Neutron Scattering and Magnetism
Laboratory for Solid State Physics · ETH Zurich

BPCB

Chemical formula:

(C5H12N)2CuBr4

Lattice type:

Monoclinic, space group P21/c

How to grow:

Wet chemistry synthesis

Magnetic model:

Heisenberg S = 1/2 spin ladder with strong rungs

Why is it cool:

Field-induced quantum criticality with zero-scale-factor universality, and exotic multi-magnon bound states

BPCB crystal

Atom legend

BPCB is the strong-rung Heisenberg spin ladder: antiferromagnetic S = 1/2 dimers weakly linked into well-isolated two-leg ladders. The energy scales are experimentally perfect. The spin gap closes near 6.6 T and saturation is reached by about 14 T, so the entire phase diagram, gapped paramagnet, gapless Luttinger-liquid regime and all, fits inside a standard laboratory magnet. Indeed, the material is so well suited to neutron spectroscopy that even the tiniest details of the Hamiltonian become measurable: our high-resolution experiments resolved the minute anisotropic terms that the idealized Heisenberg model omits [1].

Two of our favorite results live here. At the critical field the gap closes at a z = 2, one-dimensional quantum critical point, where the dilute magnon gas maps onto free fermions and every scaling function is known exactly, with no adjustable parameters, not even an overall scale factor. BPCB is where this "zero-scale-factor" universality was finally measured, using the ladder's leg-exchange symmetry as a built-in filter against the parasitic non-universal scattering that had doomed previous attempts on spin chains [2]. The same experiments held a surprise: just above the critical field the spectrum near zero wave vector visibly splits. Together with our theory colleagues we identified the extra modes as genuine multi-magnon bound states, with a binding energy independent of the field and an intensity that grows with the magnon density [3].

Scaling in BPCB

Magnetic excitation spectra of BPCB at 0.35 K in magnetic fields straddling the critical field of gap closure [2]. In panels (c) and (d) the upper branch near q|| = 0 is split: the additional mode is a magnon bound state [3].