Antiferromagnetic-ferromagnetic homostructures with Dirac magnons in the van der Waals magnet ${\mathrm{CrI}}_3$

The Dirac magnon system ${\mathrm{CrI}}_3$ with a honeycomb lattice is a potential host of topological edge magnons. It ideally orders ferromagnetically (FM) $(T_c=61 \mathrm{K})$ on cooling from a monoclinic (M) to a rhombohedral (R) phase, but antiferromagnetic (AFM) order has been detected in nanometer thin flakes, attributed to M-type layer stacking. There remains confusion, however, as to the extent to which such behavior is present in bulk samples. Using a powder sample in which the sliding transition to the R phase was largely inhibited (2:1 M:R ratio), clear evidence for M-type AFM order $(T_N\sim 50 \mathrm{K})$ coexisting with R-type FM order is observed in the bulk. From inelastic neutron scattering, a lower magnon energy is observed compared to the R phase, consistent with smaller interlayer interactions expected in the M phase. While a gap at the Dirac points has been reported in the R phase, the gap is clearly observed even when the majority is M type, as in our sample, suggesting that the same nontrivial magnon topology of the R phase is present in the M phase as well.

Figure 1

(a) Crystal structure of the $R\overline{3}$ phase of ${\mathrm{CrI}}_3$. (b) A schematic showing how the spin direction would change, layer by layer, in M- and R-type stacking, with spin flips accompanying M-type stacking. (c), (d) Illustration of (c) M-type and (d) R-type layer stacking. The honeycomb lattice represents the placement of the ${\mathrm{Cr}}^{3+}$ ions, with the red lattice above the black showing one possible stacking option; the displacements for the full set of stacking options are shown as arrows.

Figure 2

(a) Data at 5 K (black points), along with curves of simulated intensity for the $R\overline{3}$ and $C2/m{\mathrm{CrI}}_3$ phases and the ${\mathrm{Cr}}_2{\mathrm{O}}_3$ impurity phase, both for the nuclear (“str”) intensity alone and with the magnetic intensity (in the M-AFM model) included. The region of focus ($2.45\le d\le 3.9$ Å) is shaded. (b), (c) Elastic intensity within (c) 70 to 200 K and (d) 200 to 275 K, with a linear background subtracted to account for its temperature dependence. Error bars in (a) are often smaller than the marker size; error bars are omitted in (b) and (c) for clarity, but uncertainty is commensurate with scatter.

Figure 3

(a) Elastic scattering intensity vs layer spacing $d$. A linear background was subtracted for each temperature. (b) Intensity with the 70 K data subtracted for $T=5$, 50, and 65 K, to show the magnetic contribution. Error bars are omitted in (a) and (b) for clarity, but uncertainty is commensurate with scatter. [(c)–(f)] Integrated intensity of the raw data within the regions labeled in (b), plotted vs temperature; red dashed lines show 50 and 60 K. (g) Fitted position vs temperature of the peak in (b) near $d=3.43$ Å.

Figure 4

Simulation of the (a) nuclear diffuse scattering intensity, and magnetic diffuse scattering intensity within the (b) M-AFM and (c) M-FM models for various percentages of M-type stacking.

Figure 5

(a) Inelastic neutron scattering intensity (Bose-factor corrected) as a function of energy transfer for temperatures taken on warming from 5 to 275 K along the low-$Q$ trajectory of VISION. (b) Temperature dependence of inelastic intensity near 10 and 17 meV, averaged within $\pm 0.5$ meV. The dashed line indicates 60 K. (c) Inelastic intensity (Bose-factor corrected) plotted vs energy transfer with averaging over two sets of data: “low T” (5, 8, 11, and 20 K) and “high T” (70, 75, 80, and 100 K). The dashed line is a polynomial background fit to the high-T data. (d) To account for phonon peaks, the high-T data (with the fitted background subtracted) were subtracted from the low-T data and plotted as the black points. Also shown are curves of simulated intensity for the “$R\overline{3}$, FM” model (calculated from the “J-DM” parameters in Ref. [41]) and for the “$C2/m$ AFM” model (same as “$R\overline{3}$, FM”, except with summed interlayer interaction of $+0.073$ meV instead of $-0.59$ meV [41, 43]). Error bars are omitted for (a), but uncertainty is commensurate with scatter; error bars are smaller than the marker size for [(b)–(d)].

Figure 6

(a) Magnetization vs temperature for a pressed pellet of ${\mathrm{CrI}}_3$ on warming (ZFC) and cooling (FC), taken at ${\mu }_{0}H=0.01$ T. (b) Derivative $dM/dT$ of the data in (a). (c) Magnetization-field hysteresis loops collected at several temperatures on a pellet of pressed ${\mathrm{CrI}}_3$ powder. A hysteresis is present at 4 and 40 K, but is gone by 54 K. (d) The coercive field ${\mu }_0{H}_c$ (the field at which $M=0$) plotted as a function of temperature, extracted from magnetization-field hysteresis loops. The hysteresis disappears around 52 K. Error bars are omitted for clarity, but uncertainty is assumed to be commensurate with scatter.