Absence of moment fragmentation in the mixed $B$-site pyrochlore ${\mathrm{Nd}}_2{\mathrm{GaSbO}}_7$

Nd-based pyrochlore oxides of the form ${\mathrm{Nd}}_2{B}_2{\mathrm{O}}_7$ have garnered a significant amount of interest owing to the moment fragmentation physics observed in ${\mathrm{Nd}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$ and speculated in ${\mathrm{Nd}}_2{\mathrm{Hf}}_2{\mathrm{O}}_7$. Notably this phenomenon is not ubiquitous in this family, as it is absent in ${\mathrm{Nd}}_2{\mathrm{Sn}}_2{\mathrm{O}}_7$, which features a smaller ionic radius on the $B$ site. Here, we explore the necessary conditions for moment fragmentation in the Nd pyrochlore family through a detailed study of the mixed $B$-site pyrochlore ${\mathrm{Nd}}_2{\mathrm{GaSbO}}_7$. The $B$ site of this system is characterized by significant disorder and an extremely small average ionic radius. Similarly to ${\mathrm{Nd}}_2{\mathrm{Sn}}_2{\mathrm{O}}_7$, we find no evidence for moment fragmentation through our bulk characterization and neutron scattering experiments, indicating that chemical pressure (and not necessarily the $B$-site disorder) plays a key role in the presence or absence of this phenomenon in this material family. Surprisingly, the presence of significant $B$-site disorder in ${\mathrm{Nd}}_2{\mathrm{GaSbO}}_7$ does not generate a spin-glass ground state and instead the same all-in-all-out magnetic order identified in other Nd pyrochlores is found here.

Figure 1

Powder-averaged neutron scattering intensity maps of polycrystalline ${\mathrm{Nd}}_2{\mathrm{GaSbO}}_7$ measured on SEQUOIA at 5 K using incident energies (a) $E_i=$ 60 $\mathrm{meV}$ and (b) $E_i=$ 150 $\mathrm{meV}$. The corresponding $Q$-cuts have integration ranges of $Q=$ [1, 3] ${\AA }^{-1}$ and [3, 6] ${\AA }^{-1}$, respectively. Dashed lines indicate approximate energies of the observed excitations. (c) Calculated energy eigenvalues determined from a scaling analysis on ${\mathrm{Nd}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$ [40], exhibiting good agreement with the experimental spectra.

Figure 2

(a) Temperature dependence of the zero field cooled (ZFC) magnetic susceptibility of polycrystalline ${\mathrm{Nd}}_2{\mathrm{GaSbO}}_7$ in an external field of ${\mu }_{0}H=$ 0.1 T. A Curie-Weiss fit (dashed line) from 1.8 K to 15 K yields a Curie-Weiss temperature ${\theta }_{\mathrm{CW}}=-0.35\left(1\right)\mathrm{K}$, and an effective paramagnetic moment ${\mu }_{\mathrm{eff}}=2.415\left(1\right){\mu }_{\mathrm{B}}$/${\mathrm{Nd}}^{3+}$. (b) Field-dependence of the isothermal magnetization of polycrystalline ${\mathrm{Nd}}_2{\mathrm{GaSbO}}_7$ for various temperatures. At 1.8 K, the magnetization saturates at ${\mu }_{\mathrm{sat}}\sim 1.2{\mu }_{\mathrm{B}}/{\mathrm{Nd}}^{3+}$. (c) Temperature dependence of the ZFC magnetic susceptibility of polycrystalline ${\mathrm{Nd}}_2{\mathrm{GaSbO}}_7$ in an external field of ${\mu }_{0}H=$ 0.1 T extended into the ${}^3\mathrm{He}$ regime reveals a sharp transition at $T{}_{\mathrm{N}}$=1.1 K, corresponding to the onset of long-range antiferromagnetic order.

Figure 3

(a) Temperature dependence of the magnetic component of the heat capacity at 0 T for polycrystalline ${\mathrm{Nd}}_2{\mathrm{GaSbO}}_7$ revealing a $\lambda$ anomaly at 1.1 K, indicative of a transition to long range magnetic order. The magnetic component for ${\mathrm{Nd}}_2{\mathrm{GaSbO}}_7$ was isolated by subtracting off the normalized lattice contribution of the nonmagnetic analog ${\mathrm{Lu}}_2{\mathrm{GaSbO}}_7$. The raw heat capacity data for both systems is shown in the inset. (b) Corresponding entropy release for ${\mathrm{Nd}}_2{\mathrm{GaSbO}}_7$ approaching $Rln\left(2\right)$, as expected for a magnetic ground state doublet.

Figure 4

(a) Rietveld fits to neutron powder diffraction profiles for polycrystalline ${\mathrm{Nd}}_2{\mathrm{GaSbO}}_7$ collected on HB-2A at 10 K and 475 mK. A small fluorite-related ${\mathrm{Nd}}_3{\mathrm{SbO}}_7$ magnetic impurity ($<4\%$) is present. Contributions from the Bragg reflections of the sample can were fit using a Pawley refinement. (b) Enlarged version of the neutron powder diffraction data presented in (a), shown over a limited $Q$ range only. Additional scattering with a magnetic origin appears below $T_{\mathrm{N}}$ at the (220) and (311) Bragg peak positions. (c) A schematic of the all-in-all-out antiferromagnetic structure that is realized for ${\mathrm{Nd}}_2{\mathrm{GaSbO}}_7$ below $T_{\mathrm{N}}$. To improve clarity, only the ${\mathrm{Nd}}^{3+}$ ions are shown.

Figure 5

(a) Low-$Q$ neutron powder diffraction profiles and profile fits for polycrystalline ${\mathrm{Nd}}_2{\mathrm{GaSbO}}_7$ collected on HB-2A at 1.5 K under various applied fields between 0 T and 5 T. Additional scattering of magnetic origin appears for fields of 0.5 T and greater at the low $Q$ (111), (002), and (311) nuclear Bragg reflections, consistent with a ${\mathrm{\Gamma }}_9$ magnetic structure. (b) Field dependence of the refined ordered moment from magnetic Rietveld refinements for ${\mathrm{Nd}}_2{\mathrm{GaSbO}}_7$ at 1.5 K highlighting a field-induced transition between ${\mu }_{0}H=$ 0.1 and 0.5 $\mathrm{T}$. (c) Pictorial representation of the field-induced ferromagnetic ${\mathrm{\Gamma }}_9$ “ordered spin ice” magnetic structure identified by magnetic Rietveld refinements for ${\mathrm{Nd}}_2{\mathrm{GaSbO}}_7$ at 1.5 K and fields of 0.5 T and greater. For the purposes of clarity, only ${\mathrm{Nd}}^{3+}$ ions are shown.

Figure 6

Color contour maps and corresponding $Q$ cuts (integration range of $Q=$ [0.5, 1.0]${\AA }^{-1}$) of the neutron scattering intensity for polycrystalline ${\mathrm{Nd}}_2{\mathrm{GaSbO}}_7$ measured on IRIS using an $E_f=$ 1.84 meV for [(a), (b)] $T<T_{\mathrm{N}}$ and [(c), (d)] $T>T_{\mathrm{N}}$. The constant $Q$ cuts are well-described by the lineshape given by Eq. (13), as described in the main text. [(e), (f)] Temperature dependence of the lineshape fit parameters are consistent with the behavior of a spin-wave mode associated with long-range antiferromagnetic order.

Figure 7

Comparison of the $Q$ dependence of the spin-polarized, energy-integrated ($\lambda =$ 4.2 Å) differential magnetic cross section for polycrystalline ${\mathrm{Nd}}_2{\mathrm{GaSbO}}_7$ at temperatures above and below $T{}_{\mathrm{N}}$ (Bragg peaks removed). For purposes of clarity, a vertical offset of $1\frac{\mathrm{b}}{\mathrm{sr}·\mathrm{f}.\mathrm{u}.}$ has been introduced for each successive temperature.

Figure 8

Comparison of select physical properties of Nd cubic pyrochlores for various $B$-site cations (arranged in order of increasing average ionic radius). Data was retrieved from [24] (Sn, powder), [32] (ScNb, single crystal), [33] (ScNb, powder), [23] (Hf, powder), [48] (Zr, crystal), and [47] (Zr, powder). Open and filled markers denote powder and single crystal data, respectively.