Softening of Magnetic Excitations Leading to Pressure-Induced Quantum Phase Transition in Gapped Spin System KCuCl$_3$

KCuCl$_3$ is a three dimensionally coupled spin dimer system, which undergoes a pressure-induced quantum phase transition from a gapped ground state to an antiferromagnetic state at a critical pressure of $P_{\rm c} \simeq 8.2$ kbar. Magnetic excitations in KCuCl$_3$ at a hydrostatic pressure of 4.7 kbar have been investigated by conducting neutron inelastic scattering experiments using a newly designed cylindrical high-pressure clamp cell. A well-defined single excitation mode is observed. The softening of the excitation mode due to the applied pressure is clearly observed. From the analysis of the dispersion relations, it is found that an intradimer interaction decreases under hydrostatic pressure, while most interdimer interactions increase.