# Physics – Investigation of Molecular Magnetism by Interferometry

Physics 15, 137

A material wave interferometer can probe magnetism for a wide variety of types, from single atoms to very large and weak magnetic particles.

This year marks the centenary of the pioneering experiment by Otto Stern and Walter Gerlach that demonstrated the quantization of the atom’s spin angular momentum. [1]. Evidence came from the observation that a beam of silver atoms, when passing through a spatially changing magnetic field, split into two beams. The spatial splitting of the spin and down atoms corresponds to the atomic magnetic moment of a single Bohr magnet – the magnetic moment of a single spindle electron. The deflection of particle beams in a spatially variable magnetic field remains the basis of techniques for characterizing the magnetic properties of isolated atoms and molecules. However, such techniques are not sensitive enough to study very large and weak magnetic particles, including many biological ones. Now a team led by Marcus Arendt at the University of Vienna has developed a Stern-Gerlach material-wave interferometer that can resolve nanometer-scale aberrations. [2]. This “mass” interferometer is applicable to species with vastly different magnetic moments, ranging from Bohr magnetization to less than nuclear magnetization – about 1/1836 of the Bohr magnetron. These features allowed the researchers to use the same interferometer to study cesium atoms and large molecules, including free organic radicals and weakly magnetic fullerenes.

The historical Stern and Gerlach experiment included an intense parallel atomic beam, a spatially varying magnetic field, and a position-resolution detector that measures the transverse spatial distribution of the outgoing atomic beams. This configuration produced a beam deflection that was scaled inversely to the particle mass, making it difficult to measure the small deviations that heavy particles would experience. [3].

A major breakthrough occurred six decades later when physicist David Pritchard and his team at the Massachusetts Institute of Technology reflected an atomic beam from a standing-wave optical network. [4] And then from nanomechanical grating [5]. This allowed an atomic beam to split and recombine coherently to achieve the first atomic matter wave interferometer. [6]. Material wave interferometry has made it possible to greatly enhance the sensitivity of techniques for investigating the magnetism of isolated atoms and molecules [7].

In 1999, Arndt and colleagues demonstrated the diffraction of the most massive objects to that date, C60 Fullerene particles, which are scattered on a 100 nm long transport network [8]. With the de Broglie wavelength of C.60 Particles of about 1 picometer and diffraction angles of about 10 microradians, the experiment reached the limits imposed by the available beam collimation and the spatial resolution of the particle detector. These limits depend on “far-field” diffraction – that is, on scales much larger than the particle’s wavelength. But, as in optics, working in the “near field” offers the possibility to overcome diffraction limits. This is the approach taken by Arendt and his colleagues in their new work.

The researchers demonstrated a universal, highly sensitive Stern-Gerlach matter wave interferometer that can examine magnetism in atoms and in a wide range of large molecular species. The interferometer has a so-called Talbot-Lau configuration with a baseline of 2 m in length (Fig. 1a). 1) [9]. This interferometer consists of three identical, equidistant transmission gratings separated by multiples of the “Talbot length” (the square of the grid period divided by the Broglie wavelength). In the third grating, the near field diffraction creates a pattern that is a self-image of the second grating printed in the wave beam of the material hitting the second grating. Between the second and third lattices, either an array of “anti-Helmholtz” coils or permanent magnets produces a magnetic field gradient, which in turn causes small deviations in the path due to the magnetic susceptibility of the particles. Since the third lattice is tangentially scanned, the multiple paths create interference fringes that depend on the beam aberrations and affect the wave intensity of the material hitting the detector. Based on the detected intensities, Arendt and colleagues can determine the smallest deviations (of a few nanometers) associated with the magnetically weaker species under study.

The measurement capabilities of the setup stem from two main advantages of the Talbot-Lau near-field interferometer over conventional far-field interferometers. First, this interferometer has less stringent requirements on the beam coherence required to produce high-contrast interference, allowing the use of relatively unbalanced particle beams and thus greater throughput. This gain is due to the fact that each slit in the first transmission grating acts as a coherent source for the second network, with many packet paths from the first network being recombined in phase at the position of the third network thus producing a strong signal. Second, the minimum solvable de Broglie wavelength for near-field diffractometers as square-grooved spacing, in contrast to the linear measurement of far-field deflection. Thus, to detect particles with a mass ten times larger, the near-field interferometer requires gratings with a period of about three times smaller barriers—compared to a period that is ten times smaller for the far-field interferometer. These two features allow Talbot-Lau charts to have moderately long baselines and easily achievable grooved periods to reach a very large mass range.

The researchers used the highly sensitive matter wave interferometer to probe magnetic phenomena in isolated species ranging from atomic cesium – with a single non-double electron spin – to large molecules (Fig. 2). These molecules included organic free radical TEMPO molecules and weakly magnetic fullerenes, such as the spherical “football” molecule (C60), a diffuse ‘rugby ball’ molecule (C70), and a molecule with a non-double nuclear spin (12c6913c). The team obtained, as expected, a weak magnetically induced response to C70corresponding to an induced magnetic moment of about 0.4 nuclear magnetons, and a stronger response to 12c6913C, generated by nuclear spin, corresponding to 0.7 nuclear magnetons. Surprisingly, the response to C60 It was ten times stronger than C70: About 7 nuclear magnets. The researchers performed calculations indicating that the larger magnetic moment arises due to a large rotational contribution. (C . rotation states60 Even Quantum Number 466 seemed excited. in C70there is also a rotational contribution, but this contribution is much smaller due to the lower symmetry of the prolite molecule.)

The new general matter-wave interferometer Stern-Gerlach should allow researchers to extend matter-wave interferometry to ever larger molecules and more complex species, including large biological molecules and possibly even organisms such as bacteria. It should also allow researchers to explore the interface of quantum physics with chemistry, biology and the classical, macroscopic world. [3, 10]. There is currently great interest in deciphering the role of molecular magnetism in complex animal phenomena, such as the ability of migratory birds to obtain directional information from the Earth’s magnetic field. Finally, accurate measurements of the magnetic moment will help further our understanding of the magnetism of very large complex particles.

## references

1. W. Gerlach and O. Stern, “Experimental Evidence for Directional Quantization in a Magnetic Field,” Z. Physik 9 (1922).
2. yy fine et al.“Nanomagnetism Examined in a Matter Wave Interferometer,” Phys. Reverend Litt. 129123001 (2022).
3. S Gerlich et al.Otto Stern’s legacy in quantum optics: matter waves and the measurement of diffraction,” in Molecular beams in physics and chemistryedited by S. Friedrich and H. Schmidt-Böching (Springer, Cham, 2021).
4. B Moskovitz et al.“Diffraction of an atomic ray by standing wave radiation,” Phys. Reverend Litt. 51 (1983).
5. DW Keith et al.“Diffraction of Atoms by Transmission Grid,” Phys. Reverend Litt. 61 (1988).
6. DW Keith et al.“interferometer for atoms,” Phys. Reverend Litt. 662693 (1991).
7. AD Cronin et al.“Optics and Interferometry with Atoms and Molecules,” Rev. DoD. Phys. 81 (2009).
8. Im Arendt et al.“Wave-particle duality of
${\text{c}}_{60}$

molecules,” temper nature 401 (1999).

9. J.F. Clauser and S. Li, “Talbot-vonLau atom interferometry with cold slow potassium,” Phys. Reverend A 49 (1994).
10. Im Arendt et al.“Quantum Physics Meets Biology,” HFSP J. 3 (2009).

Peter Hannaford is Professor Emeritus and University Distinguished Professor at the Center for Visual Science at Swinburne University of Technology in Melbourne, Australia. He received his Ph.D. in Condensed Matter Physics from the University of Melbourne. His current research interests include atomic optics, ultracold quantum gases, and time crystals.

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