Tweaking the spin-wave dispersion and suppressing the incommensurate phase in ${\text{LiNiPO}}_4$ by iron substitution

Elastic and inelastic neutron-scattering studies of $\text{Li}\left({\text{Ni}}_{1-x}{\text{Fe}}_x\right){\text{PO}}_4$ single crystals reveal anomalous spin-wave dispersions along the crystallographic direction parallel to the characteristic wave vector of the magnetic incommensurate phase. The anomalous spin-wave dispersion (magnetic soft mode) indicates the instability of the Ising-type ground state that eventually evolves into the incommensurate phase as the temperature is raised. The pure ${\text{LiNiPO}}_4$ system $\left(x=0\right)$ undergoes a first-order magnetic phase transition from a long-range incommensurate phase to an antiferromagnetic (AFM) ground state at $T_N=20.8\text{K}$. At 20% Fe concentrations, although the AFM ground state is to a large extent preserved as that of the pure system, the phase transition is second order, and the incommensurate phase is completely suppressed. Analysis of the dispersion curves using a Heisenberg spin Hamiltonian that includes interplane and in-plane nearest- and next-nearest-neighbor couplings reveals frustration due to strong competing interactions between nearest- and next-nearest-neighbor sites, consistent with the observed incommensurate structure. The Fe substitution only slightly lowers the extent of the frustration, sufficient to suppress the incommensurate phase. An energy gap in the dispersion curves gradually decreases with the increase in Fe content from $\sim 2\text{meV}$ for the pure system $\left(x=0\right)$ to $\sim 0.9\text{meV}$ for $x=0.2$.

Figure 1

(Color online) (a) Susceptibility measurements of ${\text{LiNiPO}}_4$ (solid line) and $\text{Li}\left({\text{Ni}}_{0.8}{\text{Fe}}_{0.2}\right){\text{NiPO}}_4$ (dashed line). (b) The respective derivatives of the susceptibilities with respect to temperature, showing the two features due to the transitions to IC and AFM in pure ${\text{LiNiPO}}_4$ and a single broad feature (second-order transition) in $\text{Li}\left({\text{Ni}}_{0.8}{\text{Fe}}_{0.2}\right){\text{PO}}_4$.

Figure 2

(Color online) Magnetic order parameter of pure ${\text{LiNiPO}}_4$ and $\text{Li}\left({\text{Ni}}_{0.8}{\text{Fe}}_{0.2}\right){\text{PO}}_4$ versus temperature. ${\text{LiNiPO}}_4$ undergoes a first-order phase transition from antiferromagnetic ground state to long-range incommensurate structure at $T_N=20.8\text{K}$ and at $T_{\text{IC}}\approx 21.7\text{K}$ the IC structure transforms to the paramagnetic state. The incommensurate spin correlations become negligible at about 35–40 K. By comparison, $\text{Li}\left({\text{Ni}}_{0.8}{\text{Fe}}_{0.2}\right){\text{PO}}_4$ transforms from the collinear ground state to the paramagnetic state by a second-order phase transition at $T_N=20.6\text{K}$. The labeled temperature regions refer to phases of pure ${\text{LiNiPO}}_4$.

Figure 3

(Color online) Longitudinal scans along the $\left(0k0\right)$ direction for (a) $\text{Li}\left({\text{Ni}}_{0.8}{\text{Fe}}_{0.2}\right){\text{PO}}_4$ and (b) ${\text{LiNiPO}}_4$. Above the Néel temperature no satellite peaks, due to the long-range incommensurate structure, were observed for ${\text{LiNi}}_{0.8}{\text{Fe}}_{0.2}{\text{PO}}_4$ in the temperature range between 18 and 22 K with 0.25 K temperature steps. The error bars in this paper are statistical in origin and represent one standard deviation. (r.l.u. stands for reciprocal-lattice units, for example, for the $\left(0q0\right)$ direction $q$ is normalized to $b^{\ast }=2\pi /b$.)

Figure 4

(Color online) Constant-$Q$ energy scans along the $\left(0q0\right)$ (a) for a single-crystal ${\text{LiNiPO}}_4$ at 10 K and (b) for $\text{Li}\left({\text{Ni}}_{0.8}{\text{Fe}}_{0.2}\right){\text{PO}}_4$ at 4 K. The solid lines are Guassian fits including constant background. All modes were measured from the (010) zone center.

Figure 5

(Color online) Spin-wave dispersion curves along the $\left(00q\right)$, $\left(0q0\right)$, and $\left(q00\right)$ directions at (a) 10 K for ${\text{LiNiPO}}_4$ and (b) at 4 K for $\text{Li}\left({\text{Ni}}_{0.8}{\text{Fe}}_{0.2}\right){\text{PO}}_4$. The solid and dashed lines are fits using the spin wave Eq. (2). The dotted line starting at the zone center indicates the spin-wave optical branch.

Figure 6

(Color online) (a) Atomic structure of ${\text{LiNiPO}}_4$. The magnetic moments of ${\text{Ni}}^{2+}$ are along the $c$ axis in ${\text{LiNiPO}}_4$. (b) Illustration of spin couplings in ${\text{LiNiPO}}_4$. The same definitions of bonding are used in the spin-wave Hamiltonian.