (NV) magnetometry [3]. We find that the DW mimics an elastic surface with specific mechanical properties, determined by the interaction with the topographic features of the sample where the DW is (i) deflected from the straight plane crossing the mesa; (ii) bent around mesa corners. To address the DW behaviour theoretically, we perform large-scale spin-lattice simulations with GPU speed-up [4]. The analytical Ansatz is developed based on the numerically-obtained, three-dimensional DW profile. All main features of the DW behaviour can be determined taking into account the nearest-neighbour exchange and uniaxial anisotropy for a general model of a bipartite AFM. Crossing the mesa, the DW experiences an S-shaped distortion observed at the mesa surface, which is the result of exchange-driven boundary conditions at the side faces of the mesa, see Fig. 1. Below the top surface, the DW possesses a twist to match this distortion with the straight plane far below the sample’s surface. We find that the DW surface is deflected from the plane over a characteristic depth of 0.34w. Comparison of the equilibrium DW direction in bulk and at the mesa’s top surface allows us to derive an effective Snell’s law for the DW behaviour at the sample’s surface with the given incidence and refraction angles θ1 and θ2. The effective refraction coefficient is determined by the analytical energy minimization and reads neff = 1 + 3.1t/w + O(θ1). Controlled manipulation via laser not only enables DW dragging through the mesa, but also pinning at mesa corners. The shape of the DW surface is governed by its intrinsic elasticity. In terms of mechanics of an elastic ribbon, the corresponding tension coefficient is determined by the temperature-dependent exchange stiffness and anisotropy coefficient. This allows for curved DW states in which it is pinned at the opposite mesa sides. Using mesas as bistable pinning sites, we propose a potential DW-based AFM memory concept. Here, the memory state “0” or “1” is associated with the direction of the Neel order parameter at the mesa surface. We have realized such pinning sites experimentally and have shown manipulation of the state via laser dragging. In summary, we realize engineered DW potentials and control over DW trajectories by topographic structuring and manipulation of the DW position by means. The physics of AFM DWs in a single crystal with non-trivial surface topography is described theoretically by means of spin-lattice simulations and analytical model. A novel nanoscale AFM memory architecture is suggested.

**References:**

[1] T. Jungwirth, J. Sinova, A. Manchon et al, Nat. Phys. Vol. 14, p. 200 (2018); T. Jungwirth, X. Marti, P. Wadley et al, Nat. Nano. Vol. 11, p. 231 (2016); V. Baltz, A. Manchon, M. Tsoi et al, Rev. Mod. Phys. Vol. 90, p. 015005 (2018); O. V. Pylypovskyi, D. Y. Kononenko, K. V. Yershov et al, Nano Lett. Vol. 20, p. 8157 (2020) [2] N. Hedrich, K. Wagner, O. V. Pylypovskyi et al, arXiv:2009.08086 [3] L. Rondin, J.-P. Tetienne, T. Hingant et al, Rep. Prog. Phys. Vol. 77, p. 056503 (2014); N. Hedrich, D. Rohner, M. Batzer et al, Phys. Rev. Applied, Vol. 14, p. 064007 (2020) [4] SLaSi simulation package, http://slasi.knu.ua; O. V. Pylypovskyi, D. D. Sheka, Book of Abstracts, EUROPT Workshop, p. 11 (2013)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/53f177df2920dadc9b01b189e65f13fb.jpg)
Fig. 1. The deflection of the DW from the straight path and distortion at the mesa surface shown by the stray magnetic field image taken using Nitrogen Vacancy microscopy. Inset shows the DW trajectory in spin-lattice simulations.

![](https://assets.underline.io/uploads/markdown_image/1/image/468d98b21c2bc9cd432573e88f7fb894.jpg)
Fig. 2. Concept of DW-based AFM memory with bits defined by the direction of the Neel order parameter at the mesa top surface (red or blue color, respectively).

 Domain walls in antiferromagnetic samples with non-trivial surface topography

Voltage-controlled magnetism, where magnetic properties are controlled via an applied electric field instead of current, could represent a significant increase in energy savings in future magnetically actuated devices. Practically, however, this approach faces several important obstacles, such as thickness limitations in electrically charged metallic films, mechanical failure in strain-mediated piezoelectric/magnetostrictive devices, and a lack of room-temperature multiferroics. Voltage-driven ionic motion (magneto-ionics) may provide a path forward by avoiding many of these drawbacks. Nevertheless, translating magneto-ionics into real world devices requires significant improvements in magneto-ionic rates, cyclability, and magnetization. Here, we report on the development of magneto-ionics in single-layer, semiconducting transition metal oxides and nitrides, and the subsequent enhancements in their performance. We first present electrolyte-gated and defect-mediated O transport in single-layer, paramagnetic Co3O4 at room temperature (i.e. without thermal assistance), which allows voltage-controlled magnetic switching (referred to here as ON-OFF ferromagnetism: Fig. 1) via internal reduction/oxidation processes[1]. Negative bias partially reduces Co3O4 to Co, resulting in films with Co- and O-rich areas (ferromagnetism: ON). Positive bias re-oxidizes Co back to Co3O4 (paramagnetism: OFF). We show that the bias-induced motion of O is caused by mixed vacancy clusters, with O motion promoted at grain boundaries and assisted by the development of O-rich diffusion channels. The generated ferromagnetism is shown to be stable, and easily erased by sufficient positive bias. This voltage-induced process is demonstrated to be compositionally, structurally, and magnetically reversible and self-contained. We then show that room-temperature magneto-ionic effects in electrolyte-gated paramagnetic Co3O4 films can be significantly increased, both in terms of generated magnetization (6 times larger) and speed (35 times faster), if the electric field is applied using an electrochemical capacitor configuration (utilizing an underlying conducting buffer layer: Fig. 2) instead of electric-double-layer transistor-like configuration (placing the electric contacts at the side of the semiconductor)[2]. In addition to gains in speed, magnetization measurements show a marked increase in the squareness ratio and a decrease in the switching field distribution of the hysteresis loops in Co3O4 biased in the capacitor configuration, the result of the formation of more uniform ferromagnetic regions. These results are attributed to the uniform electric field applied throughout the film, as confirmed by COMSOL simulations. As the measured films are quite thick, further miniaturization promises even greater magneto-ionic rates. We then demonstrate room-temperature voltage-driven nitrogen magneto-ionics (i.e., N transport) by electrolyte-gating of a CoN film[3]. Nitrogen magneto-ionics in CoN is compared to oxygen magneto-ionics in Co3O4, in films using an electrochemical capacitor configuration. Both materials are shown to be nanocrystalline (face-centered cubic structure), and show reversible voltage-driven ON-OFF ferromagnetism (Fig. 1). Nitrogen transport is found to occur uniformly throughout the film, creating a plane-wave-like migration front, without assistance of diffusion channels. Nitrogen magneto-ionics also requires lower threshold voltages and exhibits enhanced rates and cyclability, due to the combination of a lower critical electric field required to overcome the energy barrier for ion diffusion and the lower electronegativity of nitrogen with respect to oxygen, consistent with ab initio calculations contrasting N vs. O motion in cobalt stacks. These results place nitrogen magneto-ionics as a robust alternative for efficient voltage-driven effects and, along with oxygen magneto-ionics, may enable the use of magneto-ionics in devices that require endurance and moderate speeds of operation, such as brain-inspired/stochastic computing or magnetic micro-electro-mechanical systems.

**References:**

[1] A. Quintana, E. Menéndez, M. O. Liedke et al., ACS Nano, Vol. 12, p. 10291 (2018) [2] J. de Rojas, A. Quintana, A. Lopeandía et al., Advanced Functional Materials, Vol. 30, p. 2003704 (2020) [3] J. de Rojas, A. Quintana, A. Lopeandía et al., Nature Communications, Vol. 11, p. 5871 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/2bda3c2e7c2cf2043f08b607447b7fbe.jpg)
Fig. 1. Hysteresis loops (M vs. H) of as-prepared, negatively-biased, and positively-biased CoN films at magneto-ionic activation voltages.

![](https://assets.underline.io/uploads/markdown_image/1/image/12893d420d32ae333459d12c5c0e4b71.jpg)
Fig. 2. A schematic of the electrochemical capacitor configuration used to bias cobalt-oxide (Co3O4) and cobalt-nitride (CoN) films.

 Oxygen vs. Nitogen Magneto-ionics

Interfacial electrochemical effects on magnetism, often also named magneto-ionic effects, are an emerging room-temperature and low-voltage approach in the research area of voltage control of magnetism [1]. In magneto-ionic systems, the magnetic layer is gated via a solid or liquid electrolyte and the applied voltage triggers ion migration and interfacial redox reactions, which impact the magnetic properties. In contrast to multiferroic systems and capacitive electronic charging, magneto-ionic concepts make significant magnetic property changes possible at room temperature and without the need for strain mediation [2], [3]. Since the mechanism is based on electrochemical charge transfer at the electrode/electrolyte interface, the morphology and the composition may be key to the magneto-ionic efficiency. We report magneto-ionic manipulation of ultrathin films in extended and stripe geometry and 3D nanoplatelet structures. In situ magnetic transport measurements are used in this study to determine and analyze the magneto-ionic effect. For FeOOH nanoplatelets, the application of a low voltage via liquid electrolyte gating yields an ON switching of magnetization (deduced from changes of the anomalous Hall resistance, see Figure 1a) [4]. The transformation proceeds via voltage-induced dissolution/redeposition, with the initially paramagnetic FeOOH structure as iron ion reservoir. The time-dependency of the reduction reaction enables the non-volatile setting of magnetic layers with different total magnetic moments. A large reversible magneto-ionic change of magnetization of up to 15% is achieved in the resulting iron films, which is explained by the enhanced roughness of the iron films obtained from the nanoplatelet structure. For thin Fe3O4/Fe films in stripe geometry, we achieved a tunable magnetoresistance by electrolytic gating (Figure 1b) [5]. Here, the tuning mechanism relies on voltage-triggered redox reactions, which locally affect the Fe3O4 regions. In the low-magnetic-field region (&lt;1 T), a crossover from positive to negative magnetoresistance is achieved by a voltage change of only 1.72 V. We will further present first results on the impact of the composition in iron triad magneto-ionic systems on magnetic properties by going beyond iron structures. The proposed approach is promising for the development of energy-efficient magnetic switches, sensors, and magnetic actuation, and may offer new avenues in magnetoelectronic devices.

**References:**

[1] K. Leistner, Current Opinion in Electrochemistry Vol. 25, p. 100636 (2021) [2] C. Navarro-Senent et al., APL Materials, Vol. 7, p. 030701 (2019) [3] K. Duschek et al., J. Mater. Chem. C, Vol. 6, p. 8411 (2018) [4] M. Nichterwitz et al., J. Phys. D: Appl. Phys., Vol. 53, p. 084001 (2020) [5] M. Nichterwitz et al., ACS Appl. Electron. Mater., Vol. 2, p. 2543 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/e678a85b2d151bfa98d2f7b3f748549d.jpg)
Fig. 1 (a) electric “ON” switching of magnetism via electrolytic gating of FeOOH nanoplatelets. Magnetization curves as measured by anomalous Hall effect (AHE) after reduction at −1.27 V for different reduction times. The inset shows the cross-sectional REM image of a FeOOH pristine sample. (Adapted from [4]). (b) Voltage-control of the magnitude and the sign of magnetoresistance (MR) of FeOx/Fe nanocomposite thin films by electrolytic gating in LiOH. The inset shows a cross-sectional HR-TEM image of the pristine iron oxide-iron nanocomposite film. (Adapted from [5]).

 Magneto-ionic effect in iron triad nanostructures with different shapes and composition

Heterostructured artificial multiferroics have opened up the possibility for novel applications like multi-state memory or magnetic field sensors, as well as enhance performance of energy harvesters or tunable antennae or phase shifters. Magnetic thin films have been grown under strain with the goal of utilizing the large strain generated with a stress-induced interferroelectric phase transition in single crystal Pb(In1/2Nb1/2)O3-Pb(Mg1/3Nb2/3)O3-PbTiO3 (PIN-PMN-PT) [1] to optimized the magnetoelectric (ME) coupling. It was previously observed that for magnetostrictive phases laminated under zero stress, this phase transitional stress did not result in any ME coupling [2]. In this work, FeCo/Ag multilayered films were grown on (011) PIN-PMN-PT single crystals using sputter deposition. The FeCo/Ag multilayers were deposited onto two substrates: One with zero stress, while another was grown simultaneously with the substrate under an in-situ strain of ~1400 με along the [001] direction using a home-built stress fixture. The magnetic easy axes varied significant between the two films after the strain had been released due to the difference in the stresses in the film. The sample grown under zero strain showed a 90o rotation of the magnetic easy axis under the collective effect of tensile and compressive stresses in-plane imposed by the piezocrystal. The change in magnetization with applied voltage was large at zero stress but decreases with increased external stress applied to the sample, which is expected resulting from a stress-induced change in magnetic anisotropy that limits the effects of magnetoelastic-imposed stresses. In contrast, the magnetization loops for the sample grown in the stress fixture was unchanged with application of stress during the measurements, and zero magnetoelectric effect was observed. The possibility of high stresses beyond the plastic limit of FeCo due to both applied pre-stress and the intrinsic stress from sputter deposition are investigated, and the results will be compared.

**References:**

[1] P. Finkel, M. Staruch A. Amin, M. Ahart, and S.E. Lofland, Scientific Reports 5, 13770 (2015). [2] M. Staruch, J.F. Li, Y. Wang, D. Viehland, and P. Finkel, Appl. Phys. Lett. 105, 152902 (2014).

**Images:**

 The Impact of Stress on the Magnetoelectric Coupling Between a Multilayered Ferromagnet and a Ferroelectric Single Crystal

Melilite-type multiferroic oxides such as Ba2MGe2O7 (M = Cu, Mn, Co) are the potential candidates for studying exotic quantum phenomena including low-energy magnetic, electronic and structural properties along with the magnetoelectric effect. Spontaneous electric polarization in Ba2MnGe2O7 arises due to the spin-dependent d-p hybridization mechanism between the transition metal 3d and ligand p orbitals like its sister compounds Ba2CoGe2O7 and Ba2CuGe2O7 [1-3]. While all the three compounds exhibit similar non-centrosymmetric tetragonal nuclear structure with space group P-421m (n.113) below the corresponding Néel temperatures (TN), they differ from each other mainly by their local spin microstructure [1, 4-6]. But there is no single report on any structural phase transition if exists in these materials from high-T to below TN. This is crucial to investigate in detail the structural evolution with temperature as the spin-dependent d-p hybridization mechanism involving the coupling between transition metal ions and ligand oxygen atoms strongly depends on the corresponding bond-length inside the MO4 terahedron. Here we report a systematic structural study of the magnetoelectric Ba2MnGe2O7 under varying temperature from RT to 673 K and cooling from 673 K to 110 K using single crystal synchrotron radiation diffraction at BM01, ESRF. Within this entire temperature range the structure was described in the same crystallographic space group P-421m with slight change in lattice parameters. From the reconstructed 2D reciprocal map obtained at the all temperatures we have observed no appearance of extra reflection or any extra symmetry extinction compared to RT phase (sg:P-421m), therefore no phase transition has been detected from 673 K down to 110 K. Interestingly, the forbidden reflections, which arise from multiple diffraction so called “Renninger effect” [7], observed at all temperatures. However, the structural parameters e.g. bond-lengths in the MnO4 tetrahedron, anisotropic displacement parameters (ADP) and lattice constant changes with temperature continuously. We have refined the structures in the space group P-421m using JANA2006 [8] and the results are presented in the Fig. 1. Lattice parameters were refined before the data reduction using CrysAlisPro [9] which give nice agreements with the reported values e.g. a = b = 8.4847(3) Å and c = 5.5162(4) Å at RT. ADP ellipsoids of oxygen atoms at 673 K are enlarged due to high temperature effects while after cooling back to RT resemble well the starting value before heating. While cooling at 110 K, ADP ellipsoids of O3 atoms are flattened in one directions. Local arrangements of MnO4 tetrahedron and the electron density distributions are slightly different for those different temperatures. This feature could have a direct consequences to the observed dielectric relaxation (dipole relaxation) in Ba2MnGe2O7 around 150 – 210 K [10], which was suggested to be results of changeable valence state of Mn transition metal ions though be observed in ceramic material. Changeable valence state of Mn atoms in Ba2MnGe2O7 is more likely not the case, rather high-spin (S = 5/2) or low-spin (S =1/2) magnetic ground state is possible in the d-p hybridization process [6]. Figure 2 shows the reconstructed (0KL) planes obtained at RT (starting phase), 673 K and 110 K. It is immediately noticeable that all the allowed structural Bragg reflections did not change with temperature except the intensity. In this space group forbidden reflections are found at (h00) and (0k0) = 2n+1 which are marked as yellow circle. The evolution of the intensity of the main Bragg peak shown in fig. 2(d) is completely reversible while cooling from 673 K, whereas the change in intensity of the forbidden reflections are quite dramatic only during heating. In summary, our first systematic temperature dependent structural study on Ba2MnGe2O7 single crystal using synchrotron radiation diffraction indicates that no structural phase transition take place in the large temperature range from 673 to 110 K. The observed forbidden peaks of weak intensity are of purely parasitic nature (Renninger scattering). Their intensity ratio to the main Bragg peaks in the range of RT to 110 K are well consistent with our previous neutron diffraction study at 10 K and RT only. Detailed investigation of the structural parameters, especially the flattened electron density of O3 atoms in the MnO4 tetrahedral at 110 K, could relate the reported dielectric properties at low temperature region [10]. This study may sheds lights on the structural dependent d-p hybridization mechanism when a finite electric polarization exist under the external magnetic field [1] far above the antiferromagnetic ordering temperature (TN ~ 4 K). In our opinion this is the advanced and novel study in these Melilite multiferroic oxides where the knowledge of such structural information are crucial in the field of magnetoelectric coupling based device applications and important to have beforehand for studying magnetic structure, strongly correlated electronic properties and the temperature dependent crystal-electric-field (CEF) excitations.

**References:**

[1] H. Murakawa et al., Phys. Rev. B 85, 174106 (2012). [2] S. Miyahara et al., Journal of the Physical Society of Japan 80, 073708 (2011). [3] H. Murakawa et al., Phys. Rev. Lett. 105, 137202 (2010). [4] A. Zheludev et al., Phys. Rev. B 54, 15163 (1996). [5] A. Zheludev et al., Phys. Rev. B 68, 024428 (2003). [6] T. Masuda et al., Phys. Rev. B 81, 100402(R) (2010). [7] A. Sazonov et al., Inorg. Chem., 57, 5089−5095 (2018). [8] V. Petricek et al., Z. Kristallogr. 229 (5), 345-352 (2014). [9] CrysAlisPRO v.46, (2018), Oxford Diffraction /Agilent Technologies, England. [10] J. Su et al., (ISAF/ECAPD/PFM), 2012, vol. 1–3, pp. 9–13, doi: http://dx.doi.org/10.1109/ISAF.2012.6297818.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/8c80799df7cf5583e2f5a3be8c8d1ca8.jpg)
Figure 1: (a) Chemical unit cell of Ba2MnGe2O7 structure at RT. (b-d) Refined ADPs of all atoms in the unit cell at RT, 673 and 110 K where “R” denotes the refinement R-factor.

![](https://assets.underline.io/uploads/markdown_image/1/image/71503811fdc31e6e8aade34c26cdb309.png)
Figure 2: (a-c) reconstructed (0KL) reciprocal maps. (d) Intensity vs. temperature plot for main Bragg reflection (060) and forbidden reflection (050).

 In-situ single crystal synchrotron X-ray diffraction study on the structure of multiferroic antiferromagnet Ba2MnGe2O7 from low- to high-temperature

Multiferroics (MFs) are materials that can combine at least two primary ferroic properties: ferromagnetism, ferroelectricity and ferroelasticity.[1] In the case of magnetoelectric (ME) MFs, coupling between ferroelectricity and ferromagnetism occurs. Throughout the history of MFs, the static ME coupling has peaked the interest of the MF community. However, there is great significance in what happens away from the static regime in MF systems; hence the popular movement toward the exploration of the dynamical ME effect in recent years.[2] Both cases share the same quantum-level microscopic mechanisms, but in the latter case the magnetization and polarization order parameters are not static, but oscillatory. This oscillating behaviour of polarization and magnetization manifests in the hybrid elementary excitations known as electromagnons, which very often lie in the terahertz (THz) or far infrared (IR) region of the spectrum. As the very word indicates, the electromagnons are electro-active magnons,[3] namely collective spin and lattice excitations that couple the dielectric and magnetic properties. Therefore, both the electric and magnetic component of the electromagnetic radiation can be brought into play to excite and detect such dynamical behaviour. The polar antiferromagnet Ni3TeO6 transcends the ME performance of most single-phase MFs, exhibiting non-hysteretic colossal ME coupling.[4] A collinear antiferromagnetic (AFM) order appears below TN = 53 K, inducing a tremendous increase in the existing - but negligible - polarization of the R3 polar structure (up to 3,280 μC m-2 at 2 K). The highest ME coupling value occurs at the spin-flop transition at 8 T. The presence of dynamical ME coupling in Ni3TeO6 was reported in 2017 by Skiadopoulou et al..[5] Two spin excitations were observed simultaneously in Raman and time-domain THz spectra below the Néel temperature TN=53 K. These magnons showed high tunability in external magnetic field. Due to symmetry considerations, these excitations were assigned to electromagnons. Since Ni3TeO6 presents a collinear AFM spin structure, the symmetric exchange striction is most probably responsible for the emergent dynamical ME effect. The quest for compounds with enhanced ME coupling led to the investigation of a series of compounds of the form A3-xBxTeO6 (A, B = Ni, Mn, Co, x=1-2), inspired by the highly praised ME behaviour of Ni3TeO6. In Ni2MnTeO6, although the spin order and magnon spectra closely resemble Ni3TeO6,[6] partial substitution of Ni by Mn shows increased TN by 20 K, while preserving the non-centrosymmetric structure R3.[6],[7] In addition, the spin-flop transition takes place at an external magnetic field of 5 T, which is 3 T lower than in Ni3TeO6. The increase in Neel temperature and decrease of the critical magnetic field which may trigger a colossal ME effect are in favour of possible ME applications. More recently, Ni2CoTeO6 and NiCo2TeO6 compounds were synthesised for the first time, in the form of single crystals and ceramics.[8] The ME properties are preserved by Co-substitution. The non-centrosymmetric R3 space group is maintained at least up to RT for both Ni2CoTeO6 and NiCo2TeO6. The AFM ordering appears at TN = 54 and 49 K for Ni2CoTeO6 and NiCo2TeO6, respectively (Fig. 1). As anticipated, both compounds evidence an interplay of magnetic and dielectric properties, indicated by the dielectric anomaly seen at TN (Fig. 1). In contrast to the magnetic ordering in the previously studied Ni3TeO6 and Ni2MnTeO6, which are collinear along the c-axis, both Co-based compounds present a helical non-collinear structure with the spins in the ab-plane. The magnetic structures of both compounds are quite similar, with a small difference between the magnetic propagation vectors: k1=(0, 0, 1.299(4)) and k2=(0, 0, 1.2109(1)), for Ni2CoTeO6 and NiCo2TeO6, respectively. Hysteretic spin-flop transitions were observed near 8 T (Ni2CoTeO6) and 4 T (NiCo2TeO6), unlike Ni3TeO6 and Ni2MnTeO6, which did not show any hysteretic behavior. Below TN both compounds demonstrate numerous spin-excitations in the THz range, which are considerably influenced by external magnetic field, with clear modifications at the spin-flop transition of ∼4 T for the case of NiCo2TeO6 (Fig. 2). Six magnons strongly dependent on magnetic field are present in the THz spectra of the Co-richer compound NiCo2TeO6. Both compounds present at least one magnetic excitation simultaneously seen by Raman spectroscopy, possibly revealing the magnetoelectric character of the magnon.

**References:**

[1] H. Schmid, Ferroelectrics Vol. 162, p.317 (1994). [2] Y. Tokura, S. Shinichiro, and N. Naoto, Reports Prog. Phys., Vol. 77, p.76501 (2014). [3] M. Bibes, J.E. Villegas, and A. Barthélémy, Adv. Phys., Vol. 60, p.5 (2011). [4] Y.S. Oh, S. Artyukhin, J.J. Yang, et al., Nat Commun, Vol. 5, p.3201 (2014). [5] S. Skiadopoulou, F. Borodavka, C. Kadlec, et al., Phys. Rev. B, Vol. 95, p.184435 (2017). [6] M. Retuerto, S. Skiadopoulou, F. Borodavka, et al., Phys. Rev. B, Vol. 97, p.144418 (2018) [7] R. Mathieu, S.A. Ivanov, P. Nordblad, et al., Eur. Phys. J. B, Vol. 86, p.1 (2013). [8] S. Skiadopoulou, M. Retuerto, F. Borodavka, et al. Phys. Rev. B, Vol. 101, p.14429 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/8dc50332dce6488ac503a54f3b083124.jpg)
Temperature dependences of magnetization (at 0.1 T) and permittivity (at 0.1 MHz) for Ni2CoTeO6 and NiCo2TeO6 ceramics, presenting AFM phase transition at 54 and 49 K, respectively. The dielectric anomalies also appear at the same temperatures for each compound.

![](https://assets.underline.io/uploads/markdown_image/1/image/22df1213d703c61618b95eaffb4cd2fa.jpg)
Magnetic field dependence of spin-wave frequencies in the THz range for NiCo2TeO6, at 5 K. The spin-flop transition is clearly seen at approximately 3 T (dotted line), by the steps on the magnon branches, as well as both the appearance of new modes and extinction of ones present in the low-field phase.

 Magnetoelectric Excitations in the Polar Antiferromagnets Ni-based Tellurates A3-xBxTeO6 (A, B = Ni, Mn, Co, x=1-2)

The antiferromagnetic Ba2CoGe2O7 has aroused great interest in current condensed matter research over the last decade, starting in 2008 when the appearance of ferroelectricity below the magnetic ordering temperature and a strong in-plane anisotropy were first reported [1]. Since the observed unique behaviour of the electric polarization with changing magnetic field in Ba2CoGe2O7 could not be explained by existing models, they accounted these effects to the presence of Dzyaloshinskii-Moriya interaction (DMI) [2,3], which is allowed by its non-centrosymmetric space group P-421m. Subsequently, to better explain this unconventional phenomena, a novel spin-dependent p-d hybridization mechanism of multiferroicity [4] and a spontaneous toroidic effect mechanism [5] were proposed. Also spin-nematic interactions were suggested as origin for the experimentally observed peculiar behaviour of the induced polarization [6]. This large variety of new models instigated further detailed studies of Ba2CoGe2O7, including a detailed determination of the crystal structure [7] and a theoretical symmetry analysis, identifying most of the observed peculiar effects as symmetry-forced results of the weak ferromagnetic (WF) canting, resulting from DMI [8]. This further endorses the DMI as a fundamental basis for the emergence and understanding of the unconventional multiferroic behavior observed in Ba2CoGe2O7. Therefore, not only the magnitude of the DMI exchange constant, but also its sign is of particular interest. In general, polarized neutron diffraction (PND) was proposed as one of the most suitable methods to determine this absolute DMI-sign in WF materials [9]. PND provides a direct access to the scattering contribution from nuclear-magnetic interference and thus reveals the phase difference between the nuclear and magnetic structure. This permits to determine the absolute direction of the individual magnetic moments with respect to the atomic arrangement, distinguishing between two equivalent AFM arrangements. In our study we performed PND measurements on a high quality Ba2CoGe2O7 single crystal at the polarized diffractometer VIP at the Orphée reactor of LLB (Saclay, France) [10]. The crystal was placed in a high magnetic field of 6 T along the [100] direction to obtain a single domain state with the WF moments aligned along and the AFM structure perpendicular to the applied field direction. The asymmetry values A=(I+-I-)/( I++I-) for 545 Bragg reflections were measured. Here, I± is the measured intensity for the two antiparallel spin orientations of the incoming neutron beam. Using these values and the crystal structure reported previously [7], we could refine the precise orientation of the AFM moments in Ba2CoGe2O7 at 2 K (Fig. 1). Overall, we observed a good fit agreement between the calculated and experimentally measured asymmetry values (Fig. 2). The resulting magnetic moment value of around 2.6 μB/Co2+ is in good agreement with previous non-polarized neutron and macroscopic studies [11]. Performing a detailed symmetry analysis of the magnetic structure, including the symmetry averaging of the DMI vector, we deduced its restriction along the z-axis. Depending on the absolute sign of the Dz component, two symmetry-equivalent AFM spin configurations could be realized. By comparison with the experimentally observed magnetic moment directions in regard to the quantization field (Fig. 1), we can finally and unambiguously determine the negative sign of Dz in Ba2CoGe2O7. To further emphasize the power of the presented PND method, we additionally relate the Dz-sign to the expected asymmetry-sign of the single exemplary (210) reflection. By evaluating the nuclear and magnetic scattering factors, we obtain an opposite signed asymmetry value A(210) and mb (the AFM moment in b-direction for the central Co atom in Fig. 1). Moreover, utilizing the general equation for the DMI energy, the sign of Dz must be opposite to mb to be energetically favored, leading finally to same signed A(210) and Dz values. Thus, the experimentally determined negative asymmetry value for just one reflection allows one to conclude about the negative sign of Dz in the whole compound. In fact, all the asymmetry points shown in Fig. 2 within the two white areas support the negative sign of Dz, whereas asymmetry points in the gray areas would support an inverted sign. All experimental asymmetries lie in the white areas proving that PND allows to determine such a fundamental information as the sign of the DMI from the measurement of a single reflection. This is especially powerful for difficult samples or/and technically challenging experiments (e.g. high pressure) where the collection of large datasets is impossible. Within this study, we could for the first time experimentally determine the absolute sign of the DMI in the peculiar non-centrosymmetric multiferroic Ba2CoGe2O7. The precise spin arrangement and its evolution with applied in-plane magnetic field up to 6 T could be established. On one side, our results provide new input for theoretical modeling on this intriguing material. On the other side, they demonstrate the capability of PND to straightforwardly determine the DMI-sign in the large class of WF materials with zero propagation vector.

**References:**

[1] H. T. Yi, Y. J. Choi, S. Lee et al., Appl. Phys. Lett. 92(21), 212904 (2008), [2] I. E. Dzyaloshinskii, Sov. Phys. – JETP 5, 1259 (1957), [3] T. Moriya, Phys. Rev. 120, 91 (1960), [4] H. Murakawa, Y. Onose, S. Miyahara et al., Phys. Rev. Lett. 105(13), 137202 (2010), [5] P. Toledano, D. D. Khalyavin, L. C. Chapon, Phys. Rev. B 84, 094421 (2011), [6] M. Soda, M. Matsumoto, M. Månsson et al., Phys. Rev. Lett. 112(12), 127205 (2014), [7] V. Hutanu, A. Sazonov, H. Murakawa et al., Phys. Rev. B 84, 212101 (2011), [8] J. M. Perez-Mato, J. L. Ribeiro, Acta Crystallogr., Sect. A: Found. Crystallogr. 67(3), 264–268 (2011), [9] V. E. Dmitrienko, E. N. Ovchinnikova, S. P. Collins et al., Nat. Phys. 10, 202 (2014), [10] A. Gukasov, S. Rodrigues, J.-L. Meuriot et al., Physics Procedia 42, 150 (2013), [11] V. Hutanu, A. Sazonov, M. Meven et al., Phys. Rev. B 86, 104401 (2012)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/67f2b487a31aa0bb4475f5fcbd63238f.jpg)
Fig. 1: Refined magnetic moment arrangement in Ba2CoGe2O7 in the WF phase at 2 K with applied magnetic field of 6 T along the a-axis as results from PND data.

![](https://assets.underline.io/uploads/markdown_image/1/image/b31ab3fd0f3326595e81e86161e5a354.jpg)
Fig. 2: Comparison between the calculated and observed asymmetry values for the refinement of the magnetic structure shown in Fig. 1.

 New insight about the magnetic order in peculiar multiferroic Ba2CoGe2O7 by revealing the sign of the Dzyaloshinskii-Moriya Interaction by Polarized Neutron Diffraction.

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