Helimagnetism in the candidate ferroelectric ${\mathrm{CrI}}_{2}$

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Helimagnetism in the candidate ferroelectric ${CrI}_{2}$

John A. Schneeloch, Shunshun Liu, Prasanna V. Balachandran, Qiang Zhang, and Despina Louca

Phys. Rev. B 109, 144403 – Published 3 April 2024

Abstract

${CrI}_{2}$ is a van der Waals layered material that exhibits helimagnetism that propagates along ribbon chains. This is determined from neutron time-of-flight diffraction measurements. Below $T_{N} = 17$ K in the orthorhombic structure, a screwlike helimagnetic order develops with an incommensurate wave vector of $q \approx (0.2492, 0, 0)$ at 8 K. Using density functional theory ( $DFT) + U$ calculations, the $J_{1} − J_{2}$ model is leveraged to describe the helimagnetism, where $J_{1} (> 0)$ and $J_{2} (< 0)$ correspond, respectively, to a ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor intrachain interaction. The $DFT + U$ calculations suggest that orthorhombic ${CrI}_{2}$ satisfies conditions that favor formation of helimagnetic order.

Received 31 October 2023
Revised 18 March 2024
Accepted 20 March 2024

DOI:https://doi.org/10.1103/PhysRevB.109.144403

Physics Subject Headings (PhySH)

Magnetic order Magnetic susceptibility

Van der Waals systems

Density functional calculations Neutron diffraction Powder metallurgy Time-of-flight neutron spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

John A. Schneeloch ¹, Shunshun Liu ², Prasanna V. Balachandran ^2,3, Qiang Zhang⁴, and Despina Louca^1,*

¹Department of Physics, University of Virginia, Charlottesville, Virginia 22904, USA
²Department of Materials Science and Engineering, University of Virginia, Charlottesville, Virginia 22904, USA
³Department of Mechanical and Aerospace Engineering, University of Virginia, Charlottesville, Virginia 22904, USA
⁴Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA

^*Corresponding author: louca@virginia.edu

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Vol. 109, Iss. 14 — 1 April 2024

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Figure 1
(a) Crystal structure of orthorhombic ${CrI}_{2}$ , showing ribbon chains along the $a$ axis. (b) One layer of ${CrI}_{2}$ in the $a b$ plane. (c) Both twins of orthorhombic ${CrI}_{2}$ depicted in the $b c$ plane, constructed by A- and B-type stacking, respectively. (d) An illustration that A- and B-type stacking are related by translations along the $b$ axis. (e) Photo of a ${CrI}_{2}$ synthesis attempt, in which the ampoule (with stoichiometric Cr and I) was hung in a vertical tube furnace at 600 $^{\circ} C$ . The boundary between the silvery ( ${CrI}_{3}$ ) and red ( ${CrI}_{2}$ ) powder suggests the influence of a temperature gradient, where ${CrI}_{3}$ formed in a slightly cooler region of the ampoule. The outer diameter of the ampoule was 23 mm. (f) Photo of a 0.5 g melt-grown piece of ${CrI}_{2}$ , in a vial of outer diameter 24 mm. Crystal structures plotted using VESTA [7].
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Figure 2
(a) Single-crystal x-ray diffraction (SCXRD) intensity in the 0KL plane. In addition to the orthorhombic phase peaks, additional peaks from the monoclinic polytype [8] are seen, with two monoclinic peaks indicated by arrows. The gray grid lines and the labels on the axes correspond to the orthorhombic phase. The red lines show the monoclinic-phase ${(H 0 L)}_{M}$ lines for integer $L$ ; $K_{orth} = H_{mono}$ and $L_{orth} = 2 (L_{mono} - ε H_{mono})$ , with $ε \approx 0.43$ . Both phases share the same vertical axis. (b) Lattice parameters plotted vs temperature, normalized to their 100 K values. Open circles denote SCXRD values, measured for $T \geq 100$ K, and dots denote neutron diffraction values, measured for $T \leq 100$ K.
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Figure 3
(a), (b) Neutron diffraction intensity (blue curves) at (a) 8 K and (b) 30 K, compared to calculated intensity from the model described in the text, shaded orange and gray for nuclear and magnetic intensity, respectively. The green curve is the difference between the data and the calculation. The locations of nuclear and magnetic peaks (with $+ / - / \pm$ superscripts omitted) are indicated below the data, colored blue for $(00 L)$ , magenta for $(03 L)$ , red for $(10 L)$ , green for $(13 L)$ , cyan for $(20 L)$ , yellow for $(23 L)$ , and gray for the remaining peaks. Selected peaks are labeled. The asterisk (*) denotes the possible (111) peak of the monoclinic polytype. (c) Neutron diffraction data at 8, 30, 40, and 100 K. No peaks were present above $d = 7$ Å.
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Figure 4
(a) Depiction of the proposed “untwisted” spin structure in the $b c$ plane, i.e., the orientation of the spins before applying the helimagnetic spin rotation along the chain direction. (b), (c) The temperature dependence of (b) the intensity of the magnetic ${(101)}^{-}$ peak [divided by the intensity of (200)] and (c) the magnitude of the modulation vector $(δ, 0, 0)$ . The “X” in (b) denotes zero intensity. (d) Magnetic intensity near selected peaks, obtained from the 11 to 20 K data by subtracting a background of the average intensity from 20 to 29 K. (e) Depiction of helical spin rotation along the $a$ axis for a pair of neighboring ribbon chains within a layer. For visual clarity, these spins are depicted rotating normal to the layers, but the helical plane determined from our data is $b c$ .
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Figure 5
(a) Magnetic susceptibility of a melt-grown ${CrI}_{2}$ crystal with a 1 T magnetic field applied in-plane. (b) The derivative $d (1 / χ) / d T$ for the data in (a). $T_{N} = 17$ K is depicted as a red dashed line.
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Figure 6
Definition of $J_{n}$ of ${CrI}_{2}$ supercell. The dark blue color represents Cr atoms and the cyan color corresponds to I atoms. (a) $J_{1}$ and $J_{2}$ is nearest- and next-nearest-neighbor intrachain Cr-Cr interaction. $J_{3}$ and $J_{5}$ is nearest- and next-nearest-neighbor intralayer interchain Cr-Cr interaction. (b) $J_{4}$ is nearest-neighbor interlayer Cr-Cr interaction.
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Physical Review B

covering condensed matter and materials physics

Helimagnetism in the candidate ferroelectric ${CrI}_{2}$

John A. Schneeloch, Shunshun Liu, Prasanna V. Balachandran, Qiang Zhang, and Despina Louca

Phys. Rev. B 109, 144403 – Published 3 April 2024

Abstract

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Physical Review B

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Helimagnetism in the candidate ferroelectric CrI2

John A. Schneeloch, Shunshun Liu, Prasanna V. Balachandran, Qiang Zhang, and Despina Louca

Phys. Rev. B 109, 144403 – Published 3 April 2024

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Helimagnetism in the candidate ferroelectric ${CrI}_{2}$