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Sub 1 K Adiabatic Demagnetization Refrigeration with Rare-Earth Borates Ba$_3$XB$_9$O$_{18}$ and Ba$_3$XB$_3$O$_9$, X = (Yb, Gd)

Marvin Klinger, Tim Treu, Felix Kreisberger, Christian Heil, Anna Klinger, Anton Jesche, Philipp Gegenwart

TL;DR

This work addresses the challenge of achieving ADR below 1 K without relying on helium-3 by examining four rare-earth borates, Ba3YbB9O18, Ba3YbB3O9, Ba3GdB9O18, and Ba3GdB3O9. The study combines structural, magnetic and thermodynamic measurements with direct ADR tests, revealing that Yb-containing compounds remain paramagnetic down to tens of millikelvin and can reach $T_{ADR}$ around 37–40 mK, while Gd-containing compounds show stronger interactions and magnetic ordering tendencies, achieving higher end temperatures but higher magnetic entropy. A key finding is that geometric frustration together with high moment density enhances ADR performance, though the studied borates still underperform benchmark compounds like KBaX(BO3)2 in entropy density. Overall, the results highlight the potential of frustrated rare-earth oxides for ADR at sub-K temperatures and underscore the trade-offs between entropy density and achievable end temperatures.

Abstract

Adiabatic demagnetization refrigeration (ADR) is regaining relevance for the refrigeration to temperatures below 1 K as global helium-3 supply is increasingly strained. While ADR at these temperatures is long established with paramagnetic hydrated salts, more recently frustrated rare-earth oxides were found to offer higher entropy densities and practical advantages since they do not degrade under heating or evacuation. We report structural, magnetic and thermodynamic properties of the rare-earth borates Ba$_3$XB$_9$O$_{18}$ and Ba$_3$XB$_3$O$_9$ with X = (Yb, Gd). Except for Ba$_3$GdB$_9$O$_{18}$, which orders at 108 mK, the three other materials remain paramagnetic down to their lowest measured temperatures. ADR performance starting at 2 K in a field of 5 T is analyzed and compared to literature results.

Sub 1 K Adiabatic Demagnetization Refrigeration with Rare-Earth Borates Ba$_3$XB$_9$O$_{18}$ and Ba$_3$XB$_3$O$_9$, X = (Yb, Gd)

TL;DR

This work addresses the challenge of achieving ADR below 1 K without relying on helium-3 by examining four rare-earth borates, Ba3YbB9O18, Ba3YbB3O9, Ba3GdB9O18, and Ba3GdB3O9. The study combines structural, magnetic and thermodynamic measurements with direct ADR tests, revealing that Yb-containing compounds remain paramagnetic down to tens of millikelvin and can reach around 37–40 mK, while Gd-containing compounds show stronger interactions and magnetic ordering tendencies, achieving higher end temperatures but higher magnetic entropy. A key finding is that geometric frustration together with high moment density enhances ADR performance, though the studied borates still underperform benchmark compounds like KBaX(BO3)2 in entropy density. Overall, the results highlight the potential of frustrated rare-earth oxides for ADR at sub-K temperatures and underscore the trade-offs between entropy density and achievable end temperatures.

Abstract

Adiabatic demagnetization refrigeration (ADR) is regaining relevance for the refrigeration to temperatures below 1 K as global helium-3 supply is increasingly strained. While ADR at these temperatures is long established with paramagnetic hydrated salts, more recently frustrated rare-earth oxides were found to offer higher entropy densities and practical advantages since they do not degrade under heating or evacuation. We report structural, magnetic and thermodynamic properties of the rare-earth borates BaXBO and BaXBO with X = (Yb, Gd). Except for BaGdBO, which orders at 108 mK, the three other materials remain paramagnetic down to their lowest measured temperatures. ADR performance starting at 2 K in a field of 5 T is analyzed and compared to literature results.

Paper Structure

This paper contains 8 sections, 8 equations, 7 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Materials and Methods
  3. Results
  4. Structure
  5. Magnetic properties
  6. Specific heat
  7. Actual refrigeration performance
  8. Conclusion

Figures (7)

  • Figure 1: PXRD data and literature peak positions for the product (green) as well as the most common foreign phase (red). The insets show the crystal structures with rare earth ions surrounded by oxygen octahedra (Yb: blue, Gd: purple) and separated by boron (orange) and barium (green). Oxygen atoms have been omitted for clarity and solid lines represent unit cells.
  • Figure 2: Magnetic moment $\mu$ in units of Bohr magneton $\mu_\mathrm{B}$ per magnetic ion versus applied field $H$ for different temperatures for Ba$_3$YbB$_3$O$_9$ (A), Ba$_3$YbB$_9$O$_{18}$ (B), Ba$_3$GdB$_3$O$_9$ (C) and Ba$_3$GdB$_9$O$_{18}$ (D). The black dotted lines show calculated moments from eq. \ref{['eq:freeIon']} for a free ion. The dashed pink lines show a mean field approximation according to eq. \ref{['eq:meanField']}.
  • Figure 3: Inverse magnetic susceptibility at an applied field of $7\,\mathrm{T}$ and fitted with eq. \ref{['eq:invChi']} with the listed parameters for Ba$_3$YbB$_3$O$_9$ (A), Ba$_3$YbB$_9$O$_{18}$ (B), Ba$_3$GdB$_3$O$_9$ (C) and Ba$_3$GdB$_9$O$_{18}$ (D).
  • Figure 4: Inverse susceptibility for low temperatures was measured at an applied field of $5\,\mathrm{mT}$, empty symbols were measured with helium-4, filled symbols with helium-3. This data was fitted with eq. \ref{['eq:invChi']} with $\chi_0 = 0$.
  • Figure 5: Specific heat and magnetic entropy for Ba$_3$GdB$_3$O$_9$(A,C) and Ba$_3$GdB$_9$O$_{18}$ (B,D) in various different fields. Colored lines display model calculations from eq. \ref{['eq:hcGd']} with "effective" field values as indicated.
  • ...and 2 more figures