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Scientists at ETH Zurich have identified new ferromagnetism in a custom-engineered moiré material, challenging traditional magnetic theories. This magnetism, based on electron spin alignment to minimize kinetic energy, offers new insights into quantum effects and solid-state magnetism.
For a magnet to stick to a refrigerator door, several physical effects must be perfectly aligned. The magnetic moments of its electrons all point in the same direction, a phenomenon that occurs even without an external magnetic field.
This is due to the exchange interaction, a complex interaction of electrostatic repulsion between electrons, and the quantum mechanical properties of the electron spins, which generate magnetic moments. This mechanism explains why materials like iron and nickel are ferromagnetic, meaning they are permanently magnetic unless they are heated above a specific temperature.
At ETH Zurich, a team of researchers led by Ataç Imamoğlu from the Institute of Quantum Electronics and Eugene Demler from the Institute of Theoretical Physics has now detected a new type of ferromagnetism in an artificially produced material, in which the alignment of magnetic moments occurs in a way completely different. They recently published their results in the scientific journal Nature.
Artificial material with electron filling
In Imamoğlu’s lab, PhD student Livio Ciorciaro, postdoc Tomasz Smolenski and their colleagues produced a special material by placing atomically thin layers of two different semiconductor materials (molybdenum diselenide and tungsten disulfide) on top of each other.
In the contact plane, the different lattice constants of the two materials – the separation between their atoms – lead to the formation of a two-dimensional periodic potential with a large lattice constant (thirty times greater than those of the two materials).
In the moiré material produced at ETH, the electron spins are disordered if there is exactly one electron per lattice site (left). Once there are more electrons than there are lattice sites (right) and electron pairs can form doubloons (red), the spins will align ferromagnetically, as this minimizes kinetic energy. Credit: ETH Zurich
“These moiré materials have attracted great interest in recent years, as they can be very well used to investigate the quantum effects of strongly interacting electrons,” says Imamoğlu. “However, until now very little was known about its magnetic properties.”
To investigate these magnetic properties, Imamoğlu and his colleagues measured whether, for a given electron fill, the moiré material was paramagnetic, with its magnetic moments randomly oriented, or ferromagnetic. They illuminated the material with laser light and measured the intensity with which the light was reflected for different polarizations.
Polarization indicates in which direction the laser light’s electromagnetic field oscillates, and depending on the orientation of the magnetic moments – and therefore the spins of the electron – the material will reflect one polarization more strongly than the other. From this difference, one can then calculate whether the spins point in the same direction or in different directions, from which the magnetization can be determined.
Stunning evidence
By constantly increasing the voltage, physicists filled the material with electrons and measured the corresponding magnetization. Until the filling of exactly one electron per moiré lattice site (also known as Mott insulator), the material remained paramagnetic. As the researchers added electrons to the lattice, something unexpected happened: The material suddenly behaved much like a ferromagnet.
“This was stunning evidence for a new type of magnetism that cannot be explained by exchange interaction,” says Imamoğlu. In fact, if the exchange interaction was responsible for magnetism, this should also have appeared with fewer electrons in the lattice. The sudden onset therefore pointed to a different effect.
Kinetic magnetism
Eugene Demler, in collaboration with postdoc Ivan Morera, finally came up with the crucial idea: they could be looking at a mechanism that Japanese physicist Yosuke Nagaoka had theoretically predicted as early as 1966. In this mechanism, by making its spins point in the same direction , electrons minimize their kinetic energy (energy of movement), which is much greater than the exchange energy. I
In the experiment carried out by ETH researchers, this happens as soon as there is more than one electron per lattice site within the moiré material. As a consequence, pairs of electrons can come together to form so-called doubloons. Kinetic energy is minimized when doubloons can spread throughout the network through quantum mechanical tunneling.
This, however, is only possible if the individual electrons in the lattice align their spins ferromagnetically, otherwise the quantum mechanical superposition effects that allow the free expansion of doubloons will be disturbed.
“Until now, such mechanisms of kinetic magnetism have only been detected in model systems, for example in four coupled quantum dots,” says Imamoğlu, “but never in extended solid-state systems like the one we use.”
As a next step, he wants to change the parameters of the moiré grating to investigate whether ferromagnetism is preserved at higher temperatures; in the current experiment, the material still needed to be cooled to a tenth of a degree above
