Magnetic excitations of the spin-1/2 tetramer substance Cu${}_2$${}^{114}$Cd${}^{11}$B${}_2$O${}_6$ obtained by inelastic neutron scattering experiments

We performed inelastic neutron scattering experiments on Cu${}_2$${}^{114}$Cd${}^{11}$B${}_2$O${}_6$ powder. The magnetic excitations at low temperatures are similar to those of the interacting spin-1/2 tetramers in the ordered state. The weak excitations existing above 3 meV suggest that the Higgs mode appears in Cu${}_2$CdB${}_2$O${}_6$ at ambient pressure and zero magnetic field. We evaluated $J_1=27.3\pm 1.0$ and $J_2=-14.0\pm 1.4$ meV for the intra-tetramer interactions and $J_3=-0.4\pm 0.2$ and $J_4=1.4\pm 0.2$ meV for the inter-tetramer interactions. The spin gap in the isolated spin tetramer was calculated to be 1.6 meV, which is less than the effective inter-tetramer interaction value ($3.6\pm 0.8$ meV). Therefore, antiferromagnetic long-range order is possible, although the ground state of the isolated spin tetramer is the spin-singlet state. We discuss the temperature dependence of the magnetic excitations.