Magnetic ground state and exchange interactions in the Ising chain ferromagnet <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>Co</mml:mi><mml:msub><mml:mi>Nb</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>6</mml:mn></mml:msub></mml:mrow></mml:math>

Abstract

Reported here are measurements and analysis of the magnetization ($M$) versus temperature (1.9--400 K) in magnetic fields $H$ up to 90 kOe for a polycrystalline sample of Ising chain ferromagnet $\mathrm{Co}{\mathrm{Nb}}_{2}{\mathrm{O}}_{6}$ with ${T}_{C}=2.9\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. For $T&gt;{T}_{C}$, the fit of magnetic susceptibility $\ensuremath{\chi}=M/H$ ($H=300\phantom{\rule{0.16em}{0ex}}\mathrm{Oe}$) to $\ensuremath{\chi}={\ensuremath{\chi}}_{0}+C/(T\ensuremath{-}\mathrm{\ensuremath{\Theta}})$ with ${\ensuremath{\chi}}_{0}=0.0009\phantom{\rule{0.28em}{0ex}}\mathrm{emu}\phantom{\rule{0.28em}{0ex}}\mathrm{mo}{\mathrm{l}}^{--1\phantom{\rule{0.16em}{0ex}}}\phantom{\rule{0.16em}{0ex}}{\mathrm{Oe}}^{--1}$ determined from high-$T$ data yields $\mathrm{\ensuremath{\Theta}}=11\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ and magnetic moment $\ensuremath{\mu}\phantom{\rule{0.16em}{0ex}}=4.994\phantom{\rule{0.16em}{0ex}}{\ensuremath{\mu}}_{B}$ per ${\mathrm{Co}}^{2+}$ ion calculated from experimental $C=3.12\phantom{\rule{0.16em}{0ex}}\mathrm{emu}\phantom{\rule{0.16em}{0ex}}\mathrm{K}\phantom{\rule{0.16em}{0ex}}\mathrm{mo}{\mathrm{l}}^{--1}\phantom{\rule{0.16em}{0ex}}{\mathrm{Oe}}^{--1}$. Values of $g$ obtained from ${\ensuremath{\mu}}^{2}/{{\ensuremath{\mu}}_{B}}^{2}={g}^{2}S(S+1)$ for spin $S=1/2$ and 3/2 are used to determine ${\ensuremath{\mu}}_{Z}=g\phantom{\rule{0.16em}{0ex}}S\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}{\ensuremath{\mu}}_{B}$ and compared with ${\ensuremath{\mu}}_{Z}$ obtained from saturation magnetization and neutron diffraction for $T\ensuremath{\ll}{T}_{C}$. This analysis of the data for both above and below ${T}_{C}$ shows that the ground state of ${\mathrm{Co}}^{2+}$ in $\mathrm{Co}{\mathrm{Nb}}_{2}{\mathrm{O}}_{6}$ has the effective spin $S=1/2$ and not $S=3/2$ expected from Hund's rules, the $S=1/2$ ground state resulting from the combined effects of a noncubic crystalline field and spin-orbit coupling. The fit of the data for $T&gt;{T}_{C}$ to $\ensuremath{\chi}=\phantom{\rule{4pt}{0ex}}{\ensuremath{\chi}}_{0}+(C/T)\phantom{\rule{0.16em}{0ex}}\mathrm{exp}({J}_{0}/2{k}_{B}T)$ valid for an Ising chain with $S=1/2$ yields the intrachain ferromagnetic exchange constant ${J}_{0}/{k}_{B}=6.2\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, whereas the $g$ value with $S=1/2$ and the experimental critical fields for spin flips yields interchain antiferromagnetic exchange constants ${J}_{1}/{k}_{B}=\ensuremath{-}0.42\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ and ${J}_{2}/{k}_{B}=\ensuremath{-}0.67\phantom{\rule{0.16em}{0ex}}\mathrm{K}$.

Topics & Concepts