Intrinsic magnetic order in ${\mathrm{Cs}}_{\mathbf{2}}{\mathrm{AgF}}_{\mathbf{4}}$ detected by muon-spin relaxation

We present the results of a muon-spin relaxation study of the high-$T_{\mathrm{c}}$ analog material ${\mathrm{Cs}}_2{\mathrm{AgF}}_4$. We find unambiguous evidence for magnetic order, intrinsic to the material, below $T_C=13.95\left(3\right)\mathrm{K}$. The ratio of interplane to intraplane coupling is estimated to be $\mid J^{\prime }∕J\mid =1.9\times {10}^{-2}$, while fits of the temperature dependence of the order parameter reveal a critical exponent $\beta =0.292\left(3\right)$, implying an intermediate character between pure two- and three-dimensional magnetism in the critical regime. Above $T_C$ we observe a signal characteristic of dipolar interactions due to linear $F\text{−}{\mu }^{+}\text{−}\mathrm{F}$ bonds, allowing the muon stopping sites in this compound to be characterized.

Figure 1

(Color online) Structure of ${\mathrm{Cs}}_2{\mathrm{AgF}}_4$ showing a possible magnetic structure. Candidate muon sites occur in both the $\left[\mathrm{CsF}\right]$ and $\left[{\mathrm{AgF}}_2\right]$ planes.

Figure 2

(a) Temperature evolution of ZF ${\mu }^{+}\mathrm{SR}$ spectra measured on ${\mathrm{Cs}}_2{\mathrm{AgF}}_4$ between 1.3 and $59.7\mathrm{K}$. (b) Above $T_C$ low-frequency oscillations are observed due to the dipole-dipole coupling of $\mathrm{F}\text{−}{\mu }^{+}\text{−}\mathrm{F}$ states. Inset: The energy level structure allows three transitions, leading to three observed frequencies. (c) Below $T_C$ higher-frequency oscillations are observed due to quasistatic magnetic fields at the muon sites. Inset: Maximum entropy analysis reveals two magnetic frequencies corresponding to two magnetically inequivalent muon sites.

Figure 3

(Color online) Results of fitting data measured below $T_C$ to Eq. (1). (a) Evolution of the muon-spin precession frequencies ${\nu }_1$ (closed circles) and ${\nu }_2$ (open circles) with temperature. Solid lines are fits to the function ${\nu }_i\left(T\right)={\nu }_i\left(0\right)(1-T∕T_C{)}^{\beta }$ as described in the text. Inset: Scaling plot of the precession frequencies with parameters $T_C=13.95\left(3\right)\mathrm{K}$ and $\beta =0.292$. Dotted lines show the results expected for the 2D Ising model $(\beta =0.125)$, 2D $XY$ model $(\beta =0.23)$, and 3D Heisenberg model $(\beta =0.367)$. (b) Relaxation rates ${\lambda }_1$ (closed circles), ${\lambda }_2$ (open circles), and ${\lambda }_3$ (closed triangles), as a function of temperature showing a rapid increase as $T_C$ is approached from below. Inset: Relaxation rates ${\lambda }_4$ (closed squares) and ${\lambda }_5$ (open squares) for $T>T_C$, which also increase close to $T_C$.