We report on a low-temperature magnetovolume study of single-crystalline heavy-fermion CeCu₆ . Magnetostriction data (B∥c) taken at temperatures below 100 mK reveal two distinct anomalies at B₁=2.2 T and B₂=4.0 T, that are rapidly washed out by increasing the temperature. Thermal expansion measurements in fields up to 8 T (B∥c) reveal an anomalous field suppression of the term linear in temperature. The field B₁ and B₂ are likely related to a change in magnetic correlations. Their interrelation is investigated by a scaling approach.