Absence of magnetic long-range order in ${\mathrm{Y}}_2{\mathrm{CrSbO}}_7$: Bond-disorder-induced magnetic frustration in a ferromagnetic pyrochlore

The consequences of random nonmagnetic-ion dilution for the pyrochlore family ${\mathrm{Y}}_2$($M{}_{1-x}N{}_x$)${}_2{\mathrm{O}}_7$ ($M$ = magnetic ion, $N$ = nonmagnetic ion) have been investigated. As a first step, we experimentally examine the magnetic properties of ${\mathrm{Y}}_2{\mathrm{CrSbO}}_7$ ($x=0.5$), in which the magnetic sites (${\mathrm{Cr}}^{3+}$) are percolative. Although the effective Cr-Cr spin exchange is ferromagnetic, as evidenced by a positive Curie-Weiss temperature, ${\mathrm{\Theta }}_{\mathrm{CW}} \simeq 19.5 \mathrm{K}$, our high-resolution neutron powder diffraction measurements detect no sign of magnetic long-range order down to 2 K. In order to understand our observations, we construct a lattice model to numerically study the bond disorder introduced by the ionic size mismatch between $M$ and $N$, which reveals that the bond disorder percolates at $x_b \simeq 0.23$, explaining the absence of magnetic long-range order. This model could be applied to a series of frustrated magnets with a pyrochlore sublattice, for example, the spinel compound $\mathrm{Zn}({\mathrm{Cr}}_{1-x}{\mathrm{Ga}}_x$)${}_2{\mathrm{O}}_4$, wherein a Néel to spin glass phase transition occurs between $x=0.2$ and 0.25 [Lee et al., Phys. Rev. B 77, 014405 (2008)]. Our study stresses the non-negligible role of bond disorder on magnetic frustration, even in ferromagnets.

Figure 1

(a) Main panel: ZFC $\chi -T$ curve of ${\mathrm{Y}}_2{\mathrm{CrSbO}}_7$ (S1) measured at ${\mu }_{0}H$ = 0.01 T. The black solid line is a Curie-Weiss fit to the data between 50 and 120 K using Eq. (2). Inset: ZFC and FC $\chi -T$ curves of S1 and S2 measured at ${\mu }_{0}H$ = 0.01 T. (b) HRNPD pattern (red solids) of ${\mathrm{Y}}_2{\mathrm{CrSbO}}_7$ (S1) measured at $T$ = 2.0 K, and $B$ = 0 T. Calculated pattern (black line), nuclear Bragg positions (blue vertical line), and difference (purple line) are also displayed. Inset: Enlarged version of a selected angle region. Additional peaks from ${\mathrm{YCrO}}_3$ (red arrows) and the vanadium sample can (black arrow) can be seen.

Figure 2

(a) Five possible configurations of an $M/N$-tetrahedron. (b) The percolation thresholds produced by our simulations on a $D$ $\times$ $D$ $\times$ $D$ pyrochlore lattice with $s$ sampling times of bond disorder (red, $D$ = 64 and $s$ = 100); Cr clusters with at least five (green, $D$ = 64 and $s$ = 16), four (blue, $D$ = 48 and $s$ = 16), and three (cyan, $D$ = 48 and $s$ = 16) nearest neighbor Cr sites; and site disorder (magenta, $D$ = 64 and $s$ = 50). (c) The evolution of the fraction of percolative bond- (circles) and site- (squares) ordered clusters as a function of the nonmagnetic fraction $x$ (blue closed: $D$ = 48, black open: $D$ = 64). The red (magenta) area marks the percolation region of bond (site) disorder. The gray hatched areas in (b) and (c) mark the position of ${\mathrm{Y}}_2{\mathrm{CrSbO}}_7$ with $\mathrm{\Delta }x$ = 0.01.

Figure 3

(a) Susceptibility ($M/H$) of ${\mathrm{Y}}_2{\mathrm{CrSbO}}_7$ (S1) vs temperature curves in the high field region. (b) Field scan of the magnetization of ${\mathrm{Y}}_2{\mathrm{CrSbO}}_7$ at 1.8 K. The black line is a linear fit to the data above 3.5 T. (c) Magnetic field dependence of the transition temperature $T_{\mathrm{t}}$ in ${\mathrm{Y}}_2{\mathrm{CrSbO}}_7$. (d) $x$ dependence of $T_{\mathrm{t}}$ measured at 5 T, showing the recovery of site percolation. The vertical arrow marks the position of $x_s$.