Competition between commensurate and incommensurate magnetic ordering in Fe${}_{1+y}$Te

The Fe${}_{1+y}$Te${}_{1-x}$Se${}_x$ compounds belong to the family of iron-based high-temperature superconductors, in which superconductivity often appears upon doping antiferromagnetic parent compounds. Unlike other Fe-based superconductors (in which the antiferromagnetic order is at the Fermi-surface nesting wave vector $[\frac{1}{2},\frac{1}{2},1]$), Fe${}_{1+y}$Te orders at a different wave vector, $[\frac{1}{2},0,\frac{1}{2}]$. Furthermore, the ordering wave vector depends on $y$, the occupation of interstitial sites with excess iron; the origin of this behavior is controversial. Using inelastic neutron scattering on Fe${}_{1.08}$Te, we find incommensurate magnetic fluctuations above the Néel temperature, even though the ordered state is bicollinear and commensurate with gapped spin waves. This behavior can be understood in terms of a competition between commensurate and incommensurate order, which we explain as a lock-in transition caused by the magnetic anisotropy.

Figure 1

Scans through $[H,0,\frac{1}{2}]$ with $E=6$ meV, taken above and below $T_N=67.5$ K. The black horizontal bar shows the estimated resolution width. The shift of the spin fluctuations from the commensurate to incommensurate position (when warming from the ordered to paramagnetic state) is also shown. Data are background-subtracted, and offset for clarity.

Figure 2

Temperature dependence of the magnetic and structural behavior. (a) Peak intensities of the incommensurate magnetic excitation and the $[1.5,0,0.5]$ magnetic Bragg peak as a function of temperature. Inset: Map of reciprocal space, showing the locations of the scans. (b) Width of the $[0,0,4]$ nuclear Bragg peak (an indicator of monoclinic splitting) as a function of temperature, showing the structural transition at 67.5 K. This is plotted together with the intensity of the $[2.5,0,0.5]$ magnetic Bragg peak, demonstrating the close coincidence between the structural and magnetic transitions.

Figure 3

Energy dependence of the spin excitations. (a), (b) $S(q,\omega )$ at $T=70$ K (a) and 11 K (b). The data have been smoothed and background-subtracted. Intensity is plotted on a logarithmic scale (arb. units). (c) Linewidths of the incommensurate (solid green circles) and commensurate (open blue diamonds) peaks, as a function of energy. (d) Constant-$Q$ scans taken at the center of the incommensurate and commensurate spin excitations.

Figure 4

Scans along the $c$-axis direction. The black horizontal bar shows the estimated full width at half maximum (FWHM) of the resolution function. The integrated intensity is approximately constant for temperatures above $T_N$, indicating that the number of spins is constant, but the correlation length decreases with $T$.

Figure 5

Schematic of the magnetic energy in Fe${}_{1+y}$Te at zero temperature as a function of the ordering wave vector, for two values of the excess iron concentration $y$. The exchange energy $E_{\text{exchange}}$ is represented as a parabola (dashed line); the structural anisotropy at the commensurate wave vector lowers the total energy$E_{\text{total}}$ further by $\Delta E_{\text{anisotropy}}$. The system always settles at the global energy minimum, marked with an “X.” (a) For values of $y<0.12$, the minimum of $E_{\text{exchange}}$ is close to the commensurate wave vector, and so the global minimum is at the commensurate position. Above $T_N$ the anisotropy well becomes filled, thus spin fluctuations appear at ${\mathbf{q}}_{\text{inc}}=[0.45,0,0.5]$, the exchange energy minimum. (b) For $y>0.12$, the energy minimum for $E_{\text{exchange}}$ is far from the commensurate position, which puts the global minimum at an incommensurate wave vector near ${\mathbf{q}}_{\text{inc}}=[0.38,0,\frac{1}{2}]$ (Refs. 5 and 11).