Manifestation of memory and butterfly in the photon echo on erbium ions in LuLiF$_4$ and YLiF$_4$

The memory effect in the form of hysteresis has been detected in the measured dependence of the intensity of the photon echo in YLiF$_4$ and LuLiF$_4$ samples with E$^{3+}$ impurity ions on the orientation, strength, and variation direction of the magnetic field. The prehistory of the location of a sample in the magnetic field with a certain direction and strength is written and stored for no less than $6$ h at a temperature of $2$ K. The effect crucially depends on the orientation of the optical axis of the sample with respect to the external magnetic field.