  The co-occurrence of phase transitions with local and global order
parameters, such as the entangled magnetization and topological invariant, is
attractive but has been seldom realized experimentally. Here, by using
high-pressure in-situ X-ray diffraction, high-pressure electric transport
measurements and high-pressure first-principles calculations, we report a
magneto-topological phase transition, i.e., the phenomenon of magnetic
materials undergoing different magnetic and topological phases during the
process of pressure loading, in a recently discovered magnetic Weyl semimetal
Co3Sn2S2. By considering both out-of-plane ferromagnetic and in-plane
anti-ferromagnetic components, the calculated results can well fit the
experimental data. The calculation results furtherly reveal a pristine Weyl
phase with four more pairs of Weyl nodes under low pressures, and a
generally-defined Z2 topological insulator phase after the restoration of
time-reversal symmetry. Remarkably, the present magneto-topological phase
transition involves a pair of crossing bands of two spin channels becoming
degenerate. Thus, all the chiral Weyl nodes annihilate with their counterparts
from another spin channel, in contrast to the typical annihilation of Weyl
pairs from the same bands in inversion-asymmetric systems. Our experiments and
theoretical calculations uncover a manner to modulate the diverse topological
states by controlling the internal exchange splitting via external physical
knobs in topological magnets.
