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Motility-induced phase separation (MIPS) is of great importance and has been extensively researched in overdamped systems, nevertheless, what impacts inertia will bring on kinetics of MIPS is lack of investigation. Here, we find a nucleation-like MIPS instead of spinodal decomposition in the overdamped case, i.e. not only the phase transition changes from continuous to discontinuous, but also the formation of clusters does not exhibit any coarsening regime. This remarkable kinetics of MIPS stems from a competition between activity-induced accumulation of particles and inertia-induced suppression of clustering process. More interestingly, the discontinuity of MIPS still exists even when the ratio of particle mass to the friction coefficient reduces to be very small such as 10−4. Our findings emphasize the importance of inertia induced kinetics of MIPS, and may open a new perspective on understanding the nature of MIPS in active systems.

The ultrasonic velocity (V) and attenuation (α) have been measured for both longitudinal and transverse waves in the single-phase polycrystalline colossal-magnetoresistance compound La0.67Ca0.33MnO3 near the Curie temperature Tc. A dramatic increase in V is observed at the ferromagnetic transition temperature and accompanied by a sharp peak in α for both longitudinal and transverse waves. This simultaneous occurrence of magnetic, transport, and lattice anomalous features implies extremely strong spin–phonon and electron–phonon interaction, and gives direct evidence for the spontaneous linear magnetostriction effect. The longitudinal attenuation (αI) was carefully measured over a wide temperature range. The temperature dependence of critical attenuation is given by (T−Tc)−1.55 for T>Tc.

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