Excitations in the spin-1 trimer chain compound $\mathrm{CaN}{\mathrm{i}}_3{\mathrm{P}}_4{\mathrm{O}}_{14}$: From gapped dispersive spin waves to gapless magnetic excitations

Magnetic excitations and the spin Hamiltonian of the spin-1 trimer chain compound $\mathrm{CaN}{\mathrm{i}}_3{\mathrm{P}}_4{\mathrm{O}}_{14}$ have been investigated by inelastic neutron scattering. The trimer spin chains in $\mathrm{CaN}{\mathrm{i}}_3{\mathrm{P}}_4{\mathrm{O}}_{14}$ result from the crystal structure that provides a special periodicity of the exchange interactions ($J_1\text{−}{J}_1\text{−}{J}_2$) comprising intratrimer ($J_1$) and intertrimer ($J_2$) exchange interactions along the crystallographic $b$ axis. Experimental data reveal gapped dispersive spin-wave excitations in the 3D long-range ordered magnetic state ($T_C=16\mathrm{K}$), and gapless magnetic excitations above the $T_C$ due to the low-dimensional spin-spin correlations within chains. Simulated magnetic excitations, by using the linear spin-wave theory, for a model of coupled trimer spin chains provide a good description of the observed experimental data. The analysis reveals both ferromagnetic $J_1$ and $J_2$ interactions within the chains, and an antiferromagnetic interchain interaction $J_3$ between chains. The strengths of the $J_1$ and $J_2$ are found to be closer ($J_2/J_1\sim 0.81$), and $J_3$ is determined to be weaker ($|J_3/J_1|\sim 0.69$), which is consistent with the spin-chain-type crystal structure. Presence of a weak single-ion anisotropy ($D/J=0.19$) is also revealed. The strengths and signs of exchange interactions explain why the 1/3 magnetization is absent in the studied spin-1 compound $\mathrm{CaN}{\mathrm{i}}_3{\mathrm{P}}_4{\mathrm{O}}_{14}$ in contrast to its $S=5/2$ counterpart Mn-based isostructural compound. The signs of the exchange interactions are in agreement with that obtained from the reported density-functional theory calculations, whereas their strengths are found to be significantly different. The relatively strong value of the $J_3$ in $\mathrm{CaN}{\mathrm{i}}_3{\mathrm{P}}_4{\mathrm{O}}_{14}$ gives a conventional 3D-type magnetic ordering behavior below the $T_C$ with full ordered moment at 1.5 K, however, retains its 1D character above the $T_C$. The present experimental study also reveals a sharp change of single-ion anisotropy across the $T_C$, indicating that the stability of the 3D magnetic ordering in $\mathrm{CaN}{\mathrm{i}}_3{\mathrm{P}}_4{\mathrm{O}}_{14}$ is ascribed to the local magnetic anisotropy in addition to interchain interactions. The present study divulges the importance of full knowledge of the exchange interactions in trimer spin-chain compounds to understand their exotic magnetic properties, such as 1/3 magnetization plateau. The importance of the observed gapless magnetic excitations of the strongly correlated spin chains above the $T_C$ is also discussed.

Figure 1

(a) Experimentally observed (circles) and calculated (line through the data points) neutron diffraction patterns for $\mathrm{CaN}{\mathrm{i}}_3{\mathrm{P}}_4{\mathrm{O}}_{14}$ at 6 K over $Q=2.1–9.4{\AA }^{-1}$. The difference between observed and calculated patterns is shown by the solid blue line at the bottom. The vertical bars indicate the positions of allowed nuclear Bragg peaks for the main phase $\mathrm{CaN}{\mathrm{i}}_3{\mathrm{P}}_4{\mathrm{O}}_{14}$ (top row) and the minor secondary phase $\mathrm{N}{\mathrm{i}}_3{\mathrm{P}}_2{\mathrm{O}}_8$ (bottom row), respectively. (b) A schematic view of the exchange interactions in $\mathrm{CaN}{\mathrm{i}}_3{\mathrm{P}}_4{\mathrm{O}}_{14}$. The Ni(1), Ni(2), P, and O ions are shown by green, blue, yellow, and red spheres, respectively. Ca ions are omitted for clarity. The intrachain exchange interactions between Ni(1) and Ni(2) ions are denoted by $J_1$, whereas between Ni(1) and Ni(1) ions are denoted by $J_2$. The interchain interaction between two Ni ions having shortest distance ($d_{\mathrm{Ni}\left(1\right)-\mathrm{Ni}\left(2\right)}=4.663\AA$) is shown by $J_3$. The individual trimer units are marked by ellipsoid.

Figure 2

2D color map of the INS intensity of $\mathrm{CaN}{\mathrm{i}}_3{\mathrm{P}}_4{\mathrm{O}}_{14}$ as a function of energy transfer (ћω) and momentum transfer ($\left|Q\right|$), measured at 4 K on the MERLIN spectrometer, with incident neutron energy of $E_{\mathrm{i}}=8$, 13, 21, and 40 meV. The color scales show the scattering intensity $S\left(\right|Q|,\omega )$ in an arbitrary unit. The sharp features with strong intensities (on the lower edge of the spectra, over 5–7 meV for $E_{\mathrm{i}}=8\mathrm{meV}$, over 1–4 meV for $E_{\mathrm{i}}=13\mathrm{meV}$, and over 2–8 meV for $E_{\mathrm{i}}=21\mathrm{meV}$) are experimental artifacts caused by defective detector elements. The sharp feature that is observable at the lower energies around $\left|Q\right|\sim 2{\AA }^{-1}$ for $E_{\mathrm{i}}=13\mathrm{meV},\left|Q\right|\sim 2.5{\AA }^{-1}$ for $E_{\mathrm{i}}=21\mathrm{meV}$, and $\left|Q\right|\sim 3.5{\AA }^{-1}$ for $E_{\mathrm{i}}=40\mathrm{meV}$ could be due to some electronic instability in data accusation units in time channels which automatically becomes stable with time [high-temperature patterns above 25 K (Fig. 3)].

Figure 3

2D Color map of the INS intensity of $\mathrm{CaN}{\mathrm{i}}_3{\mathrm{P}}_4{\mathrm{O}}_{14}$ as a function of energy transfer ($ћ\omega$) vs momentum transfer ($\left|Q\right|$) measured on the MERLIN spectrometer. (a)–(c) The inelastic spectra measured with incident neutron energy of $E_{\mathrm{i}}=8\mathrm{meV}$ at 4, 12, and 18 K, respectively. (e)–(l) The INS spectra measured with incident neutron energy of $E_{\mathrm{i}}=21\mathrm{meV}$ at 4, 8, 12, 15, 18, 25, 50, and 100 K, respectively. The color scales show the scattering intensity $S\left(\left|Q\right|,\omega \right)$ in arbitrary units. (d), (m), and (n) The intensity vs energy transfer curves for $E_{\mathrm{i}}=8$ and 21 meV, respectively. For $E_{\mathrm{i}}=8\mathrm{meV}$, the intensities were obtained by integrations over $\left|Q\right|=0–3.5{\AA }^{-1}$ and for $E_{\mathrm{i}}=21$ meV, the integrations were performed over $\left|Q\right|=0–2.3{\AA }^{-1}$).

Figure 4

(a) The measured intensity vs energy transfer curves for $E_{\mathrm{i}}=13$ meV at different temperatures. The instrumental profile is shown by the dashed line (vanadium curve). The intensities were obtained by integrations over $\left|Q\right|=0–1.8{\AA }^{-1}$. The curves are shifted vertically for clarity. (b) The measured curves after subtraction of V curve at 4, 8, 12, 15, 18, 25, and 50 K. (c), (d) The temperature variation of the energy gaps and the integrated intensity, respectively.

Figure 5

(a) Experimentally measured (at 4 K) and (b) simulated (by the spinw program) spin-wave excitation spectra. The strong intensity over 5–7 meV on the lower edge of the experimental spectrum is an artifact caused by defective detector elements. (c) The constant energy cuts as a function of momentum transfer; summed over 0.7–0.8, 0.8–0.9, 0.9–1.0, 1.0–1.1, and 1.1–1.2 meV, respectively. (d) The constant momentum transfer $\left|Q\right|$ cuts over the lower edge of the lowest-energy excitation band illustrating the dispersion of the excitation mode. The solid lines are the guide to the eyes. Cuts are taken for $\left|Q\right|=0.35$, 0.45, 0.55, 0.65, 0.75, 0.85, 0.95, 1.05, 1.15, and $1.25{\AA }^{-1}$ with a width of $0.1{\AA }^{-1}\left(\right|Q|\pm 0.05{\AA }^{-1})$. (e) The momentum dependence of the lower edge of the lowest-energy band. The experimental scattering intensity as a function of (f) energy transfer (integrated over $\left|Q\right|$ range $0–3.5{\AA }^{-1}$) and (g) momentum transfer (integrated over $\mathrm{\Delta }E=1–2.5\mathrm{meV}$), respectively. The spin-wave calculated intensities (red solid lines) are also plotted for comparison. To match with the experimental intensity, a constant scale factor to the calculated intensity has been applied in addition to a constant background. The addition intensity for the experimental spectra over 5–7 meV in (f) appears from the defective detector elements (for details see caption of Fig. 2).

Figure 6

The powder averaged spin-wave excitation spectra for the values, predicted by the DFT calculation for $\mathrm{CaN}{\mathrm{i}}_3{\mathrm{P}}_4{\mathrm{O}}_{14}$, (a) GGA model $J_1=-2.85,J_2=-1.49,J_3=5.63$ and $D=-0.25\mathrm{meV}$, and (b) $\mathrm{GGA}+{\mathrm{U}}_{\mathrm{eff}}$ model $J_1=-1.54,J_2=-0.578,J_3=2.66$ and $D=-0.25\mathrm{meV}$. Color bar represents the intensity in the arb. units.

Figure 7

(a) The simulated dispersion curves along the different crystallographic directions with the derived parameters $J_1=-1.3$, $J_2=-1.05$, $J_3=0.9$, and $D=-0.25$ meV. The intensity variation of the dispersion patterns shown by the color map. (b) The dispersion curves (solid blue lines) along the chain direction ($b$ axis) with the derived parameters $J_2/J_1=0.81$, $J_3/J_1=-0.69$, and $D/J_1=0.19$. The dashed curves represent the nature of the dispersion curves in the absence of the interchain interactions ($J_3=0$). (c) The variation of the dispersion curves with $J_2/J_1$ and $J_3=0$. Discrete energy levels are evident for $J_2=0$.

Figure 8

The local crystal structure of $\mathrm{CaN}{\mathrm{i}}_3{\mathrm{P}}_4{\mathrm{O}}_{14}$ highlighting (by solid ovals) the inter trimer superexchange interaction $J_2$. The arrows indicate the possible movements of the O3 ions upon substitution of a larger ion of similar type such as arsenic (As) at the P1 position.