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Low-temperature spin dynamics of the double-layered perovskiteLa_2-2x_Sr_1+2x_Mn_2_O_7 (LSMO327) was systematically studied in a wide holeconcentration range (0.3 <= x < 0.5). The spin-wave dispersion, which is almostperfectly 2D, has two branches due to a coupling between layers within adouble-layer. Each branch exhibits a characteristic intensity oscillation alongthe out-of-plane direction. We found that the in-plane spin stiffness constantand the gap between the two branches strongly depend on x. By fitting tocalculated dispersion relations and cross sections assuming Heisenberg models,we have obtained the in-plane (J_para), intra-bilayer (J_perp) andinter-bilayer (J') exchange interactions at each x. At x=0.30, J_para=-4meV andJ_perp=-5meV, namely almost isotropic and ferromagnetic. Upon increasing x,J_perp rapidly approaches zero while |J_para| increases slightly, indicating anenhancement of the planar magnetic anisotropy. At x=0.48, J_para reaches -9meV,while J_perp turns to +1meV indicating an antiferromagnetic interaction. Such adrastic change of the exchange interactions can be ascribed to the change ofthe relative stability of the d_x^2-y^2 and d_3z^2-r^2 orbital states upondoping. However, a simple linear combination of the two states results in anorbital state with an orthorhombic symmetry, which is inconsistent with thetetragonal symmetry of the crystal structure. We thus propose that an ``orbitalliquid'' state realizes in LSMO327, where the charge distribution symmetry iskept tetragonal around each Mn site.Comment: 10 pages including 7 figure

physical review. b, condensed matter

Spin dynamical properties and orbital states of the layered perovskite<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">La</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:mi>−</mml:mi><mml:mn>2</mml:mn><mml:mi>x</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Sr</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mn>2</mml:mn><mml:mi>x</mml…

Spin dynamical properties and orbital states of the layered perovskiteLa2−2xSr1+2x