Magnetic structure and magnon dynamics of the quasi-two-dimensional antiferromagnet ${\mathrm{FePS}}_3$

Neutron scattering from single crystals has been used to determine the magnetic structure and magnon dynamics of ${\text{FePS}}_3$, an $S=2$ Ising-like quasi-two-dimensional antiferromagnet with a honeycomb lattice. The magnetic structure has been confirmed to have a magnetic propagation vector of ${\mathbf{k}}_M=\left[01\frac{1}{2}\right]$ and the moments are collinear with the normal to the $ab$ planes. The magnon data could be modeled using a Heisenberg Hamiltonian with a single-ion anisotropy. Magnetic interactions up to the third in-plane nearest neighbor needed to be included for a suitable fit. The best fit parameters for the in-plane exchange interactions were $J_1=1.46, J_2=-0.04$, and $J_3=-0.96$ meV. The single-ion anisotropy is large, $\mathrm{\Delta }=2.66$ meV, explaining the Ising-like behavior of the magnetism in the compound. The interlayer exchange is very small, $J^{\prime }=-0.0073$ meV, proving that ${\text{FePS}}_3$ is a very good approximation to a two-dimensional magnet.

Figure 1

Neutron elastic scattering scans along $l$ for three fixed $\left(hk\right)$, measured using IN3. The successive $\left(hk\right)$ correspond to ${60}^{\circ }$ rotations about c${}^{*}$. All the data were measured at 2 K.

Figure 2

The observed versus calculated crystal and magnetic structure factors for ${\text{FePS}}_3$ at 2 K from the refinement of neutron scattering data from D10. The crystal structure refinement was performed first, and the resulting atomic coordinates and thermal factors were fixed in the refinement of the magnetic data.

Figure 3

The magnetic structure for ${\text{FePS}}_3$, shown for two orientations. The moments all have a magnitude of $4.52\pm 0.05{\mu }_B$ and are color-coded to differentiate between the two moment orientations. The figure was created using the VESTA program [31].

Figure 4

The monoclinic unit cell (solid lines), and one of the four interlocking primitive lattices (dashed lines) used to construct the magnetic structure for the calculation of $S\left(\mathbf{Q},\omega \right)$. The red spheres indicate those ${\mathrm{Fe}}^{2+}$ ions with moments up, and the blue indicate those with moments down. The lattice parameters for the magnetic unit cell are approximately $a_{\text{mag}}=a, b_{\text{mag}}=2a, c_{\text{mag}}=\frac{a}{3}\sqrt{7+{tan}^2\beta }, {\alpha }_{\text{mag}}=126.7^{\circ }, {\beta }_{\text{mag}}=83.1^{\circ }, {\gamma }_{\text{mag}}={120}^{\circ }$, with ${\mathbf{a}}_{\text{mag}}=\mathbf{a}$.

Figure 5

View down the ${\mathbf{c}}^{☆}$ axis for ${\text{FePS}}_3$, showing the inter- and intraplanar exchange parameters. The black circles represent the ${\mathrm{Fe}}^{2+}$ positions in the $ab$ basal plane, while the gray circles are the ${\mathrm{Fe}}^{2+}$ positions in the plane displaced one lattice unit along $\mathbf{c}$.

Figure 6

Constant-Q scans at $\left(01l\right)$ using IN20 (left) and $\left(02l\right)$ using IN8 (right) for various values of $l$. Fits to the data of $S_{\text{mag}}\left(\mathbf{Q},\omega \right)$ convoluted with the instrument resolution are shown as dashed lines. The spectra are shifted vertically for clarity.

Figure 7

The magnon energies as a function of $l$. The data at $\mathrm{\Delta }E\sim 15.8$ meV result from fitting the magnons along $\left(01l\right)$. Note that the magnetic Bragg peaks are found at $\left(01\overline{\frac{3}{2}}\right)$ and $\left(01\overline{\frac{5}{2}}\right)$. The data at $\mathrm{\Delta }E\sim 40.3$ meV result from the magnons along $\left(02l\right)$.

Figure 8

Neutron inelastic data from ${\text{FePS}}_3$, measured using time-of-flight spectroscopy on MERLIN at 5K, for various $\left(\mathbf{Q},\mathrm{\Delta }E\right)$ slices through reciprocal space. Panels (a)–(c) show the experimental data for slices perpendicular to the nominal ${\mathbf{b}}^{*}$ axis, centered at $k=\frac{1}{2}$, 1, and $\frac{3}{2}$ respectively. Panel (d) shows data for a slice along the nominal ${\mathbf{b}}^{*}$ axis. Panels (e)–(h) show corresponding calculations for $S_{\text{mag}}\left(\mathbf{Q},\omega \right)$. The magnon energies for the two ${120}^{\circ }$ twinned domains are shown as dashed white lines.

Figure 9

Neutron spin-flip scattering from powdered ${\text{FePS}}_3$ at 2 K using D7. The neutron polarization was normal to the scattering plane. The scattering is due to a combination of two-thirds of the nuclear spin-incoherent cross-section and, in the absence of preferred orientation, one half of the magnetic cross-section.

Figure 10

Schematic showing the relationship between the monoclinic and orthohexagonal unit cells for ${\text{FePS}}_3$. The positions of the ${\mathrm{Fe}}^{2+}$ positions are shown as spheres. Dark gray spheres represent ions that are in the hexagonal unit cell, while light gray spheres are only in the monoclinic unit cell.

Figure 11

(a) Schematic showing the $ab$ plane with the three twinned crystalline domains for the monoclinic cell. The points mark the positions for the ${\mathrm{Fe}}^{2+}$ ions. (b) The magnetic structure with an in-plane propagation vector ${\mathbf{k}}_M=\left(01\right)$ is drawn with respect to domain $R1$. Open circles represent a moment out of the page and closed circles represent moments into the page. The other two domains are also shown.