Anomalous spin waves and the commensurate-incommensurate magnetic phase transition in ${\text{LiNiPO}}_4$

Detailed spin-wave spectra of magnetoelectric ${\text{LiNiPO}}_4$ have been measured by neutron scattering at low temperatures in the commensurate (C) antiferromagnetic (AF) phase below $T_N=20.8\text{K}$. An anomalous shallow minimum is observed at the modulation vector of the incommensurate (IC) AF phase appearing above $T_N$. A linear spin-wave model based on Heisenberg exchange couplings and single-ion anisotropies accounts for all the observed spin-wave dispersions and intensities. Along the $b$ axis an unusually strong next-nearest-neighbor AF coupling competes with the dominant nearest-neighbor AF exchange interaction and causes the IC structure.

Figure 1

(Color online) Measured (filled circles) spin-wave dispersion along three reciprocal directions, compared with a Holstein-Primakoff spin-wave calculation (full and dotted lines) as explained in the text. The insets show the corresponding measured and calculated intensities (in arbitrary units) as function of wave vector. The dispersions along $\left(H,1,0\right)$ and $\left(0,K,0\right)$ were measured at $T=2\text{K}$ on RITA-II, while the dispersion along $\left(0,1,L\right)$ was measured at $T=10\text{K}$ on HB1A.

Figure 2

(Color online) (a) Spin-wave energy gap at $\mathbf{Q}=\left(0,1,0\right)$ as function of temperature measured at RITA-II. The dashed line is a guide to the eyes. The inset shows constant $\mathbf{Q}=\left(0,1.055,0\right)$ scans at different temperatures with $\hslash \omega$ (in meV) along the $x$ axis and measured intensity (in counts per minute) along $y$. (b) The magnetic unit cell of ${\text{LiNiPO}}_4$ showing only ${\text{Ni}}^{2+}$ ions. The depicted spin configuration and exchange interactions are the ones used in the spin-wave model.

Figure 3

(Color online) Spin-wave dispersions in the $\left(0,K,L\right)$ plane corresponding to the most intense branch. In colors we present spin-wave intensities with red for high and blue for low intensity. (a) Experimental data from IN8 at ILL. (b) Calculated data using the spin-wave model described in the text. The mesh around 0 meV shows the deviation in energy between (a) and (b).

Figure 4

(Color online) (a) Constant $\mathbf{Q}=\left(0,1,L\right)$ cuts from IN8. At $\mathbf{Q}=\left(0,1,0.4\right)$ and (0,1,1.4) only a single branch is visible, but at $\mathbf{Q}=\left(0,1,1.8\right)$ and (0,1,2) both branches are observed. (b) Dispersions along $\left(0,1,L\right)$ measured at IN8 [blue (black) and red (gray) circles compared to the calculated spin-wave energies (full and dotted lines). The inset shows the calculated intensity of the dispersions. Two branches are observed at $\mathbf{Q}$ where the model predicts spin-waves with finite intensity that are well separated in energy. (c) Dispersions along $\left(0,K,2\right)$ measured at IN8 and compared to the calculated spin-wave energies. The inset shows the calculated intensity of the branches. Along $\left(0,K,0\right)$ [Fig. 1b] the intensity of the second branch is always zero, but here, along $\left(0,K,2\right)$, there are $\mathbf{Q}$-values where both branches have intensity and can be observed.