Nanoscale Magnetism Probed in a Matter-Wave Interferometer

We explore a wide range of fundamental magnetic phenomena by measuring the dephasing of matter-wave interference fringes upon application of a variable magnetic gradient. The versatility of our interferometric Stern-Gerlach technique enables us to study the magnetic properties of alkali atoms, organic radicals, and fullerenes in the same device, with magnetic moments ranging from a Bohr magneton to less than a nuclear magneton. We find evidence for magnetization of a supersonic beam of organic radicals and, most notably, observe a strong magnetic response of a thermal ${\mathrm{C}}_{60}$ beam consistent with high-temperature atomlike deflection of rotational magnetic moments.

Figure 1

The interferometer with three equidistantly spaced gratings $G_{1-3}$ and the magnetic interaction region between $G_2$ and $G_3$. The latter consists of an anti-Helmholtz coil pair for the atomic experiments and a permanent magnet for the molecular experiments. $G_3$ is scanned along the $x$ axis to mask the sinusoidal interference fringes before mass selection and detection of the transmitted flux. The studied species are shown with their corresponding point groups, the origin of their dominant magnetism observed in our scheme, and typical magnitudes of the associated magnetic moments.

Figure 2

Cesium interference visibility as a function of the anti-Helmholtz coil current. The solid curves are obtained from Eq. (4), where we fit a small constant offset to the calculated $C$ factor. The inset shows the high-current behavior, with the line indicating the expected asymptote. Each point consists of multiple interference scans, and error bars are standard errors. Visibilities are normalized using the asymptotic value rather than the zero-current point (see Supplemental Material [22]).

Figure 3

TEMPO interference visibility as a function of the magnet distance. We consider three models: a symmetric deflection model of the unpaired electronic spin (dashed line), a one-sided deflection model assuming a purely Langevin-like response at 10 K (dotted line), and a one-sided deflection model assuming ${\mu }_{\mathrm{eff}}=0.1{\mu }_B$ (solid line). The nonzero baseline of the data is likely a fitting artifact, also seen for the ${\mathrm{C}}_{60}$ isotopomers in the Supplemental Material [22]. Visibilities are normalized to the first data point (magnet withdrawn) and error bars are standard errors.

Figure 4

${\mathrm{C}}_{60}$ (all isotopomers), ${}^{12}{\mathrm{C}}_{70}$ and ${}^{12}{\mathrm{C}}_{69}{}^{13}\mathrm{C}$ interference visibility as a function of the magnet distance. There are three distinct magnetic phenomena on display here: one-sided diamagnetic deflection of ${}^{12}{\mathrm{C}}_{70}$, symmetric deflection of the nuclear spin of ${}^{12}{\mathrm{C}}_{69}{}^{13}\mathrm{C}$, and symmetric deflection of rotational moments of ${\mathrm{C}}_{60}$. Visibilities are normalized to the first data point (magnet withdrawn) and error bars are standard errors. There are no free parameters in the theory curves.