Random-field effects in the diluted two-dimensional Ising antiferromagnet<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Rb</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Co</mml:mi></mml:mrow><mml:mrow><mml:mn>0.7</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Mg</mml:mi></mml:mrow><mml:mrow><mml:mn>0.3</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">F</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>

We report a comprehensive neutron scattering study of the spin correlationsin the diluted two-dimensional (2D) Ising antiferromagnet ${\mathrm{Rb}}_{2}$${\mathrm{Co}}_{0.7}$${\mathrm{Mg}}_{0.3}$${\mathrm{F}}_{4}$ in an applied magnetic field. As predicted by Fishman and Aharony, an applied field in this system produces a random staggered magnetic field. Random fields are expected to have drastic effects on the cooperative behavior of magnets although the detailed behavior remains controversial. It is found that the applied magnetic field, and by inference the concomitant random staggered fields, destroy the 2D long-range order for all temperatures and fields. The structure factor ${\mathcal{J}}^{\mathrm{zz}}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{Q}})=\ensuremath{\Sigma}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}}}^{}{e}^{i\stackrel{\ensuremath{\rightarrow}}{\mathrm{Q}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}}}{〈{S}_{\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}}}^{z}\ifmmode\cdot\else\textperiodcentered\fi{}{S}_{\stackrel{\ensuremath{\rightarrow}}{0}}^{z}〉}_{T}$ is well described as the sum of a Lorentzian plus a Lorentzian squared with the Lorentzian-squared term dominating at low temperatures. The integrated intensity of the Lorentzian-squared term exhibits the same temperature dependence as the Bragg intensity at zero field. The correlation length $\ensuremath{\kappa}$ and structure-factor peak intensity ${\mathcal{J}}^{\mathrm{zz}}({\stackrel{\ensuremath{\rightarrow}}{\mathrm{Q}}}_{0})$ exhibit power-law dependences on the applied field $H$, $\ensuremath{\kappa}\ensuremath{\sim}{H}^{1.6}$, and ${\mathcal{J}}^{\mathrm{zz}}({\stackrel{\ensuremath{\rightarrow}}{\mathrm{Q}}}_{0})\ensuremath{\sim}{H}^{\ensuremath{-}3.2}$ at low temperatures; the measured exponents agree reasonably with the values 2 and -4, respectively, deduced from theories with the lower marginal dimensionality ${d}_{l}=3$. The effective exponents initially increase slightly with increasing temperature and then decrease dramatically as $T\ensuremath{\rightarrow}{T}_{N}$, taking on values of about 0.7 and -1.2, respectively, at ${T}_{N}=42.5$ K. For small but nonzero applied fields the inverse correlation length may be factorized into a random-field part and a thermal part, $\ensuremath{\kappa}={\ensuremath{\kappa}}_{\mathrm{RF}}+{\ensuremath{\kappa}}_{T}$, with ${\ensuremath{\kappa}}_{T}\ensuremath{\sim}{e}^{\frac{\ensuremath{-}3.4{J}^{\mathrm{zz}}}{{k}_{B}T}}$ where ${J}^{\mathrm{zz}}$ is the Ising exchange constant. It is also found that for $T&lt;20$ K reproducible results are only obtained when the sample is cooled in the presence of the applied field; this history-dependent behavior is analogous to that found in spinglasses.

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