Unconventional Temperature Enhanced Magnetism in ${\mathrm{Fe}}_{1.1}\mathrm{Te}$

Our inelastic neutron scattering study of spin excitations in iron telluride reveals remarkable thermal evolution of the collective magnetism. In the temperature range relevant for the superconductivity in ${\mathrm{FeTe}}_{1-x}{\mathrm{Se}}_x$ materials, where the local-moment behavior is dominated by liquidlike correlations of emergent spin plaquettes, we observe unusual, marked increase of magnetic fluctuations upon heating. The effective spin per Fe at $T\approx 10\mathrm{K}$, in the phase with weak antiferromagnetic order, corresponds to $S\approx 1$, consistent with the recent analyses that emphasize importance of Hund’s coupling [K. Haule and G. Kotliar, New J. Phys. 11, 025021 (2009).]. However, it grows to $S\approx 3/2$ in the high-$T$ disordered phase, suggestive of the Kondo-type behavior, where local magnetic moments are entangled with the itinerant electrons.

Figure 1

Magnetic scattering intensity measured in ${\mathrm{Fe}}_{1.1}\mathrm{Te}$ at $T=10\mathrm{K}$ for energy transfers $(0\pm 0.5)\mathrm{meV}$, (a), $(7.5\pm 0.5)\mathrm{meV}$, (b) and $(20\pm 0.5)\mathrm{meV}$, (c). (d)–(f), fits to a model cross section consisting of four lattice Lorentzian (LL) peaks at (0, $\pm \zeta$) and ($\pm \zeta$, 0), $\zeta \lesssim 0.5$. A Gaussian ring of scattering centered at (0, 0) is included in (e) to account for the dispersive acoustic mode clearly visible in Fig. 2a. (g)–(i), two-parameter fits to the checkerboard cluster model described in the text. All fits assume the magnetic form factor of ${\mathrm{Fe}}^{2+}$.

Figure 2

Energy dependence of the imaginary part of the dynamical magnetic susceptibility, ${\chi }^{\prime \prime }(\mathit{Q},E)=\pi (1-e^{-E/(k_{B}T)})S(\mathit{Q},E)$ at $T=10\mathrm{K}$, (a), 80 K, (d), and 300 K, (g), as a function of wave vector (0, $K$). (b),(e),(h) and (c),(f),(i) show fits to the same models as in Fig. 1.

Figure 3

Peak positions at $T=10\mathrm{K}$, (a), 80 K, (b), and 300 K, (c), obtained by fitting constant-$E$ slices to a single-component LL cross-section (filled symbols). Horizontal bars show the FWHM of LL peaks. Open symbols are positions of the LL (black) and the ring (light blue with error bars) in the two-component model of Fig. 2e. Solid line in (a) is a fit of the ring mode dispersion to $E(q)\sim \sin (\pi k/2)$, folded into a small (magnetic) Brillouin zone, [$-0.5$, 0.5]. (d), (e), (f) Integral intensity of magnetic scattering as a function of energy. Error bars account for the uncertainty of absolute normalization. Solid lines are fits consisting of a quasielastic (QE) central peak (shaded yellow) and a damped harmonic oscillator (DHO, red), used to interpolate the data for integration. Green-shaded peak in (d) is magnetic Bragg intensity. Insets show the correlation length in lattice units for the LL (closed circles) and the cluster (open rhombi) models.

Figure 4

(a) ${\chi }^{\prime \prime }(\mathit{Q},E)$ as a function of energy for $\mathit{Q}=(0,0.45)$ at 10 K, 80 K and 300 K. Lines are fits shown in Figs. 2b, 2e, 2h. (b) Temperature dependence of $S(E)$, excluding Bragg scattering. Solid lines are fits of Figs. 3d, 3e, 3f, dashed lines show DHO fits of the inelastic part. (c) Square of the effective magnetic moment obtained by integrating the $S(E)$, as a function of temperature. Upper (blue) symbols show the total response, bottom (red) symbols are the Bragg contribution, green symbols are the quasielastic contribution.