Neutron diffraction study of the magnetic and structural phase transitions in ${\text{BaFe}}_2{\text{As}}_2$

We present the results of an investigation of both the magnetic and structural phase transitions in a high quality single crystalline sample of the undoped iron pnictide compound ${\text{BaFe}}_2{\text{As}}_2$. Both phase transitions are characterized via neutron diffraction measurements which reveal simultaneous, continuous magnetic and structural orderings with no evidence of hysteresis, consistent with a single second-order phase transition. The onset of long-range antiferromagnetic order can be described by a simple power-law dependence $\varphi {\left(T\right)}^2\propto {\left(1-\frac{T}{T_N}\right)}^{2\beta }$ with $\beta =0.103\pm 0.018$; a value near the $\beta =0.125$ expected for a two-dimensional Ising system. Biquadratic coupling between the structural and magnetic order parameters is also inferred along with evidence of three-dimensional critical scattering in this system.

Figure 1

(Color online) (a) Bulk susceptibility measurements showing the dc magnetization measured with the magnetic field applied parallel to the $ab$ plane. Dashed line denotes the AF transition temperature at $T=136\text{K}$. (b) Neutron characterization showing a rocking curve illustrating the mosaic of our crystal. The resolution-limited peak FWHM of $0.32°$ demonstrates the high quality of our single crystals. The measurement was taken with collimation of $30^{\prime }\text{−}12^{\prime }$-sample-$12^{\prime }\text{−}72^{\prime }$. (c) Resistivity measurements on a small crystal of ${\text{BaFe}}_2{\text{As}}_2$ showing a linear decrease with decreasing temperature and a sharp drop at $T=135\text{K}$. The drop in resistivity is indicative of the simultaneous magnetic and structural phase transitions in this system. (d) The derivative $\frac{\partial \rho }{\partial T}$ upon both warming and cooling showing a sharp peak indicative of the slope change at the transition temperature. The peaks during both sample warming and cooling overlap perfectly showing no evidence for hysteresis in the simultaneous magnetic and structural phase transitions of our samples.

Figure 2

(Color online) (a) Radial scans through magnetic peaks at the $\left(1,0,L\right)$; $L=1,3,5,7$ positions along with the (3, 0, 3) position. (b) Rocking curves through the corresponding magnetic peaks in panel (a). Insets in each panel qualitatively show the direction that the resolution ellipsoid intersects the magnetic Bragg position.

Figure 3

(Color online) $\mathbf{Q}$ mapping through mesh scans about the (3, 0, 3) magnetic Bragg reflection with (a) the PG filter out of the beam and (b) the PG filter in the beam. The resulting nuclear scattering from the (6, 0, 6) position in panel (a) shows the structural twinning below $T_s$ which is absent in the purely magnetic scattering from the (3, 0, 3) reflection in panel (b). This indicates that the moments are aligned along the longer $a$ axis in agreement with previous reports (Refs. 9, 18).

Figure 4

(Color online) Measurements of the magnetic order parameter upon warming and cooling at the (1, 0, 3) reflection. Both the peak intensity measured at $\mathbf{Q}=\left(1,0,3\right)$ and the radially integrated (1, 0, 3) peak area are plotted upon both (a) cooling and (b) warming through $T_N$. The perfect overlap between the peak intensity and integrated area measurements indicates that the peak intensity can be safely used as a measure of the magnetic order parameter, ${\varphi }^2$. (c) Integrated (1, 0, 3) peak areas overplotted as a function of cooling and warming. There is no sign of hysteresis and the onset of magnetic order is seemingly continuous. (d) Peak intensities at $\mathbf{Q}=\left(1,0,3\right)$ overplotted upon both cooling and warming the sample. Dashed line represents the results of the power-law fit described in the text with $\beta =0.103$ while the solid line displays the results of a power-law fit with $\beta$ fixed at 1/8.

Figure 5

(Color online) Continued analysis of the magnetic order parameter in different regimes of reduced temperature. Top panel shows a power-law fit to the $\mathbf{Q}=\left(1,0,3\right)$ peak intensity data in the reduced temperature regime $t\approx 0.10$ while the bottom panel shows a power-law fit to the data in the $t\approx 0.05$ regime. For both fits, only data below $T=135.5\text{K}$ were included. Power-law fits are denoted by the solid yellow lines in both panels. Inset in the upper panel replots the magnetic phase transition zoomed in to within $\pm 1\text{K}$ of the phase transition. A linear fit to the data between 135.6 and 136.3 K is plotted as a solid line through the data and illustrates the maximum possible range for a linear trade-off between the paramagnetic and ordered magnetic phases required by a first-order phase transition.

Figure 6

(Color online) The evolution of the structural order parameter as a function of temperature. (a) Longitudinal $H$ scans through the (2, 0, 0) nuclear Bragg reflection both below and above the structural phase transition $T_s$. Solid lines are the results of fits of two Gaussians to the broadened peak below $T_s$ with the splitting, $\delta \left(T\right)$, determined as described in the text. (b) $\delta {\left(T\right)}^2$ plotted upon both warming and cooling. The onset of the structural splitting shows no hysteresis, identical to the development of the magnetic order in this material. $\delta {\left(T\right)}^2$ is overplotted with the integrated area of the (1, 0, 3) magnetic reflection as a function of (c) warming and (d) cooling showing a remarkable tracking between the structural order parameter squared and the magnetic order parameter squared. The exact tracking within the errors verifies previous suggestions of a strong coupling between the onset of magnetic order and the structural lattice distortion in this material (Ref. 9).

Figure 7

(Color online) Critical scattering above $T_N$ at the (1, 0, 3) magnetic reflection. (a) Radially integrated area of the (1, 0, 3) magnetic peak as a function of temperature. The critical scattering above $T_N$ is denoted by the shaded area. Dashed line denotes the level of $\lambda /2$ contamination in our measurements which can be treated as background. Radial scans at select temperatures are plotted in panel (b). The large $\lambda /2$ peak apparent at 148 K renders this measurement of critical scattering only preliminary. $\mathbf{Q}$ scans through (1, 0, 3) along both the $H$ and $L$ directions in reciprocal space are plotted in panels (c) and (d), respectively. The nuclear background scattering from the $148\text{K}\lambda /2$ peak was subtracted off in order to isolate the magnetic portion of the peaks. Sharp resolution-limited peaks in both in-plane and out-of-plane scans demonstrate that the critical scattering observed is fully three dimensional. Solid lines in panels (b)–(d) are the results of Gaussian fits to the data.