(Rb/Cs)₂Cu₂Mo₃O₁₂

Chemical formula:

Rb₂Cu₂Mo₃O₁₂ and Cs₂Cu₂Mo₃O₁₂

Lattice type:

Monoclinic, space group C2/c

How to grow:

Bridgman furnace

Magnetic model:

Frustrated ferro-antiferromagnetic spin chains

Why is it cool:

Inverse Dzyaloshinskii-Moriya interactions make these chains quantum multiferroics

Growing single crystals of these copper molybdates is extremely challenging: the ones grown in our group are the first, and quite possibly the only ones ever obtained in any laboratory. The effort is well justified. Both materials realize spin chains with competing ferro- and antiferromagnetic interactions: the Rb compound is a gapped quantum paramagnet that orders only inside a "dome" of applied magnetic fields [1], while its Cs sibling orders already in zero field and has a rich phase diagram of its own [2]. In both, inverse Dzyaloshinskii-Moriya interactions couple the electric polarization linearly to the magnetic order parameter: these chains are quantum multiferroics.

In Rb₂Cu₂Mo₃O₁₂ that coupling resolves a problem of principle. Field-induced ordering of a gapped quantum paramagnet is a Bose-Einstein condensation of magnons, but the critical susceptibility of a BEC corresponds to no observable: the field conjugate to the order parameter is a magnetic field that reverses direction from one atom to the next, which no laboratory magnet can produce. Here the polarization is tied linearly to that very order parameter, so an ordinary capacitor measurement becomes the "impossible" experiment: along the quantum critical trajectory the dielectric susceptibility diverges with the exponent γ = 1.64(1), in excellent agreement with the value 3/2 predicted for a three-dimensional BEC. This was the first direct measurement of that quantity in any system [3].

Cs₂Cu₂Mo₃O₁₂ supplied a genuine surprise on top: a new kind of dielectric relaxation in which the activation barrier is set not by an optical phonon but by a magnon, an excitation whose energy is dialed by the applied field and collapses to zero at the 7.7 T quantum critical point [4,5]. The electric dipoles of the lattice thus relax by exchanging energy with individual quantum-critical magnons, which works only because, as this experiment proves, the magnons themselves carry an electric dipole moment.

Phase diagram of Cs₂Cu₂Mo₃O₁₂ in differently applied magnetic fields, obtained from specific heat measurements and torque magnetometry.

• [1] S. Hayashida, D. Blosser, K. Yu. Povarov, Z. Yan, S. Gvasaliya, A. N. Ponomaryov, S. A. Zvyagin, A. Zheludev, One- and three-dimensional quantum phase transitions and anisotropy in Rb₂Cu₂Mo₃O₁₂ , Phys. Rev. B 100, 134427 (2019); arXiv:1908.07739.

• [2] D. Flavián, S. Hayashida, L. Huberich, D. Blosser, K. Yu. Povarov, Z. Yan, S. Gvasaliya, A. Zheludev, Magnetic phase diagram of the linear quantum ferro-antiferromagnet Cs₂Cu₂Mo₃O₁₂ , Phys. Rev. B 101, 224408 (2020); arXiv:2004.10636.

• [3] S. Hayashida, L. Huberich, D. Flavián, Z. Yan, K. Yu. Povarov, S. Gvasaliya, A. Zheludev, Critical dielectric susceptibility at a magnetic BEC quantum critical point , Phys. Rev. Research 3, 033053 (2021); arXiv:2011.00107.

• [4] D. Flavián, P. A. Volkov, S. Hayashida, K. Yu. Povarov, S. Gvasaliya, P. Chandra, A. Zheludev, Dielectric Relaxation by Quantum Critical Magnons , Phys. Rev. Lett. 130, 216501 (2023); arXiv:2302.04234.

• [5] D. Flavián, P. A. Volkov, S. Hayashida, K. Yu. Povarov, S. Gvasaliya, P. Chandra, A. Zheludev, Dielectric relaxation in the quantum multiferroics Rb₂Cu₂Mo₃O₁₂ and Cs₂Cu₂Mo₃O₁₂ , Phys. Rev. B 110, 174433 (2024); arXiv:2406.12690.