Phase transitions and iron-ordered moment form factor in LaFeAsO

Elastic neutron-scattering studies of single-crystal LaFeAsO reveal that upon cooling, an onset of the tetragonal (T)-to-orthorhombic (O) structural transition occurs at $T_{\text{S}}\approx 156\text{K}$, and it exhibits a sharp transition at $T_{\text{P}}\approx 148\text{K}$. We argue that in the temperature range $T_{\text{S}}$ to $T_{\text{P}}$, T and O structures may dynamically coexist possibly due to nematic spin correlations recently proposed for the iron pnictides, and we attribute $T_{\text{P}}$ to the formation of long-range O domains from the finite local precursors. The antiferromagnetic structure emerges at $T_{\text{N}}\approx 140\text{K}$, with the iron moment direction along the O $a$ axis. We extract the iron magnetic form factor and use the tabulated $⟨j_0⟩$ of Fe, ${\text{Fe}}^{2+}$, and ${\text{Fe}}^{3+}$ to obtain a magnetic moment size of $\sim 0.8{\mu }_{\text{B}}$ at 9.5 K.

Figure 1

(Color online) (a) Crystal structure $\left(P4/nmm\right)$ above $T_{\text{S}}=156\left(1\right)\text{K}$ with two unit cells (solid lines). (b) Crystal structure $\left(Cmma\right)$ below $T_{\text{S}}$ with two unit cells (solid lines) and AFM structure below $T_{\text{N}}=140\left(1\right)\text{K}$ in one AFM unit cell. The arrows on the Fe ions in (b) represent the spins of iron in single-crystal LaFeAsO. The unit cells of $P4/nmm$ (T), $Cmma$ (O) and AFM structures are $\left(abc\right)$ $\left(a=b\right)$, $\left(\sqrt{2}a\sqrt{2}bc\right)$ and $\left(\sqrt{2}a\sqrt{2}b2c\right)$, respectively.

Figure 2

(Color online) Observed (dots) and calculated (solid line) x-ray powder-diffraction patterns for pulverized LaFeAsO single crystals at ambient conditions obtained on an in-house diffractometer employing the copper $K_{\alpha 1}=1.54056\text{Å}$ and $K_{\alpha 2}=1.54439\text{Å}$ with $I_{\alpha 2}/I_{\alpha 1}=0.5$ as the radiation. The vertical bars mark the positions of Bragg reflections. The lower curve represents the difference between the observed and calculated patterns.

Figure 3

(Color online) Temperature dependence of the normalized integrated intensities of (a) $\theta \text{−}2\theta$ (void symbols) and rocking-curve $\theta$ (solid symbols) neutron-diffraction scans of the nuclear Bragg ${\left(400\right)}_{\text{O}}$ (circles) and ${\left(006\right)}_{\text{O}}$ (triangles) reflections, and (b) the neutron rocking-curve scan of the AFM (103) reflection (down-solid-triangles) of single-crystal LaFeAsO measured upon warming up the crystal from 9.5 K. (c) and (d) are the enlargements of (a) and (b) near the structural and AFM transitions, respectively. The integrated intensities of ${\left(400\right)}_{\text{O}}$ and ${\left(006\right)}_{\text{O}}$ rocking curves are rescaled by 1.66 and 2.10, respectively, as indicated to make them coincide with the respective $\theta \text{−}2\theta$ scans at low temperatures.

Figure 4

(Color online) Synchrotron x-ray powder-diffraction data of pulverized LaFeAsO single crystals above (158 K), during (150 K) and below (130 K) the O-T transition (circles). The solid lines are fits of the Lorentzian line shape.

Figure 5

(Color online) Temperature variation in FWHM of the ${\left(004\right)}_{\text{O}/\text{T}}$ (a) and ${\left(220\right)}_{\text{T}}$ (circles) (b) reflections from synchrotron x-ray powder-diffraction study of pulverized LaFeAsO single crystals. Below the O-T structural transition, the FWHM of the ${\left(220\right)}_{\text{T}}$ reflection was averaged from the ${\left(400\right)}_{\text{O}}$ and ${\left(040\right)}_{\text{O}}$ reflections. To avoid the influence of systematic errors, we normalized the FWHM of the ${\left(220\right)}_{\text{T}}$ reflection to that of the ${\left(004\right)}_{\text{O}/\text{T}}$ shown as squares in (b). The lines in (b) are guides to the eye.

Figure 6

(Color online) (a) $q$ dependence of the collected factor $C_{\text{N}}\left(q\right)$ (circles) in Eq. (2) at 9.5 K as described in the text. The nuclear Bragg reflections were chosen to cover the $q$ range of the measured AFM reflections as possible. The intensities of nuclear reflections were integrated from their respective rocking curves, taking into account the domain effect, and normalized to the corresponding structure factors and the Lorentz factors. The collected factor $C_{\text{N}}\left(q\right)$ contains the DWF and other effects such as extinctions and absorption. The solid line is the best DWF-like curve that best fits the data and is used to normalize the AFM peaks to obtain the magnetic form factor of iron in single-crystal LaFeAsO. (b) Measured magnetic form factor of iron (circles) at the AFM phase (9.5 K) of single-crystal LaFeAsO. The lines as indicated are the best fits of the data with the magnetic moment $M\left({\mu }_{\text{B}}\right)$ multiplied by the calculated form factors $⟨j_0⟩$ of Fe, ${\text{Fe}}^{2+}$ and ${\text{Fe}}^{3+}$ with spin contribution only (Ref. 20), and the form factor of a homogeneous sphere (details in text), respectively. The fitted results are shown in Table . The deviation of A and B points from the smooth curves is discussed in the text.