The crystallographic and magnetic phase diagram of the $n=2\mathrm{}$ layered manganite ${\mathrm{La}}_{2-2x}{\mathrm{Sr}}_{1+2x}{\mathrm{Mn}}_2{\mathrm{O}}_7$ in the region $x>~0.5$ has been studied using temperature-dependent neutron powder diffraction. The magnetic phase diagram reveals a progression of ordered magnetic structures generally paralleling that of three-dimensional (3D) perovskites with similar electronic doping: A $(0.5\mathrm{}<~x<~0.66)\to C$ $(0.75\mathrm{}<~x<~0.90)\to G$ $(0.90\mathrm{}<~x<~1.0).$ However, the quasi-2D structure amplifies this progression to expose features of manganite physics uniquely accessible in the layered systems: (i) a “frustrated” region between the A and C regimes where no long-range magnetic order is observed; (ii) magnetic polytypism arising from weak interbilayer magnetic exchange in the type-C regime; and (iii) a tetragonal-to-orthorhombic phase transition whose temperature evolution directly measures ordering of $d_{{3y}^2-r^2}$ orbitals in the $a-b$ plane. This orbital-ordering transition is precursory to type-C magnetic ordering, where ferromagnetic rods lie parallel to the b axis. These observations support the notion that $e_g$ orbital polarization is the driving force behind magnetic spin ordering. Finally, in the crossover region between type-C and type-G states, we see some evidence for the development of local type-C clusters embedded in a type-G framework, directly addressing proposals of similar short-range magnetic ordering in highly doped ${\mathrm{La}}_{1-x}{\mathrm{Ca}}_x{\mathrm{MnO}}_3$ perovskites.

We report on the temperature dependence of the crystal and magnetic structure of the layered colossal magnetoresistive manganite, ${\mathrm{La}}_{2-2x}{\mathrm{Sr}}_{1+2x}{\mathrm{Mn}}_2{\mathrm{O}}_7,\hspace{0.5em}x=0.3\mathrm{}$. Neutron-diffraction measurements show that the insulator-metal (IM) transition ${(T}_{\mathrm{IM}})$ at ∼100 K is accompanied by a ferromagnetic (FM) ordering of spins within ${\mathrm{MnO}}_6$ bilayers (intrabilayer coupling), but with an antiferromagnetic coupling between neighboring bilayers (interbilayer coupling). Below $T_{\mathrm{IM}},$ the Mn spins rotate from ∼45° inclination to the c axis until they are almost parallel to the c axis at 5 K. Coincident with this spin reorientation, a FM c axis component develops below 75 K. Evidence from both neutron and synchrotron x-ray-diffraction experiments suggest that the FM c-axis magnetic moment results from a second layered manganite phase with composition $0.3\lesssim x\lesssim 0.32$. This observation emphasizes the need for thorough examination of the homogeneity when measuring bulk properties (e.g., magnetization, transport) of nominally x=0.3 samples. Associated with the electronic and magnetic transitions, a pronounced lattice response along the c axis (observed in both phases) signals a transfer of charge into $d_{x^2-y^2}$ orbitals in the low-temperature phase. That the lattice effects here are opposite in sign to those observed in the x=0.4 layered manganite points to the sensitivity of the spin-lattice-charge coupling to dopant concentration in these reduced-dimensionality manganites.

Charge-lattice fluctuations are observed in the layered perovskite manganite ${\mathrm{LaSr}}_2{\mathrm{Mn}}_2{\mathrm{O}}_7$ by Raman spectroscopy at temperatures as high as 340 K, and with decreasing temperature they become static, forming a charge-ordered (CO) phase below $T_{\mathrm{CO}}=210\mathrm{}\mathrm{K}.$ In the static regime, superlattice reflections are observed by neutron and x-ray diffraction with a propagation vector (1/4, -1/4, 0). Crystallographic analysis of the CO state demonstrates that the degree of charge and orbital ordering in this manganite is weaker than that in the three-dimensional perovskite manganites. Below $T_N=170\mathrm{}\mathrm{K},$ type-A antiferromagnetism (AF) develops and competes with the charge ordering, causing it to eventually melt below $T^{*}=100\mathrm{}\mathrm{K}.$ High-resolution diffraction measurements suggest that the CO and AF states do not coincide within the same region of material, but rather coexist as separate phases. The transition to type-A antiferromagnetism at lower temperatures is characterized by the competition between these two phases.