Correlations and dynamics of spins in an XY-like spin-glass(Ni0.4Mn0.6)TiO3single-crystal system

Elastic and inelastic neutron scattering (ENS and INS) experiments were performed on a single crystal of $(\mathrm{N}{\mathrm{i}}_0.4\mathrm{M}{\mathrm{n}}_0.6)\mathrm{Ti}{\mathrm{O}}₃$ (NMTO) to study the spatial correlations and dynamics of spins in the XY-like spin-glass (SG) state. Magnetization measurements reveal signatures of SG behavior in NMTO with a freezing temperature of ${T}_{\mathrm{SG}}\ensuremath{\sim}9.1\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. The ENS experiments indicate that the intensity of magnetic diffuse scattering starts to increase around 12 K, which is close to ${T}_{\mathrm{SG}}$. Also, spin-spin correlation lengths $(\ensuremath{\xi})$ at 1.5 K are approximately $(21\ifmmode\pm\else\textpm\fi{}1)$ and $(73\ifmmode\pm\else\textpm\fi{}2)\phantom{\rule{0.16em}{0ex}}\AA{}$ in the interlayer and the in-plane directions, respectively, demonstrating that magnetic correlations in NMTO exhibit quasi-two-dimensional antiferromagnetic order. In addition, critical exponent $(\ensuremath{\beta})$ is determined to be $0.37\ifmmode\pm\else\textpm\fi{}0.02$ from the intensity of magnetic diffuse scattering confirms the XY-like SG state of NMTO. INS results show quasielastic neutron scattering (QENS) profiles below ${T}_{\mathrm{SG}}$. The lifetime of dynamic correlations $\ensuremath{\tau}\ensuremath{\sim}\ensuremath{\hbar}/{\mathrm{\ensuremath{\Gamma}}}_L$, obtained from the half-width at half-maximum of the Lorentzian $({\mathrm{\ensuremath{\Gamma}}}_L)$ QENS profiles, are approximately $(16\ifmmode\pm\else\textpm\fi{}1)$ and $(16\ifmmode\pm\else\textpm\fi{}2)$ ps at 10 K for two positions (0.00, 0.00, 1.52) and (0.01, 0.01, 1.50), respectively. Therefore, our experimental findings demonstrate that short-range-ordered antiferromagnetic clusters with short-lived spin correlations are present in the XY-like SG state of NMTO.