DTN
Chemical formula:
NiCl2·4SC(NH2)2
Lattice type:
Tetragonal, space group I4
How to grow:
Wet chemistry synthesis
Magnetic model:
Ideal S = 1 easy-plane quantum paramagnet
Why is it cool:
Magnetic order induced by field (z = 2 quantum phase transition), pressure (z = 1) or "chemical pressure"
A gapped quantum paramagnet can be pushed into a magnetically ordered state along entirely different routes: a magnetic field closes the gap at a z = 2 quantum critical point, where the magnon dispersion is quadratic and the transition is a magnon BEC, while pressure or chemical tuning close it at a z = 1, "relativistic" critical point with a linear spectrum. DTN, with its S = 1 nickel ions, strong easy-plane single-ion anisotropy and high tetragonal symmetry, was long considered the prototype for the field-induced route: the symmetry seemingly guarantees a Hamiltonian free of the anisotropic exchange terms that spoil BEC universality elsewhere. For a combination of reasons, it is not: our precision measurements found critical exponents inconsistent with magnon BEC and an intrinsic smearing of the transition [1].
The other routes proved more rewarding. A gap-closing transition to an ordered phase can be induced by chemical substitution on the non-magnetic site, replacing a few percent of chlorine with bromine: quantum criticality at zero field and ambient pressure [2]. The price is chemical disorder, which produces rather unusual spin dynamics near the critical composition [3]. Finally, combining high-frequency susceptibility, ultrasound and ESR measurements under pressure, we discovered a similar transition that is not affected by disorder: the spin gap closes at about 4.2 kbar of hydrostatic pressure, with no lattice distortion and the high spin symmetry fully preserved, establishing DTN as a perfect platform for z = 1 quantum criticality [4].
Magnetic excitations in bond-disordered DTNX with 6% bromine, measured by time-of-flight neutron spectroscopy at 60 mK [3]. A single magnon branch disperses across the entire Brillouin zone (inset: the reciprocal-space path); the small residual gap Δ at the dispersion minimum shows the material sitting close to, but not quite at, the composition-induced quantum critical point.
- [1] E. Wulf, D. Hüvonen, R. Schönemann, H. Kühne, T. Herrmannsdörfer, I. Glavatskyy, S. Gerischer, K. Kiefer, S. Gvasaliya, A. Zheludev, Critical exponents and intrinsic broadening of the field-induced transition in NiCl2·4SC(NH2)2 , Phys. Rev. B 91, 014406 (2015); arXiv:1412.0545.
- [2] K. Yu. Povarov, A. Mannig, G. Perren, J. S. Möller, E. Wulf, J. Ollivier, A. Zheludev, Quantum criticality in a three-dimensional spin system at zero field and pressure , Phys. Rev. B 96, 140414(R) (2017); arXiv:1708.02776.
- [3] L. Facheris, D. Blosser, R. Bewley, S. Gvasaliya, A. Zheludev, Finite-temperature dynamics and role of disorder in almost-critical Ni(Cl1−xBrx)2·4SC(NH2)2 , Phys. Rev. B 102, 224405 (2020); arXiv:2008.04037.
- [4] K. Yu. Povarov, D. E. Graf, A. Hauspurg, S. Zherlitsyn, J. Wosnitza, T. Sakurai, H. Ohta, S. Kimura, H. Nojiri, V. O. Garlea, A. Zheludev, A. Paduan-Filho, M. Nicklas, S. A. Zvyagin, Pressure-tuned quantum criticality in the large-D antiferromagnet DTN , Nat. Commun. 15, 2295 (2024); arXiv:2306.15450.