Fig. 4: Composition–temperature phase diagram and carrier evolution in La₄Ni_3-xCu_xO_10+δ.

Phase diagram of La₄Ni_3-xCu_xO_10+δ showing the evolution of the density wave transition temperature (T_dw) as a function of Cu content. Blue square markers correspond to values extracted from resistivity data, and orange circle markers from magnetic susceptibility. The resistive transition temperature decreases linearly with Cu substitution and vanishes near x ≈ 0.20, indicating the complete suppression of long-range spin-density wave order, whereas the magnetic transition isn’t fully suppressed until \(x\approx 0.3\). The linear fit shown has a slope of -13.8 K per 1% Cu-substitution, with \({R}^{2}=0.98\). The error bars were taken using the full-width half maximum/minimum of the peak seen in \(\frac{d\rho }{{dT}}\) and \(\frac{d\chi }{{dT}}\). The green star markers represent the carrier concentration, where it increases for \(x < 0.3\) and subsequently plateaus for \(x > 0.3\), which matches the location of the full suppression of density wave phase in the magnetic susceptibility, or when T_dw approaches zero.