Size-induced moment formation on isolated Fe atoms embedded in a nanocrystalline Ta matrix: Experiment and theory

Employing the time differential perturbed angular distribution (TDPAD) technique, we have measured the local susceptibility (${\chi }_{\text{loc}}$) of isolated Fe probe atoms implanted in nanocrystalline $\alpha$-Ta as well as $\beta$-Ta host matrices. While Fe dopants in bulk Ta and $\beta$-Ta exhibit no magnetic response, the temperature dependence of ${\chi }_{\text{loc}}$ in nanocrystalline $\alpha$-Ta reveals the emergence of a local magnetic moment on Fe below a critical size of $\approx$8 nm. Using ab initio electronic structure calculations, we show that the moment formation in nanocrystalline $\alpha$-Ta occurs due to Stoner enhancement arising from an unusual size-dependent lattice expansion that results in a shift in the Fermi level.

Figure 1

X-ray diffraction patterns of three $\alpha$-Ta films and one $\beta$-Ta film. The Scherrer size (coherently diffracting domain size, $d_{\text{XRD}}$) corresponding to each sample is indicated.

Figure 2

Field emission scanning electron micrographs of three $\alpha$-Ta films corresponding to the Scherrer sizes: (a) 34 nm, (b) 8 nm, and (c) 4 nm.

Figure 3

Spin rotation spectra $R\left(t\right)$ recorded at 15 K (left panel) and their Fourier transforms (right panel) for ${}^{54}$Fe in nanocrystalline Ta with varying particle size $d_{\text{XRD}}$. The bottom panel corresponds to Fe in $\beta$-Ta.

Figure 4

Temperature dependence of the local susceptibility $\beta \left(T\right)$ of ${}^{54}$Fe in bulk and nanocrystalline Ta. Data for Fe in 5 nm nano-Nb (stars) taken from Ref. [9] are shown for comparison. The solid and dotted lines represent a fit to Curie-Weiss law discussed in the text.

Figure 5

(Color online) Temperature dependence of the nuclear spin relaxation time ${\tau }_N$ of ${}^{54}$Fe in nanocrystalline Ta samples. The solid line correspond to a linear fit reflecting Korringa behavior. Symbols have the same significance as in Fig. 4.

Figure 6

Projected nonmagnetic density of states (DOS) for Fe impurity in bulk and nano-Ta hosts. Colored lines represent: black = Fe-$d$, green = $t_{2g}$, blue = $e_g$, and dotted black = Ta-$d$ ($\times 5$). The pink line in the topmost panel corresponds to Fe in bulk Ta and the red line in the lowest panel represents Fe-$d$ DOS in $\beta$-Ta. Vertical dotted line shows the position of the Fermi energy $E_F$.

Figure 7

Spin resolved $d$-projected density of states for Fe impurity in bulk and nano-Ta hosts. Color lines represent: black = Fe-$d$, green = $t_{2g}$, and blue = $e_g$. Vertical dotted line at zero energy shows the position of the Fermi energy.

Figure 8

Dependence of the Curie constant ($•$), Fe moment ($\circ$), and $N(E_F$) ($\diamond$) with a particle size of nano-Ta samples. Lines are visual guides.