R₃BWO₉

Chemical formula:

R₃BWO₉ (R = Nd, Pr)

Lattice type:

Hexagonal, space group P6₃

How to grow:

Flux method

Magnetic model:

Quantum spin chains braided into frustrated spin tubes

Why is it cool:

A completely different frustration mechanism than the breathing kagome suggested by previous studies

The rare-earth magnets R₃BWO₉ (R = Pr, Nd) entered the literature as proximate spin-liquid candidates on the breathing kagome lattice. Our experiments tell a different story [1-3]. The crystal electric field forces strongly non-collinear Ising anisotropies on the magnetic sites, which all but silence the celebrated in-plane kagome exchange. What remains are the shortest, out-of-plane bonds: two competing ferro- and antiferromagnetic couplings that braid the spin chains into twisted triangular spin tubes. This is frustration of a completely different, quasi-one-dimensional kind, and it proves no less exciting than the kagome physics it displaces.

The same magnetic architecture, it turns out, hosts two entirely different kinds of quantum matter, depending on the ion that carries it. Nd³⁺ is a Kramers ion: its ground-state doublet is protected by time-reversal symmetry, the moments are true Ising spins, and the physics is essentially classical, from a cascade of fractional magnetization plateaus to incommensurate order driven by thermally proliferating domain walls, all captured quantitatively by a two-parameter Ising model [1,3]. In the non-Kramers Pr³⁺, nothing protects the doublet: the crystal field splits it into two singlets, and every site becomes an Ising spin in a built-in transverse field. Quantum fluctuations are thus hard-wired into the Hamiltonian itself. Pr₃BWO₉ remains a quantum paramagnet down to T = 0, with a remarkable excitation spectrum in which sharp exciton-like spin waves coexist with a broad continuum that carries most of the spectral weight [2].

Magnetic excitation spectra of Pr₃BWO₉ at 0.3 K along five reciprocal-space directions (top row), compared with spin-wave theory for the minimal transverse-field Ising model (middle row) and with the full crystal-field-level calculation including structural disorder (bottom row) [2]. The minimal model captures the sharp modes; the broad continuum, which carries most of the intensity, requires the full treatment.

• [1] D. Flavián, J. Nagl, S. Hayashida, M. Yan, O. Zaharko, T. Fennell, D. Khalyavin, Z. Yan, S. Gvasaliya, A. Zheludev, Magnetic phase diagram of the breathing-kagome antiferromagnet Nd₃BWO₉ , Phys. Rev. B 107, 174406 (2023); arXiv:2301.05555.

• [2] J. Nagl, D. Flavián, S. Hayashida, K. Yu. Povarov, M. Yan, N. Murai, S. Ohira-Kawamura, G. Simutis, T. J. Hicken, H. Luetkens, C. Baines, A. Hauspurg, B. V. Schwarze, F. Husstedt, V. Pomjakushin, T. Fennell, Z. Yan, S. Gvasaliya, A. Zheludev, Excitation Spectrum and Spin Hamiltonian of the Frustrated Quantum Ising Magnet Pr₃BWO₉ , Phys. Rev. Research 6, 023267 (2024); arXiv:2402.14107.

• [3] J. Nagl, D. Flavián, B. Duncan, S. Hayashida, O. Zaharko, E. Ressouche, J. Ollivier, Z. Yan, S. Gvasaliya, A. Zheludev, Braided Ising spin-tube physics in a purported kagome magnet , Phys. Rev. B 111, L180406 (2025); arXiv:2409.07807.