The infrared absorption of charge density waves coupled to a magnetic background is first observed in two manganites La1−xCaxMnO3 with x = 0.5 and x = 0.67. In both cases a BCS-like gap 2∆(T ), which for x = 0.5 follows the hysteretic ferro-antiferromagnetic transition, fully opens at a finite T0 < T Neel , with 2∆(T0)/kBTc ≃ 5. These results may also explain the unusual coexistence of charge ordering and ferromagnetism in La0.5Ca0.5MnO3.The close interplay between transport properties and magnetic ordering in the colossal magnetoresistance (CMR) manganites La(Nd) 1−x Ca(Sr) x MnO 3 is presently explained in terms of magnetic double exchange promoted by polaronic carriers along the path Mn +3 -O −2 -Mn +4 .[1] Charge hopping promotes the alignment of Mn +3 and Mn +4 magnetic moments, and vice versa. The polaronic effects are due to the dynamic Jahn-Teller distortion of the oxygen octahedra around the Mn +3 ions. The above mechanism explains how, in manganites with 0.2 < x < 0.48, any increase in the magnetization enhances the dc conductivity, and vice versa. However, La 0.5 Ca 0.5 MnO 3 shows an unpredicted coexistence of ferromagnetism and incommensurate charge ordering (CO). This compound is paramagnetic at room temperature, becomes ferromagnetic (FM) at T c ≃ 225 K and, by further cooling (C), antiferromagnetic (AFM) at a Néel temperature T C N ≃ 155 K.[2] Upon heating the sample (H) the FM-AFM transition is instead observed at T H N ≃ 190 K .[3] The dc conductivity σ(0) of La 0.5 Ca 0.5 MnO 3 is quite insensitive to the PM-FM transition at T c . [3] Xray, neutron [4] and electron diffraction [5] show quasicommensurate charge and orbital ordering in the AFM phase with wavevector q = (2π/a)( 1 2 − ǫ, 0, 0). The incommensurability ǫ increases with temperature and follows the hysteretic behavior of the AFM-FM transition, until charge ordering disappears above the Curie point T c .[5] At higher Ca doping, for 0.5 < ∼ x < ∼ 0.75, a transition to a charge ordered phase [6] is observed in the paramagnetic phase at T CO . T CO is a maximum (265 K) for x = 0.67 ≃ 2 3 , where the charge ordering is commensurate with the lattice. Below T CO , the system enters at T N an antiferromagnetic phase. For x = 0.67, T N ≃ 140 K.

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This paper presents a digital rights protection scheme for every type of document containing images or text using a number of steps that uses cryptography and watermarking. The entities involved in this process are two: the owner of the document that has digital rights on it and a generic user who can download or view the watermarked version of the original document. The watermarked document contains a QRcode that is repeatedly inserted, and scrambled, by the document right's owner, into the frequency components of the image, thus producing the watermarked image. The signed ID uniquely identifies every users using the system. The schema, a non-blind type, achieves good perceptive quality and fair robustness using the 3rd level of the Discrete Wavelet Transform. The experimental results show that, inserting more occurrences of a scrambled QR-code, the proposed algorithm is quite resistant to JPEG compression, rotation, cropping and salt and peeper noise.

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