Spinlike Susceptibility of Metallic and Insulating Thin Films at Low Temperature

Susceptibility measurements of patterned thin films at sub-$K$ temperatures were carried out using a scanning SQUID microscope that can resolve signals corresponding to a few hundred Bohr magnetons. Several metallic and insulating thin films, even oxide-free Au films, show a paramagnetic response with a temperature dependence that indicates unpaired spins as the origin. The observed response exhibits a measurable out-of-phase component, which implies that these spins will create $1/f$-like magnetic noise. The measured spin density is consistent with recent explanations of low frequency flux noise in SQUIDs and superconducting qubits in terms of spin fluctuations, and suggests that such unexpected spins may be even more ubiquitous than already indicated by earlier measurements. Our measurements set several constraints on the nature of these spins.

Figure 1

(a) SQUID field coil and pickup loop. (b) Schematic of the layer structure of sample II: 1, bare Si; 2, Au with Al adhesion layer; 3, ALD deposited ${\mathrm{AlO}}_x$; 4,  Au on ${\mathrm{AlO}}_x$. (c)–(e) Sample II, linear in- and out-of phase signal (${\varphi }_1$, $-{\varphi }_2$) and in-phase 3rd harmonic (${\varphi }_1^{(3)}$) at 193 Hz, 43 mK. All numbers in this figure are in units of $\mu {\Phi }_0/\mathrm{mA}$ and the response over bare Si has been defined as 0. (f) Scanning electron micrograph of a region of sample I, Au films on Si with native oxide. (g) Sample I: linear in-phase signal (${\varphi }_1$) at 193 Hz, 27 mK of a region as shown in (f). (h) Line scans over the positions indicated in (g), at 25 mK and 111 Hz. Panels (i)–(k) are the same as (f)–(h), zoomed in on ring as indicated by the box in (g). The ring has a $2\mu \mathrm{m}$ diameter, 350 nm linewidth, and a connection to the $15\mu \mathrm{m}$ wide wire for heat sinking. The line scans in (k) were taken at 35 mK and the $x$ scan is offset for clarity. The temperature dependence shown in Figs. 2a, 2b was obtained from line scans as in (h) and (k), or by averaging over the rectangles in (c).

Figure 2

(a) Temperature dependence of the in-phase linear susceptibilities (${\varphi }_1$) obtained from scans as shown in Fig. 1 (see text) at 111 or 193 Hz. Numbers in parenthesis indicate the sample. The downturn at the highest $T$ can be attributed to the $T$ independent diamagnetic bulk susceptibility of $-3.4\times {10}^{-5}$ for gold [26]. (b) Out-of-phase component (${\varphi }_2$) from the same data sets. (c) Frequency dependence of ${\varphi }_2/{\varphi }_1$ from sample I at 25 mK. The data from the superconducting ring characterize the phase shift due to the finite measurement bandwidth and show that the nonzero ${\varphi }_2$ is not a measurement artifact. (d),(f) Nonlinear part of the response of the heatsunk Au ring (I), deposited directly on the Si substrate, at base temperature. (f),(g) Same for an isolated ring on sample II, deposited onto the ${\mathrm{AlO}}_x$ film. In (d) and (f), only ${\varphi }_1$ (i.e., a line) was subtracted. In (e) and (g), both ${\varphi }_1$ and ${\varphi }_2$ (i.e., an ellipse) were subtracted.