Triplon Bose-Einstein condensation and proximate magnetism in dimerized antiferromagnets

Dimerized quantum magnets provide a useful arena for novel quantum states and phases transitions with the singlet-triplet type of triplon excitations. Here we study the triplon physics and the Bose-Einstein condensation in two isostructural dimerized antiferromagnets $A$Cu(SeO$_3$)$_2$ ($A$ = Hg, Cd). With the systematic measurements, we demonstrate a dimer singlet ground state in HgCu(SeO$_3$)$_2$ with a triplon gap $\sim$ 7.9 K and a triplon Bose-Einstein condensation with an antiferromagnetic order in CdCu(SeO$_3$)$_2$ below 4.4 K. We further adopt the bond-operator technique and show that the elemental replacement preserves the Hamiltonian and allows the study in a unified theoretical framework with tunable interdimer and intradimer interactions on the opposite sides of the quantum critical point. With the peculiar Cu$_2$O$_8$ dimer configuration and effective ferromagnetic interdimer interaction, $A$Cu(SeO$_3$)$_2$ is distinguished from other $S$ = 1/2 dimerized antiferromagnets. Our results represent a global understanding of the magnetic ground states as well as the magnetic transitions in the dimerized magnets of this unusual crystal structure.