Normal-state magnetic susceptibility in ${\mathrm{TlSr}}_2$(${\mathrm{Lu}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Ca}}_{\mathit{x}}$)${\mathrm{Cu}}_2$${\mathrm{O}}_{\mathit{y}}$ from the underdoped to the overdoped regime

Analyzing the normal-state magnetic susceptibility χ for ${\mathrm{TlSr}}_2$(${\mathrm{Lu}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Ca}}_{\mathit{x}}$)${\mathrm{Cu}}_2$ ${\mathrm{O}}_{\mathit{y}}$, whose carrier density covers the entire range from the underdoped to the overdoped regime, as a function of Ca concentration x and oxygen content y, we find significant correlations between χ and the carrier density. (1) The temperature dependence of χ gradually changes from positive to negative on going from the underdoped to the overdoped regime. It is almost entirely temperature independent at the optimum carrier density (maximum ${\mathit{T}}_{\mathit{c}}$). (2) The magnitude of χ gradually increases with the carrier density. For the optimum carrier density, the spin susceptibility at 200 K is estimated to be about 1.2×${10}^{\mathrm{-}4}$ emu/mol Cu. These characteristics are typical of most high-${\mathit{T}}_{\mathit{c}}$ cuprates and seem to be closely related to the high-${\mathit{T}}_{\mathit{c}}$ superconductivity mechanism.