Magnetic-crystallographic phase diagram of the superconducting parent compound Fe${}_{1+x}$Te

Through neutron diffraction experiments, including spin-polarized measurements, we find a collinear incommensurate spin-density wave with propagation vector $\mathbf{k}=$ [$0.4481\left(4\right)0\frac{1}{2}$] at base temperature in the superconducting parent compound Fe${}_{1+x}$Te. This critical concentration of interstitial iron corresponds to $x\approx 12\%$ and leads to crystallographic phase separation at base temperature. The spin-density wave is short-range ordered with a correlation length of 22(3) Å, and as the ordering temperature is approached its propagation vector decreases linearly in the H direction and becomes long-range ordered. Upon further populating the interstitial iron site, the spin-density wave gives way to an incommensurate helical ordering with propagation vector $\mathbf{k}=$ [$0.3855\left(2\right)0\frac{1}{2}$] at base temperature. For a sample with $x\approx 9\left(1\right)\%$, we also find an incommensurate spin-density wave that competes with the bicollinear commensurate ordering close to the Néel point. The shifting of spectral weight between competing magnetic orderings observed in several samples is supporting evidence for the phase separation being electronic in nature, and hence leads to crystallographic phase separation around the critical interstitial iron concentration of 12%. With results from both powder and single crystal samples, we construct a magnetic-crystallographic phase diagram of Fe${}_{1+x}$Te for $5\%<x<17\%$.

Figure 1

(Color online) Magnetic-crystallographic phase diagram for Fe${}_{1+x}$Te constructed by plotting the $\delta$ of the propagation vector $\mathbf{k}=$ ($\delta 0\frac{1}{2}$) versus concentration of interstitial iron at base temperature. The open circles are for data from samples in this paper, triangle for data from Li et al. (Ref. 12), and diamonds from Bao et al. (Ref. 13). At right, the four different magnetic orderings in Fe${}_{1+x}$Te observed in our neutron diffraction studies. In the commensurate bicollinear antiferromagnetic (AFM) phase, the moments are along the $b$ direction only. Upon increasing interstitial iron to 12%, the bicollinear AFM phase gives way to an incommensurate spin-density wave (SDW) that is collinear and with moments pointed along the $b$ direction. Upon further increasing $x$, a spin component develops along the $c$ direction, creating first an elliptical helix (elongated along $b$ direction) and then circular helix phase. The direction of the propagation vector is shown for all. Here and throughout this paper, error bars represent plus or minus 1 sigma.

Figure 2

(Color online) The experimental setup for the neutron spin polarized diffraction studies on single crystals of Fe${}_{1+x}$Te. The neutron beam is polarized vertically as represented by the vector ${\mathbf{P}}_0$, which is normal to the scattering vector $\mathbf{Q}$, allowing one to measure the spin amplitude vector ${\mathbf{S}}_{\perp }$ in the nonspin flip (NSF) and spin flip (SF) channels. By aligning the crystals to have the $b$ axis parallel to ${\mathbf{P}}_0$, one can distinguish between a magnetic structure with collinear arrangement as the spin density wave (SDW) model or a noncollinear one such as the helical model. The interstitial iron site is shown in the crystal structures, but their moments (along with the Te atoms) are excluded for clarity.

Figure 3

(Color online) The observed and calculated neutron powder diffraction patterns of Fe${}_{1.12}$Te from the time-of-flight NPDF diffractometer with the difference pattern and phase reflection marks below. In (a) the 15 K data are fit with monoclinic and orthorhombic phases, and in (b) the 100 K data are fit with a single tetragonal phase.

Figure 4

(Color online) Lattice parameters and relevant bond distances and angles as a function of interstitial iron, $x$, obtained from the neutron analysis. (a) The $a,b$ lattice constants with the tetragonal data taken at 100 K, and the rest at base temperature (5 to 15 K). (b) The $c$ lattice constant, or interplanar spacing. (c) The iron-iron bond distances with Fe1 corresponding to the in-plane iron and Fe2 to the interstitial iron at 100 K. (d) The Te–Fe1–Te tetrahedral bond angle at 100 K.

Figure 5

(Color online) The crystal structure of Fe${}_{1+x}$Te with the layers consisting of edge-sharing FeTe${}_4$ tetrahedra. The interstitial iron sites, shown as beach ball spheres, are partially occupied and disordered. The magnetic lattice of the antiferromagnetic structure commensurate with the chemical lattice consists of bicollinear chains with moments pointing in the $b$ direction. Only the moments of the Fe atoms in the tetrahedral coordination are shown for clarity. Such ordering corresponds to a magnetic propagation vector of $\mathbf{k}=$ ($\frac{1}{2}0\frac{1}{2}$) in reciprocal lattice units.

Figure 6

(Color online) The nonspin flip (NSF) magnetic scattering of a single crystal with composition Fe${}_{1.09\left(1\right)}$Te as measured on the SPINS spectrometer with a vertically polarized neutron beam. In (a) the contour map shows the scattering versus temperature upon warming, and in (b) upon cooling. Near the Néel point, an incommensurate wave vector is shown in both maps to compete with the commensurate $\mathbf{k}=$ ($\frac{1}{2}0\frac{1}{2}$) ordering. In (c) through (e), cross sections of the scattering in the NSF and spin-flip (SF) channels is shown for various temperatures upon cooling. These data confirm a model where the moment lies only in the $b$ direction for both the incommensurate wave vector appearing close to the Néel point and the commensurate wave vector that exists in the ground state of Fe${}_{1.09\left(1\right)}$Te.

Figure 7

(Color online) Peak centers and integrated intensities from fits to the magnetic Bragg peaks of a single crystal Fe${}_{1.09\left(1\right)}$Te measured in the spin polarized experiments on the SPINS spectrometer. In (a) the peak centers and therefore the $\delta$ from the propagation vector $\mathbf{k}=$ ($\delta 0\frac{1}{2}$) is shown versus temperature upon warming and cooling. In (b) the integrated intensities for the Fe${}_{1.09\left(1\right)}$Te crystal upon cooling and warming.

Figure 8

(Color online) The nonspin flip (NSF) and spin flip (SF) magnetic scattering of a single crystal with composition Fe${}_{1.124\left(5\right)}$Te as measured on the SPINS spectrometer with a vertically polarized neutron beam. In (a) the contour map shows the NSF scattering versus temperature upon warming, and in (b) upon cooling. In (c) the contour map shows the SF scattering versus temperature upon warming, and in (d) upon cooling. What both measurements reveal is that the resolution-limited magnetic peak at H $=$ 0.3855(2) corresponds to a helical type of ordering whereas the broad magnetic peak at H $=$ 0.4481(4) corresponds to a spin density wave (SDW). In (e) through (g), cross sections of the scattering in the NSF and SF channels is shown for various temperatures upon warming.

Figure 9

(Color online) The evolution of the magnetic propagation vector with interstitial iron as evidenced by the change in the low-angle magnetic scattering from BT-1 neutron data. All data are normalized to the (001) nuclear Bragg peak at $\approx 19.1$ deg. $2\theta$. In (a) the monoclinic Fe${}_{1.051\left(3\right)}$Te has two closely separated magnetic Bragg peaks which correspond to the ($+0.50+0.5$) and ($-0.50+0.5$) satellite positions. In (b) the broad magnetic scattering is fit with two magnetic phases, slightly incommensurate at [0.489(1), 0, 0.5] and [0.460(1), 0, 0.5]. In (c) the two well separated peaks can be fit with an incommensurate and slightly incommensurate mangetic ordering. (d) Single incommensurate ordering at [0.380(2), 0, 0.5] for Fe${}_{1.143\left(3\right)}$Te.

Figure 10

(Color online) Peak centers and integrated intensities from fits to the magnetic Bragg peaks of a single crystal Fe${}_{1.124\left(5\right)}$Te measured in the spin polarized experiments on the SPINS spectrometer. In (a) the peak centers and therefore the $\delta$ from the propagation vector $\mathbf{k}=$ ($\delta 0\frac{1}{2}$) is shown versus temperature upon warming and cooling. In (b) the integrated intensities for the Fe${}_{1.124\left(5\right)}$Te crystal upon warming. In (c) the full-width at half maximum of the two competing magnetic peaks is shown upon warming.

Figure 11

(Color online) Contour maps of the (H 0 L) plane of Fe${}_{1.124\left(5\right)}$Te taken on the MACS spectrometer. The final and incident energies were set to 3.6 meV, to capture only the elastic scattering of the two magnetic peaks. The change in peak position and intensity as a function of temperature is shown in panels (a)–(d). In (f) the peaks are integrated in $L$ over a range of 0.48 to 0.52, which shows that the broad short-range magnetic scattering centered at H $=$ 0.45 dominates most of the scattering at base temperature. In (g) the width of the peak, after integrating in H over 0.45 to 0.47, shows that along the $L$ direction, the magnetic ordering is long range. The bars inside the peaks represent the instrument resolution.

Figure 12

(Color online) Labeling of the exchange parameters for the helical ordering present in Fe${}_{1.143\left(5\right)}$Te. On top, the three exchange parameters used for the in-plane iron atoms (rendered). Similar exchange parameters are present for the interstitial sites, which are shown below with filled circles representing the site at $z\approx 0.7$ and the empty circles the site at $z\approx 0.3$. The exchange parameters linking the two iron sublattices are shown to the right.