Observation of a spin-density wave node on antiferromagnetic Cr(110) islands

We have performed a detailed study of the evolution of the charge-density wave (CDW) and spin-density wave (SDW) on the surface of nanoscale Cr islands grown on W(110). Using low-temperature scanning tunneling microscopy (STM), we find a striking nonmonotonic thickness dependence of the CDW wavelength at 50 K. As the local island thickness $\Theta$ decreases from about 50 to 5.2 nm, the CDW wavelength gradually increases from the bulk value by approximately 30$\%$. We find a gap without any CDW at coverages ${\Theta }_{\mathrm{gap}}$ between 5.2 and 3.7 nm. Spin-resolved STM data reveal that within this CDW gap the SDW modulation also disappears on the Cr island surface. At $\Theta <3.7$ nm the CDW reappears. This unusual behavior of CDW and SDW in Cr nanoislands can be understood by a reorientation of the SDW wave vector Q which is potentially driven by the pinning of the SDW node at the island surface at ${\Theta }_{\mathrm{gap}}$.

Figure 1

(a) STM image of Cr islands grown on W(110). Scan parameters are $U=1.0$ V, $I=30$ pA. (b) Line profile taken along the black line across the right island in panel (a).

Figure 2

(a) Derivative ($dz/dx$) map of a topographic STM image showing the moiré pattern on top of a Cr island (scan parameters: $U=1.0$ V, $I=30$ pA). High-resolution images of the moiré pattern measured at local island thicknesses of (b) ${\Theta }_{\mathrm{loc}}=0.66$ nm and (c) ${\Theta }_{\mathrm{loc}}=2.63$ nm. These images were analyzed by taking 1D-FFT along the [(d) and (e)] perpendicular and the [(f) and (g)] horizontal direction. Panels (h) and (i) show line sections taken along the [1$\overline{1}$0] and along the [001] direction, respectively.

Figure 3

(a) Overall morphology of a large Cr island at 50 K. (b) Higher-magnification image of the island surface. Clearly, periodic stripes running along the [001] direction are present in the upper and the lower part of the image, corresponding to a CDW propagating in the [1$\overline{1}$0] direction. However, the CDW is absent in the central part (called the CDW gap. Scan parameters are $U=1.0$ V, $I=30$ pA. (c) Zoomed-in image taken inside the rectangle indicated in Panel (b). While some dark stripes are truncated, some strips connect to each others. (d) Topography with atomic resolution taken inside the CDW gap region. Scan parameters are $U=10$ mV, $I=1$ nA.

Figure 4

(a) Morphology of Cr island with thickness varying from ${\Theta }_{\mathrm{loc}}=(3.6\pm 0.2)$ nm in the lower part up to ${\Theta }_{\mathrm{loc}}=(8.0\pm 0.2)$ nm in the upper part. Scan parameters are $U=1.0$ V, $I=30$ pA. (b) Image taken on top of the island shown in panel (a) showing the wavefronts of the CDW and the CDW gap at the bottom (see area surrounded by a hatched line), Scan parameters are $U=20$ mV, $I=100$ pA. [(c) and (d)] High-resolution images taken within the framed boxes at the top and the bottom of panel (b), respectively. [(e) and (f)] Corresponding FFT analysis. (g) Comparison of line profiles reveals that the CDW wavelength increases for thinner Cr island.

Figure 5

(a) Thickness-dependent CDW wavelength (black squares) and moiré periodicity along the [001] (blue triangles) and [1$\overline{1}$0] directions (red circles), respectively. The black dashed line indicates the bulk value of CDW periodicity along the [1$\overline{1}$0] direction (${\lambda }_{\mathrm{CDW}}\approx 4.2$ nm). (b) Zoomed-in image of panel (a) to show the CDW gap region. Red and blue dashed lines are the moiré periodicities expected for Cr bulk lattice constants $a_{\left[001\right]}\approx 2.88$ Å and $a_{\left[1\overline{1}0\right]}\approx 4.07$ Å, respectively.

Figure 6

(a) Tip characterization of an Fe-coated probe tip (scan parameters are $U=150$ mV, $I=1$ nA) on a Mn monolayer on W(110) which exhibits a cycloidal AFM spin structure. As revealed by the line section (lower panel), the row-wise magnetic corrugation coincides with the maximum of the spin-orbit contrast (SOC) (periodicity 6 nm), indicating in-plane sensitivity. (b) Differentiated constant-current image image ($dz/dx$) of the boundary region of the CDW gap. measured with the same in-plane-sensitive tip characterized in panel (a) ($U=10$ mV, $I=6$ nA). (c) FFT-transform of panel (b) showing the pair of satellites characteristic for the SDW. (d) Plot of the FFT intensity associated with the CDW (red data points) and the SDW (black) as measured within the corresponding segments in panel (b).

Figure 7

(a) SP-STM measurement on 1 AL Mn/W(110) performed with Ni tip. Maximum magnetic contrast is observed near the minimum of the SOC, indicating out-of-plane sensitivity ($U=8$ mV, $I=5$ nA). (b) Differentiated constant-current image image ($dz/dx$) of the boundary region of the CDW gap measured with the same out-of-plane-sensitive tip characterized in panel (a) ($U=10$ mV, $I=6$ nA). (c) FFT-transform of panel (b) showing the pair of satellites characteristic for the SDW.

Figure 8

STM images taken at various temperatures show the evolution in the proximity between the CDW and the CDW gap (scan parameters: $U=1$ V, $I=150$ pA). Black circles mark the same impurity in different images. The CDW gap broadens as the temperature is increased from (a) $T=48$ K to (b) $T=106$ K. In addition, the CDW rearranges and occasionally forms closed loops (arrow). (c) Cooling the sample back down to 51 K almost recovers the surface distribution of the CDW and the CDW gap. (d) Further cooling to $T=35$ K has little effect on the CDW.

Figure 9

Models of SDW in Cr(110) islands. (a) Cartoon of spin structure of SDW with node at the Cr(110) surface at SDW gap region. (b) Model of apparent thickness dependence of SDW wavelength by reorientation transition of SDW (see text for details).