Spin wave spectra of single crystal ${\mathrm{CoPS}}_{3}$

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Spin wave spectra of single crystal ${CoPS}_{3}$

A. R. Wildes, B. Fåk, U. B. Hansen, M. Enderle, J. R. Stewart, L. Testa, H. M. Rønnow, C. Kim, and Je-Geun Park

Phys. Rev. B 107, 054438 – Published 27 February 2023

Abstract

The spin waves in single crystals of the layered van der Waals antiferromagnet ${CoPS}_{3}$ have been measured using inelastic neutron scattering. The data show four distinct spin wave branches with large ( $≳ 14$ meV) energy gaps at the Brillouin zone center indicating significant anisotropy. The data were modeled using linear spin wave theory derived from a Heisenberg Hamiltonian. Exchange interactions up to the third nearest-neighbor in the layered planes were required to fit the data with ferromagnetic $J_{1} = - 1.37$ meV between first neighbors, antiferromagnetic $J_{3} = 3.0$ meV between third neighbors, and a very small $J_{2} = 0.09$ meV between second neighbors. A biaxial single-ion anisotropy was required, with a collinear term $D^{x} = - 0.77$ meV for the axis parallel to the aligned moment direction and a coplanar term $D^{z} = 6.07$ meV for an axis approximately normal to the layered crystal planes.

Received 9 December 2022
Accepted 9 February 2023

DOI:https://doi.org/10.1103/PhysRevB.107.054438

Physics Subject Headings (PhySH)

Magnetism Spin dynamics

2-dimensional systems Van der Waals systems

Inelastic neutron scattering

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

A. R. Wildes ^*, B. Fåk, U. B. Hansen , and M. Enderle

Institut Laue-Langevin, 71 avenue des Martyrs CS 20156, 38042 Grenoble Cedex 9, France

J. R. Stewart

ISIS Pulsed Neutron and Muon Source, STFC Rutherford Appleton Laboratory, Harwell Campus, Didcot OX11 0QX, United Kingdom

L. Testa and H. M. Rønnow

Laboratory for Quantum Magnetism, Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland

C. Kim and Je-Geun Park

Center for Quantum Materials, Seoul National University, Seoul 08826, Korea; Center for Correlated Electron Systems, Institute for Basic Science, Seoul 08826, Korea; and Department of Physics and Astronomy, Seoul National University, Seoul 08826, Korea

^*wildes@ill.fr

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Vol. 107, Iss. 5 — 1 February 2023

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Figure 1
The magnetic structure of ${CoPS}_{3}$ [12], viewed (a) along the $c^{★}$ axis, (b) isometrically, and (c) along the $b$ axis. The magnetic exchanges between first, second, and third nearest intraplanar neighbors are labeled in (a) as $J_{1}, J_{2}$ , and $J_{3}$ respectively, and the exchanges between interplanar nearest neighbors are labeled in (b) as $J^{'}$ . The vesta software package was used to create the figure [19]. (d) The Brillouin zone for the magnetic structure of ${CoPS}_{3}$ . Selected high-symmetry points are indicated, corresponding to the magnetic space group $P_{C} 2_{1} / m$ (#11.57) as defined in the Bilbao Crystallographic Library [20, 21, 22]. (e) An $(a^{★}, b^{★})$ plane for ${CoPS}_{3}$ . Brillouin zone boundaries are shown for the crystallographic and magnetic lattices as black and red lines, respectively. Nuclear Brillouin zone centers are shown as black filled circles. Strong magnetic Bragg peaks appear at the red open squares. Selected $hk$ Miller indices and high-symmetry points are indicated.
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Figure 2
Neutron three-axis spectroscopy data and simulation for the magnetic excitations in ${CoPS}_{3}$ at 210 (left column) and $\frac{5}{2} 10$ (right column), corresponding to $Γ$ and Y points respectively. (a) and (b) show measurements from IN8, each with data at 2 K and 150 K. The data have been divided by the temperature factor. The differences between the scattering at the two temperatures are shown in (c) and (d), and the peak positions have been determined by fitting Gaussian functions. (e) - (h) show the separated contributions to the scattering determined from IN20 neutron polarization analysis data using Eq. (1). The nuclear coherent and isotopic incoherent, $N u c$ , and nuclear spin incoherent, $I n c$ , contributions are shown in (e) and (f), and the directional components of the magnetic fluctuations, $M_{Y}$ and $M_{Z}$ , are shown in (g) and (h). SpinW calculations of the modeled spin waves are shown in (i) and (j). $S^{⊥}$ refers to the components of the spin fluctuations that are perpendicular to the neutron scattering vector, $Q$ . Instrument resolution has not been included in the calculations, and the magnons have been broadened by an arbitrary width of 1 meV.
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Figure 3
Neutron inelastic scattering data from MAPS for slices parallel to the $c^{★}$ axis, collected at 5 K. Equivalent reciprocal lattice points were shown to be qualitatively the same and the data have been combined for better statistics. The trajectories have fixed ${h k}$ of (a) ${12}$ , (b) ${11},$ and ( $c) {10}$ , thus incorporating Brillouin zone centres. The slice widths are $\pm 0.1$ in both $h$ and $k$ .
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Figure 4
Neutron inelastic scattering data from MAPS for slices parallel to the $a^{★}$ axis, collected at 5 K. Data and models have been integrated for $0 \leq l \leq 2$ . Slices centered at $\pm k$ were shown to be equivalent and have been combined for statistics with a slice width of $| k | \pm 0.1$ . Slices along (a) $h 0$ , (c) $h | \frac{1}{2} |$ , and (e) $h | 1 |$ are shown with corresponding calculations in (b), (d), and (f).
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Figure 5
Neutron inelastic scattering data from MAPS for slices parallel to the $b^{★}$ axis, collected at 5 K. Data and models have been integrated for $0 \leq l \leq 2$ . Slices centered at $\pm h$ were shown to be equivalent and have been combined for statistics with a slice width of $| h | \pm 0.1$ . Slices along (a) $0 k$ , (c) $| \frac{1}{2} | k$ , and (e) $| 1 | k$ are shown with corresponding calculations in (b), (d), and (f).
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Figure 6
The spin wave dispersions calculated with the fitted exchange parameters for ${CoPS}_{3}$ . The red lines show the dispersion using the parameters from Kim et al. [23], derived from fitting neutron data from powders using Eq. (3), while the black lines show the results from the current work using Eq. (2). The data points at the high-symmetry positions correspond to an average of the fitted spin wave energies for each of the equivalent eigenvalues listed in Table 2.
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Physical Review B

covering condensed matter and materials physics

Spin wave spectra of single crystal ${CoPS}_{3}$

A. R. Wildes, B. Fåk, U. B. Hansen, M. Enderle, J. R. Stewart, L. Testa, H. M. Rønnow, C. Kim, and Je-Geun Park

Phys. Rev. B 107, 054438 – Published 27 February 2023

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Physical Review B

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Spin wave spectra of single crystal CoPS3

A. R. Wildes, B. Fåk, U. B. Hansen, M. Enderle, J. R. Stewart, L. Testa, H. M. Rønnow, C. Kim, and Je-Geun Park

Phys. Rev. B 107, 054438 – Published 27 February 2023

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Spin wave spectra of single crystal ${CoPS}_{3}$