Exceptional field dependence of antiferromagnetic magnons in ${\mathrm{LiFePO}}_4$

Low-energy magnon excitations in magnetoelectric ${\mathrm{LiFePO}}_4$ have been investigated by high-frequency–high-field electron spin resonance spectroscopy in magnetic fields up to $B=58\mathrm{T}$ and frequencies up to $f=745\mathrm{GHz}$. For magnetic fields applied along the easy magnetic axis, the excitation gap softens and vanishes at the spin-flop field of $B_{\mathrm{SF}}=32\mathrm{T}$ before hardening again at higher fields. In addition, for $B\lesssim B_{\mathrm{SF}}$ we observe a resonance mode assigned to excitations due to Dzyaloshinskii-Moriya (DM) interactions, thereby evidencing a sizable DM interaction of $\approx 150\mu \mathrm{eV}$ in ${\mathrm{LiFePO}}_4$. Both the magnetization and the excitations up to high magnetic fields are described in terms of a mean-field theory model which extends recent zero-field inelastic neutron scattering results. Our results imply that magnetic interactions as well as magnetic anisotropy have a sizable quadratic field dependence which we attribute to significant magnetostriction.

Figure 1

Schematic view of magnetic structure of ${\mathrm{LiFePO}}_4$ at zero field, based on Refs. [15] and [32]. Numbers illustrate how the Fe moments are associated with four antiferromagnetic sublattices. $J_{ab}, J_{ac}, J_{bc}$, and $J_b$ are the leading magnetic interactions [note that $J_b$ does not significantly affect the AFMR model at $B<B_{\mathrm{SF}}$ and hence is omitted in the Hamiltonian equation (1)]. The figure was generated with vesta [33].

Figure 2

(a) Pulsed-field magnetization of ${\mathrm{LiFePO}}_4$ with $B\left|\right|b$ at $T=1.5\mathrm{K}$ [35]. The red line is a simulation of the data; see the text. Vertical dashed lines indicate the spin-flop field $B_{\mathrm{SF}}$ and the saturation field $B_{\mathrm{sat}}$. (b) Pulsed-field electron spin resonance up-sweep ($\to$) and down-sweep ($\leftarrow$) spectra at $T=4\mathrm{K}$ and $f=708\mathrm{GHz}$. The resonances are labeled with ${\omega }_{\mathrm{lin}}$ for the linear resonance branch and ${\omega }_{1,\mathrm{DM},\mathrm{SF}}$ (see Fig. 4). Pictograms indicate the magnetic structure with respect to the model for $B\left|\right|b$ (a) at $B<B_{\mathrm{SF}}$ (adapted from Ref. [15]) and (b) in the spin-flop phase.

Figure 3

Pulsed-field electron spin resonance up-sweep transmission spectra at $T\sim 4\mathrm{K}$ in the frequency range between $f=130\mathrm{GHz}$ and $f=708\mathrm{GHz}$. The vertical dashed line indicates the spin-flop field $B_{\mathrm{SF}}$.

Figure 4

Resonance fields at different frequencies (data points, cf. Fig. 3). Vertical dashed lines indicate the spin-flop field, and gray short-dashed lines are guides to the eye. Solid lines are model calculations (a) with exchange interactions $J$ and anisotropy $D_{\mathrm{b}}$ being magnetic-field-dependent parameters (model 1), (b) with additional Dzyaloshinskii-Moriya interaction (model 2), and (c) with a magnetic-field-dependent anisotropy tensor $D$ (model 3). See Table 1 for simulation parameters and Fig. S1 of the Supplemental Material [41] for a further comparison of the models.

Figure 5

HF-ESR transmission spectra measured at $f=348\mathrm{GHz}$ in the temperature regime between 2.6 and $\sim 20\mathrm{K}$. The vertical dashed line indicates the spin-flop field. Inset: Magnetic phase diagram of ${\mathrm{LiFePO}}_4$; data are from Ref. [35]. The horizontal dashed (red) line marks the position where the $T=19.8\mathrm{K}$ spectrum was measured.