France



Frustrated magnetic structures hold configurations wherein localized magnetic moments or spins interact through competing exchange interactions, rendering macroscopic degeneracy of exotic ground states like spin ice and providing an excellent platform for discovering novel states and properties. One example is the pyrochlore spin ice, in which four nearest-neighbor Ising-like spins on the vertices of the corner-sharing tetrahedra are forced to form the local “2-in-2-out” configuration for each tetrahedron, which forms spin ice in analogy to the water ice[1]. In two dimensions (2D), ice rules can be similarly defined for in-plane Ising like classical spins residing on the kagome lattice, which require “2-in-1-out” or “1-in-2-out” local arrangements of the spins on its triangles[2]. A √3×√3 ground state can be selected by further neighbor exchange couplings or the long-range dipolar interaction. As a result, kagome spin ices show a characteristic multi-stage ordering behavior under changing temperature. Experimentally, kagome spin ices have only been realized in artificial spin ice systems formed by nanorods of ferromagnets organized into honeycomb networks[3-5]. However, the large magnetic energy scales and system sizes make it challenging to explore the rich phase diagram of spin ices in the thermodynamic limit.&lt;br/&gt;Neutron scattering, though measuring the energy and momentum of in-coming and out-going neutrons, offers one of the most powerful tools in the study of magnetic structures and dynamics of magnets. Through neutron scattering and other experimental and theoretical approaches, we discover that the intermetallic compound HoAgGe is a naturally existing kagome spin ice that exhibits a fully ordered ground state[6]. The multi-stage ordering behavior was confirmed by Single-crystal neutron diffraction: below 11.6 K the Ho spins enter a partially ordered state with one-third of them still fluctuating, while below ~7 K, all spins order into the √3×√3 ground state of the kagome ice with crystalized magnetic monopoles. All these observations are in good agreement with Monte Carlo simulations of a classical spin model including both dipolar interactions and up to 4th nearest-neighbor exchange couplings on the noncentrosymmetric kagome lattice of HoAgGe.

**References:**

[1] Bramwell, S. T., and Gingras, M. J. P. &lt;i&gt;Science&lt;/i&gt; 294, 1495–1501 (2001)&lt;br/&gt;[2] Chern, G.-W. et al. &lt;i&gt;Phys. Rev. Lett.&lt;/i&gt; 106, 207202 (2011)&lt;br/&gt;[3] A. S. Wills, R. Ballou and C. Lacroix, &lt;i&gt;Phys. Rev. B&lt;/i&gt; 66, 144407 (2002)&lt;br/&gt;[4]G. Möller, R. Moessner, &lt;i&gt;Phys. Rev. B&lt;/i&gt; 80, 140409 (2009)&lt;br/&gt;[5]G.-W. Chern, P. Mellado and O. Tchernyshyov, &lt;i&gt;Phys. Rev. Lett.&lt;/i&gt; 106, 207202 (2011)&lt;br/&gt;[6] Zhao, K., Deng, H., Chen, H. et al. &lt;i&gt;Science&lt;/i&gt; 367, 1218–1223 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/d4ab6a1eaf76a141378b86c81da328f8.jpg)
The refined magnetic structures of HoAgGe at 10K and 4K



INTERMAG 2021

 Neutron Scattering Revealing Kagome Spin Ice in a Frustrated Intermetallic Compound

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2022 Joint MMM-INTERMAG

This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

Frustrated magnetic structures hold configurations wherein localized magnetic moments or spins interact through competing exchange interactions, rendering macroscopic degeneracy of exotic ground states like spin ice and providing an excellent platform for discovering novel states and properties. One example is the pyrochlore spin ice, in which four nearest-neighbor Ising-like spins on the vertices of the corner-sharing tetrahedra are forced to form the local “2-in-2-out” configuration for each tetrahedron, which forms spin ice in analogy to the water ice[1]. In two dimensions (2D), ice rules can be similarly defined for in-plane Ising like classical spins residing on the kagome lattice, which require “2-in-1-out” or “1-in-2-out” local arrangements of the spins on its triangles[2]. A √3×√3 ground state can be selected by further neighbor exchange couplings or the long-range dipolar interaction. As a result, kagome spin ices show a characteristic multi-stage ordering behavior under changing temperature. Experimentally, kagome spin ices have only been realized in artificial spin ice systems formed by nanorods of ferromagnets organized into honeycomb networks[3-5]. However, the large magnetic energy scales and system sizes make it challenging to explore the rich phase diagram of spin ices in the thermodynamic limit. Neutron scattering, though measuring the energy and momentum of in-coming and out-going neutrons, offers one of the most powerful tools in the study of magnetic structures and dynamics of magnets. Through neutron scattering and other experimental and theoretical approaches, we discover that the intermetallic compound HoAgGe is a naturally existing kagome spin ice that exhibits a fully ordered ground state[6]. The multi-stage ordering behavior was confirmed by Single-crystal neutron diffraction: below 11.6 K the Ho spins enter a partially ordered state with one-third of them still fluctuating, while below ~7 K, all spins order into the √3×√3 ground state of the kagome ice with crystalized magnetic monopoles. All these observations are in good agreement with Monte Carlo simulations of a classical spin model including both dipolar interactions and up to 4th nearest-neighbor exchange couplings on the noncentrosymmetric kagome lattice of HoAgGe.

**References:**

[1] Bramwell, S. T., and Gingras, M. J. P. Science 294, 1495–1501 (2001) [2] Chern, G.-W. et al. Phys. Rev. Lett. 106, 207202 (2011) [3] A. S. Wills, R. Ballou and C. Lacroix, Phys. Rev. B 66, 144407 (2002) [4]G. Möller, R. Moessner, Phys. Rev. B 80, 140409 (2009) [5]G.-W. Chern, P. Mellado and O. Tchernyshyov, Phys. Rev. Lett. 106, 207202 (2011) [6] Zhao, K., Deng, H., Chen, H. et al. Science 367, 1218–1223 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/d4ab6a1eaf76a141378b86c81da328f8.jpg)
The refined magnetic structures of HoAgGe at 10K and 4K

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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

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.

Manganite oxides family RMn2O5 (R – rare-earth element) represents example of a multiferroics with extremely interesting and close relationship between magnetism and ferroelectricity [1-3]. The particularities of the magnetic alignment seems to play the decisive role in this M-E coupling. In order to go deep in the understanding in explicit the microscopic mechanisms responsible for spin-driven ferroelectricity in these compounds the investigations of the magnetic ordering in the Nd0.8Tb0.2Mn2O5 single crystal were performed. The magnetic phase diagram in both parent compounds is rather complicate, and is different for them. TbMn2O5 is characterized by several successive phases - high-temperature incommensurate, at TCP &lt; T &lt; TN (TCP = 35 ÷ 37 K, TN = 45K), commensurate at TLTIC &lt; T &lt; TCP (TLTIC = 20 ÷ 24 K) and low-temperature incommensurate, at T &lt; TLTIC [4]. The ferroelectric ordering in TbMn2O5 can also be represented as successive ferroelectric phases in the same temperature ranges. In TbMn2O5, chiral scattering was detected in all magnetically ordered phases [4]. In contrast to TbMn2O5, chiral scattering was observed in multiferroic NdMn2O5 only below the temperature T ~ 20 K, i.e., below this temperature, the transition from a incommensurate non-chiral magnetic phase to a chiral one occurs [5]. The temperature of this chiral transition corresponds to the temperature of the ferroelectric transition TCE [6], while the value of the ferroelectric polarization is extremely small. The temperature and electric field dependences of magnetic ordering in single crystal Nd0.8Tb0.2Mn2O5 were investigated using diffraction of unpolarized and polarized neutrons. The temperature dependence of the propagation vectors of the observed magnetic phases is shown at Fig. 1. Our results demonstrate that two magnetic phases coexist in a broad temperature range, indicating magnetic phase separation. One of them bears features of TbMn2O5, another – of NdMn2O5. Thus, phase 1 or “Tb-phase” has higher temperature of alignment TN ≈ 37 K, but it is still lower than that of TbMn2O5. The propagation vector k1 = (0.5 0 kz1) is commensurate along a-axis and incommensurate along c-axis at all temperatures of alignment, while for TbMn2O5 propagation vector k = (½-δx, 0, ¼+δz) is non-commensurate in both a and c directions in two incommensurate phases – HTIC and LTIC. It was possible to change the ratio of "right" and "left" spirals in Nd0.8Tb0.2Mn2O5 crystals by an external electric field. The features of phase 2 – “Nd-phase” – are close to those of magnetic order at NdMn2O5. It has transition temperature the same as TN = 30 K in NdMn2O5, the propagation vector k2 = (0.5 0 kz2) has the same component along a* and kz2 value is close to that of NdMn2O5. It is difficult to say whether this “Nd-phase” is chiral in whole temperature range of existence or it is chiral below some definite temperature TCh, which takes place in NdMn2O5, with its TCh = 20 K. Compared to NdMn2O5, the system Nd0.8Tb0.2Mn2O5 exhibits even greater ability to generate ordered magnetic phases of the same type. This leads to the fact that, in the narrow temperature range of 20 K – 30 K two more magnetic incommensurate phases were observed. Such phenomena were observed in the compounds of this family like TbMn2O5 in narrow temperature range [7, 8], in NdMn2O5 – in a broad temperature range [5, 9]. This feature should be connected with the magnetic inhomogeneity of the system. This inhomogeneity could follow from the non-rigidity of the Mn3+ - Mn4+ bonding at RMn2O5 family. From another side, at RMn2O5 series the bond lengths and angles in the Mn3+ and Mn4+ polyhedra are in the critical position for the superexchange interactions or close to it [10]. The small deviation in the geometrical arrangement of Mn3+ - Mn4+ bonding provide different magnetic interaction strength. The coexistence of two rare earth ions with different types of ground state: Kramers-like Nd3+ and non-Kramers one Tb3+, could lead to different types of site anisotropies. The system energy lowers by phase separation state for two main phases with their characteristic resembling those of phases of pure compounds. The broadening of the incommensurate reflections at low temperature (Fig.2) could be connected with the existence of several propagation vectors, distributed around the two main values k1,2. At the temperature region 22 K – 30 K, the competing interactions lead to more phases with similar vectors k3,4. Approximately at the same temperature region competing interactions stabilize the commensurate structure in TbMn2O5. The studied system Nd0.8Tb0.2Mn2O5 at this temperature range corresponds to the least homogeneous state, when the energy minimum achieved by the separation on three and four magnetic phases. This fact can be one more indication that CM phase in RMn2O5 is not really commensurate. Propagation vector component kz in this phase could be not precisely commensurate and it arises as not very stable result of interplay of different interaction. Recent work [8] witnesses in favor of that where kz component of propagation vector in TbMn2O5 changed value in magnetic field from 0.25 to 0.32. As another argument can be the “reverse” transition from CM to LTIC phase. The work was supported by the Russian Foundation for Basic Research grant # 19-52-12047, and DFG grant # SA 3688/1-1.

**References:**

1. N. Hur, S. Park, P. A. Sharma, et al. Nature 429, 392 (2004). 2. Y. Noda, H. Kimura, M. Fukunaga, et al. J. Phys.: Condens. Matter 20, 434206 (2008). 3. G. R. Blake, L. C. Chapon, P. G. Radaelli, et al. Phys. Rev. B 71, 214402 (2005). 4. I.A. Zobkalo, S.V. Gavrilov, A. Sazonov, et al. J. Phys.: Condens. Matter 30, 205804 (2018). 5. I.A. Zobkalo, A.N. Matveeva, A. Sazonov, et al. Phys. Rev. B 101, 064425 (2020). 6. S. Chattopadhyay, V. Baledent, et al., Phys. Rev. B 93, 104406 (2016). 7. I.A. Zobkalo, S.V. Gavrilov, V.A. Sanina, et al. Physics of the Solid State 56, 51 (2014). 8. T. Chatterji, P. J. Brown. J. Appl. Phys. 116, 203904 (2014). 9. I. A. Zobkalo, S. V. Gavrilov, et al., J. Magn. Magn. Mater. 354, 85 (2014). 10. L. M. Volkova, D. V. Marinin.J. Phys.: Condens. Matter 21, 015903 (2009).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/07c5c5ebce767eccbe77e3ed92b7d489.jpg)
Temperature dependence of propagation vectors for four magnetic phases in heating mode

![](https://assets.underline.io/uploads/markdown_image/1/image/07e625659faaba34826e7cd116e02b03.jpg)
Temperature dependence of peak width of satellites (0 1 0)+k1 and (0 1 0)+k2 in heating mode

 Magnetic phases and chirality control in magnetic multiferroics Nd0.8Tb0.2Mn2O5 by the neutron scattering

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.

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

Direct magnetoelectric (ME) coupling in single-phase multiferroic materials is limited to high magnetic fields and/or cryogenic temperatures. More robust ME behavior has been achieved in multi-phase composites that combine magnetostrictive and piezoelectric materials in a matrix 1–3. The ME effect in such composites is due to the induced stresses within the magnetostrictive or piezoelectric phases controlled by the application of external magnetic or electric fields, which transfer through the interface to the piezoelectric or magnetostrictive phases, respectively 4. Therefore, two factors play a crucial role in the effectiveness of the ferroic phases conjugation: resistivity of the ceramic, which directly governs the electrical poling effectiveness of the ferroelectric phase, and the interface of the two materials, which influences the strain transfer 5. Wide choice of materials, volume fraction, and microstructure in multi-phase composites allow addressing these challenges 1,3. There are multiple applications for magnetoelectric (ME) materials in sensors, energy harvesting, magnetoelectric random access memory, antennas, drug delivery, etc 2. The implementation of ME materials in some of these applications demands the use of nano-multiferroic samples. Although, the characterization methods to study the ME coupling in bulk materials are well-developed; however, the measurement of ME coupling at the nanoscale is still challenging 6. In this work, high magnetoelectric coupling coefficient CoFe2O4-BaTiO3 composites were developed using commercial CoFe2O4 and BaTiO3 powders as precursors. The bulk magnetoelectric coefficient in the optimized CoFe2O4-BaTiO3 composite where individual CoFe2O4 grains are fully enclosed by the BaTiO3 matrix was found to be comparable with the numbers reported for the composites based on core-shell structures 7, 8. This presentation will detail the physical (magnetic, electric, magnetoelectrical, and magneto-mechanical) and microstructural properties of the developed composites, offer the analysis of the observed behaviors, and outline the routes for further improvements. The composites were produced by dry ball-milling of precursor powders followed by annealing at 1200 °C. Properties of the composite as a function of synthesis precursor choice and precursor mixture composition were explored. The microstructural characterization (focused ion-beam depth profiling of pellet composites etched in hydrochloric acid to selectively remove CoFe2O4 and piezo-force microscopy of polished pellets) of the synthesized CoFe2O4-BaTiO3 composited clearly revealed a dramatic dependence on the size and phase (cubic vs. tetragonal) of BaTiO3 precursor. This dependence has translated into a dramatic difference between magnetoelectric coupling coefficients observed in the composites synthesized with cubic and tetragonal BaTiO3 precursors. Utilizing 50 nm cubic BaTiO3 precursor powder results in a material, in which relatively large individual CoFe2O4 grains are fully embedded into and well-insulated by a BaTiO3 matrix. This microstructure enhances the strain-mediated coupling between CoFe2O4 and BaTiO3 grain. Furthermore, it leads to higher electrical resistivity, which, in turn, enables effective electrical poling. The highest magnetoelectric coupling coefficient is exhibited in CoFe2O4-BaTiO3: 20-80% composites that utilize a 50 nm cubic BaTiO3 powder as precursor with a value as high as 4.3 mV/Oe.cm. The dependence of magnetoelectric coupling coefficient on the value of the external DC magnetic field for different compositions of CoFe2O4-BaTiO3 composites is shown in Fig. 1 and, as will be shown in this presentation, correlates well with magnetic and magnetostrictive properties and is in agreement with theoretical analysis. In addition to the detailed characterization of bulk properties, the dependence of the local surface potential on the magnitude of external DC magnetic fields was studied using Kelvin Probe Force Microscopy (KPFM). The line profile of the surface potential for the (CoFe2O4-BaTiO3 (50 nm cubic):30-70%) sample for different values of external magnetic field is shown in Fig. 2.

**References:**

 1 J.S. Andrew, J.D. Starr, and M.A.K. Budi, Scripta Materialia 74, 38 (2014). 2 Y. Cheng, B. Peng, Z. Hu, Z. Zhou, and M. Liu, Physics Letters A 382, 3018 (2018). 3 N. Ortega, A. Kumar, J.F. Scott, and R.S. Katiyar, Journal of Physics: Condensed Matter 27, 504002 (2015). 4 J. Ma, J. Hu, Z. Li, and C.-W. Nan, Advanced Materials 23, 1061 (2011). 5 M. Fiebig, ChemInform 36, (2005). 6 G. Caruntu, A. Yourdkhani, M. Vopsaroiu, and G. Srinivasan, Nanoscale 4, 3218 (2012). 7 G.V. Duong and R. Groessinger, Journal of Magnetism and Magnetic Materials 316, e624 (2007). 8 G.V. Duong, R. Sato Turtelli, and R. Groessinger, Journal of Magnetism and Magnetic Materials 322, 1581 (2010).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/533f7d4795f3b2dce4084f139aac20cc.jpg)
 
Fig. 1. ME coefficient vs DC magnetic field for different CoFe2O4-BaTiO3 compositions prepared with 50 nm cubic BaTiO3 precursor

![](https://assets.underline.io/uploads/markdown_image/1/image/3a5b6f51cb43efe25e14ee1da2a1dd8e.jpg)
 
Fig. 2. Contact Potential Difference (CPD) measured for CoFe2O4-BaTiO3 (50 nm cubic):30-70% using KPFM at different external magnetic fields.

 Development and analysis of highly-efficient magnetoelectric cobalt ferrite/barium titanate composites using a scalable synthesis technique

Artificial spin ice (ASI) is a magnetic metamaterial designed to exhibit frustration [1]. It consists of an array of magnetostatically interacting nanomagnets arranged in a geometry that prevents these interactions to be all satisfied simultaneously. They were originally conceived to replicate, in an artificial manner, interesting frustration induced phenomena found in natural frustrated magnets known as spin ices [2]. One of those most remarkable phenomena is the emergence of quasiparticles similar to magnetic monopoles when such materials are excited above the ground state [3]. In ASI, this behavior is experimentally reproduced by subjecting the system to a magnetization cycle [4]. The magnetization reversal proceeds by creation of one-dimensional strings of flipped nanomagnets, referred as Dirac strings, that host the magnetic monopoles at their ends. This reversal mechanism has been already reproduced by Monte Carlo-based simulations, where the nanomagnets are treated as Ising variables and a phenomenological random switching field distribution is employed [5]. In this work, we reproduced the same behavior using a more fundamental approach, that was lacking in literature, based on micromagnetic simulations, applied particularly to a large scale (more than a thousand magnets) kagome lattice arrangement of ASI [6]. We regarded a more realistic description of the shape of each nanomagnet, including its finite size and roughness at the edges, in such a way that no a priori switching field distribution was required but that came out naturally. Furthermore, our simulations predict a critical angle between the applied field and the direction of a sublattice that separates different reversal regimes: the process is mostly 2D for angles above the critical value, and it is 1D (i.e., via Dirac strings and monopoles) otherwise.

**References:**

[1] S. H. Skjærvø, C. H. Marrows and R. L. Stamps, Nature Review Physics, Vol. 2, p. 13–28 (2020) [2] R. F. Wang, C. Nisoli and R. S. Freitas, Nature, Vol. 439, pp. 303–306 (2006) [3] C. Castelnovo, R. Moessner and S. L. Sondhi, Nature, Vol. 451, p. 42–45 (2008) [4] E. Mengotti, L. J. Heyderman and A. F. Rodríguez, Nature Physics, Vol. 7, p. 68–74 (2011) [5] R. V. Hügli G., G. Duff and B. O'Conchuir, Philos. Trans. R. Soc. A Math. Phys. Eng. Sci., Vol. 370, p. 5767–5782 (2012 [6] M. F. Velo, B. M. Cecchi, and K. R. Pirota, Physical Review B, Vol. 102, p. 224420 (2020)

**Images:**

 Micromagnetic simulations of magnetization reversal in kagome artificial spin ice

The vertical stacking of the 2D materials into the vdW heterotructures has attracted much attention during last years [1], mostly due to a new phenomena that can be observed is such heterostructures. Just recently the 2D magnetic crystals have been experimentally reported [2], opening the possibility to study the vdW layered magnets, exhibiting different magnetic phases [3,4]. Proximity between magnetic 2D crystals might serve as sensitive tool to examine details of the magnetic structure. Here, we present a comprehensive ab initio study of the prototypical example of vdW magnetic system NiPS3/FeS3. The individual layers are the members of large family of transition metal phosphorus trichalcogenides MPX3 [5], which are antiferomagnets. The impact the intralayer and interlayer magnetism on the electronic properties of heterobilayer is examined in the framework of the density functional theory. In particular, the bands alignments, band offsets and band gaps are investigating and compared with isolated layers. Our results have demonstrated the moderate influence of intralayer magnetism on the electronic and energetic properties of the system along with negligible impact of interlayer magnetism on these properties. In addition, spatial separation of charges at the band edges are demonstrated, implying the existence of the interlayer excitons in NiPS3/FePS3 structure. The study was accomplished thanks to the funds allotted by the National Science Centre, Poland within the framework of the research project ‘SONATA12’ no. UMO-2016/23/D/ST3/03446. Access to computing facilities of TU Dresden ZIH for the project ”TransPheMat”, PL-Grid Polish Infrastructure for Supporting Computational Science in the European Research Space, and of the Interdisciplinary Center of Modeling (ICM), University of Warsaw are gratefully acknowledged.

**References:**

 [1] D. L. Duong et al, ACS Nano 2017, Vol. 11, p. 11803−11830. [2] B. Huan et al., Nature, Vol. 546, p. 270-273 (2017). [3] D. Zhong et al. Science Advances, Vol. 3, p. 1-6 (2017). [4] M. Birowska et al. http://arxiv.org/abs/2009.05030. [5] R. Brec, Solid State Ionics ,Vol. 22, p. 3-30 (1986).

**Images:**

 The impact of the intralayer and interlayer magnetism on the electronic properties of vdW heterostructure NiPS3/FePS3 – a theoretical approach.

A particular interest to the behavior of magnetic frustrated spin systems is explained that the problem of finding a ground state, i.e., the state with the lowest energy is a very difficult task due to the macroscopic degeneracy and frustrations that are present in most realistic spin glass models. This problem is fundamentally difficult to solve since it often requires the search for potential solutions over huge spaces of possible states. Among conventional methods which are using in statistical physics, one of the most powerful approaches is the Monte Carlo simulation, consisting of stochastic sampling over a state space and an evaluation of estimators for physical quantities. However, the ability of modern machine learning techniques to classify, identify, or interpret massive data sets provides a complementary paradigm to the above approach in statistical physics to analyze the exponentially large number of states. The main research object is the two-dimensional Edwards-Anderson model, with the exchange integral J as a random function and the average value of J is zero in a system. In such the system, one half of the spins' interaction is ferromagnetic, and the other is antiferromagnetic. It is well known that critical phenomena occur in condensed matter under certain conditions, when an abrupt change in its properties occurs. Near the critical points, various phenomena may arise. The critical region can be described by a set of state parameters (order parameters), which allow one to obtain information about the anomalous behavior of thermodynamic averages, internal processes, and the nature of the objects of study. The first research direction related to the fact, that the temperature behavior of the average magnetization modulus equals to zero for the Edwards-Anderson model. Because of this, we calculated an average size of the percolation cluster, which is defined as the relative size of maximum cluster, which include spins in the ground state, to the total number of spins. The average size of the percolation was chosen as an order parameter. This order parameter, in contrast to other thermodynamic characteristics, makes it possible to describe the behavior of the system with a change in temperature. Using this parameter, we calculated main critical exponents of these two models: correlation length, magnetization, specific heat and susceptibility. The second research direction was about the problem of finding a ground state for the Edwards-Anderson model. In present work, for simulation we used a combination of our Hybrid Multispin Method (HMM) and the Restricted Boltzmann Machine (RBM) to predict the ground states for the Edwards–Anderson spin glass model. The problem of spin glass simulation is determined by the high complexity of obtaining configurations with the lowest possible energy level (ground state). At the moment, no universal algorithm exists to directly generate the ground state. To predict the GS, we used the data of the HMM to train our neural network and to predict spin glass state with a lower energy level than in the training data sets. We used small spin systems (4 x 4 and 6 x 6) to verify our results and compare them with those of the exact solution calculated by a brute-force method (BFM). Our research has shown that the ground states of spin glass systems can be predicted using a neural network. However, given the absence of an exact solution to determine the number of degenerations at the ground energy level for big systems, it is impossible to check whether our algorithms reach the global energy minimum. Nonetheless, machine-learning algorithms can make a significant contribution to solving NP-complete problems in the future. This work was supported by the state task of the MSHE of Russia No. 075-00400-19-01.

**References:**

S. Edwards, P. Anderson, Phys. F: Metal Phys., Vol. 5 (5), p. 965 (1975) A. Patashinski, V. Pokrovskii, Pergamon Press (1979) A.G. Makarov et al., JETP Letters., Vol. 110 (10), pp. 702-706 (2019) R. Salakhutdinov, A. Mnih, G. Hinton, Restricted Boltzmann machines for collaborative filtering //Proceedings of the 24th international conference on Machine learning, pp. 791-798 (2007)

**Images:**

Neutron Scattering Revealing Kagome Spin Ice in a Frustrated Intermetallic Compound

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