Magnetic excitations in long-range stripe-ordered ${\mathrm{Pr}}_2{\mathrm{NiO}}_{4+\delta }$

We report an inelastic neutron scattering study on the magnetic excitations of ${\mathrm{Pr}}_2{\mathrm{NiO}}_{4+\delta }$ ($\delta \sim 0.24\pm 0.01$) at $T=10$ K. Spin stripe ordering becomes pronounced below $\sim 220$ K with an incommensurability $\epsilon \approx 0.346$, and a strong influence of interstitial oxygen is identified on establishing a long-range spin stripe ordering. Apart from the Goldstone modes emerging from the magnetic satellites (${\mathbf{q}}_m$), multiple homologous modes are observed along the spin stripe modulation separated by $\mathrm{\Delta }{\mathbf{q}}_m\approx 0.076$ in reciprocal lattice units, which is interpreted by the internal periodicity of the long-range ordered discommensurated spin stripes.

Figure 1

(a) Structure of ${\mathrm{Pr}}_2{\mathrm{NiO}}_{4+\delta }$ (Ni in dark cyan, Pr in grey, octahedrally coordinated oxygen to the Ni sites in red, and interstitial oxygen in deep blue). The chemical unit cell is indicated in black dashed lines. Squares in blue indicate the unoccupied interstitial sites ($8f$ Wyckoff) in the unit cell. (b) Scan at 10 K along the oxygen ordering modulation through the fourth-order satellite originating from (040), (inset) RT mapping of the ($hk0$) plane around the same oxygen ordering satellite. (c) Line cut along $l$ through the oxygen ordering modulation at $l=5/2$ in the ($h1l$) plane. Horizontal bars in blue represent the instrumental $Q$ resolution for the presented scans.

Figure 2

(a) Elastic scan through spin peak at ($1.346,0,0$) along $h$. Horizontal bar in blue represents the instrumental $Q$ resolution. (b) $T$-dependent magnetic intensity of the spin stripe order satellite at ($1,0.346,0$). (c) Two-dimensional cut of ($h1l$) plane obtained from the MAPS data at 10 K. The $h=\pm 0.346$ dashed lines in red corresponding to the magnetic incommensurabilities are presented to guide the eye. (d) Line cut along $l$ through spin stripe order ($l=$ integer) and oxygen order ($l=$ half-interger) satellites. (e) DCSS unit along the $a$ axis corresponding to the $\epsilon =0.346$ presented for a single twin domain. For the other orthogonal twin domain the DCSS unit is exactly the same but rotated by ${90}^{\circ }$ around the $c$ axis. Exchange interactions are indicated by solid lines in different colors.

Figure 3

Constant-$E$ scans performed at 10 K up to 65 meV on both sides of the AFM zone centers along $h$ and $k$ as indicated in the scans. Solid lines in red represent the cumulative fit and dashed lines in black show Gaussian fit components. Horizontal bars in blue represent the instrumental $Q$ resolution. The text in the left inset shows instrument configurations (e.g., fixed final ($E_f$) or initial ($E_i$) energy of neutrons, collimation, monochomator-anlyzer, chopper frequency for TAS and TOF) with which the scans have been performed.

Figure 4

(a) Spin wave dispersion calculated from SpinW. The measured peak positions from the inelastic scans have been overlaid on the calculated dispersion. Horizontal and vertical bars represent the FWHMs of the peaks in $Q$ and $E$, respectively. (b) Calculated spin wave dispersion for 1/3 stripe. (c) Elastic scan through the magnetic satellite reflection at $(0,1.346,0)$. (d), (e) Bose corrected constant-$Q$ scans at $(3,0,0)$ and at $(3,0.5,0)$. No background correction has been performed for the presented scans. All fits have been done keeping the background constant.