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 $_{3}$ $L n$ (PO $_{4}$ ) $_{2}$ ( $L n$ = Yb, Gd), which crystallize in a monoclinic $P 2_{1} / m$ 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 $J_{e f f} = 1 / 2$ 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 $_{3}$ $L n$ (PO $_{4}$ ) $_{2}$ as a chemically robust platform for rare-earth-tunable solid-state ADR.

Rare-earth tuning of magnetic entropy and interaction scales in K $_{3}$ $L n$ (PO $_{4}$ ) $_{2}$ ( $L n$ = Yb, Gd) for adiabatic demagnetization refrigeration

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Rare-earth tuning of magnetic entropy and interaction scales in K $_{3}$ $L n$ (PO $_{4}$ ) $_{2}$ ( $L n$ = Yb, Gd) for adiabatic demagnetization refrigeration

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Rare-earth tuning of magnetic entropy and interaction scales in K33​LnLn(PO44​)22​ (LnLn = Yb, Gd) for adiabatic demagnetization refrigeration

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Rare-earth tuning of magnetic entropy and interaction scales in K33​LnLn(PO44​)22​ (LnLn = Yb, Gd) for adiabatic demagnetization refrigeration

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Rare-earth tuning of magnetic entropy and interaction scales in K $_{3}$ $L n$ (PO $_{4}$ ) $_{2}$ ( $L n$ = Yb, Gd) for adiabatic demagnetization refrigeration

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Rare-earth tuning of magnetic entropy and interaction scales in K $_{3}$ $L n$ (PO $_{4}$ ) $_{2}$ ( $L n$ = Yb, Gd) for adiabatic demagnetization refrigeration

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