Evaluating the effects of structural disorder on the magnetic properties of ${\mathrm{Nd}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$

Motivated by the variation in reported lattice parameters of floating-zone-grown ${\mathrm{Nd}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$ crystals, we have performed a detailed study of the relationship between synthesis environment, structural disorder, and magnetic properties. Using a combination of polycrystalline standards, electron-probe microanalysis, and scattering techniques, we show that crystals grown under atmospheric conditions have a reduced lattice parameter relative to pristine polycrystalline powders due to occupation of the Nd site by excess Zr (i.e., negative stuffing). In contrast, crystals grown under high-pressure Ar are nearly stoichiometric with an average lattice parameter approaching the polycrystalline value. While minimal disorder of the oxygen sublattices is observed on the scale of the average structure, neutron pair-distribution function analysis indicates a highly local disorder of the oxygen coordination, which is only weakly dependent on growth environment. Most importantly, our magnetization, heat capacity, and single-crystal neutron scattering data show that the magnetic properties of crystals grown under high-pressure Ar match closely with those of stoichiometric powders. Neutron scattering measurements reveal that the signature of magnetic moment fragmentation—the coexistence of all-in-all-out (AIAO) magnetic Bragg peaks and diffuse pinch-point scattering due to spin-ice correlations–persists in these nearly stoichiometric crystals. However, in addition to an increased AIAO transition temperature, the diffuse signal is seemingly stabilized and remains nearly unchanged upon warming to 800 mK. This behavior indicates that both the AIAO magnetic order and spin-ice correlations are sensitive to deviations of the Nd stoichiometry.

Figure 1

Comparison of lattice parameters for polycrystalline samples and single crystals from this paper and the literature [16, 22, 23]. All lattice parameters were determined from laboratory XRD on powders at $T$ = 300 K. The error bars are contained within the symbols and represent one standard deviation.

Figure 2

Illustration of some of the key defect modes for ${\mathrm{Nd}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$ considered in this paper.

Figure 3

Refined room-temperature lattice parameters from laboratory XRD versus nominal Nd/Zr ratio for polycrystalline samples of ${\mathrm{Nd}}_{2(1-x)}{\mathrm{Zr}}_{2(1+x)}{\mathrm{O}}_7$ with $x$ = 0.2, 0.05, 0, and $-0.1$. The error bars are contained within the symbols and represent one standard deviation. The Nd-enriched polycrystalline sample is biphasic (${\mathrm{Nd}}_2{\mathrm{O}}_3 +$ “${\mathrm{Nd}}_{2.2}{\mathrm{Zr}}_{1.8}{\mathrm{O}}_7$”) as is expected from the change in slope. The dashed red line is a linear fit to the phase pure samples while the dashed black lines indicate the lattice parameters found by laboratory XRD for single crystal samples grown in this work.

Figure 4

EPMA data on sample disks of the FZ crystals cut perpendicular to the growth direction. Error bars represent the statistical error reported from the measurement software. The top panels show results for a number of spot measurements taken at different points within a small central region of the sample disk for the (a) air and (b) HP-Ar samples. The measurement region is represented by the green square (not to scale) in the inset of (b). The bottom panels show results from line scans for the (c) air and (d) HP-Ar samples. The direction of the scan is shown by the green arrow in the inset of (d). The distance is measured relative to one edge of the sample disk, extending across the diameter of the slice.

Figure 5

Rietveld refinement of synchrotron XRD data collected from powdered FZ-boules grown under (a) air and (b) HP-Ar. Refinement of TOF neutron diffraction data for powders of the same boules, (c) air and (d) HP-Ar. The left inset shows a close view of the (622) peak, illustrating the variable peak shapes observed in the XRD data but not the TOF neutron data. The right inset shows a closer view of the fit to the high-$Q$ data.

Figure 6

Fits to the neutron PDF spectra in the $r$ = 1.5–5 Å range for the air (top), HP-Ar (middle), and HP-80:20 (bottom) samples. Defect fluorite phase fraction is quoted in mass %.

Figure 7

(a) Magnetic susceptibility (1 emu = ${10}^{-3}\mathrm{A}{\mathrm{m}}^2$) for powder of the HP Ar-grown crystal and the $x$ = 0 polycrystalline powder taken at ${\mu }_{0}H$ = .1 T (1 T = 10 000 Oe). The inset shows the inverse susceptibility for same; the dashed red lines are the Curie-Weiss fits. (b) Magnetization versus field data for powder of the HP Ar-grown sample and the polycrystalline sample. The Van Vleck contribution has been subtracted. The dashed black line is the expected powder saturation value for a previously reported reduced lattice parameter (LP) single-crystal sample [24]. The inset shows magnetization data out to ${\mu }_{0}H$ = 14 T prior to subtraction of the Van Vleck contribution. The dashed red line is the linear fit from 8–14 T, which has been extended to low field.

Figure 8

Magnetization versus field (VSM) measurements to ${\mu }_{0}H$ = 14 T at $T$ = 2 K on polycrystalline ${\mathrm{Nd}}_{2(1-x)}{\mathrm{Zr}}_{2(1+x)}{\mathrm{O}}_7$ samples. The Van Vleck contribution ($M_{\text{VV}}$) has been subtracted.

Figure 9

Low-temperature $C_P$(T) data on the air, HP-Ar, and HP-80:20 samples. The inset shows $T_{\text{AFM}}$ (taken as the peak of the $C_P$(T) curve) versus lattice parameter from laboratory XRD.

Figure 10

(a) Order parameters collected for a HP-Ar single-crystal. The blue markers show the evolution of the integrated intensity at the (220) reflection. The error bars are extracted from the uncertainty in the Gaussian fit parameters. The orange markers show the same for the diffuse scattering along the (hhh) direction (excluding Bragg peaks and scaled to be comparable) (b) Map of the static diffuse scattering in the (hhl) scattering plane at 38 mK. The red box indicates the integration area. A 10 K background scan has been subtracted. The concentrated intensity at the (111) is due to the imperfect removal of the nuclear Bragg scattering. (c) Map of of the diffuse scattering around the (220) at 500 mK. Both (b) and (c) have been averaged according to the symmetry of the lattice.