Electronic transport in gadolinium atomic-size contacts

We report on the fabrication, transport measurements, and density functional theory (DFT) calculations of atomic-size contacts made of gadolinium (Gd). Gd is known to have local moments mainly associated with $f$ electrons. These coexist with itinerant $s$ and $d$ bands that account for its metallic character. Here we explore whether and how the local moments influence electronic transport properties at the atomic scale. Using both scanning tunneling microscope and lithographic mechanically controllable break junction techniques under cryogenic conditions, we study the conductance of Gd when only few atoms form the junction between bulk electrodes made of the very same material. Thousands of measurements show that Gd has an average lowest conductance, attributed to single-atom contact, below $\frac{2e^2}{h}$. Our DFT calculations for monostrand chains anticipate that the $f$ bands are fully spin polarized and insulating and that the conduction may be dominated by $s$, $p$, and $d$ bands. We also analyze the electronic transport for model nanocontacts using the nonequilibrium Green's function formalism in combination with DFT. We obtain an overall good agreement with the experimental results for zero bias and show that the contribution to the electronic transport from the $f$ channels is negligible and that from the $d$ channels is marginal.

Figure 1

Typical conductance traces for atomic-size contacts made of Gd. Bright (dark) curves stand for breaking (creating) contacts, as the arrows indicate. (Top) Measurements taken with the STM technique in equilibrium with liquid He bath and at ${10}^{-8}\mathrm{mbar}$. All traces have been taken at $100\mathrm{mV}$ bias voltage. (Inset) Artistic representation of nanocontacts; hcp ball stacking is pictured, where balls represent atoms. (Bottom) Measurements taken with the lithographic MCBJ technique in equilibrium with liquid He bath and at ${10}^{-5}\mathrm{mbar}$. Red and green traces and their return traces have been taken at $5\mathrm{mV}$ bias voltage; the yellow curve has been taken at $10\mathrm{mV}$.

Figure 2

Histograms of conductance calculated from conductance traces for Gd atomic-size contacts. The top (bottom) plot stands for breaking (creating) contact mode. Same colors for top and bottom plots stand for a set of traces with electrodes that have not been modified with deep indentations (i.e., less than $\approx 20\frac{2e^2}{h}$). The different colors (red, purple, yellow, black, green) illustrate the variability in the histograms between contacts, or for different choices of depth of indentations. All measurements have been taken with the STM technique at $100\mathrm{mV}$ bias voltage in equilibrium with liquid He bath and ${10}^{-8}\mathrm{mbar}$, except the purple curve, that has been taken with the MCBJ technique, where a bias voltage of $10\mathrm{mV}$ has been applied. For STM histograms, a few (from 1 to 10) thousands of traces are considered. For MCBJ $\approx 500$ traces are included.

Figure 3

(Linear color scale) Overlapped Gd conductance traces measured with STM. Breaking contact (left plot) and creating contact (right plot) situations are shown. Traces are centered to $1\mathrm{nm}$ when $0.01\frac{2e^2}{h}$ is reached from higher (lower) to lower (higher) conductance values for breaking (creating) contacts. Total number of traces are 2524 and 2511 for breaking and creating contact cases, respectively.

Figure 4

Sketch of the projected DOS onto the $d$ and $f$ manifold for Gd in chain (a) and bulk (b). The $d$ manifold acquires a large spin splitting only in the chain case, while the $f$ manifold is spin polarized in both cases. Panels (c),(d) show the DOS projected onto the $d$ manifold as calculated by the first-principles full potential method for the chain (c) and bulk (d) Gd, in agreement with the sketch (a),(b).

Figure 5

Spin-resolved density of states of Gd in chain structures calculated with elk (LAPW) projected onto the manifolds $s$ (a), $p$ (b), $d$ (c), and $f$ (d). Same cases calculated with crystal14 (LCAO) [$s$ (e), $p$ (f), $d$ (g), and $f$ (h)].

Figure 6

Gd $〈111〉$ nanocontact calculated conductance-distance characteristic. (Top) Two atomically sharp tips in the $〈111〉$ direction forming a dimeric contact. The distance $\mathrm{\Delta }z$ equals 0 when the distance between both tip apex atoms equals the nearest-neighbor distance in bulk. (Bottom) An atomically sharp tip in the $〈111〉$ direction against a blunt $〈111〉$ one. Both tips touch to form a monomeric contact. The distance $\mathrm{\Delta }z$ equals 0 when the distance between the tip apex atom in the atomically sharp tip and each tip apex atom in the blunt one equals the nearest-neighbor distance in bulk.

Figure 7

(a) Spin-resolved principal eigenchannel projected onto all the magnetic shells of a Gd dimeric nanocontact at a tip-tip displacement of $1.0\AA$; (b) and (c) the same but for a monomeric contact at tip-tip displacement of $\mathrm{\Delta }z=1.0\AA$ and $\mathrm{\Delta }z=2.2\AA$, respectively. “Up” electrons correspond to the “minority” spin component, while “down” electrons correspond to the “majority” one.