Direct evidence for the all-in/all-out magnetic structure in the pyrochlore iridates from muon spin relaxation

In the pyrochlore iridates R${}_2$Ir${}_2$O${}_7$ (R = lanthanide, Y) determination of the magnetic structure of the iridium moments remains an outstanding problem despite the role this is expected to play in the formation of novel band structures and topologies in these materials. In this work, an analysis of the experimentally measured spontaneous muon spin precession frequency is presented which incorporates both probabilistic and ab initio modeling techniques to determine the ground state magnetic structure. It is shown that the experimentally observed results are consistent only with a magnetically ordered Ir${}^{4+}$ sublattice with the so-called “all-in/all-out” magnetic structure, and that the electronic state of the Ir${}^{4+}$ is best described by the $J_{\mathrm{eff}}=\frac{1}{2}$ model in several member compounds. Through this approach it is also demonstrated that such a simple structure is not likely to be present on the rare-earth sublattice which contains much larger localized moments.

Figure 1

The three spin configurations of the Ir${}^{4+}$ sublattice examined in this work. Each configuration is denoted by the single appropriate basis function following the notation in Ref. [21].

Figure 2

(a) PDF for the frequency distribution $f\left(\nu \right|\mu )$ calculated for Y${}_2$Ir${}_2$O${}_7$ by applying Eq. (1) to each of the spin configurations as described in the text. (b) Calculated probability distribution of the local Ir${}^{4+}$ moments $g\left(\mu \right|\nu )$ after application of Bayes' theorem for each of the configurations considered above.

Figure 3

Maps of the electrostatic potential inside the unit cell of Y${}_2$Ir${}_2$O${}_7$ for the (a) [001] plane located at $c=0.05a$ and (b) [110] plane passing through the origin which intersects the muon stopping site, and visualized using vesta [29]. Ir ions are shown as blue, Y as green, O as red, and the muon as black.

Figure 4

(a) PDFs $g\left(\mu \right|\nu )$ for Y${}_2$Ir${}_2$O${}_7$ and Eu${}_2$Ir${}_2$O${}_7$ for the ${\psi }_1$ configuration; the inset shows the variation of the peak in $f\left(\nu \right|\mu )$ calculated for an ideal $J=\frac{1}{2}$ moment as a function of $a$ and $x/a$ with $a=10.1669$ Å for variable x/a and $\mathit{x}/\mathit{a}=0.335$ for variable a; the error bars are given by the full width at half maximum of the peak. (b) and (c) show the $g\left(\mu \right|\nu )$ for Y${}_2$Ir${}_2$O${}_7$ and Eu${}_2$Ir${}_2$O${}_7$ in the ${\psi }_3$ and ${\psi }_6$ configurations, respectively. (d) $g\left(\mu \right|\nu )$ calculated for Nd${}_2$Ir${}_2$O${}_7$ where either the Ir or Nd lattice is ordered with the ${\psi }_1$ configuration.