Mössbauer study of the Ising antiferromagnet DyPO4: Hyperfine parameters,g-factor anisotropy, and spin-lattice relaxation

Abstract

M\"ossbauer spectroscopy of the 26-keV $\ensuremath{\gamma}$-ray transition in $^{161}\mathrm{Dy}$ was employed to study nuclear hyperfine interactions in Ising-like DyP${\mathrm{O}}_{4}$. Single-crystal and polycrystalline samples were studied over the temperature range $1.8\ensuremath{\le}T\ensuremath{\lesssim}300$ K, which included the N\'eel temperature ${T}_{N}=3.39$ K. For $0\ensuremath{\le}T\ensuremath{\lesssim}10$ K the spectra could be analyzed in terms of a "static" $S=\frac{1}{2}$ spin Hamiltonian $\mathcal{H}={A}_{z}{I}_{z}{S}_{z}+(\frac{{A}_{\ensuremath{\perp}}}{2})({I}^{+}{S}^{\ensuremath{-}}+{I}^{\ensuremath{-}}{S}^{+})+P[3{I}_{z}^{2}\ensuremath{-}I(I+1)]$. The measured components of the magnetic hyperfine tensor parallel and perpendicular to the tetragonal $c$ axis are, respectively, $\frac{{A}_{z}}{2}=\ensuremath{-}831\ifmmode\pm\else\textpm\fi{}4$ MHz and ${A}_{\ensuremath{\perp}}=\ensuremath{-}14\ifmmode\pm\else\textpm\fi{}5$ MHz. This is the first reported measurement of an ${A}_{\ensuremath{\perp}}$ term in M\"ossbauer studies of dysprosium compounds. Using the known ionic $g$-factor component, ${g}_{z}=19.32\ifmmode\pm\else\textpm\fi{}0.01$, we calculate $k=\frac{{A}_{z}}{2h{g}_{z}}=43.0\ifmmode\pm\else\textpm\fi{}0.2$ and hence ${g}_{\ensuremath{\perp}}=0.3\ifmmode\pm\else\textpm\fi{}0.1$. The ratio of quadrupole parameters for the excited and ground nuclear states of $^{161}\mathrm{Dy}$ is $\frac{{P}_{e}}{{P}_{g}}=0.986\ifmmode\pm\else\textpm\fi{}0.003$ with $\frac{{P}_{g}}{h}=60.3\ifmmode\pm\else\textpm\fi{}0.6$ MHz. For $T\ensuremath{\gtrsim}10$ K the spectra are relaxation broadened and can be described well using the time-dependent Hamiltonian $\mathcal{H}(t)=f(t){A}_{z}{I}_{z}{S}_{z}+P[3{I}_{z}^{2}\ensuremath{-}I(I+1)]$, where $f(t)=\ifmmode\pm\else\textpm\fi{}1$. These spectra were analyzed using a random-fluctuation stochastic model for $f(t)$ and incorporating the exchange splittings obtained from previous optical work on the ground Kramers doublet. The analysis then depends on a single relaxation parameter $\ensuremath{\Omega}(T)$. Between $T=16\mathrm{and}36$ K the relaxation is dominated by an Orbach spin-lattice process of the form $\ensuremath{\Omega}={\ensuremath{\Omega}}_{0}{e}^{\frac{\ensuremath{-}{\ensuremath{\Delta}}_{G}}{T}}$, where ${\ensuremath{\Delta}}_{G}\ensuremath{\simeq}70$ ${\mathrm{cm}}^{\ensuremath{-}1}$.