Frustrated magnetism in the two-dimensional triangular lattice of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mi>Li</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:msub><mml:mi>CoO</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math>

Magnetism of the simplest layered cobaltite ${\mathrm{Li}}_{x}{\mathrm{CoO}}_{2}$ with $x=1.0$, 0.95, and 0.7 has been investigated by positive muon spin rotation and relaxation $({\ensuremath{\mu}}^{+}\mathrm{SR})$ spectroscopy together with magnetic susceptibility measurements, using polycrystalline samples in the temperature range between 300 and 1.8 K. Weak transverse field ${\ensuremath{\mu}}^{+}\mathrm{SR}$ showed the appearance of magnetism below $\ensuremath{\sim}65\phantom{\rule{0.3em}{0ex}}\mathrm{K}\phantom{\rule{0.3em}{0ex}}(={T}_{c}^{\text{on}})$ for the sample with $x=1.0$. The volume fraction of the magnetic phase at 1.8 K is determined to be $\ensuremath{\sim}20%$ for ${\mathrm{LiCoO}}_{2}$, strongly suggesting that the observed magnetism is not induced by impurities but is an intrinsic behavior. This indicates that either a charge disproportionation $(2{\mathrm{Co}}^{3+}\ensuremath{\rightarrow}{\mathrm{Co}}^{2+}+{\mathrm{Co}}^{4+})$, a spin state transition $({t}_{2g}^{6}\ensuremath{\rightarrow}{t}_{2g}^{5}{e}_{g}^{1})$, or an appearance of magnetic ${\mathrm{Co}}^{3+}$ at surface occurs below 65 K. Zero field ${\ensuremath{\mu}}^{+}\mathrm{SR}$ spectra of ${\mathrm{LiCoO}}_{2}$ consist mainly of a slow relaxing signal due to random fields even at 1.8 K plus a small amount of a fast relaxing signal and an oscillating component, implying the presence of an antiferromagnetic order, as in the case of ${\mathrm{Na}}_{x}{\mathrm{CoO}}_{2}$ with $x\ensuremath{\geqslant}0.75$. For Li-deficient ${\mathrm{Li}}_{x}{\mathrm{CoO}}_{2}$ samples, ${T}_{c}^{\text{on}}$ decreases with decreasing $x$ from 50 K for $x=0.95$ to 25 K for $x=0.7$. The volume fraction of the magnetic phase is however almost independent of $x$ and is estimated as 20% at 1.8 K, but no oscillations were observed in the zero field spectrum.

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