Magnetism in Pd: Magnetoconductance and transport spectroscopy of atomic contacts

Since the rapid technological progress demands for ever smaller storage units, the emergence of stable magnetic order in nanomaterials down to the single-atom regime has attracted huge scientific attention to date. Electronic transport spectroscopy has been proven to be a versatile tool for the investigation of electronic, magnetic, and mechanical properties of atomic contacts. Here we report a comprehensive experimental study of the magnetoconductance and electronic properties of Pd atomic contacts at low temperature. The analysis of electronic transport $\left(dI/dV\right)$ spectra and the magnetoconductance curves yields a diverse behavior of Pd single-atom contacts, which is attributed to different contact configurations. The magnetoconductance shows a nonmonotonous but mostly continuous behavior, comparable to those found in atomic contacts of band ferromagnets. In the $dI/dV$ spectra, frequently, a pronounced zero-bias anomaly (ZBA) as well as an aperiodic and nonsymmetric fluctuation pattern are observed. While the ZBA can be interpreted as a sign of the Kondo effect, suggesting the presence of magnetic impurity, the fluctuations are evaluated in the framework of conductance fluctuations in relation to the magnetoconductance traces and to previous findings in Au atomic contacts. This thorough analysis reveals that the magnetoconductance and transport spectrum of Au atomic contacts can completely be accounted for by conductance fluctuations, while in Pd contacts the presence of local magnetic order is required.

Figure 1

(a) Scheme of a mechanically controllable break junction (MCBJ) setup. Freestanding atomic contacts and chains are created from a thin constriction, which connects two broad leads, when the sample is bent in a three-point breaking mechanism. The movements of the pushing rod and countersupport are indicated by the arrows. The upper panel shows a SEM micrograph of a Pd sample. (b) Conductance histogram calculated from 349 opening traces of an electromigrated Pd-MCBJ. A broad peak in the conductance histogram between 1.0 and 2.$5G_0$ indicates the preferred conductance of a single-atom contact.

Figure 2

Selected magnetoconductance curves of atom-sized Pd contacts, where the magnetic field was applied perpendicular to the sample plane $(z$ direction). The colors indicate the sweep direction of the external magnetic field between the limits of $\pm 8\text{T}$ as indicated by the arrows. All curves feature an extremum near zero magnetic field and additional extrema of inverse character symmetrically located at fields of $3–5\text{T}$. The labels on the left axis $\left(MC{R}_{\max }\right)$ indicate the relative differences between these extrema of each curve. The label on the right axis denotes the zero-field conductance of each contact. The hysteresis $2\mathrm{\Delta }$, i.e., the shift of the low-field extrema in the sweep direction of the magnetic field, is indicated exemplarily in curve VI.

Figure 3

An irregular MC trace of an atom-sized Pd contact recorded in magnetic field applied in $x$ direction. A large conductance change $\left(MC{R}_{\max }=70\%\right)$ occurs in the range of 2–2.8 T depending on the sweep direction, indicated by the arrows. In contrast, the majority of Pd contacts show parabolic magnetoconductance curves when the field is applied in $x$ direction with moderate $|MC{R}_{\max }|$ between $1\%–15\%$.

Figure 4

Typical anisotropic magnetoconductance $\left(AMC\right)$ of an atom-sized Pd contact with zero-field conductance of $2.4G_0$. The field is rotated in the $xz$ plane at a constant field amplitude of 3 T; the field angle $\theta =0$ corresponds to a magnetic field in $x$ direction. The AMC amplitude is approximately $10\%$, similar to that in atomic contacts of ferromagnets.

Figure 5

The magnetic state in an atomic-size contact is defined by contributions of different parts: the electrodes (blue), the apex atoms (magenta), and the central atom (cyan). Each of these parts is characterized by a different magnetic moment and magnetic anisotropy energy, which depend on the electronic and geometric environment. The direction of local magnetic moments is indicated by the arrows. Panel (a) shows a ferromagnetic (collinear) alignment of the magnetic moments. This is the most likely ground-state configuration, which results in a negative $MC{R}_{\max }$ as observed in the majority of Pd contacts, e.g., curves IV–X in Fig. 2. (b) The interpretation of MC curves with a positive $MC{R}_{\max }>0$ (e.g., curves I–III in Fig. 2) requires a noncollinear ground state; four possible configurations are shown.

Figure 6

Two examples of $dI/dV$ spectra of atom-sized Pd contacts showing a zero-bias anomaly (ZBA). (a) ZBA described by a single Kondo resonance fitted with a Fano function (red) and $T_K=198\text{K}$. (b) Example in which the spectrum is fitted by two independent Fano functions, one for a low-voltage ZBA (pink) and a more pronounced feature vanishing at higher voltages (red).

Figure 7

Histogram of Kondo temperatures $T_{\mathrm{K}}$ extracted from $394dI/dV$ spectra of different contacts. (a) The Kondo temperatures are mainly distributed between 20 and 100 K, with a maximum at $\sim 30\text{K}$, but there are also Kondo temperatures up to almost $500\text{K}$. (b) The same data as shown in (a) in log-normal presentation. As a guide to the eye a log-normal distribution (blue solid line) matching the data is shown. In this representation a second maximum appears at higher $T_{\mathrm{K}}$, indicating the presence of another Kondo resonance.

Figure 8

Distribution of the occupation number of the $d$ orbital, extracted from the fit parameters of ZBAs. The maximum of the distribution is slightly above 1 and the FWHM is $\sim 0.5$ irrespective of the application of the distribution functions (Gauss and Lorentzian).

Figure 9

Typical temperature dependence of transport spectra $\left(dI/dV\right)$ without pronounced ZBA, recorded in a single-atom Pd contact with a conductance of 2.$5G_0$. All of the features decrease in amplitude with increasing temperature; most of them eventually vanish at temperatures comparable to the temperature scaling of conductance fluctuations.

Figure 10

MC curve of an atom-sized Pd contact with a zero-field conductance of $2.3G_0$ and its symmetric (blue) and antisymmetric (orange) components; the MC data and the symmetric component are shifted for clarity by $-1.9G_0$. The antisymmetric part shows a smaller amplitude $\left(\delta G_{\mathrm{rms},\mathrm{B}}=0.092e^2/h\right)$ than the symmetric part $\left(\delta G_{\mathrm{rms},\mathrm{B}}=0.488e^2/h\right)$, which only slightly deviates from the MC $\left(\delta G_{\mathrm{rms},\mathrm{B}}=0.496e^2/h\right)$.

Figure 11

Representative illustration of the FFT and Wiener analysis of MC characteristics of Pd atomic contacts. (a) The graph shows the original MC curve (blue), the low-frequency background (yellow), and the remaining fluctuation pattern (orange) after applying a band pass, which reduces the influence of the noise and removes low-frequency contributions. (b) The logarithmic power spectrum of the FFT of the original curve (blue). The Wiener noise filter is defined by a linear fit on the high-frequency contributions of the data (cyan). The essential signal range is determined by a polynomial fit (violet). (c) Shows a zoom-in of (b); the cutoff frequency for the long-wave contributions is indicated by the red line at $f_c=0.25{\mathrm{T}}^{-1}$. Right before this cutoff minimum, the spectra always show a pronounced peak (green line) corresponding to the dominant long-wave contributions.