Structural and magnetic properties of ${\mathrm{FeMn}}_x$ chains $\left(x=1–6\right)$ supported on ${\mathrm{Cu}}_2\mathrm{N}/\mathrm{Cu}$ (100)

Heterogeneous atomic magnetic chains are built by atom manipulation on a ${\mathrm{Cu}}_2\mathrm{N}/\mathrm{Cu}$ (100) substrate. Their magnetic properties are studied and rationalized by a combined scanning tunneling microscopy (STM) and density functional theory (DFT) work completed by model Hamiltonian studies. The chains are built using Fe and Mn atoms ontop of the Cu atoms along the N rows of the ${\mathrm{Cu}}_2\mathrm{N}$ surface. Here, we present results for ${\mathrm{FeMn}}_x$ chains $\left(x=1–6\right)$ emphasizing the evolution of the geometrical, electronic, and magnetic properties with chain size. By fitting our results to a Heisenberg Hamiltonian we have studied the exchange-coupling matrix elements $J$ for different chains. For the shorter chains, $x\le 2$, we have included spin-orbit effects in the DFT calculations, extracting the magnetic anisotropy energy. Our results are also fitted to a simple anisotropic spin Hamiltonian and we have extracted values for the longitudinal-anisotropy $D$ and transversal-anisotropy $E$ constants. These parameters together with the values for $J$ allow us to compute the magnetic excitation energies of the system and to compare them with the experimental data.

Figure 1

Constant current STM image of a ${\mathrm{FeMn}}_3$ chain assembled on a ${\mathrm{Cu}}_2\mathrm{N}$ layer and atomic scheme (on the right of the figure) that can be inferred from the position of the upper-right Fe atom and manipulation with the STM tip. The STM image was scanned at 10 mV and 100 pA. The scanned area is $6\times 6{\mathrm{nm}}^2$. The transition-metal atoms were always placed on top of a Cu atom between two nitrogen atoms. The topography was processed with wsxm [25].

Figure 2

Top (top panel) and side (bottom panel) views of the relaxed geometry of ${\mathrm{FeMn}}_2$. We show Fe atoms in red; Mn atoms in green; N atoms in blue; Cu atoms in the first layer in brown; the rest of Cu atoms in pink. Blue lines delimit the unit cell used in the calculations. The vacuum side of the unit cell and the three bottom Cu layers have been removed for pictorial reasons.

Figure 3

Atomization energy, $E_{\mathrm{at}}$ from Eq. (3), (black x's) and the gain in energy by adding one more Mn atom to the chain, ${\mathrm{\Delta }}_x{E}_F$ from Eq. (4), (red stars). As we can see, atomization of the chain becomes less difficult as the chain becomes longer, and correspondingly, adding one more atom does not reduce the total energy as much for longer chains. These values reveal an increasing destabilization of the chain as it size increases. The dotted lines are a guide for the eye.

Figure 4

Spin density of the ${\mathrm{FeMn}}_3$ chain. Red (yellow) indicates majority (minority) spin areas. The chosen isovalue is $0.01\text{eV}/{\AA }^3$. The color code of the atoms is the same of Fig. 2.

Figure 5

Evolution of $J_{12}$ for FeMn with respect to the variation of $U_{\text{eff}}$. We have changed one of the values of $U$ while keeping constant the other one.

Figure 6

Inelastic electron tunneling spectra (IETS) of different ${\mathrm{FeMn}}_x$ chains obtained by measuring the differential conductance with the STM tip placed on a central Mn atom.

Figure 7

Inelastic electron tunneling spectra (IETS) of ${\mathrm{FeMn}}_3$: (a) experimental and (b) two computed solution using our calculated spin-chain parameters for ${(U-J)}_{\text{Mn}}=4$ eV and ${(U-J)}_{\text{Fe}}=1$ eV (blue) or scaling the computed exchange coupling by a 1.6 factor as found for FeMn with ${(U-J)}_{\text{Mn}}=3$ eV and ${(U-J)}_{\text{Fe}}=1$ eV (green), Sec. 4c. The STM tip is placed on the edge Mn atom.

Figure 8

(a) Inelastic electron tunneling spectra (IETS) for ${\mathrm{FeMn}}_3$ with a magnetic field applied perpendicular to the surface increasing until 9 T. (b) The behavior of the different magnetic states (black dots) obtained from the experimental figure follows the Zeeman trend expected for a Zeeman term with the atomic $g$ factors $(g_{\mathrm{Fe}}=2.1$ and $g_{\mathrm{Mn}}=1.9$ from Ref. [22]).