Effects of magnetic ordering on dynamical conductivity: Optical investigations of ${\text{EuFe}}_2{\text{As}}_2$ single crystals

The magnetic, transport, and optical properties of ${\text{EuFe}}_2{\text{As}}_2$ single crystals have been investigated parallel and perpendicular to the $ab$ plane. The anisotropy ${\rho }_c/{\rho }_{ab}\approx 8$ depends only slightly on temperature. In both orientations, the spin-density-wave transition at $T_{\text{SDW}}=189\text{K}$ shows up as a considerable increase in the dc resistivity. Susceptibility measurements evidence the magnetic order of the ${\text{Eu}}^{2+}$ moments at $T_N=19\text{K}$ with little influence on the electronic transport taking place in the FeAs layers. Polarization-dependent infrared spectroscopy reveals strongly anisotropic optical properties and yields a carrier density of only $4.2\times {10}^{21}{\text{cm}}^{-3}$ and a bandmass of $m_b=2m_0$. A sizeable Drude contribution is present at all temperatures and narrows upon cooling. Below $T_{\text{SDW}}$, the spin-density-wave gap develops in the in-plane optical conductivity; no appreciable change is detected for the perpendicular polarization. Modifications in the phonon features are associated with changes in the electronic properties at $T_{\text{SDW}}$. The extended Drude analysis yields a linear behavior of the frequency-dependent scattering rate below $T_{\text{SDW}}$, indicating an interaction between the charge carriers and spin fluctuations in the spin-density-wave state.

Figure 1

(Color online) Temperature dependence of resistivity ${\rho }_{ab}$ (black squares, left axis) in the $ab$ plane and ${\rho }_c$ (red crosses, right axis) in the perpendicular direction of single crystalline ${\text{EuFe}}_2{\text{As}}_2$. The spin-density-wave transition $T_{\text{SDW}}$ and the antiferromagnetic order of Eu at $T_N$ are indicated by arrows.

Figure 2

(Color online) Magnetic susceptibility of ${\text{EuFe}}_2{\text{As}}_2$ for (a) the $ab$ plane and (b) the $c$ direction from $T=2\text{K}$ to 100 K (left axes). Corresponding to the right axes the inverse susceptibility $1/\chi$ is plotted for both orientations. The inset shows the inverse susceptibility after subtracting the temperature-independent terms for $H\parallel c$ (red curve) in a wider temperature range $\left(2\text{K}<T<300\text{K}\right)$ (Ref. 10); the blue line indicates the Curie-Weiss fit up to 300 K. $1/{\chi }_{ab}$ (not shown) has the same trend as ${\chi }_c$ above 200 K.

Figure 3

(Color online) Temperature dependence of the magnetization of ${\text{EuFe}}_2{\text{As}}_2$ under various fields up to 2 T; the development with magnetic field strength is indicated by the arrows. For both orientations, $M_{ab}$ and $M_c$ continuously increase with rising magnetic field $H$, as indicated by the black arrows. The inset shows a schematic diagram for the Eu magnetic structure. The long axis represents the $c$ axis; the red arrows indicate the spins of Eu which are not completely within the $ab$ plane.

Figure 4

(Color online) Optical properties of ${\text{EuFe}}_2{\text{As}}_2$ in the $ab$ plane measured in a broad frequency range at different temperatures. (a) The reflectivity $R\left(\omega \right)$ drops around $1250{\text{cm}}^{-1}$ for $T=170\text{K}$ and lower since the SDW state is entered at $T_{\text{SDW}}=189\text{K}$. (b) The corresponding optical conductivity indicates the development of the SDW gap around $1000{\text{cm}}^{-1}$; nevertheless there remains a strong background of excitations in the gap. (c) The spectral weight calculated according to Eq. (1) is displayed in a double-logarithmic fashion.

Figure 5

(Color online) Optical properties of ${\text{EuFe}}_2{\text{As}}_2$ measured at various temperatures with the electric field $E$ polarized in the $c$ direction. (a) The mid-infrared reflectivity is much lower compared to the $ab$-plane reflectance and decreases even further when the temperature is reduced. (b) The optical conductivity is dominated by the mid-infrared band around $5000{\text{cm}}^{-1}$ ascribed to an interband transition.

Figure 6

(Color online) Low-frequency optical properties (up to $1500{\text{cm}}^{-1}$) of ${\text{EuFe}}_2{\text{As}}_2$ at various temperatures for $E\parallel ab$. (a) The optical conductivity can be decomposed in two Drude-type contributions (olive pattern and orange shaded), and an oscillator to mimic the SDW gap (violet shaded), as depicted for the 10 K data for instance. (b) The frequency dependence of the dielectric constant exhibits a zero crossing $\left(d{ϵ}_1/d\omega >0\right)$ as low as $500{\text{cm}}^{-1}$.

Figure 7

(Color online) (a) In-plane conductivity of ${\text{EuFe}}_2{\text{As}}_2$ in the far-infrared spectral range. (b) Frequency-dependent scattering rate and (c) frequency-dependent effective mass as obtained from an extended Drude analysis of the optical spectra. The dashed line in panel (b) indicates the linear behavior of $1/\tau \left(\omega \right)$.

Figure 8

(Color online) Temperature development of the conductivity in the region of the phonon mode of ${\text{EuFe}}_2{\text{As}}_2$. The different spectra are displaced for clarity reasons.