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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.