Transverse and longitudinal lattice modulations in the charge-orbital- ordered manganite Sr _2-xLa _xMnO ₄ around x=0.5

For Sr _2-xLa _xMnO ₄, having a nearly two-dimensional electronic system of e _g electrons, we have examined the crystallographic features of the charge-orbital-ordered (COO) and charge-exchange (CE)-type magnetic states for 0.40 ≤ x ≤ 0.55 by transmission electron microscopy. Incommensurate and commensurate longitudinal lattice modulations were found below ∼150 K for 0.47 ≤ x ≤ 0.51, while the cooling from the disordered tetragonal state resulted in the appearance of transverse modulations below T _COO for 0.40 ≤ x ≤ 0.52. For 0.47 ≤ x ≤ 0.51, thus, the longitudinal and transverse modulations were present in both the lower-temperature region of the COO state and the CE-type magnetic state. In addition to these two states, the COO state for 0.40 ≤ x < 0.47 and 0.51 < x ≤ 0.52 accompanies only the transverse modulation and should be referred to as the orbital modulated state without a charge modulation.