United States

Current magnetic sensors have been used to detect position, angle, rotation and magnetic fields, based on three key types of technologies: Hall, anisotropic and giant
magnetoresistance effects [1]. Hall sensors are made by patterning Silicon into a cross-bar, where sensitivity can be increased by replacing Si with compound semiconductors such as InAs
and GaAs. However, these sensors suffer from large temperature dependence of their output in a finite magnetic field and have limitations in their working temperature range (between -40
and 120oC) as well as their detectable field range (between 10-2 and 102 T). We have demonstrated a linear response in magnetisation under a small magnetic field (up to +/-50 mT) in an
antidot structure consisting of ferromagnetic Fe nanoparticles dispersed in insulating MgO matrix [2]. In this study, we have adopted this system to replace ferromagnetic Fe dots with Co
and have measured magnetisation dynamics.
We co-deposited Co and MgO at the ratio of 2:1 by electron-beam evaporation on MgO(001) and (011) substrates in ultrahigh vacuum molecular beam epitaxy. The total film thickness
was 30 nm. The films were ex-situ annealed at 400oC for up to 3 hours under vacuum. All the samples show very strong magnetic anisotropy, which is different from the Fe:MgO films
previously reported [2]. The MgO[010] direction is found to be the easy axis, while the MgO[100] is the hard axis. The squareness is estimated to be 0.936 for the as-deposited film,
improving up to 0.939 for the 3-h annealed film. Along the hard axis, the magnetisation curve shows almost linear response within ± 750 Oe, which is broader than that for the Fe:MgO
films (± 500 Oe) [2]. This may indicate the Co nanoparticles dispersed in the MgO matrix are crystallised in fcc. with the epitaxial relationship of Co(001)[010]//MgO(001)[010] [3]. We
will also report the results on the Co:MgO films grown on MgO(011) and discuss the steps towards the sensor applications.&lt;br&gt;

**References:**&lt;br&gt;

[1] M. A. Khan et al., Eng. Res. Exp. 3, 022005 (2021).&lt;br&gt;
[2] M. Rummey et al., IEEE Trans. Magn. 48, 4010 (2012).&lt;br&gt;
[3] M. Hashimoto et al., J. Cryst. Growth 166, 792 (1996).&lt;br&gt;


MMM 2022

Development of a Magnetic Sensor Using Co:MgO Antidots

Current magnetic sensors have been used to detect position, angle, rotation and magnetic fields, based on three key types of technologies: Hall, anisotropic and giant
magnetoresistance effects [1]. Hall sensors are made by patterning Silicon into a cross-bar, where sensitivity can be increased by replacing Si with compound semiconductors such as InAs
and GaAs. However, these sensors suffer from large temperature dependence of their output in a finite magnetic field and have limitations in their working temperature range (between -40
and 120oC) as well as their detectable field range (between 10-2 and 102 T). We have demonstrated a linear response in magnetisation under a small magnetic field (up to +/-50 mT) in an
antidot structure consisting of ferromagnetic Fe nanoparticles dispersed in insulating MgO matrix [2]. In this study, we have adopted this system to replace ferromagnetic Fe dots with Co
and have measured magnetisation dynamics.
We co-deposited Co and MgO at the ratio of 2:1 by electron-beam evaporation on MgO(001) and (011) substrates in ultrahigh vacuum molecular beam epitaxy. The total film thickness
was 30 nm. The films were ex-situ annealed at 400oC for up to 3 hours under vacuum. All the samples show very strong magnetic anisotropy, which is different from the Fe:MgO films
previously reported [2]. The MgO[010] direction is found to be the easy axis, while the MgO[100] is the hard axis. The squareness is estimated to be 0.936 for the as-deposited film,
improving up to 0.939 for the 3-h annealed film. Along the hard axis, the magnetisation curve shows almost linear response within ± 750 Oe, which is broader than that for the Fe:MgO
films (± 500 Oe) [2]. This may indicate the Co nanoparticles dispersed in the MgO matrix are crystallised in fcc. with the epitaxial relationship of Co(001)[010]//MgO(001)[010] [3]. We
will also report the results on the Co:MgO films grown on MgO(011) and discuss the steps towards the sensor applications. 

**References:** 

[1] M. A. Khan et al., Eng. Res. Exp. 3, 022005 (2021). 
[2] M. Rummey et al., IEEE Trans. Magn. 48, 4010 (2012). 
[3] M. Hashimoto et al., J. Cryst. Growth 166, 792 (1996).

technical paper

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All of the polymorphs of pure ammonium iodide NH4I have space groups that are non-polar. However, we identify that when a fraction of the hydrogen is replaced by deuterons or when small percentages of iodide are replaced by bromide or potassium, polar phases can be established. In particular, the electric polarization of the following compounds can be switched by an applied electric field: (NH4)0.67(ND4)0.33I (where D is deuteron), NH4I0.91Br0.09 and NH4I0.94K0.06 according to pyroelectric current measurements. Magnetic susceptibility measurements indicate that the polar phases may be magnetic in origin. We explain our results by taking into account the notion that every reorienting NH4+ possesses a molecular magnetic moment that can couple with that of neighboring NH4+. The magnetic moments arise from the protons (H+) having to orbit in concert about the central nitrogen atom when the ion reorients. In the room-temperature phases, enough orbits are available to avoid mutual resonance, but below a critical temperature, a subset of these orbits become energetically inaccessible so neighboring NH4+ become mutually resonant. To avoid lattice instabilities from resonant forces, the NH4+ become ordered to establish a spiral modulation of its magnetic moments. A replacement of a fraction of H with D or I with Br or K breaks the spatial-inversion symmetry of the modulating vector so an electric polarization emerges. Our findings provide the potential of adding an extra ferroelectric dimension to hydrogen-bonded materials. 

**References:** 
F. Yen, Z. Zheng and Z. Si, Angewandte Chemie, 129(44), 13863-13866 (2017) 
L. Meng, C. He and F. Yen, The Journal of Physical Chemistry C, 124, 17255−17261 (2020)

Inducing ferroelectricity in NH4I via doping of deuterons, bromide and potassium

Ultrathin ferromagnetic strips, sandwiched between a heavy metal and an oxide, have been suggested as potential platforms for recording devices where the information is coded in perpendicular magnetized domains (up or down) separated domain walls (DWs). Due to the Dzyaloshinskii-Moriya interaction, such DWs depict a homochiral Néel configuration [1,2] and are displaced with high velocity (~500 m/s) by current pulses (J~1 TA/m2) [3]. However, the writing mechanism for such DW-based devices, that is, a controlled nucleation of domains and DWs, is still challenging. Nucleation is conventionally performed by injecting an electrical current pulse along an orthogonal conducting wire [1]. However, the resulting Oersted field that nucleates a new domain also annihilates an already shifted one unless an intricate device layout is used [4]. Although some ideas have been proposed to solve this issue [5,6], a simple nucleation scheme remains elusive.
Here we propose a simple geometrical design where both the nucleation and the shifting can be purely achieved by current pulses (Fig. 1(a)). A DW is initially located in the bottom-left arm of the two symmetrical arms close to its junction with the longitudinal strip (LS), where the bits will be coded and shifted. By applying a proper voltage pulse (V2 in Fig. 1(b)), the DW is pushed towards the LS, and split in two new DWs: one at the top-left arm and other entering in the LS. A second pulse along the same bottom-left arm (V2) will shift the new DW along the LS. If injected along the top-left arm (V1), another DW and domain will be nucleated whereas the former DW will be also driven along the LS. Based on this method, new domains (bits) and DWs can be simultaneously nucleated (written) and driven by alternatively applying voltage pulses between one of the two left arms and the LS of the structure. In the talk, we will show by means of realistic simulations the potential of this idea to perform the writing operation in DW-based recording devices. 
**References** [1] S. Emori et al. Nat. Mater. 12, 611 (2013).
[2] K.-S. Ryu et al. Nat. Nanotechnol. 8, 527 (2013).
[3] I. M. Miron et al. Nat. Mater. 10, 419 (2011).
[4] O. Alejos et al. Scientific Reports, 7, 11909 (2017).
[5] Z. Luo et al. Appl. Phys. Lett. 111, 162404 (2017).
[6] T. Phuong Dao et al. Nano Lett. 19, 9, 5930 (2019).
 
![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/685344f1d53b63eaa04ed5c1ea27dc65.png)

Purely current driven writing mechanism for domain wall

Wood's anomaly is a phenomenon discovered in 1902 [1], manifesting as a decrease of the reflected waves amplitude due to the excitation of a surface mode that is still investigated in photonics [2]. Another curious effect observed in the reflection of obliquely incident waves is the Goos-Hanchen effect (GHE) [3,4], which causes a spatial shift of the reflected waves. One of the configurations suitable for observing both phenomena for spin waves (SWs) is the Gires-Tournois interferometer (GTI) proposed in Ref. [5,6], made of a magnetic stripe placed above the edge of a magnetic layer. We use micromagnetic simulations to study the reflection of an oblique incident SW beam at such a GTI. We identified the resonance conditions required to efficiently excite SW modes in the GTI by the incident SW beam, which give rise to magnonic Wood's anomaly in our system. The amplitude of these modes is confined in the stripe and emits SWs back to the layer; therefore, these modes can be classified as 'leaky-modes'. The consequence of the leaky-mode is the creation of multiple spatially shifted SW beams in the layer parallel to one another. Furthermore, the excitation of the leaky-modes is accompanied by a significant GHE for the primary reflected beam with values spanning between -175 nm and 225 nm with respect to the non-resonant case. In Fig. 1a and 1b we show the distributions of SW intensity for the case with the resonant excitation of a leaky-mode and without the excitation, respectively. In Fig. 1b multiple reflected SW beams are evident. Our findings contribute to understanding and utilizing the interaction of propagating SWs in thin films with the localized leaky-modes. Additionally, an incident beam's excitation of modes in GTI provides a platform for investigations of SWs inelastic scattering on interferometer's modes. We acknowledge the funding from the Polish National Science Centre project No. UMO-2019/33/B/ST5/02013.

Magnonic interferometer’s leaky mode influence on spin

It is important to understand physically how to reliably control the domain wall (DW), because the promising applications such as solid-state spintronic memories utilizing
DW displacements along ferromagnetic nanowires (NWs) [1] are directly connected to the reproducibility of repeatable DW motion. As those are based on operations at room temperature,
extensive studies on how the thermal effect on DW depinning can be controlled by various geometrical and methodological considerations should be required for enhancing controllabilty
of the DW motion. In the previous study, we have found that their depinning fields from artificial constraints (notches) on ferromagnetic NWs can be experimentally oscillated under a
magnetic field HT transverse to the nanowire [2]. Interestingly, this study is focused on the thermal fluctuation of the 2D magnetization (M) vector, m(r,t)=mx
(r,t)x+my
(r,t)y [3]. Figure
1(a) shows noise spectra in magnetization components at specific frequencies under HT. Figure 1(b) depicts schematics of thermal M fluctuation at each frequency corresponding to Fig.
1(a), which means the red region indicates the highest magnetization fluctuation at each mode. It is clearly seen that the specific modes of thermal M fluctuations in the DWs exist and the
trend of tilting-angle difference between magnetizations at mode 4 of Fig. 2(a) is consistent with that of depinning field from notches as shown in Fig. 2(b). This depinning behavior is
related to the thermal M fluctuation in the DWs pinned at the notches, as confirmed by a micromagnetic simulation. 
**References** [1] S. Parkin and S. –H. Yang, Nature Nanotech. 10, 195 (2015).
[2] S.-M. Ahn et al., J. Nanosci. Nanotechnol. 11, 6472 (2011).
[3] N. Smith, J. Appl. Phys. 90, 5768 (2001). 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/a4d93e2ed8785583d2cd80fc9529fafc.png) 

Fig. 1 (a) Noise spectra in magnetization components (mx and my
). (b) Schematic maps of thermal M fluctuations at specific frequencies, (1) 1.52 GHz, (2) 2.28 GHz, (3) 3.58 GHz, and
(4) 4.52 GHz. 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/a181122f90dc2dfdb65d9bbac50bf50a.png) 
Fig. 2 (a) Tilting-angle difference for the depinning field with respect to HT (simulation). (b) The depinning field as a function of HT. Inset : High resolution image of U-shaped 350-nm- wide Permalloy nanowire structure with double notches.

Role of the thermal magnetization fluctuation in depinning of domain wall from constraints on the ferromagnetic nanowire

Scaling TMR reader down to sub 20 nm for magnetic storage technology beyond 4 Tb/in2 is challenging, due to its complex film stack and increasing noise at smaller size. Recently, a spin-orbit torque (SOT) reader based on the inverse spin Hall effect was proposed as an alternative candidate [1]. The SOT reader consists of a SOT layer and a ferromagnetic layer (FM). A spin-polarized current is injected from the FM layer to the SOT layer, which generates an output voltage via the inverse spin Hall effect. However, the output voltage and signal-to-noise ratio (SNR) of SOT reader using traditional heavy metals are insufficient due to the relatively small spin Hall angle (SHA) and low sheet resistance [2]. Hence, a SOT material with large SHA is essential to generate a large output and sufficient SNR. The topological insulator (TI) BiSb emerges as potential candidate for SOT reader thanks to its giant SHA [3] and larger sheet resistance. In this work, we demonstrate a proof-of-concept for a BiSb-based SOT reader with large output voltage and SNR. Figure 1 shows the schematic structure of our device. The SOT reader is a 20 μm × 20 μm pillar of CoFe (5 nm)/MgO (2 nm)/BiSb (10 nm) on top of a 20 nm-thick Ta/Pt bottom current electrode deposited on an oxidized silicon substrate. Then, a top current electrode was deposited on top of the pillar. A perpendicular bias current was applied to the pillar, and the output voltage of the inverse spin Hall effect was read out during sweeping an in-plane magnetic field. Figure 2(a) shows a representative data at Japp = 6.25 kA/cm2 for the inverse spin Hall resistance RISHE = VISHE/Iapp of the reader. Figure 2(b) shows the characteristics of the reader. The output is as large as 15 mV, which is 3 orders of magnitude larger than that of Pt-based devices [2]. We project a giant inverse spin Hall angle of 24 for this device, which demonstrates the potential of BiSb for SOT reader application. 
**References** 
[1] P. A. V. Heijden, Q. Le, K. S. Ho, US patent US9947347B1 (2016). 
[2] V. T. Pham, I. Groen, S. Manipatruni, Nat. Elec. 3, 309 (2020). 
[3] N. H. D. Khang, Y. Ueda, and P. N. Hai, Nat. Mater. 17, 808 (2018). 
![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/876d0c64ad5b253f6d4185bcb1e6882f.png) 
Schematic device structure of our BiSb-based SOT reader. 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/caa4f1c75de584c6a6127f7610c871a9.png) 
(a) Inverse spin Hall resistance at Japp = 6.25 kA/cm2. (b) Output voltage at various applied current density.

Giant inverse spin Hall effect in BiSb topological insulator for SOT reader

2D bi-material artificial spin ice systems have been well studied [1-4] but restricting spins to 2D limits functionality. Extending into 3D provides an extra degree of
freedom, but the underlying physics need deeper understanding. We show how spin stability can be controlled via introduction of mixed materials and overlap layer (OL) in 3D
nanostructures (NS), with potential applications in computation and memory [5].
Self-aligned hexagonally arranged Py and Co NS were fabricated via stepwise nanosphere lithography [6] via a two-step deposition at different orientation. A mixture of Co NS, Py NS and
3D overlapped Co/Py NS (OLNS) comprising of a Co parallelogram on top of a Co/Py base layer is formed (Fig 1a&b).
Magnetization reversal studies were done via MFM. Fig 1c-f show remanant domain configurations at different field values. After +3 kOe saturation (Fig 1c), most Py NS (circled)
reversed at -300 Oe (Fig 1d). At -700 Oe (Fig 1e), a Co NS reversed (circled) while OLNS exhibited stable transition states (arrows). OOMMF [7] simulations showed a Néel wall (circled)
in Fig 2a but none in Fig 2b for NS without OL. Shape anisotropy causes spins in the OL to lie along the geometrical easy axis. Vertical spins of the Néel wall also connect spins in the base
layer and OL via strong exchange coupling, causing in-plane spins to remain unperturbed over large fields.
The in-plane spins were seen in Fig 2a to also pin nearby spins in the base layer outside the OL in the same direction (light blue), resulting in the stable transition state in Fig 1e. In contrast,
reversal begins at the constituent NS' corners without any OL, as seen in Fig 2b (circled).
The tunability of spin stability via OL's shape and area, material and size will be further discussed via experiments and simulations. These interesting static observations in 3D show
promise for new dynamic spin wave propagation behavior in 3D. This study aims to extend well-established static and dynamic magnetic behavior of 2D structures into 3D. 


**References:** 

[1] A. Rodríguez, L. Heyderman, F. Nolting, Appl. Phys. Lett., vol. 89, p. 142508 (2006) 
[2] S. Choudhury, S. Saha, R. Mandal, ACS Appl. Mater. Interfaces, vol. 8, p. 18339 – 18346 (2016) 
[3] A. O. Adeyeye, S. Jain, and Y. Ren, IEEE Trans. Magn., vol. 47, p. 1639 – 1643 (2011) 
[4] S. Choudhury, S. Pan, S. Barman, J. Magn. Magn. Mater., vol. 490, p. 165484 (2019) 
[5] S. Sahoo, A. May, A. van Den Berg, Nano Letters, vol. 21, no. 11, p. 4629-4635 (2021) 
[6] B. Myint, D. Yap and V. Ng, Nano Express, vol. 1, p. 020029 (2020) 
[7] M. Donahue and D. Porter, OOMMF User’s Guide, Version 1.0 Interagency Report NISTIR 6376 (1999) 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/a34e0d2f1abba981e622df78b10125da.png)

Controlling Spin Stability in Three Dimensional Bi

The development of functional printable materials enables the production of electronic components in unconventional materials and different form factors[1]. Here, we
show magnetically sensitive inks/pastes based on magnetoresistive powder that can be printed via stencil, dispenser, or screen printing. We employ bismuth microparticles[2] as well as
[Co/Cu], [Py/Cu],[3] and permalloy [4] flakes showing giant, anisotropic, or non-saturating large magnetoresistance, respectively.
We demonstrate that magnetic field sensors based on various types of magnetoresistive flakes can be printed onto rigid, flexible, and deformable substrates. We employed blockcopolymers
and elastic binders to enable mechanical resilience of these sensors: they can withstand bending down to 16 μm, 100% of stretching, and bending for hundreds of cycles
without losing functionality.[3]
Additionally, by automatizing the dispenser printing process of bismuth-based pastes, we demonstrate the production of fully printed magnetic field sensors. The use of a micro-optically
optimized high-power diode laser array provided a versatile approach for selective sintering of sensors over flexible foils in areas exceeding several square centimeters. In this work we
experimentally confirm that such sensors retain their non-saturating magnetoresistive performance (MR = 146%) in high field conditions, allowing operation above 5 T. [2]
Our printed magnetic field sensors can be used to create interfaces that are responsive to magnetic fields through remote human input. Being flexible, they can be laminated on the skin, or
stuck onto any object, from a desk to a house wall. We demonstrate the capabilities of printed magnetic field sensors to work as an interface to navigate through digital maps, as input
panels for smart home applications, and as interactive wallpapers. 

**References:** 

[1] A. Kamyshny, S. Magdassi. Chem. Soc. Rev. Vol. 48, p.1712 (2019) 
[2] E.S. Oliveros-Mata, G.S. Cañón Bermúdez, M. Ha, et al. Appl. Phys. A Vol. 127, p.280 (2021) 
[3] M. Ha, G.S. Cañón Bermúdez, T. Kosub, et al. Adv. Mater. Vol. 33, p.2005521 (2021) 
[4] E.S. Oliveros-Mata, C. Voigt, G.S. Cañón Bermúdez, et al. Adv. Mater. Technol. p.2200227 (2022)

Detecting Magnetic Fields with Printed Magnetoresistive Sensors on Rigid and Flexible Substrates

The recent development of magnetic tomography [1] and laminography [2] techniques has allowed the quantitative characterization of 3D magnetization vector maps in thin films and nanostructures. Thus, vector analysis methods can be used to understand the experimental magnetization configurations and obtain a unified description of the different types of 3D domain walls and magnetic singularities. In this work we have studied by X-ray vector magnetic tomography (XVMT) the 3D magnetization configuration of a 140 nm thick permalloy microstructure [3] and a ferrimagnetic GdCo/NdCo/GdCoâ€™ trilayer [4]. In the Py microstructure, we observe a domain wall with non-trivial 3D configuration decorated by Bloch points such as the one in Fig. 1: composed of a linear tail-to-tail wall and a circulating vortex across the sample thickness. The corresponding emergent field Be (calculated in the right part of Fig. 1) reveals the underlying topological singularity with charge -1, that acts as a sink of Be lines. Changes in domain wall chirality are mediated by topological dipoles and triplets linked by horizontal bundles of emergent field lines. In addition, surface magnetic textures and helical vortices are found at the cross sections of vertical bundles of Be lines [3]. In the GdCo/NdCo/GdCoâ€™ trilayer, the competition between anisotropy, exchange and magnetostatic interactions creates a peculiar stripe domain pattern with an exchange spring wall across the thickness at the top GdCo/NdCo interface [4]. The role of this boundary as a preferred site for nucleation of singularities will be discussed in detail (see e.g. the emergent field dipole in Fig. 2, composed of two Bloch points at different sample depths and opposite topological charges). Work supported by Spanish MICIN and Asturias FICYT.

X ray vector magnetic tomography of Bloch points in magnetic microstructures and multilayers

Geometrical transformations, such as rolling a 2D ferromagnetic film into a 3D cylinder provide means to tune its magnetic properties generating different magnetic ground states [1]. Rolled-up magnetic membranes with azimuthal magnetic anisotropy are very attractive due to expected much higher domain wall velocity (compare to their planar counterparts) [2] and for applications as impedance-based field sensors [1]. However, a clear recipe for acquiring highly mobile azimuthal domains in a soft ferromagnetic tubular geometry is unclear. State of the art studies report the rolling of an extended ferromagnetic film (of hundreds of micro-meters), which after rolling converts into tubular geometry with 2-3 windings [1]. Changes in the magnetic domain configuration in such tubular geometries may arise from modifications of the shape anisotropy in addition to stress-induced anisotropy due to rolling. In our work, we report on rolling-induced azimuthal anisotropy in Ni78Fe22 stripes (as shown in figure 1a) purely due to strain, considering that curvature induced changes in shape anisotropy can be neglected due to reduced dimensions of our magnetic stripe in the azimuthal direction. For that, we employed a self-assembly rolling technology based on a polymeric platform, which allows choosing the shape and size of the magnetic structure willingly. Magnetic structures patterned on the polymeric platform can be bent controllably and hence the sign and magnitude of strain on the magnetic structure can be adjusted. We quantify the induced azimuthal magnetic anisotropy (figure 1c) by electrical measurements (figure 1b) capable of providing magnetic properties of magnetic structures hidden under the 3D polymer architecture.

Self Assembly as a Tool to Study Strain

Multiferroic materials have garnered wide interest for their exceptional static and dynamical magnetoelectric properties (1). In particular, type-II multiferroics exhibit an inversion-symmetry-breaking magnetic order which directly induces a ferroelectric polarization through various mechanisms, such as the spin-current or the inverse Dzyaloshinskii-Moriya effect. This intrinsic coupling between the magnetic and dipolar order parameters results in record-strength magnetoelectric effects (2). In this context, there has been a recent surge of interest in 2D materials possessing such intrinsic multiferroic properties, enabling the integration and control of magnetoelectric effects in artificial heterostructures and nanoelectronic devices (3,4).
In this talk, I will present our recent study and realization of type-II multiferroic order in a single atomic layer of the transition metal-based van der Waals material NiI2 (5). The multiferroic state of NiI2 is characterized by an inversion-symmetry-breaking helimagnetic order which induces a chirality-dependent electrical polarization. Using circular dichroic Raman measurements, we directly probed the magneto-chiral ground state and its electromagnon modes originating from dynamic magnetoelectric coupling. Using birefringence and second-harmonic generation measurements, we observed a highly anisotropic electronic state simultaneously breaking three-fold rotational and inversion symmetry to support polar order. The evolution of the optical signatures as a function of temperature and layer number surprisingly revealed an ordered magnetic, polar state that persists down to the ultrathin limit of monolayer NiI2 (6). 

**References:** 
(1) Matsukura, F., Tokura, Y. and Ohno, H. Control of magnetism by electric fields. Nat. Nanotech. 10, 209 (2015). 
(2) Spaldin, N. A. and Ramesh, R. Advances in magnetoelectric multiferroics. Nat. Mater. 18, 203 (2019). 
(3) Huang, B. et al. Electrical control of 2D magnetism in bilayer CrI3. Nat. Nanotech. 13, 544 (2018). 
(4) Jiang, S., Li, L., Wang, Z., Mak, K. F. and Shan, J. Controlling magnetism in 2D CrI3 by electrostatic doping. Nat. Nanotech. 13, 549 (2018). 
(5) Kurumaji, T. et al. Magnetoelectric responses induced by domain rearrangement and spin structural change in triangular-lattice helimagnets NiI2 and CoI2. Phys. Rev. B 87, 014429 (2013). 
(6) Song, Q. et al. Evidence for a single-layer van der Waals multiferroic. Nature 602, 601 (2022) 
![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/16d0bed0aa8cc8b53b6d7e52bbf8d944.png)

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