Ordering and Excitations in the Field-Induced Magnetic Phase of Cs$_{3}$Cr$_{2}$Br$_{9}$

Cs$_{3}$Cr$_{2}$Br$_{9}$ is an interesting example of interacting spin-dimer system. As in other isotropic antiferromagnets such as Haldane or alternating chains and ladders, the ground state in zero field is a total spin singlet separated from the excited triplet by an energy gap. In a magnetic field $H$, a phase transition occurs at a critical field $H_{c1}$, where the gap to the lowest component of the Zeeman-split triplet closes. Above $H_{c1}$, field-induced magnetic order (FIMO) for spin components perpendicular to $H$ is induced by inter-dimer or inter-chain couplings. The FIMO transition may be considered as a Bose-Einstein Condensation. Cs$_{3}$Cr$_{2}$Br$_{9}$ differs from other dimer systems currently studied ($e$.$g$. PHCC, TlCuCl$_{3})$ in two main ways: each Cr$^{3+}$ ion of the dimer has spin 3/2 rather than 1/2 for Cu-based systems and the arrangement of the dimers is hexagonal. This gives rise to anisotropy and frustration in a 3D lattice, respectively. The possibility of studying the magnetic ordering and the spin dynamics in a FIMO with sufficient detail to bring out features of frustration and anisotropy motivated the present neutron scattering study in Cs$_{3}$Cr$_{2}$Br$_{9}$*. Two field orientations have been exploited, perpendicular and parallel to the easy axis \textbf{c} (direction of the dimers). First, I present the diffraction study: the FIMO displays large hysteresis incommensurability, showing the importance of frustration. The impact of anisotropy is seen in the magnetic structure, whose nature strongly depends on the field direction. Second, I focus on spin dynamics: it quantifies the presence of anisotropy and shows its crucial role on the energy gap at $H_{c1}$, which is measurably open or not, depending on whether $H$ is perpendicular or parallel to \textbf{c}. Third, an explanation is proposed for the large value of the gap at higher field: it involves the mixing of higher order states (\textit{extended}-FIMO), reflected by the absence of magnetization plateaus. Comparison with the sister Cs$_{3}$Cr$_{2}$Cl$_{9}$ compound provides a test of this hypothesis. *B. Grenier \textit{et al.,} Phys. Rev. Lett. \textbf{92}, 177202 (2004)