Magnetically Hindered Chain Formation in Transition-Metal Break Junctions

Based on first-principles calculations, we demonstrate that magnetism impedes the formation of long chains in break junctions. We find a distinct softening of the binding energy of atomic chains due to the creation of magnetic moments that crucially reduces the probability of successful chain formation. Thereby, we are able to explain the long standing puzzle why most of the transition metals do not assemble as long chains in break junctions and thus provide indirect evidence that in general suspended atomic chains in transition-metal break junctions are magnetic.

Figure 1

Calculated MW energy $\mathcal{E}(d)$ (circles) as a function of interatomic distance $d$ (throughout the Letter given in $\mathrm{a}.\mathrm{u}.=0.0529\mathrm{nm}$) for both nonmagnetic (NM) (black) and magnetic ($\mathrm{M}$) state (green or gray) are shown for (a) Fe and (b) W. The Morse fit (lines) provides a universal fit to these points well below the required accuracy of about 100 meV for chemical bonding and can be characterized by the equilibrium interatomic distance $d_0$ and the inflection point $\widehat{d}$. $\mathcal{E}(d)$ and the magnetic moments $M$ in (c) and (d) correspond to the FM and AFM ground state for Fe and W, respectively.

Figure 2

(a) Cohesion energy difference $\Delta E_{\mathrm{Lead}}$, (b) difference $\widehat{d}-d_0=\ln 2/\gamma$ and (c) break force $F_0$ for nonmagnetic (marked as NM, black squares) and magnetic (marked as FM or AFM, green circles) $5d$-TM chains. Broken line in (c) stands for the break force $F_0^{\mathrm{M}}$ calculated according to Eq. (2). As indicated by the gray shaded area, W and Re MWs reveal an AFM ground state at all interatomic distances, while the rest of the chains are FM. With orange squares in (c) the break force for the FM W and Re MWs is shown for comparison.

Figure 3

Phase diagrams for Fe, Ru, and W-BJs with (a), (c), (e) and without (b), (d), (f) spin polarization of the chain atoms. Plots indicate regions of stability ($S$, gray), producibility ($P$, light gray), separated by a white region or overlapping in the $SP$ region (in green or dark gray). The starting point along the $x$ axis is $d_0$ and the assumed surface orientations of the leads are indicated. The input parameters for W are given in Figs. 2a, 2b, 2c and for Fe and Ru in [26]. (g) provides a schematic summary of our results. Shown is the chain formation probability, proportional to the size of $SP$ regions, versus chain length, proportional to the highest $N$ for which an $SP$ region exists, with (green boxes) and without spin polarization (gray circles) in relation to the experimental findings (bold red) [10, 13, 14, 16, 18, 29] in all cases in arbitrary units relative to Au. Arrows indicate (exemplified for Fe, Ru, and W) the consequence on the chain formation caused by switching off the finite magnetization in the chain.