Structure of Cr monolayer on Ag(001): A buried two-dimensional $c(2\times 2)$ antiferromagnet

The growth, morphology, and magnetic structure of ultrathin Cr films grown on a Ag(001) substrate are studied using low-energy electron diffraction (LEED), angle-resolved photoemission spectroscopy (ARPES), and ab initio density functional theory (DFT) calculations. The presence and temperature dependence of $c(2\times 2)$ half-order spots in the LEED pattern, for low electron energies, along with the presence of characteristic Cr $3d$ bands in the ARPES spectra, confirm the existence of antiferromagnetic ordering for the Cr monolayer case. Our experiments are also consistent with the presence of a $p(1\times 1)$ Ag overlayer on top of the Cr layer, suggesting the existence of a Ag/Cr/Ag(001) sandwich structure at the surface. Our DFT calculations confirm that this is the most favored geometric and magnetic structure of the system. The Cr layer is found to retain a “two-dimensional” character with enhanced Cr $3d$ magnetic moments, despite being buried below a Ag monolayer, due to the absence of significant hybridization between Cr $3d$ and Ag $4d$ electronic states. The coverage dependence of the magnetic ordering indicates a maximum ordering above the expected monolayer coverage, possibly due to intermixing between Ag and Cr atoms in the overlayer.

Figure 1

(a) LEED pattern for 1 ML of Cr deposited on Ag(001) at RT, for a primary electron energy $E_p$ of 40 eV, indicating sharp $p(1\times 1)$ spots. The surface Brillouin zone and corresponding high-symmetry directions are marked. (b) LEED pattern for $E_p=23$ eV at RT, showing the absence of half-order spots. (c) LEED pattern for 1 ML of Cr deposited on Ag(001) at 428 K ($E_p=40$ eV), showing weak $c(2\times 2)$ half-order spots (enclosed in white circles), along with integer-order spots. (d) For $E_p=23$ eV, clear half-order spots are shown. (e) Line profile along the half-order spots ($-1/2$, 1/2) and (1/2, 1/2) [boxed region in (d)]. (f) Average intensity variation of the half-order spots at 23 eV $\left(E_p\right)$, as a function of the sample temperature, confirming AFM order with a transition temperature of $\sim 450$ K.

Figure 2

(a) Average intensity of $c(2\times 2)$ half-order spots (for $E_p=23\text{eV}$) measured at RT from Cr deposited on Ag(001), for a deposition temperature of 428 K, as a function of the film coverage. Error bars indicate intensity variations for different half-order spots. (b) ARPES spectra at the $\overline{\mathrm{M}}$ point measured at RT using He $I_{\alpha }$, showing the emergence of AFM Cr $3d$ bands as a function of Cr coverage. (c) Variation of the extracted Cr $3d$ band intensity from (b), for different Cr coverages, with a deposition temperature of 428 K.

Figure 3

ARPES spectra at the $\overline{\mathrm{M}}$ point in the surface Brillouin zone, over a wide binding energy range, using He $I_{\alpha }$, for the cases of bare Ag (001), 1 ML of Cr deposited at 428 K, and 1 ML of Cr deposited at RT. See text for details.

Figure 4

Geometry of the energetically most favored structure, $c(2\times 2)$ AFM 1Ag/Cr/Ag(001): (a) top and (b) side views of the system. Light-gray and dark-gray (green) spheres represent Ag and Cr atoms, respectively. The (red) arrows indicate the directions of spins. Note that in the absence of spin-orbit interactions, the in-plane and out-of-plane spin directions are equivalent. (c) ${\Delta }_{ij}$, the percentage change in interlayer separations, for the first few surface layers. See text for the definition of ${\Delta }_{ij}$ and (b) for the convention used in numbering layers.

Figure 5

Theoretically calculated results for the spin-polarized projected density of states (PDOS) of 1Ag/Cr/Ag(001) in the $c(2\times 2)$ AFM configuration. Dashed (red) line, PDOS from first-layer Ag $4d$ states; solid (green) line, PDOS from second-layer Cr $3d$ states; and shaded (gray) area, PDOS from third layer Ag $4d$ states.