Rare-earth tuning of magnetic entropy and interaction scales in K$_3$$Ln$(PO$_4$)$_2$ ($Ln$ = Yb, Gd) for adiabatic demagnetization refrigeration

Adiabatic demagnetization refrigeration (ADR) based on frustrated rare-earth magnets provides a promising route toward helium-free sub-Kelvin cooling, while balancing magnetic entropy and interaction scales is essential for optimizing the ADR functionalities. Here we investigate the low-temperature magnetic and ADR properties of the alkali rare-earth double phosphates K$_3$$Ln$(PO$_4$)$_2$ ($Ln$ = Yb, Gd), which crystallize in a monoclinic $P2_1/m$ structure containing distorted isosceles triangular lattices of rare-earth ions. Magnetization and specific heat measurements confirm the absence of long-range magnetic ordering down to 0.1 K in both compounds. Direct quasi-ADR measurements demonstrate strongly contrasting refrigeration behaviors: K$_3$Yb(PO$_4$)$_2$ reaches a minimum temperature of 29.8 mK from an initial state of 2 K and 6 T, whereas K$_3$Gd(PO$_4$)$_2$ exhibits extended hold times below 150 mK associated with its larger magnetic entropy reservoir. Crystal-electric-field calculations confirm a $J_{\mathrm{eff}} = 1/2$ ground-state doublet in K$_3$Yb(PO$_4$)$_2$, while thermodynamic analysis based on magnetic entropy and interaction scales accounts for the distinct ADR performance of the two compounds. These results identify K$_3$$Ln$(PO$_4$)$_2$ as a chemically robust platform for rare-earth-tunable solid-state ADR.