$\mu \mathrm{SR}$ and neutron diffraction studies on the tuning of spin-glass phases in the partially ordered double perovskites $\mathrm{SrM}{\mathrm{n}}_{1-x}{\mathrm{W}}_x{\mathrm{O}}_3$

We have studied the partially ordered double perovskite (PODP) and spin-glass phase in $\mathrm{Sr}\left(\mathrm{M}{\mathrm{n}}_{1-x}{\mathrm{W}}_x\right){\mathrm{O}}_3$ ($x=0.20$ to 0.40) using neutron powder diffraction (NPD), muon spin relaxation (μSR), magnetic susceptibility (χ), and x-ray photoelectron spectroscopy measurements. Structural studies reveal that $\mathrm{SrM}{\mathrm{n}}_{1-x}{\mathrm{W}}_x{\mathrm{O}}_3$ undergoes a quasicontinuous transformation from simple perovskite ($Pm-3m$) to PODP ($P{2}_1/n$) phase as $x$ increases. ${\chi }_{\mathrm{dc}}\left(T\right)$ and ${\chi }_{\mathrm{ac}}\left(T\right)$ measurements show a sharp cusplike peak at spin-glass transition $T_g$. The muon relaxation rate (λ) peaks at $T_g$ following a critical growth, given by $\lambda =\lambda \left(0\right){\tau }^{-w}\left[\tau =\left(T-T_g\right)/T_g\right]$. No long-range magnetic order is observed in NPD below $T_g$. These measurements confirm a tunable spin-glass state of $\mathrm{SrM}{\mathrm{n}}_{1-x}{\mathrm{W}}_x{\mathrm{O}}_3$ for $0.2<x<0.4$. The spin-glass phase appears with the onset of $\mathrm{M}{\mathrm{n}}^{2+}$ cations, which induce competing ferro-antiferro interactions leading to exchange frustration. The $T_g$ decreases as the W content and $\mathrm{M}{\mathrm{n}}^{2+}$ concentration increase. Our results suggest that the spin-glass phase can be tuned through the relative concentration of 2+, 3+, and 4+ Mn ions.

Figure 1

(a) Rietveld refined time-of-flight (TOF) neutron powder diffraction profile of $\mathrm{Sr}\left(\mathrm{M}{\mathrm{n}}_{1-x}{\mathrm{W}}_x\right){\mathrm{O}}_3$ for $x=0.30$. Inset shows the structure of a double perovskite phase, highlighting the presence of tetrahedral topology of $B/B$′ cations. (b) A typical crystal structure model of a partially ordered double perovskite of $\mathrm{Sr}\left(\mathrm{M}{\mathrm{n}}_{1-x}{\mathrm{W}}_x\right){\mathrm{O}}_3$ obtained after Rietveld refinement. (c) It depicts the biased occupancies of Mn at $2c$ and W at $2d$ sites for $x=0.30$. Atoms have been indicated in different colors.

Figure 2

(a), (b) The temperature variation of ${\chi }_{\mathrm{dc}}\left(T\right)$ for $\mathrm{Sr}\left(\mathrm{M}{\mathrm{n}}_{1-x}{\mathrm{W}}_x\right){\mathrm{O}}_3$, respectively, for $x=0.2$ and 0.3. The cusplike peak can be clearly seen. (c), (d) ${\chi }_{\mathrm{ac}}$($T$) variation of $\mathrm{Sr}\left(\mathrm{M}{\mathrm{n}}_{1-x}{\mathrm{W}}_x\right){\mathrm{O}}_3$, for $x=0.20$ and 0.30. Frequency dispersion of the cusplike peaks can be clearly seen in the insets.

Figure 3

Variation of spin-glass transition temperature $T_g$ and the ${\chi }_{\mathrm{dc}}\left(T_g\right)$, i.e., value of ${\chi }_{\mathrm{dc}}\left(T\right)$ at $T_g$, as a function of W concentration ($x$). $T_g$ marks the cusp of ${\chi }_{\mathrm{dc}}\left(T\right)$.

Figure 4

Enlarged view of the low-$q$ (high-$d$) regions of the bank-2 TOF-NPD profiles of $\mathrm{Sr}\left(\mathrm{M}{\mathrm{n}}_{1-x}{\mathrm{W}}_x\right){\mathrm{O}}_3$ samples with $x=0.30$, 0.32, and 0.40. Unlike Ref. [26] these profiles clearly depict (dashed vertical line) the absence of any peak at ∼9.2 Å showing AFM order in the PODP phase.

Figure 5

The temperature variation of $A_r, A_c$, and λ obtained from the $A$($t$) data. The relaxing asymmetry $A_r$ decreases sharply and λ peaks at $T_g$.

Figure 6

(a) log(λ) vs $\log \left\{\left(T-T_g\right)/T_g\right\}$ plot showing critical behavior of the spin freezing across the glass transition. Here ($w$) is the critical exponent of λ. (b) Zero to 0.3 T longitudinal field dependence of $A$($t$) spectra for $x=0.30$ sample at 5 K.

Figure 7

(a) Some of the possible superexchange models showing antiferro- or ferromagnetic interactions between given Mn charge states. (b) 2D schematic showing proposition of the possible cause of exchange frustration arising due to random distribution of mixed charge states of Mn leading to competing (FM/AFM) superexchange interactios in $\mathrm{Sr}\left(\mathrm{M}{\mathrm{n}}_{1-x}{\mathrm{W}}_x\right){\mathrm{O}}_3$, generally expected to occur for samples with $x\ge 0.20$.

Figure 8

Phase diagram showing various magnetic phases of $\mathrm{Sr}\left(\mathrm{M}{\mathrm{n}}_{1-x}{\mathrm{W}}_x\right){\mathrm{O}}_3$ as a function of ($x$).