Sul-Cu₂Cl₄

Chemical formula:

Cu₂Cl₄·C₄H₈SO₂

Lattice type:

Triclinic, space group P1̄

How to grow:

Wet chemistry synthesis

Magnetic model:

Frustrated Heisenberg 4-leg spin tubes

Why is it cool:

A quantum paramagnet with incommensurate correlations, and a field-induced transition to a helimagnetic state

In Sul-Cu₂Cl₄ the S = 1/2 spins form highly frustrated four-leg tubes with a gapped, quantum-disordered ground state whose short-range correlations are already incommensurate. An applied magnetic field closes the tiny gap, and the condensing magnons freeze into an incommensurate helimagnetic spiral. The spiral breaks inversion symmetry and therefore carries a uniform electric polarization: this was the first observed field-induced Bose-Einstein condensation transition taking a material from a paramagnetic, paraelectric state directly into a quantum multiferroic [1].

The same transition solved a long-standing experimental problem. Many groups have tried to measure the hallmark critical exponent of magnon BEC, φ = 2/3, which governs the shape of the phase boundary, and the lattice keeps getting in the way. If the crystal symmetry is lower than tetragonal, the residual anisotropy breaks the required rotational symmetry and the transition is actually of the Ising class; if the symmetry is tetragonal, magnetoelastic coupling destroys the critical point altogether and the transition turns first order. Sul-Cu₂Cl₄ evades both traps: because the high-field phase is incommensurate, the broken U(1) symmetry is not a rotation of the spins but a translation, a sliding of the spiral made frictionless by its very incommensurability, with the lattice fully decoupled. Better yet, the multiferroic coupling lets the transition be tracked through the dielectric channel with millikelvin precision: the measured boundary exponent φ = 0.63(3) is the textbook BEC value [2].

Magnetocapacitive effect in Sul-Cu₂Cl₄: the anomalous contribution to the sample capacitance as a function of magnetic field and temperature [2]. The sharp dielectric anomaly tracks the magnon BEC transition down to millikelvin temperatures; the peak positions map out the critical phase boundary with the textbook BEC exponent φ = 2/3.

• [1] F. Schrettle, S. Krohns, P. Lunkenheimer, A. Loidl, E. Wulf, T. Yankova, A. Zheludev, Magnetic-field induced multiferroicity in a quantum critical frustrated spin liquid , Phys. Rev. B 87, 121105(R) (2013); arXiv:1203.3127.

• [2] K. Yu. Povarov, A. Reichert, E. Wulf, A. Zheludev, Giant dielectric nonlinearities at a magnetic Bose-Einstein condensation , Phys. Rev. B 92, 140410(R) (2015); arXiv:1503.08173.