# Intrinsic Magnetism and Field-Driven Spin Alignment in NiI2 Revealed by X-ray Magnetic Spectroscopy

Ethan L Arnold, Emily Heppell, Rabindra Basnet, Binshuo Zhang, Jieyi Liu, Javier Herrero-Martín, Charles Guillemard, Yanfeng Guo, Jin Hu, Dirk Backes, et al.

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## To cite this version:

Ethan L Arnold, Emily Heppell, Rabindra Basnet, Binshuo Zhang, Jieyi Liu, et al. Intrinsic Magnetism and Field-Driven Spin Alignment in NiI2 Revealed by X-ray Magnetic Spectroscopy. physica status solidi (RRL) - Rapid Research Letters (pss RRL), In press, 10.1002/pssr.202500130. hal-05128040

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Submitted on 24 Jun 2025

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# Intrinsic Magnetism and Field-Driven Spin Alignment in NiI₂ Revealed by X-ray Magnetic Spectroscopy

Ethan L. Arnold, Emily Heppell, Rabindra Basnet, Binshuo Zhang, Jieyi Liu, Javier Herrero-Martín, Charles Guillemard, Yanfeng Guo, Jin Hu, Dirk Backes, Gerrit van der Laan,* and Thorsten Hesjedal*

This study investigates the intrinsic magnetism and field-driven spin alignment in NiI₂ using X-ray absorption spectroscopy and X-ray magnetic circular dichroism (XMCD). NiI₂, a van der Waals material, exhibits helimagnetic and type-II multiferroic behavior. This study reveals robust XMCD signals across paramagnetic, antiferromagnetic, and helimagnetic phases under applied out-of-plane fields up to 6 T, while no net moment emerges at zero field. Atomic multiplet calculations confirm a covalent Ni 3d ground state with a significantly reduced spin moment. The results establish the intrinsic nature of NiI₂'s magnetism and clarify its field-driven spin alignment mechanism. This comprehensive spectroscopic characterization lays the foundation for future applications of NiI₂ in advanced spintronic and multiferroic devices, despite challenges posed by its low transition temperature in the monolayer limit. Future research should focus on enhancing its critical temperature through doping, strain engineering, or heterostructure fabrication.

## 1. Introduction

Magnetic van der Waals (vdW) semiconductors hold great promise for future spintronic and multiferroic technologies[1,2] due to their intrinsic magnetism persisting down to the monolayer limit[3-5] and their tunability via external stimuli such as magnetic fields, strain, and electric fields.[6-8] Among these

materials, nickel diiodide (NiI₂) stands out for its rich magnetic phase diagram and unique multiferroic properties.[9] At room temperature, bulk NiI₂ is paramagnetic, but upon cooling, it undergoes a series of intriguing magnetic transitions—first to an antiferromagnetic state below 75 K, and subsequently to a helimagnetic phase below 59 K. The latter transition involves a rhombohedral-to-monoclinic structural distortion, enabling an inversion-symmetry-breaking spin spiral that couples magnetism and electric polarization.[10,11] Consequently, NiI₂ is classified as an improper type-II multiferroic, with multiferroicity extending down to monolayer thickness,[12] albeit at a reduced critical temperature of around 21 K, highlighting the crucial role of dimensionality.[5]

Recent research has confirmed that exfoliated NiI₂ retains strong magnetic correlations in its 2D limit, exhibiting phenomena such as chiral magnetoelectric oscillations,[13] electromagnons,[5,14,15] and quantum-entangled magnetic states.[8] These properties position NiI₂ as an ideal candidate for applications in advanced spin-based devices.[3,4] Despite significant interest, a detailed spectroscopic characterization of the electronic and magnetic ground states of NiI₂ is still lacking.

E. L. Arnold, E. Heppell, J. Liu, T. Hesjedal
Department of Physics
Clarendon Laboratory
University of Oxford
Oxford OX1 3PU, UK
E-mail: thorsten.hesjedal@physics.ox.ac.uk

E. L. Arnold, E. Heppell, J. Liu, D. Backes, G. van der Laan, T. Hesjedal
Diamond Light Source
Harwell Science and Innovation Campus
Didcot OX11 0DE, UK
E-mail: gerrit.vanderlaan@diamond.ac.uk

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The ORCID identification number(s) for the author(s) of this article can be found under https://doi.org/10.1002/pssr.202500130.

© 2025 The Author(s). physica status solidi (RRL) Rapid Research Letters published by Wiley-VCH GmbH. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

DOI: 10.1002/pssr.202500130

E. Heppell
Rutherford Appleton Laboratory
ISIS
Harwell Science and Innovation Campus
Didcot OX11 0QX, UK

R. Basnet, J. Hu
Department of Physics
Institute for Nanoscience and Engineering
University of Arkansas
Fayetteville, AR 72701, USA

B. Zhang, Y. Guo
School of Physical Science and Technology and Shanghai Tech Laboratory for Topological Physics
ShanghaiTech University
Shanghai 201210, China

J. Herrero-Martín, C. Guillemard
ALBA Synchrotron
Carrer de Llum 2-26, Cerdanyola del Vallès 08290, Barcelona, Spain
In this work, we bridge this gap by providing a comprehensive X-ray absorption spectroscopy (XAS) and X-ray magnetic circular dichroism (XMCD) study of bulk NiI₂ single crystals as a function of temperature and applied magnetic field. Our experimental results, supported by atomic multiplet calculations, clarify the intrinsic nature of NiI₂'s magnetism and lay the foundation for the future use of its unique magnetoelectric phenomena in advanced 2D heterostructures.

**2. Experimental Section**

At room temperature, NiI₂ adopts the CdCl₂-type (R³m) crystal structure, shown in **Figure 1**, featuring Ni²⁺ ions arranged on triangular planes separated by I⁻ layers. These I⁻·Ni²⁺·I⁻ triple slabs stack along the c-axis, with neighboring layers bound by weak vdW interactions.

The NiI₂ crystal was grown using chemical vapor transport. Owing to NiI₂'s hygroscopic nature, which results in rapid degradation in air, the crystal was cleaved at the beamline right before the measurements in an Ar glove box that is directly interfaced with the ultrahigh vacuum (UHV) end station, thus ensuring that the sample remained in an inert environment throughout the transfer process. The sample was oriented such that the c-axis was in the out-of-plane (OOP) direction. The sample was transferred to the XMCD end-station in UHV, thus limiting degradation as far as possible. Note that the XMCD spectra show no signs of Ni oxide, indicating that there has been no deterioration of the sample.

XAS and XMCD offer the most direct way to determine the local electronic and magnetic structure of 3d transition metals due to their element-, valence-, site-, and symmetry-selectivity.[16] In particular, XMCD—defined as the difference between X-ray absorption spectra for photons with left and right circular polarization—enables a direct, quantitative assessment of spin

and orbital moments via the well-established sum rules.[17] The XAS and XMCD measurements reported here were carried out at the BOREAS beamline at the ALBA Synchrotron (Barcelona, Spain), spanning temperatures from 2 to 300 K in a superconducting magnet. All data were collected in the total electron yield (TEY) mode, which is surface-sensitive with a typical probing depth of ≈4 nm. The incident X-ray beam was along the applied field.

Atomic multiplet calculations were performed to obtain the Ni L<sub>2,3</sub> XAS and XMCD spectra for the electric-dipole transitions, 3d<sup>n</sup> → 2p<sup>5</sup>3d<sup>n+1</sup>, with the spin-orbit and electrostatic interactions treated on an equal footing.[18,19] The wave functions of the initial- and final-state configurations were calculated in intermediate coupling using Cowan's atomic Hartree-Fock (HF) code with relativistic corrections.[18,20] The atomic electrostatic interactions included the 3d-3d and 2p-3d Coulomb and exchange interactions, which were reduced to 80% of their atomic HF value to account for intra-atomic screening. An octahedral crystal field of 10Dq = 2 eV was included, which splits the 3d-orbitals in states of e<sub>g</sub> and t<sub>2g</sub> symmetry. Hybridization in a cluster-model mixes the 3d<sup>n+1</sup> *L* and 3d<sup>n</sup> wave functions, where *L* represents a hole on the neighboring atoms in states of appropriate symmetry. Specifically, for NiI<sub>2</sub>, the hybridization parameter T = ⟨Ψ(d<sup>n</sup>)|H|Ψ(d<sup>n+1</sup> *L*)⟩ was taken as T(e<sub>g</sub>) = 1.5 and T(t<sub>2g</sub>) = 0.75 eV. The relative values of the average energy of the configurations in the initial state were taken as E(3d<sup>8</sup>) = 0, E(3d<sup>9</sup> *L*) = -1.5, and E(3d<sup>10</sup> *L<sup>2</sup>) = 5 eV and those in the final state as E(2p<sup>5</sup>3d<sup>9</sup>) = 0 and E(2p<sup>5</sup>3d<sup>10</sup> *L*) = -2.5 eV. This resulted in a high spin <sup>3</sup>A<sub>2g</sub> ground state with 54.8% d<sup>8</sup>, 43.4% d<sup>9</sup>, and 1.8% d<sup>10</sup> character, yielding a *d*-count of n<sub>d</sub> = 8.47—in good agreement with earlier performed Anderson impurity model calculations for the XAS of Ni dihalides and NiO.[21] The computed Ni L<sub>3</sub> (L<sub>2</sub>) line spectra were convoluted by a Lorentzian with a half width of Γ = 0.2 eV (0.6 eV) for intrinsic lifetime broadening and a Gaussian with a standard deviation of σ = 0.15 eV for instrumental broadening.

<figure><img src="image_4.png" /><figcaption>**Figure 1.** Crystal structure and magnetic phase diagram of NiI₂. a) At room temperature, NiI₂ adopts a CdCl₂-type structure (space group R3m), comprising alternating layers of Ni²⁺ and I⁻ ions, weakly coupled via vdW interactions. b) Top-down view of the crystal structure along the c-axis, highlighting its triangular symmetry. c) Temperature-dependent magnetic phase diagram illustrating NiI₂'s transition from a paramagnetic state at room temperature to an antiferromagnetic phase below 75 K, followed by a helimagnetic phase emerging below 59 K.</figcaption></figure>
We note that the magnetic transition into the helimagnetic phase is accompanied by a structural distortion from rhombohedral to monoclinic symmetry, as reported in earlier work.[10,11] While our XMCD measurements do not directly track changes in lattice parameters, these structural modifications likely play a role in the evolution of the magnetic ground state. A detailed temperature-dependent structural analysis would be a valuable complement to the present study.

**3. Results and Discussion**

We begin by comparing the experimental and calculated XAS and XMCD at 65 K in a 6 T out-of-plane magnetic field, as shown in **Figure 2**. The primary peaks at the $L_3$ and $L_2$ edges, located at 851.6 and 868.7 eV, respectively, are dominated by the $2p^5 3d^{10} L$ configuration, whereas the satellite structure at ≈3.5 eV higher photon energy corresponds mainly to $2p^5 3d^9$, split by ≈2 eV due to the core-valence exchange interaction. In the XMCD spectrum, the satellite structure displays a characteristic (−,+)$\sigma$-signature. The spectral structure is markedly different from a pure $3d^8$ ground state, as reported in ref. [22], and instead aligns well with earlier work on Ni metal for which an impurity-model analysis revealed a significantly hybridized Ni $3d$ ground state.[23] The strong agreement between the experimental and calculated XAS confirms the high quality of the $NiI_2$ crystal and establishes that the XMCD signals originate from $NiI_2$ itself, rather than from spurious nickel metal impurities or other contamination. The observed step in the XAS intensity at ≈858 eV corresponds to the onset of the $L_3$ continuum states,[21] which are not taken into account in the calculation and which show no dichroism.

The element-specific spin and orbital magnetic moments were obtained from the integrated intensities of the dichroic spectra using the XMCD sum rule analysis.[24] Consider the integrated XMCD spectra, with *p* and *q* the integrated intensities over the $L_3$ and $L_{2,3}$ edges, respectively. Using the integrated intensity *r* over the $L_{2,3}$ edge of the sum spectrum as the normalization factor accounting for the number of *d* holes $n_h = (10 - n_d) = 1.53$, the spin and orbital moments per atom are then given by $m_L = -\langle L_Z \rangle = -(4/3)qn_h/r$ and $m_S = -\langle 2S_{eff,z} \rangle = -(6p-4q)n_h/r$.[16] For the calculated spectra, we obtain $m_L = 0.103 \mu_B$/Ni and $m_S = 1.36 \mu_B$/Ni, yielding $m_L/m_S = 0.076$. By contrast, sum rule analysis on the experimental data at 65 K and 6 T (as shown in Figure 2), after background subtraction, give $m_L = 0.005 \mu_B$/Ni and $m_S = 0.08 \mu_B$/Ni, yielding $m_L/m_S = 0.063$. Although the ratio of orbital to spin moment, $m_L/m_S$, is comparable in both cases, i.e., a 17% difference, the spin moment observed experimentally is ≈17 times smaller than in the theoretical calculation. Such a strong reduction is expected and arises from the geometrical projection of the spin moment along the direction of the incoming X-ray beam. In zero field, the antiferromagnetic or helical spin textures in $NiI_2$ result in no net magnetization along any fixed axis, thereby suppressing the XMCD signal. Even under finite field, unless full spin alignment is achieved, only the projected component contributes to the dichroic signal. Thus, the apparent discrepancy reflects the noncollinearity of the spin structure rather than a fundamental disagreement in moment size. A detailed quantitative analysis of this reduction would

<figure><img src="image_5.png" /><figcaption>**Figure 2.** Comparison between experimental and calculated a) XAS, averaged over both polarizations, and b) XMCD spectra at the Ni $L_{2,3}$ edge of $NiI_2$. The experimental data were collected at 65 K in an out-of-plane magnetic field of 6 T in normal incidence using TEY mode. The theoretical spectra were calculated in intermediate coupling using Cowan's atomic Hartree-Fock code with relativistic corrections. Transitions to the continuum states, showing a step-like onset at ≈858 eV, as indicated by the green arrow, were not included in the calculation. The experimental XAS and XMCD spectra have been scaled to the calculated spectra in order to allow for a better comparison of the multiplet structure. To do this, the experimental XMCD intensity had to be multiplied by a factor ≈20 compared to the experimental XAS intensity. The need to scale reflects the fact that the atomic multiplet model assumes fully aligned moments and does not account for the antiferromagnetic or helical spin structures present in $NiI_2$.</figcaption></figure>

require modeling the spin texture and its projection along the beam, which goes beyond the current multiplet framework.

Next, we examine the XMCD as a function of temperature. **Figure 3** shows the XMCD spectra at temperatures from 2 to 300 K, in an out-of-plane field of 6 T. The XAS spectra are normalized such that the sum of both circular polarizations has an $L_3$ peak intensity of unity. At lower temperatures, the XMCD spectra exhibit noticeable linewidth broadening, which is not observed in the corresponding XAS data. Moreover, the XMCD peak intensity diminishes with decreasing temperature, suggesting partial suppression of the net spin alignment, possibly due to enhanced spin-orbit interactions or domain effects
<figure><img src="image_6.png" /><figcaption>**Figure 3.** a) Normalized XAS sum spectrum measured at 2 K and b) temperature-dependent XMCD spectra at the Ni L<sub>2,3</sub> edge. All spectra were acquired at a fixed out-of-plane field of 6 T with incoming X-rays at normal incidence. The XMCD spectra have been vertically offset for clarity.</figcaption></figure>

near the surface. In addition to the reduction in XMCD intensity, an effect that may seem counterintuitive from the perspective of conventional ferromagnetic ordering, we also observe a gradual broadening of the spectral features below 59 K. In the monoclinically distorted low-temperature crystal structure, the various spins will feel slightly different exchange interactions, which can lead to slight shifts in energy, resulting in a broadened XMCD response. Although no XMCD studies on helimagnetic materials reporting similar broadening effects are currently known, related temperature-dependent changes in hybridization, localization, or magnetic interactions influencing the XMCD line shape have been observed in other 3d transition metal compounds. For example, XMCD studies on Co<sub>2</sub>MnGe revealed multiplet features in the Mn L<sub>2,3</sub> spectra attributed to localized 3d electrons and temperature-dependent hybridization effects.<sup>[25]</sup> Likewise, in GdNi, strong hybridization between Ni 3d and Gd states leads to significant temperature-dependent changes in the XMCD spectral profile.<sup>[26]</sup>

Finally, we investigate the XMCD behavior in the intermediate antiferromagnetic phase between 59 and 75 K. **Figure 4** shows XMCD spectra acquired at 65 K in out-of-plane magnetic fields from 0 T to 6 T. To estimate the magnetization, we use the peak asymmetry, defined as the L₃ XMCD amplitude divided by the XAS sum intensity (see Supporting Information for ref. [27]). To determine the asymmetry values, we evaluated the XMCD amplitude for each field by identifying the minimum of the L₃ edge within a narrow energy window around the peak, rather than taking the value at a fixed energy, minimizing the influence of noise and slight peak shifts across the field-dependent spectra. From these data, we extract the average Ni magnetic moment along the field direction at each field value, which is plotted in **Figure 5**. The measurement at 0 T is excluded because it lacks

<figure><img src="image_7.png" /><figcaption>**Figure 4.** a) Normalized XAS sum spectrum at the Ni L<sub>2,3</sub> edge, measured at 65 K in an applied field out-of-plane field of 6 T. b) Corresponding XMCD spectra as a function of field from 0 T to 6 T. Measurements were performed at normal incidence of the X-rays, and the XMCD spectra are vertically offset for clarity.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>**Figure 5.** XMCD asymmetry (i.e., maximum peak XMCD divided by sum XAS) at 65 K as a function of the applied out-of-plane magnetic field. The data points (dots) are derived from the L₃ edges in the XMCD spectra shown in Figure 4. Note that the uncertainty in the asymmetry is expected to be greater at low fields due to reduced signal strength and less well-defined spectral features. The solid line represents a linear fit to highlight the nearly linear proportional relationship between magnetization along the field direction and magnetic field for fields up to 6 T.</figcaption></figure>

a discernible ferromagnetic-like XMCD lineshape. The linear trend observed above 0 T is therefore extrapolated down to 0 T to emphasize the apparent proportionality between magnetization and applied field at 65 K. Similar behavior was observed for the same set of measurements for X-rays in grazing incidence.

Although NiI₂ hosts paramagnetic, antiferromagnetic and helimagnetic phases at low fields, we observe XMCD at all studied temperatures once the out-of-plane field is sufficiently large.
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