Nature of the ferromagnet-paramagnet transition in Y$_{1-x}$Ca$_{x}$TiO$_{3}$

Neutron scattering, magnetometry, and muon spin rotation ($\mu$SR) measurements were performed to investigate the magnetic order and spin dynamics across the ferromagnet-to-paramagnet transition in the hole-doped Mott insulator Y$_{1-x}$Ca$_x$TiO$_3$. We find that the transition proceeds through a volume-wise phase separation into ferromagnetic and paramagnetic regions. Spin fluctuations with a characteristic timescale of $\sim$ 0.1 $\mu$s, as detected via $\mu$SR, are observed to appear at Ca concentrations $x \geq 0.10$. The magnetic phase separation, accompanied by a modest dynamic response, represents a novel behavior in Mott systems near the loss of magnetic order. It is linked to a previously observed insulator-metal transition and the associated electronic phase separation into hole-poor Mott insulating and hole-rich metallic phases for $0 < x < 0.50$. In particular, the $x$-dependence of the paramagnetic volume fraction strongly correlates with that of the volume fraction of the hole-rich metallic phase. The spin-wave spectra reveal a doping-induced crossover from isotropic to two-dimensional anisotropic exchange interactions, reflecting substantial changes in the orbital state with increasing Ca content.