Nonlinear susceptibilities as a probe to unambiguously distinguish between canonical and cluster spin glasses

Abstract

Treating the randomly Fe-substituted optimally hole-doped manganite ${\text{La}}_{0.7}{\text{Pb}}_{0.3}({\text{Mn}}_{1\ensuremath{-}y}{\text{Fe}}_{y}){\text{O}}_{3}$ ($y=0.2,0.3$) as a test case, we demonstrate that a combined investigation of both odd and even harmonics of the ac magnetic response permits an unambiguous distinction between the canonical and cluster spin glasses. As expected for a spin glass (SG), the nonlinear ac magnetic susceptibilities ${\ensuremath{\chi}}_{3}(T,\ensuremath{\omega})$ and ${\ensuremath{\chi}}_{5}(T,\ensuremath{\omega})$ (odd harmonics) diverge at the SG freezing temperature ${T}_{g}=80.00(3)$ K [${T}_{g}=56.25(5)$ K] in the static limit and, like the imaginary part of the linear susceptibility, follow dynamic scaling with the critical exponents $\ensuremath{\beta}=0.56(3)$ [$\ensuremath{\beta}=0.63(3)$], $\ensuremath{\gamma}=1.80(5)$ [$\ensuremath{\gamma}=2.0(1)$], and $z\ensuremath{\nu}=10.1(1)$ [$z\ensuremath{\nu}=8.0(5)$] in the sample with composition $y=0.2$ ($y=0.3$). The nonlinear susceptibility ${\ensuremath{\chi}}_{NL}$, which has contributions from both ${\ensuremath{\chi}}_{3}$ and ${\ensuremath{\chi}}_{5}$, satisfies static scaling with the same choice of ${T}_{g}$, $\ensuremath{\beta}$, and $\ensuremath{\gamma}$. Irrespective of the Fe concentration, the values of the critical exponents $\ensuremath{\gamma}$, $\ensuremath{\nu}$, and $\ensuremath{\eta}$ are in much better agreement with those theoretically predicted for a three-dimensional ($d=3$) Heisenberg chiral SG than for a $d=3$ Ising SG. The true thermodynamic nature of the ``zero-field'' spin-glass transition is preserved even in finite magnetic fields. Unlike odd harmonics, even harmonics ${\ensuremath{\chi}}_{2}(T,\ensuremath{\omega})$ and ${\ensuremath{\chi}}_{4}(T,\ensuremath{\omega})$ make it evident that, apart from the macroscopic length scale of the spin-glass order in the static limit, there exists a length scale that corresponds to the short-range ferromagnetic order.