**2. Experimental techniques**

We prepared the polycrystalline samples by solid-state sintering of oxides (Y<sup>2</sup> O3 , Sm<sup>2</sup> O3 , CuO) with a purity of 99.999% and carbonates (SrCO<sup>3</sup> 99.999% pure, BaCO<sup>3</sup> with a purity of 99.99%). All these chemicals were thoroughly mixed in desired proportions and calcined at 950°C in air for 12–18 h. The obtained ceramic was ground, mixed, pelletized and heated in air at 980°C for 16–24 h. This was repeated twice. For each sample, the circular pellets were subjected to heat treatment in oxygen at 450°C for 60–72 h and furnace cooled. This was denoted as sample [O].

X-ray diffraction spectra of the samples were measured with Philips diffractometer fitted with a secondary beam graphite monochromator and using Cu Kα (40 kV/20 mA) radiation. The angle 2θ was varied from 20° to 120° in steps of 0.025°and the counting time per step was 10 s. The XRD spectra were resolved with Rietveld refinement.

A detailed description of the basic arrangement of the experiment of the AC magnetic susceptibility can be found in [6]. The sample in the form of a slab is placed in the magnetic field Hext = Hdc + Hac cos(ωt) with the static component Hdc and the AC component with the amplitude Hac and the frequency f = ω/2π. The sample's magnetic response was detected by a pick-up coil surrounding the sample. Superconducting transitions were determined by the measure of the real (χ′) and the imaginary (χ″) parts of the AC magnetic susceptibility as a function of temperature in Hac = 0.11 Oe and at f = 1500 Hz. Also, χ′ and χ″ were measured in 0 < Hdc < 150 Oe with applied Hac.

We used the Van Der Pauw method [7] for measuring resistivity ρ(T). The sample was attached to a cane in a cryostat with closed helium circuit with a cryogenic pump, a regulator of temperature (1 μA–10 mA) and 1 μV resolution digital voltmeter controlled with a computer. Tc was determined by both the measured χ′(T) and ρ(T).

For each x, the same sample [O] was then heated in argon at 850°C for about 12 h, cooled to 20°C and oxygen was allowed to flow instead of argon and the sample was annealed at 450°C for about 72 h. This sample is denoted as [AO]. XRD, resistivity and AC susceptibility measurements were done on a part of this sample. We measured 6 + z by iodometry technique on a part of each sample.
