Dimensional Crossover of Antiferromagnetism in Half-Doped La$_{0.5}$Sr$_{1.5}$MnO$_{4}$

Like cuprates which exhibits high-temperature superconductivity, half-doped single-layered manganites such as La$_{0.5}$Sr$_{1.5}$MnO$_{4}$ have distinct features of the MnO$_{2}$ plane in the perovskite structure. In addition to charge-orbital order, of particular interest is the antiferromagnetism in half-doped manganites with the so called CE-type antiferromagnetic (AF) structure, which is essentially composed of ferromagnetic zigzag chains antiferromagnetically coupled to one-another. In this talk, we will report critical behavior and dimensional crossover of AF order in La$_{0.5}$Sr$_ {1.5}$MnO$_{4}$, based on measurements of resonant soft-x-ray magnetic scattering. A 2D incommensurate AF order exists at temperatures above the Neel temperature $T_N$. As the temperature cools across $T_N$, the interlayer exchange coupling prevails and the 2D incommensurability collapses to stabilize the 3D AF order. The measurements unravel spin correlations in the classical renormalized region for a non- standard (CE-type) antiferromagnet.