Magneto-optic response of the metallic antiferromagnet ${\mathrm{Fe}}_2\mathrm{As}$ to ultrafast temperature excursions

The linear magneto-optic Kerr effect (MOKE) is often used to probe magnetism of ferromagnetic materials, but MOKE cannot be applied to collinear antiferromagnets due to the cancellation of sublattice magnetization. Magneto-optic constants that are quadratic in magnetization, however, provide an approach for studying antiferromagnets on picosecond timescales. Here, we combine transient measurements of linear birefringence and optical reflectivity to study the optical response of ${\mathrm{Fe}}_2\mathrm{As}$ to small ultrafast temperature excursions. We performed temperature-dependent pump-probe measurements on crystallographically isotropic (001) and anisotropic (010) faces of ${\mathrm{Fe}}_2\mathrm{As}$ bulk crystals. We find that the largest optical signals arise from changes in the index of refraction along the $z$ axis, perpendicular to the Néel vector. Both real and imaginary parts of the transient optical birefringence signal approximately follow the temperature dependence of the magnetic heat capacity, as expected if the changes in dielectric function are dominated by contributions of exchange interactions to the dielectric function.

Figure 1

(a) Tetragonal magnetic unit cell of ${\mathrm{Fe}}_2\mathrm{As}$. Arsenic atoms are depicted as green spheres; Fe as brown spheres. Arrows denote the local magnetic moment of the Fe atoms. Fe atoms labeled with the same color arrows (blue or pink) are crystallographically equivalent. The Cartesian coordinates $x,y,z$ are aligned along the crystallographic $a,b,c$ axes. (b) Experimental geometry for time-domain thermo-birefringence (TDTB) and time-domain thermoreflectance (TDTR) experiments with the probe beam normal to the (010) face of the ${\mathrm{Fe}}_2\mathrm{As}$ crystal. In TDTR measurements, the polarization of the probe is along $x$ or $z$. In TDTB measurements, the polarization of the electric field $E$ of the probe is at an angle of ${45}^{\circ }$ from the $x$ axis.

Figure 2

Heat capacity and thermal conductivity of ${\mathrm{Fe}}_2\mathrm{As}$. (a) The measured total heat capacity $C_{\mathrm{tot}}$ of ${\mathrm{Fe}}_2\mathrm{As}$ and contributions to $C_{\mathrm{tot}}$ from excitations of electrons (e), phonons (ph), and magnons (m). The electronic and phonon contributions are calculated by density-functional theory (DFT). The magnon contribution is derived by subtracting the calculated phonon and electronic contributions from $C_{\mathrm{tot}}$. (b) The thermal conductivity in the direction normal to the (001) face (black circles) and (100) face (blue circles) shows a small anisotropy. The electrical contribution to the thermal conductivity (green circles) is calculated from the Wiedemann-Franz law and measurements of the electrical conductivity.

Figure 3

(a) Calculated electronic band structure and electronic density of states (DOS) of ${\mathrm{Fe}}_2\mathrm{As}$. The electronic band structure includes spin-orbit coupling effects through a noncollinear magnetism calculation. (b) Calculated phonon dispersion and phonon DOS of ${\mathrm{Fe}}_2\mathrm{As}$. For panel (a), the units of the electronic DOS are the number of states per magnetic unit cell per eV; for panel (b), the units of the phonon DOS are the number of states per magnetic unit cell per THz.

Figure 4

(a) The real part of the time-domain thermo-birefringence (TDTB) signal measured on the (010) face of ${\mathrm{Fe}}_2\mathrm{As}$; and (b) the imaginary part of the TDTB signal. The temperature in the legend is the temperature of the sample stage; the spatially averaged temperature of the area of the sample that is measured in the TDTB experiment is the sum of the stage temperature and the steady-state heating of 13 K. When stage temperature is at 338 K, the temperature of the measured region of the sample is close to $T_N=350$ K. Empty symbols denote data acquired at $T<T_N$; filled circles are data for $T>T_N$. We attribute the slower response at $T\approx T_N$ to the peak in the magnetic heat capacity at $T_N$.

Figure 5

Time-domain thermoreflectance (TDTR) data for the (010) face of ${\mathrm{Fe}}_2\mathrm{As}$ with (a) probe polarization aligned along the $z$ axis and (b) probe polarization aligned along the $x$ axis. TDTR data for $\mathrm{\Delta }{R}_z/\mathrm{\Delta }T$ shown in panel (a) is approximately an order of magnitude larger than TDTR data for $\mathrm{\Delta }{R}_x/\mathrm{\Delta }T$ shown in panel (b). The temperature in the legend is the temperature of the sample stage; the spatially averaged temperature of the area of the sample that is measured in the TDTR experiment is the sum of stage temperature and the steady-state heating of 13 K. Empty symbols denote data for temperatures $T<T_N$; filled symbols are for data acquired at $T>T_N$.

Figure 6

Comparison between $\mathrm{\Delta }\mathrm{\Theta }/\mathrm{\Delta }T$ and magnetic specific heat as a function of sample temperature. The values for $\mathrm{\Delta }\mathrm{\Theta }$ are for 100 ps delay time. For each sample temperature $T$, $\mathrm{\Delta }T$ at 100 ps at is calculated from a thermal model that uses the measured total heat capacity and thermal conductivity of ${\mathrm{Fe}}_2\mathrm{As}$ as inputs to the model. The sample temperature $T$ includes the effects of steady-state heating of measurement area that is created by the absorbed laser power. The real and imaginary parts $\mathrm{\Delta }\mathrm{\Theta }/\mathrm{\Delta }T$ measured for the (010) face have a similar temperature dependence as the magnetic specific heat $C_m$.