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

To reach temperatures colder than the surface of any known planet, scientists must strip away the heat that permeates the universe. This is the realm of sub-Kelvin physics, where matter behaves in strange, quantum ways that are invisible at warmer temperatures. For decades, the standard tool for achieving this extreme cold has been the dilution refrigerator, a complex machine that relies on a mixture of two rare isotopes of helium. However, helium is becoming scarce and expensive, prompting a global search for alternative cooling methods. One promising path is adiabatic demagnetization refrigeration, a technique that uses magnetic fields to chill solid materials without any moving parts or liquid gases. The process works by first applying a strong magnetic field to align the tiny magnetic spins inside a material, which releases heat. When the field is removed while the material is isolated, the spins scramble back into disorder, absorbing heat from their surroundings and driving the temperature down. The challenge lies in finding the perfect solid material: it must hold enough magnetic disorder to absorb significant heat, yet interact so weakly with itself that it does not freeze into an ordered state before reaching the target temperature.

A team of researchers has now identified a new family of solid materials that offers a tunable solution to this problem. By swapping different rare-earth elements into the same crystal structure, they created two distinct refrigerants that excel at different stages of the cooling process. The materials are potassium-based phosphates containing either ytterbium or gadolinium, two heavy metals from the rare-earth series. When the scientists tested these compounds, they found that the ytterbium version could reach a bone-chilling 29.8 millikelvin, a temperature just a fraction of a degree above absolute zero. In contrast, the gadolinium version could not get quite as cold, stopping at 135.5 millikelvin, but it could hold that cold temperature for a much longer time. This difference arises because the two elements possess different internal magnetic structures. The ytterbium ions act like tiny, isolated magnets that barely talk to each other, allowing them to scramble easily and reach extreme cold. The gadolinium ions, however, carry a much larger magnetic charge and interact more strongly, creating a massive reservoir of disorder that can absorb heat for a longer duration, even if it cannot reach the same depth of cold.

The researchers synthesized these crystals in a laboratory by mixing high-purity powders of potassium carbonate, ammonium phosphate, and the respective rare-earth oxides. They heated the mixtures in a furnace to fuse the atoms into a solid lattice, then carefully ground and reheated the material to ensure it was pure. To understand the internal arrangement of the atoms, they fired neutrons at the ytterbium sample, a technique that reveals the positions of light atoms like oxygen which X-rays often miss. They discovered that in both compounds, the rare-earth ions form a distorted triangular pattern within the crystal. This geometry is known to create "frustration," a state where the magnetic spins cannot all align perfectly with their neighbors, keeping the material disordered and ready to absorb heat even at very low temperatures.

When the team measured how these materials responded to magnetic fields and temperature changes, the differences between the two became clear. The ytterbium compound behaves as if its magnetic spins are isolated pairs, a state that allows it to remain disordered down to the lowest temperatures tested. Its magnetic entropy, or the measure of its disorder, is limited to a specific, small amount, but this limitation is actually an advantage for reaching the lowest possible temperatures. The gadolinium compound, on the other hand, retains a much larger capacity for disorder because its spins are more complex and numerous. However, these spins interact more strongly with one another, which prevents the material from cooling as deeply as the ytterbium version.

In a direct test of their cooling power, the researchers placed samples of both materials in a magnetic field and then slowly reduced the field to zero while isolating them from heat. The ytterbium sample dropped from an initial temperature of 2 Kelvin to a record-low 29.8 millikelvin, staying below 40 millikelvin for about an hour. The gadolinium sample only reached 135.5 millikelvin, but it maintained a temperature below 150 millikelvin for over an hour and a half. This demonstrates that the two materials serve complementary roles: the gadolinium version acts as a high-capacity buffer that can hold a moderate level of cold for a long time, while the ytterbium version acts as a deep-freeze agent capable of reaching the most extreme temperatures.

The study confirms that these potassium rare-earth phosphates are chemically stable and do not contain water, unlike older cooling salts that tend to dry out and lose their effectiveness. This stability, combined with the ability to tune the cooling properties simply by changing the rare-earth element, suggests a new path for building compact, helium-free cooling systems. The work does not claim to have solved all cooling challenges, but it provides a clear blueprint for how to engineer solid materials that can balance the need for extreme cold with the need for long-lasting thermal stability. By understanding how the specific magnetic nature of different rare-earth elements influences the cooling process, scientists can now design multi-stage refrigeration systems that use one material to pre-cool a sample and another to push it into the deepest reaches of the quantum world.