Pressurizing the van der Waals magnet FeOCl at low temperatures: Phase transitions and structural evolution

Magnetic order is frustrated on the orthorhombic lattice of van der Waals layered FeOCl. Antiferromagnetic (AFM) order is attained at ambient pressure upon cooling through $T_N=81$ K, due to an accompanying monoclinic lattice distortion lifting the magnetic frustration. Within the paramagnetic state at 293 K, an incommensurate structural modulation appears above a critical pressure of $p_c\approx 15$ GPa, while orthorhombic symmetry is retained. This modulation is related to an optimization of the packing of chlorine atoms within the van der Waals gap. Here, we report four new phases in the pressure-temperature $(p,T)$ phase diagram of FeOCl below room temperature. High-pressure–low-temperature single-crystal x-ray diffraction (SXRD) up to 37.8 GPa reveals that, at 100 K, the AFM transition occurs at $p=7.3\pm 1.3$ GPa. The pressure coefficient of $\mathrm{\Delta }{T}_N/\mathrm{\Delta }p=2.13$ K/GPa explains that FeOCl remains paramagnetic up to the highest measured pressure of 33.3 GPa at 293 K. At 6 and 100 K, the structural modulation appears around $p_c\approx 15$ GPa within the AFM ordered phase with monoclinic symmetry. The monoclinic and triclinic lattice distortions increase with pressure up to $\gamma =90.64{\left(1\right)}^{\circ }$, much larger than the maximum value of $90.1^{\circ }$, that can be reached upon cooling at ambient pressure. The structural evolution provides the geometrical basis for the increase with the pressure of direct $3d-3d$ exchange and superexchange interactions. It is proposed, that a strong monoclinic lattice distortion may be of importance for understanding the properties of single-layer FeOCl materials.

Figure 1

Perspective view of the crystal structure of FeOCl with space group $Pmmn$ at ambient conditions [1]. The unit cell is indicated by solid (black) lines. Distorted $M{\mathrm{Cl}}_2{\mathrm{O}}_4$ octahedra are displayed for the central layer. Drawn with the software vesta [2].

Figure 2

Schematic representation of the $(p,T)$ phase diagram of FeOCl for temperatures below room temperature and pressures up to 37.8 GPa (compare to Table 1). The space group (phase I) and the superspace groups (phases II–VIII) are given at the top of the phase diagram. Data compiled from x-ray diffraction at $T=6$ and 100 K (this study) and at $T=293$ K [42]. Each measured $(p,T)$ combination is indicated by a square marker for SXRD or by a cross for x-ray powder diffraction. No data are available for the hatched pressure ranges. The bar diagrams for $T=6$ and 100 K are used in Figs. 3, and 4 6, and 7.

Figure 3

Lattice parameters as a function of pressure for $T=6$ K (open symbols) and $T=100$ K (filled symbols). (a) Volume of the unit cell; lines represent fits to the data points of 3BM-EOS functions [Eq. (1)]. (b) Lattice parameters $\alpha$ and $\beta$. (c) $\gamma$; solid lines represent fits of Eq. (2) to all data points; the dashed line is a fit to the first five data points above the transition at 100 K (compare Table 3). (d) Normalized lattice parameters $a/a_0$ with $a_{0,6\mathrm{K}}=3.7650\left(4\right)$ and $a_{0,100\mathrm{K}}=3.7645\left(1\right)$ Å. (e) $b/b_0$ with $b_{0,6\mathrm{K}}=3.2959\left(2\right)$ and $b_{0,100\mathrm{K}}=3.2940\left(2\right)$ Å. (f) $c/c_0$, with $c_{0,6\mathrm{K}}=7.809\left(9\right)$ and $c_{0,100\mathrm{K}}=7.882\left(9\right)$ Å. Error bars are not shown if they are smaller than the size of the symbol. The upper bar indicates the phase diagram at $T=100$ K; the lower bar is the phase diagram at $T=6$ K (compare to Fig. 2).

Figure 4

Components of the modulation wave vector, ${\mathbf{q}}_X=({\sigma }_1,{\sigma }_2,{\sigma }_3)$, as a function of pressure for $p>14$ GPa at $T=6$ K (open symbols) and $14<p<39$ GPa at $T=100$ K (filled symbols). (a) ${\sigma }_1$ with dashed lines at the rational values $1/5$ and $1/4$. (b) ${\sigma }_2$ with a dashed line at 0. (c) ${\sigma }_3$ with a dashed line at $1/2$. Error bars are not shown if they are smaller than the size of the symbol. The upper bar indicates the phase diagram at $T=100$ K; the lower bar is the phase diagram at $T=6$ K (compare to Fig. 2).

Figure 5

Projection of one layer FeOCl onto the ($\mathbf{a},\mathbf{b}$) plane. The unit cell is outlined in the lower left quadrant. Fe atom chains parallel $\mathbf{b}$ are located above ($+c$) and below ($-c$) the plane of projection. Exchange parameters are defined according to Zhang et al. [64]. $J_1$ is between Fe atoms of neighboring ribbons (“diagonal,” $\mathbf{a}\mathbf{\text{and}}\mathbf{b}$ directions). $J_2$ is between Fe atoms separated by $\mathbf{b}$. And $J_3$ is between Fe atoms separated by $\mathbf{a}$.

Figure 6

Pressure dependence of selected interatomic distances and bond angles for the crystal structures at [(a), (c), (d), and (f)] $T=100$ and [(b), (c), (e), and (f)] 6 K. Vertically placed gray ribbons reflect the range of values as present in the structurally modulated phases, with the superimposed symbol indicating the average value. [(a) and (b)] Distances Fe–O and Fe–Cl within the ribbons FeOCl along $\mathbf{b}$ parallel to the $\mathbf{b},\mathbf{c}$ plane, and distance Fe–O into the $\mathbf{a}$ direction. (c) Distance Fe–Fe along $\mathbf{a}$; this distance is equal to $a$ in the basic structure. [(d) and (e)] Bond angle Fe–O–Fe and Fe–Cl–Fe within the ribbons FeOCl along $\mathbf{b}$ parallel to the $\mathbf{b},\mathbf{c}$ plane, and bond angle Fe–O–Fe with the Fe atoms separated by the $\mathbf{a}$ lattice translation in the basic structure. (f) Distance Fe–Fe between neighboring FeOCl ribbons (diagonal $\mathbf{a},\mathbf{b}$ direction). The shortest distance is shown of two nearly equal Fe–Fe distances (monoclinic symmetry) or of four Fe–Fe distances (triclinic symmetry). Differences between these distances are smaller than 0.021 Å (see Fig. S5 in Ref. [50]). Error bars are not shown if they are smaller than the size of the symbol. The upper bar indicates the phase diagram at $T=100$ K; the lower bar is the phase diagram at $T=6$ K (compare to Fig. 2).

Figure 7

Shortest interlayer $\mathrm{Cl}\cdots \mathrm{Cl}$ distance at $T=6$ K (open symbols) and at $T=100$ K (filled symbols). Vertically placed gray ribbons reflect the range of values as present in the structurally modulated phases, with the superimposed symbol indicating the average value. The dashed line indicates 3 Å. The shortest distances are shown of two nearly equal $\mathrm{Cl}\cdots \mathrm{Cl}$ distances (for monoclinic symmetry) or of four $\mathrm{Cl}\cdots \mathrm{Cl}$ distances (for triclinic symmetry). Differences between these distances go up to 0.02 Å in phase III and up to 0.04 Å in phases IV and V (see Fig. S5 in Ref. [50]). Error bars are not shown if they are smaller than the size of the symbol. The upper bar indicates the phase diagram at $T=100$ K; the lower bar is the phase diagram at $T=6$ K (compare to Fig. 2).

Figure 8

Projection of the $4\mathbf{a}\times 2\mathbf{c}$ approximate superstructure at $T=100$ K and $p=23.0\left(3\right)$ GPa (phase IV). (a) Cl atoms omitted, showing the Fe-O distances (Å) across the van der Waals gap, and (b) with the Cl atoms shown, revealing their large modulation amplitude along $\mathbf{a}$.