Magnetism in quasi-two-dimensional tri-layer La_2.1Sr_1.9Mn₃O₁₀ manganite

The tri-layer La[Formula: see text]Sr[Formula: see text]Mn[Formula: see text]O[Formula: see text] manganites of Ruddlesden-Popper (RP) series are naturally arranged layered structure with alternate stacking of ω-MnO[Formula: see text] (ω = 3) planes and rock-salt type block layers (La, Sr)[Formula: see text]O[Formula: see text] along c-axis. The dimensionality of the RP series manganites depends on the number of perovskite layers and significantly affects the magnetic and transport properties of the system. Generally, when a ferromagnetic material undergoes a magnetic phase transition from ferromagnetic to paramagnetic state, the magnetic moment of the system becomes zero above the transition temperature (T[Formula: see text]). However, the tri-layer La[Formula: see text]Sr[Formula: see text]Mn[Formula: see text]O[Formula: see text] shows non-zero magnetic moment above T[Formula: see text] and also another transition at higher temperature T[Formula: see text] 263 K. The non-zero magnetization above T[Formula: see text] emphasizes that the phase transition in tri-layer La[Formula: see text]Sr[Formula: see text]Mn[Formula: see text]O[Formula: see text] not a ferromagnetic to paramagnetic state. We show here the non-zero magnetic moment above T[Formula: see text] is due to the quasi-two-dimensional nature of the tri-layer La[Formula: see text]Sr[Formula: see text]Mn[Formula: see text]O[Formula: see text] manganite. The scaling of the magnetic entropy change confirms the second-order phase transition and the critical behavior of phase transition has been studied around T[Formula: see text] to understand the low dimensional magnetism in tri-layer La[Formula: see text]Sr[Formula: see text]Mn[Formula: see text]O[Formula: see text]. We have obtained the critical exponents for tri-layer La[Formula: see text]Sr[Formula: see text]Mn[Formula: see text]O[Formula: see text], which belong to the short-range two-dimensional (2D)-Ising universality class. The low dimensional magnetism in tri-layer La[Formula: see text]Sr[Formula: see text]Mn[Formula: see text]O[Formula: see text] manganite is also explained with the help of renormalization group theoretical approach for short-range 2D-Ising systems. It has been shown that the layered structure of tri-layer La[Formula: see text]Sr[Formula: see text]Mn[Formula: see text]O[Formula: see text] results in three different types of interactions intra-planer ([Formula: see text]), intra-tri-layer ([Formula: see text]) and inter-tri-layer ([Formula: see text]) such that [Formula: see text] and competition among these give rise to the canted antiferromagnetic spin structure above T[Formula: see text]. Based on the similar magnetic interaction in bi-layer manganite, we propose that the tri-layer La[Formula: see text]Sr[Formula: see text]Mn[Formula: see text]O[Formula: see text] should be able to host the skyrmion below T[Formula: see text] due to its strong anisotropy and layered structure.