Researchers at TU Dortmund University have shown that separate time crystals formed in the same semiconductor can synchronize their oscillations, locking to a common frequency even when they are up to about 40 micrometers apart. The team identified the diffusion of spin-polarized electrons as the coupling mechanism. It suggests the effect could serve as a basis for networks of coupled spin oscillators in spintronic devices.
A continuous time crystal is a system that oscillates spontaneously and persistently under constant driving, rather than in response to a periodic external signal. In 2024, the same group reported such a time crystal in an electron-nuclear spin system inside an indium gallium arsenide (InGaAs) semiconductor, with oscillations that remained stable for hours. The material is a 10 μm-thick InGaAs layer containing 3% indium and doped with silicon. Each electron bound to a silicon donor interacts with roughly a million surrounding nuclear spins and forms a single oscillator. A circularly polarized pump laser aligns the electron spins, which pass their polarization to the nuclei. The resulting nuclear magnetic field then acts back on the electrons, sustaining the oscillation, which a second laser reads out. The experiments were carried out at about 6 K.
Because of small local variations in the material, oscillators at different spots on the sample have different natural frequencies. When the team illuminated a wide area of about 200 μm, however, all regions oscillated at a single frequency, even where their natural frequencies differed by up to 40%. To probe the range of the effect, the researchers used two tightly focused pump beams to create two separate oscillators. When the beams were within about 38 μm of each other, the two oscillators locked to one shared frequency lying between their individual values. At 50 μm apart, each kept its own frequency. That coupling distance is more than a thousand times the size of a single oscillator.
The team weighed several possible coupling mechanisms, including stray light between the spots, the spread of nuclear polarization and electrons hopping between donors. Of these, only electron spin diffusion acts over the observed distance. The researchers independently measured an electron spin diffusion length of about 18 μm in the sample using time-resolved Kerr microscopy, consistent with the synchronization range. In a second sample with far fewer electrons and a shorter spin lifetime, the oscillators synchronized only when the two pump spots overlapped. Simulations that add spin diffusion to the team's earlier model reproduced the experimental results.
The findings also explain why the group's earlier time crystal was so stable: its oscillations come from a large synchronized ensemble, and that collective state protects them against fluctuations and disorder. The researchers suggest that adding electrostatic gating or controlled electron drift could turn the passive coupling into a tunable one. That could lead to networks of spin oscillators for analog neuromorphic computing, in which information is processed through collective phase dynamics rather than discrete logic states, as well as to on-chip devices based on time crystals.