Thermal stability and irreversibility of skyrmion-lattice phases in   Cu$_2$OSeO$_3$
  Small angle neutron scattering measurements have been performed to study the thermodynamic stability of skyrmion-lattice phases in Cu$_2$OSeO$_3$. We found that the two distinct skyrmion-lattice phases [SkX(1) and SkX(2) phases] can be stabilized through different thermal histories; by cooling from the paramagnetic phase under finite magnetic field, the SkX(2) phase is selected. On the other hand, the 30$^{\circ}$-rotated SkX(1) phase becomes dominant by heating the sample from the ordered conical phase under finite field. This difference in stabilization is surprisingly similar to the irreversibility observed in spin glasses. The zero-field cooling results in the co-existence of the two phases. It is further found that once one of the skyrmion-lattice phases is formed, it is hardly destabilized. This indicates unusual thermal stability of the two skyrmion-lattice phases originating from an unexpectedly large energy barrier between them. 
Koya Makino and Johannes D. Reim and Daiki Higashi and Daisuke Okuyama   and Taku J. Sato and Yusuke Nambu and Elliot P. Gil...
cond-mat.str-el