Spin decoupling under a staggered field in the ${\mathrm{Gd}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ pyrochlore

The influence of a staggered molecular field in frustrated rare-earth pyrochlores, produced via the magnetic iridium occupying the transition metal site, can generate exotic ground states, such as the fragmentation of the magnetization in the Ho compound. At variance with the Ising ${\mathrm{Ho}}^{3+}$ moment, we focus on the behavior of the quasi-isotropic magnetic moment of the ${\mathrm{Gd}}^{3+}$ ion at the rare-earth site. By means of macroscopic measurements and neutron scattering, we find a complex situation where different components of the magnetic moment are decoupled and contribute to two antiferromagnetic noncollinear arrangements: a high-temperature all in–all out order induced by the Ir molecular field, and Palmer and Chalker correlations that tend to order at much lower temperatures. This is enabled by the anisotropic nature of the Gd-Gd interactions and requires a weak easy-plane anisotropy of the ${\mathrm{Gd}}^{3+}$ moment due to the mixing of the ground state with multiplets of higher spectral terms.

Figure 1

(a) Sketch of the AIAO ordering produced on the rare earth (red) by the iridium AIAO order (blue). Scheme of different spin configurations on a tetrahedron: (b) AIAO along the $\langle 111\rangle$ directions; (c) PC in the planes perpendicular to the $\langle 111\rangle$ directions [12]; (d) total magnetic moments (black) obtained from the coexistence of AIAO (red) and PC (blue) components.

Figure 2

(a) High-temperature ZFC-FC magnetization of ${\mathrm{Gd}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ for ${\mu }_{0}H=10$ mT. Inset: ZFC-FC magnetization between 0.08 and 4 K for ${\mu }_{0}H=5$ mT. (b) Magnetization curves vs field at different temperatures and powder averaged $M\left(H\right)$ calculated using RPA. Specific heat vs temperature in a semilogarithmic scale: (c) Measurements at various magnetic fields and (d) zero-field MC calculations.

Figure 3

Neutron diffraction results on ${\mathrm{Gd}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$. (a) Difference between the D1B diffractograms recorded at 200 and 1.5 K. The magnetic Bragg peaks are refined with an AIAO magnetic order on the Gd and Ir sites. (An offset was added in order to make the fullprof refinement). (b) Temperature dependence of the refined AIAO ordered ${\mathrm{Gd}}^{3+}$ magnetic moment, compared to MC calculations. (c) Difference between the D4c diffractograms, performed with a much shorter wavelength, at low temperatures (3, 10, and 20 K) and 50 K displayed only up to $6{\AA }^{-1}$. (d) mPDF obtained by Fourier transforming the 3–50 K D4c diffractogram of (c) in the $0\text{–}10{\AA }^{-1}Q$ range (blue) compared to mPDF similarly obtained from a calculated AIAO order diffractogram corrected from the square of the magnetic form factor (red) [22].

Figure 4

(a)–(d) Magnetic scattering of ${\mathrm{Gd}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ from D7 polarized neutron measurements at various temperatures. (b)–(d) Gray lines: MC simulations of equal-time scattering functions using the instrumental $Q$ resolution. (d) Red line: fullprof refinement of coexisting AIAO and PC components of the magnetic moment.

Figure 5

(a) Temperature dependence of the inelastic neutron scattering of ${\mathrm{Gd}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ measured on IN6 compared to (b) MC calculations from 100 to 1.5 K and RPA calculations in the ordered phase at 50 mK. (c) Corresponding measured (red) and calculated (blue) $Q$-integrated $S\left(\omega \right)$.