Matsukura, F., Tokura, Y. & Ohno, H. Management of magnetism by electrical fields. Nat. Nanotechnol. 10, 209–220 (2015).
Google Scholar
Kurumaji, T. et al. Magnetoelectric responses induced by area rearrangement and spin structural change in triangular-lattice helimagnets NiI2 and CoI2. Phys. Rev. B 87, 014429 (2013).
Google Scholar
Tokura, Y., Seki, S. & Nagaosa, N. Multiferroics of spin origin. Rep. Prog. Phys. 77, 076501 (2014).
Google Scholar
Pimenov, A. et al. Potential proof for electromagnons in multiferroic manganites. Nat. Phys. 2, 97–100 (2006).
Google Scholar
Rovillain, P. et al. Magnetoelectric excitations in multiferroic TbMnO3 by Raman scattering. Phys. Rev. B 81, 054428 (2010).
Google Scholar
Kibayashi, S., Takahashi, Y., Seki, S. & Tokura, Y. Magnetochiral dichroism resonant with electromagnons in a helimagnet. Nat. Commun. 5, 4583 (2014).
Google Scholar
Khomskii, D. Classifying multiferroics: mechanisms and results. Physics 2, 20 (2009).
Spaldin, N. A. & Ramesh, R. Advances in magnetoelectric multiferroics. Nat. Mater. 18, 203–212 (2019).
Google Scholar
Huang, B. et al. Electrical management of 2D magnetism in bilayer CrI3. Nat. Nanotechnol. 13, 544–548 (2018).
Google Scholar
Jiang, S., Li, L., Wang, Z., Mak, Okay. F. & Shan, J. Controlling magnetism in 2D CrI3 by electrostatic doping. Nat. Nanotechnol. 13, 549–553 (2018).
Google Scholar
Gong, C. et al. Discovery of intrinsic ferromagnetism in two-dimensional van der Waals crystals. Nature 546, 265–269 (2017).
Google Scholar
Huang, B. et al. Layer-dependent ferromagnetism in a van der Waals crystal all the way down to the monolayer restrict. Nature 546, 270–273 (2017).
Google Scholar
Burch, Okay. S., Mandrus, D. & Park, J. G. Magnetism in two-dimensional van der Waals supplies. Nature 563, 47–52 (2018).
Google Scholar
Mak, Okay. F., Shan, J. & Ralph, D. C. Probing and controlling magnetic states in 2D layered magnetic supplies. Nat. Rev. Phys. 1, 646–661 (2019).
Astrov, D. N. The magnetoelectric impact in antiferromagnetics. Sov. Phys. – JETP 11, 708 (1960).
Rado, G. T. & Folen, V. J. Statement of the magnetically induced magnetoelectric impact and proof for antiferromagnetic domains. Phys. Rev. Lett. 7, 310–311 (1961).
Google Scholar
Newnham, R. E., Kramer, J. J., Schulze, W. A. & Cross, L. E. Magnetoferroelectricity in Cr2BeO4. J. Appl. Phys. 49, 6088–6091 (1978).
Google Scholar
Kimura, T. et al. Magnetic management of ferroelectric polarization. Nature 426, 55–58 (2003).
Google Scholar
McGuire, M. A. Crystal and magnetic buildings in layered, transition steel dihalides and trihalides. Crystals 7, 121 (2017).
Lai, Y. et al. Two-dimensional ferromagnetism and pushed ferroelectricity in van der Waals CuCrP2S6. Nanoscale 11, 5163–5170 (2019).
Google Scholar
Botana, A. S. & Norman, M. R. Digital construction and magnetism of transition steel dihalides: bulk to monolayer. Phys. Rev. Mater. 3, 44001 (2019).
Google Scholar
Amoroso, D., Barone, P. & Picozzi, S. Spontaneous skyrmionic lattice from anisotropic symmetric change in a Ni-halide monolayer. Nat. Commun. 11, 5784 (2020).
Google Scholar
Pollini, I., Thomas, J. & Lenselink, A. Optical properties of layered transition-metal iodides. Phys. Rev. B 30, 2140–2148 (1984).
Google Scholar
Ju, H. et al. Potential persistence of multiferroic order all the way down to bilayer restrict of van der Waals materials NiI2. Nano Lett. 21, 5126–5132 (2021).
Google Scholar
Kurumaji, T. Spiral spin buildings and skyrmions in multiferroics. Phys. Sci. Rev. https://doi.org/10.1515/psr-2019-0016 (2020).
Amoroso, D., Barone, P. & Picozzi, S. Interaction between single-ion and two-ion anisotropies in annoyed 2D semiconductors and tuning of magnetic buildings topology. Nanomaterials 11, 1873 (2021).
Google Scholar
Friedt, J. M., Sanchez, J. P. & Shenoy, G. Okay. Digital and magnetic properties of steel diiodides MI2 (M = V, Cr, Mn, Fe, Co, Ni, and Cd) from 129I Mössbauer spectroscopy. J. Chem. Phys. 65, 5093–5102 (1976).
Google Scholar
Kuindersma, S., Sanchez, J. & Haas, C. Magnetic and structural investigations on NiI2 and CoI2. Phys. B+C 111, 231–248 (1981).
Google Scholar
Liu, H. et al. Vapor deposition of magnetic van der Waals NiI2 crystals. ACS Nano 14, 10544–10551 (2020).
Google Scholar
Kumdersma, S. R., Boudewijn, P. R. & Haas, C. Close to infrared d-d transitions of NiI2, CdI2:Ni2+, and CoI2. Phys. Stat. Sol. (b) 108, 187–194 (1981).
Google Scholar
Xiao, J. et al. Intrinsic two-dimensional ferroelectricity with dipole locking. Phys. Rev. Lett. 120, 227601 (2018).
Google Scholar
Cenker, J. et al. Direct commentary of two-dimensional magnons in atomically skinny CrI3. Nat. Phys. 17, 20–25 (2021).
Google Scholar
Jin, W. et al. Raman fingerprint of two terahertz spin wave branches in a two-dimensional honeycomb Ising ferromagnet. Nat. Commun. 9, 5122 (2018).
Google Scholar
Deng, Y. et al. Gate-tunable room-temperature ferromagnetism in two-dimensional Fe3GeTe2. Nature 563, 94–99 (2018).
Google Scholar
Sivadas, N., Okamoto, S., Xu, X., Fennie, C. J. & Xiao, D. Stacking-dependent magnetism in bilayer CrI3. Nano Lett. 18, 7658–7664 (2018).
Google Scholar
Akram, M. et al. Moiré skyrmions and chiral magnetic phases in twisted CrX3 (X = I, Br, and Cl) bilayers. Nano Lett. 21, 6633–6639 (2021).
Google Scholar
Nguyen, T. P. T., Yamauchi, Okay., Oguchi, T., Amoroso, D. & Picozzi, S. Electrical-field tuning of the magnetic properties of bilayer VI3: a first-principles examine. Phys. Rev. B 104, 014414 (2021).
Google Scholar
Xiang, H. J., Kan, E. J., Zhang, Y., Whangbo, M.-H. & Gong, X. G. Basic idea for the ferroelectric polarization induced by spin-spiral order. Phys. Rev. Lett. 107, 157202 (2011).
Google Scholar
Prayitno, T. B. Controlling section transition in monolayer steel diiodides XI2 (X: Fe, Co, and Ni) by service doping. J. Phys. Condens. Matter 33, 335803 (2021).
Google Scholar
Narayan, A., Cano, A., Balatsky, A. V. & Spaldin, N. A. Multiferroic quantum criticality. Nat. Mater. 18, 223–228 (2019).
Google Scholar
Zomer, P., Guimarães, M., Brant, J., Tombros, N. & Van Wees, B. Quick choose up method for prime quality heterostructures of bilayer graphene and hexagonal boron nitride. Appl. Phys. Lett. 105, 013101 (2014).
Google Scholar
Kresse, G. & Furthmüller, J. Environment friendly iterative schemes for ab initio total-energy calculations utilizing a plane-wave foundation set. Phys. Rev. B 54, 11169–11186 (1996).
Google Scholar
Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave methodology. Phys. Rev. B 59, 1758–1775 (1999).
Google Scholar
Blaha, P. et al. WIEN2k: an APW+lo program for calculating the properties of solids. J. Chem. Phys. 152, 074101 (2020).
Google Scholar
Perdew, J. P., Burke, Okay. & Ernzerhof, M. Generalized gradient approximation made easy. Phys. Rev. Lett. 77, 3865–3868 (1996).
Google Scholar
Rohrbach, A., Hafner, J. & Kresse, G. Digital correlation results in transition-metal sulfides. J. Phys. Condens. Matter 15, 979–996 (2003).
Google Scholar
Liechtenstein, A. I., Anisimov, V. I. & Zaanen, J. Density-functional idea and powerful interactions: Orbital ordering in Mott-Hubbard insulators. Phys. Rev. B 52, R5467–R5470 (1995).
Google Scholar
Perdew, J. P. et al. Restoring the density-gradient enlargement for change in solids and surfaces. Phys. Rev. Lett. 100, 136406 (2008).
Google Scholar
Becke, A. D. On the large-gradient conduct of the density useful change power. J. Chem. Phys. 85, 7184–7187 (1986).
Google Scholar