$\mu$SR investigation of magnetically ordered states in the $A$-site ordered perovskite manganites $R$BaMn${}_2$O${}_6$ ($R=\text{Y}$ and La)

The magnetically ordered states of the $A$-site ordered perovskite manganites LaBaMn${}_2$O${}_6$ and YBaMn${}_2$O${}_6$ have been investigated by muon spin relaxation in zero external magnetic field. Our data reveal striking differences in the nature of the magnetically ordered state between these materials. For LaBaMn${}_2$O${}_6$, the $\mu$SR time spectra in the ferromagnetic state below $\simeq$330 K reveal a strongly inhomogeneous phase, reminiscent of a Griffiths phase. Within this magnetically inhomogeneous phase, an antiferromagnetic state develops below 150 K, which displays well defined static internal magnetic fields, but reaches only 30$\%$ of the volume fraction at low temperatures. A broad distribution of $\mu$SR relaxation rates is inferred down to the lowest temperatures. This behavior is similar to that in the $A$-site disordered La${}_{0.5}$Ba${}_{0.5}$MnO${}_3$. On the other hand, for YBaMn${}_2$O${}_6$, the $\mu$SR time spectra for both (i) the charge and orbital ordered and (ii) the paramagnetic phases reveal rather homogeneous states, namely, an exponential relaxation in the paramagnetic state and well defined muon spin oscillation in the antiferromagnetic state.

Figure 1

Crystal structure of $R$BaMn${}_2$O${}_6$, where the three lattice constants $a_p$, $b_p$, and $c_p$ are associated with the cell of the corresponding $A$-site disordered $R_{0.5}$Ba${}_{0.5}$MnO${}_3$. Dashed lines indicate the tetragonal unit cell of $R$BaMn${}_2$O${}_6$ ($R=\text{La}$, Pr, and Nd). Distortions and tilting of MnO${}_6$ octahedra are not shown.

Figure 2

ZF-$\mu$SR time spectra of YBaMn${}_2$O${}_6$ at 246, 174, and 75 K.

Figure 3

Fourier transform FFT of the time spectra below $T_N$ in YBaMn${}_2$O${}_6$.

Figure 4

Temperature dependence of (a) $A$ and $A_1$, (b) $\lambda$ and ${\lambda }_1$, and (c) ${\nu }_i$ in YBaMn${}_2$O${}_6$. Filled and open symbols indicate the data measured on cooling and warming, respectively. Inset shows the BaO plane ($z=0.5$), where green filled circles, red open circles, and blue stars represent Ba, O, and muon sites, respectively.

Figure 5

Time spectra of LaBaMn${}_2$O${}_6$ at 324, 300, 240, and 160 K in zero magnetic field. The solid curves indicate the best fit by the stretched exponential model for respective temperatures.

Figure 6

Temperature dependence of (a) $A$, (b) $\lambda$, and (c) $n$ for LaBaMn${}_2$O${}_6$ data measured at zero magnetic field.

Figure 7

Time spectrum for LaBaMn${}_2$O${}_6$ at 2.5 K in zero external field. The red solid curve is the best fit of Eq. (1), indicating two components of muon oscillation frequency, ${\nu }_1=69.6$ MHz and ${\nu }_2=31.6$ MHz.

Figure 8

Temperature dependence of the zero-field muon frequencies for LaBaMn${}_2$O${}_6$.

Figure 9

Temperature dependence of fractional amplitude of $A_s$, that is, (a) $A_s/A$, (b) ${\lambda }_f$, and (c) ${\lambda }_s$ in the two-exponential model for the FM phase of LaBaMn${}_2$O${}_6$.