Evidence of discrete energy states and cluster-glass behavior in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>Sr</mml:mi><mml:mrow><mml:mn>2</mml:mn><mml:mo>−</mml:mo><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>La</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:msub><mml:mi>CoNbO</mml:mi><mml:mn>6</mml:mn></mml:msub></mml:mrow></mml:math>

Abstract

We report the detailed analysis of specific heat $[{C}_{P}(T)]$ and ac susceptibility for magnetically frustrated ${\mathrm{Sr}}_{2\ensuremath{-}x}{\mathrm{La}}_{x}{\mathrm{CoNbO}}_{6}$ $(x=0--1)$ double perovskites to understand low-temperature complex magnetic interactions and their evolution with $x$. Interestingly, the observed Schottky anomaly in the $x\ensuremath{\leqslant}0.4$ samples shifts gradually toward higher temperatures with magnetic field as well as $x$, and the analysis reveals the persistence of the discrete energy states in these samples resulting from the spin-orbit coupling and octahedral distortion. Moreover, the extracted values of the Land\'e $g$ factor indicate the existence of high-spin state ${\mathrm{Co}}^{3+}$ ions energetically close to a nonmagnetic low-spin state. The specific-heat data show the $\ensuremath{\lambda}$-type anomaly for the $x\ensuremath{\geqslant}0.6$ samples due to evolution of the long-range antiferromagnetic ordering. Our analysis of low-temperature ${C}_{P}(T)$ data for the $x\ensuremath{\geqslant}0.6$ samples demonstrates the 3D isotropic Heisenberg antiferromagnetic (AFM) interactions and the temperature-induced second-order AFM-paramagnetic phase transition. More interestingly, we demonstrate the presence of the free ${\mathrm{Co}}^{2+}$-like Kramers doublet ground state in the $x=1$ sample. Further, the ac susceptibility and time evolution of the magnetization data reveal the low-temperature cluster-glass-like behavior in the $x=0--0.4$ samples, where spin-spin correlation strength decreases with $x$.

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