Dynamics and field-induced order in the layered spin $S=1/2$ dimer system ${\left({\mathrm{C}}_5{\mathrm{H}}_6{\mathrm{N}}_2\mathrm{F}\right)}_2{\mathrm{CuCl}}_4$

The quasi-two-dimensional Heisenberg spin $S=1/2$ dimer system bis(2-amino-5-fluoro-pyridinium) tetrachlorocuprate(II) is studied by means of inelastic neutron scattering, calorimetry, and nuclear magnetic resonance (NMR) experiments. In the absence of an applied magnetic field we find dispersive triplet excitations with a spin gap of $\mathrm{\Delta }=1.112\left(15\right)$ meV and a bandwidth of 0.715(15) meV within the layers and 0.116(15) meV between the layers, respectively. In an applied magnetic field of ${\mu }_0{H}_c\approx 8.5$ T the spin gap is closed and we find a field-induced antiferromagnetically ordered phase.

Figure 1

(a) Crystal structure of (5FAP)${}_2{\mathrm{CuCl}}_4$ projected along the crystallographic $a$ direction. The blue lines show the dominant magnetic interaction $J$ forming spin dimers. These are coupled in the $b,c$ planes ($J_1$, green lines) creating 2D layers of coupled dimers. These are topologically equivalent to a honeycomb lattice or to a square lattice of dimers as sketched in (b). (c), (d) Crystal structure as projected along $c$ illustrating the buckled layers. Possible interlayer interactions are marked by orange and red lines.

Figure 2

Representative false-color slices through the four-dimensional inelastic neutron scattering data set measured in (5FAP)${}_2{\mathrm{CuCl}}_4$ at $T=100$ mK in zero magnetic field showing the dispersion of magnetic triplet excitations. The solid and dashed lines correspond to the calculated triplet dispersion branches as described in the text.

Figure 3

(a) Band extrema of the Zeeman-split triplet modes as a function of magnetic field. (b) Phase boundary of the field-induced long-range ordered antiferromagnetic phase as measured by specific heat and nuclear magnetic resonance.

Figure 4

Representative measurements of specific heat vs (a) temperature and (b) magnetic field. Peaks mark the onset of long-range antiferromagnetic order.

Figure 5

NMR data measured at ${\mu }_{0}H=9\mathrm{T}$. (a) Evolution of the ${}^{19}\mathrm{F}$ NMR spectrum upon entering the ordered phase. The splitting of the resonance indicates antiferromagnetic long-range order. (b), (c) Temperature evolution of the line splitting and (d), (e) the nuclear spin relaxation rate $1/T_1$.

Figure 6

(a) NMR line broadening and splitting and (b) $1/T_1$ relaxation rate vs magnetic field at $T=206$ mK.