Magnetic ground states and magnetodielectric effect of $R$Cr(BO$_3$)$_2$ ($R$ = Y and Ho)

The magnetic, electric, and structural properties of polycrystalline $R$Cr(BO$_3$)$_2$ ($R$ = Y and Ho) samples were studied using AC/DC susceptibility measurements, dielectric constant measurements, and neutron scattering experiments. Both samples' Cr$^{3+}$ ions order in a noncollinear antiferromagnetic ground state with a transition temperature $T_N$ $\sim$8 K while the Ho$^{3+}$ ions do not order down to $T$ $\sim$ 2K. When a critical magnetic field is applied below $T_{N}$, the Cr$^{3+}$ and Ho$^{3+}$ ions both adopt a canted ferromagnetic ground state. Using inelastic neutron scattering, we estimated the $R$ = Y sample's intralayer and interlayer exchange strengths, J$_{intra}$ = -4.80 meV and J$_{inter}$ = 0.215 meV. The magnetodielectric effects in this system appear to depend on these exchanges. When the nonmagnetic $R$ = Y$^{3+}$ ions are replaced by magnetic Ho$^{3+}$ ions, the system exhibits stronger magnetodielectric responses near the critical field value. Our data suggests that this behavior results from an increased magnetostriction which is dependent on the Ho$^{3+}$ ions' ordering.