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Caption : fig. s1. x-ray diffraction patterns of the la0.6sr0.4mno3 nanopowders (tann = 800, 850, and 900 °c) measured at room temperature and fitted using the rietveld method. the experimental and calculated values (black and red curves), and difference curve (blue line) normalized to a statistical error are presented. vertical bars are calculated positions of diffraction peaks corresponding to the   space group.

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Caption : fig. s2(a). sem images (top) for the lsmo-800 (left)

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Caption : fig. s2(b). sem images (top) for the lsmo-850 (center)

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Caption : fig. s2(c). sem images (top) for the lsmo-900 (right)

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Caption : fig. s2(d).eds of chemical composition (bottom) for the lsmo-800 (left).

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Caption : fig. s2(e).eds of chemical composition (bottom) for the lsmo-850 (center).

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Caption : fig. s2(f).eds of chemical composition (bottom) for the lsmo-900 (right).

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Caption : fig. s3(a). particle size distribution in the la0.6sr0.4mno3 nanopowders with tann = 800°c according to sem images (inset).

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Caption : fig. s3(b). particle size distribution in the la0.6sr0.4mno3 nanopowders with tann = 900°c according to sem images (inset).

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Caption : fig. s4(a). approximation of the experimental values of d in the la0.6sr0.4mno3 nanopowders (tann = 800°c) by the gaussian function (sm2)

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Caption : fig. s4(b). approximation of the experimental values of d in the la0.6sr0.4mno3 nanopowders (tann = 800°c) by the lorentzian function (sm3)

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Caption : fig. s4(c). approximation of the experimental values of d in the la0.6sr0.4mno3 nanopowders (tann = 800°c) by the lognormal function (sm4)

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Caption : fig. s4(d). approximation of the experimental values of d in the la0.6sr0.4mno3 nanopowders (tann = 900°c) by the gaussian function (sm2)

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Caption : fig. s4(e). approximation of the experimental values of d in the la0.6sr0.4mno3 nanopowders (tann = 900°c) by the lorentzian function (sm3)

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Caption : fig. s4(f). approximation of the experimental values of d in the la0.6sr0.4mno3 nanopowders (tann = 900°c) by the lognormal function (sm4)

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Caption : fig. s5. approximation of the particle size dispersion d in the lsmo-800 nanopowder by the gaussian function f(d) (d0sem is the average particle size from sem image, 94% of the particles have a size d ≤ 50 nm).

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Caption : fig. s6. an approximation of the inverse magnetic susceptibility χ-1(t) = h/m(t) by the curie law for the lsmo-800 nanopowder (θ is the paramagnetic curie temperature, tconset is the temperature of the appearance of fm correlations, and μeff(mn) is the effective magnetic moment of manganese).

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Caption : fig. s7(a). cv curves of lsmo-800 electrodes in ar-saturated and o2-saturated 1 m koh at a sweep rate of 10 mv•s-1.

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Caption : fig. s7(b). cv curves of lsmo-800 electrodes in ar-saturated and o2-saturated 1 m koh at a sweep rate of 50 mv•s-1.

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Caption : fig. s8(a). lsv curves of lsmo-800 electrodes in ar-saturated and o2-saturated 1 m koh at a sweep rate of 1 mv•s-1 (ir-compensation 90%).

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Caption : fig. s8(b). lsv curves of lsmo-900 electrodes in ar-saturated and o2-saturated 1 m koh at a sweep rate of 1 mv•s-1 (ir-compensation 90%).

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Caption : fig. s9(a). сhronopotentiometry test of lsmo-800 catalyst at the current density of 10 ma•cm-2: cp curve

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Caption : fig. s9(b1). сhronopotentiometry test of lsmo-800 catalyst at the current density of 10 ma•cm-2: photo of electrode corrosion

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Caption : fig. s9(b2). сhronopotentiometry test of lsmo-800 catalyst at the current density of 10 ma•cm-2: photo of electrode corrosion

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Caption : fig. s10. the equivalent scheme for eis measurement: rs – solution resistance, rсt – the resistance of electron transfer on a anode; qh – constant phase element (cpe),represents helmholtz layer capacitance; qsc – constant phase element (cpe), represents space charge layer capacitance; rsc is the space charge separation resistance q is the constant phase element (cpe).

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Caption : fig. s11(a). cv curves of lsmo electrodes in 1 m na2so4 at different sweep rate: 1 mv•s-1.

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Caption : fig. s11(b). cv curves of lsmo electrodes in 1 m na2so4 at different sweep rate: 1 mv•s-1 for within voltages from 1,0 to 1,7.

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Caption : fig. s11(c). cv curves of lsmo electrodes in 1 m na2so4 at different sweep rate: 50 mv•s-1.