Ultrafast Spin Dynamics in Photodoped Spin-Orbit Mott Insulator ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$

Ultrafast photodoping of the Mott insulators, possessing strong correlation between electronic and magnetic degrees of freedom, holds promise for launching an ultrafast dynamics of spins which cannot be described in terms of conventional models of ultrafast magnetism. Here we study the ultrafast laser-induced dynamics of the magnetic order in a novel spin-orbit Mott insulator ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ featuring an uncompensated pattern of antiferromagnetic spin ordering. Using the transient magneto-optical Kerr effect sensitive to the net magnetization, we reveal that photodoping by femtosecond laser pulses with photon energy above the Mott gap launches melting of the antiferromagnetic order seen as ultrafast demagnetization with a characteristic time of 300 fs followed by a sub-10-ps recovery. Nonequilibrium dynamical mean-field theory calculations based on the single-band Hubbard model confirm that ultrafast demagnetization is primarily governed by the laser-induced generation of electron-hole pairs, although the precise simulated time dependencies are rather different from the experimentally observed ones. To describe the experimental results, here we suggest a phenomenological model which is based on Onsager’s formalism and accounts for the photogenerated electron-hole pairs using the concepts of holons and doublons.

Popular Summary

Ultrafast magnetism, in which ultrashort laser pulses manipulate the magnetic state of material on timescales shorter than 1 ps, has enormous potential to influence information digital processing. So far, it was mainly limited to metals where laser pulses can promote sudden loss of the magnetic order in less than 0.1 ps. Although magnetic interactions in dielectrics are more versatile, the loss in magnetic order there usually takes about 10–100 ps. Materials known as Mott insulators have the potential to bridge this gap, but not a lot is known about the actual rates of their magnetic dynamics. Here, we study a novel Mott insulator, ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$, in which strong spin-orbit interaction tilts otherwise collinear magnetic moments such that the net magnetization emerges.

Mott insulators possess a strong correlation between highly energetic electronic degrees of freedom and the magnetic state, thus promising very fast magnetic dynamics. However, Mott insulators are quite difficult to study because they are intrinsically antiferromagnetic. In antiferromagnets, adjacent elementary magnetic moments are ordered antiparallel, so they carry no net macroscopic magnetization. The lack of the magnetization substantially reduces experimental access to the magnetism of the Mott insulators and requires demanding experimental facilities such as free-electron lasers. Using a simple tabletop setup exploiting the magneto-optical Kerr effect, which is sensitive to the net magnetization, we study, with high temporal resolution, ultrafast spin dynamics in the Mott insulator. We find that in such a class of materials the loss of magnetic order occurs in less than 0.3 ps.

Our findings provide a route for engineering and detecting novel out-of-equilibrium states of quantum matter, with the potential to impact terahertz spintronics technologies.

Figure 1

(a) The band structure of a Mott insulator with schematics of the electronic configuration corresponding to the lower (LHB) and upper Hubbard bands (UHB). The pink arrow indicates an above the band gap optical excitation with photon having energy $h\nu$. (b) Magnetic structure of a Mott insulator subjected to the above band gap excitation. The staggered pattern of the blue and red circles denotes lattice sites hosting electrons having spins $S$ pointing “up” or “down,” thus forming two oppositely orienting magnetic sublattices characterized by magnetizations ${\mathbf{M}}_1$ and ${\mathbf{M}}_2$, respectively. Pink arrows denote light-induced hops of electrons between individual magnetic sublattices resulting in melting of the magnetic order.

Figure 2

(a) The canted antiferromagnetic order at the distorted perovskite lattice as it is seen in a single ${\mathrm{IrO}}_2$ layer of ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$. Angle $\theta$ defines deviation of the effective magnetic moment ${\mathbf{J}}_{\mathrm{eff}}$ from the collinear alignment. Red and blue circles stand for ${\mathrm{Ir}}^{4+}$ ions belonging to interpenetrating oppositely oriented magnetic sublattices “1” and “2” magnetic sublattices having magnetic moment denoted by green arrows. Yellow circles schematically represent positions of the oxygen ions. (b) The square bipartite lattice with collinear antiferromagnetic order characterized by rotated magnetic moments ${\tilde{\mathbf{J}}}_{\mathrm{eff}}$ obtained after the gauge transformation.

Figure 3

(a) RHEED intensity oscillations of the specular spot during the growth of a 45-u.c. ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ film. Four oscillations correspond to the growth of 1-u.c. ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$. (b) Atomic force microscopy topographic image of the surface of a 10-u.c. ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ film. (c) X-ray diffraction scan of STO capped 45-u.c. ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ film. Inset: Rocking curve around the ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ ($00\underset{\_}{12}$) reflection (d). X-ray diffraction scan around the ($00\underset{\_}{12}$) reflection. The solid black line is a simulation of the diffracted intensity with 45 u.c. and $c=25.66\AA$.

Figure 4

(a) Experimental geometry employed for the longitudinal MOKE experiment. The blue arrows depict optical path and orientation of the electric field $E_p$ of the incident light. ${\theta }_K$ is the rotation of the polarization plane due to the MOKE. (b) Left axis (blue line): ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ magnetic moment per Ir atom as a function of the external magnetic field applied in the sample plane. The data are acquired with a SQUID magnetometer. Right axis (red circles): The MOKE rotation as a function of the external magnetic field applied in the sample plane. The incident angle is close to 30 deg. The data are measured at 120 K. (c) Left axis (red circles): The amplitude of the MOKE signal measured for various temperatures. Right axis (blue line): Temperature dependence of magnetization per Ir atom acquired with a SQUID. The data are acquired during cooling down with a field of 0.5 T applied in the sample plane. (d) Temperature dependence of the coercive field.

Figure 5

(a) Schematic band structure of ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$. The pink arrow indicates the optical transition launched by the pump pulse with a photon energy of 1.55 eV. Open circles and circles with a dash indicate photoinduced holes $h$ and electrons $e$, respectively. Pink spring illustrates the process of the impact ionization and relaxation of the photoinduced carriers to the bottom of the UHB and LHB. The solid blue line denotes charge-transfer transition between oxygen ($2p$) and iridium ion ($5d$) probed with the probe pulse having a photon energy of 3.1 eV. (b) Left axis: Time-resolved transient MOKE signal triggered by the pump pulse. Right axis: Time-resolved transient reflectivity signal triggered by the pump pulse. Solid lines are fits to the data. The fits are represented by an exponential decay function multiplied by the error function. Sample temperature is 80 K and the pump fluence is $100\mu \mathrm{J}/{\mathrm{cm}}^2$. The blue and violet lines show the autocorrelation functions of the probe and pump pulses, respectively. (c) Temperature dependence of the magnetization decay time (red circles) and time of the fast rising edge in the reflectivity signal (black squares). (d) Value of the pump-induced demagnetization as a function of the pump fluence. (e) Value of the pump-induced demagnetization as a function of the sample temperature. The inset shows the magnitude of the transient pump-induced MOKE rotation $\mathrm{\Delta }{\theta }_K$ as a function of the sample temperature. The fluence of the pump pulse is $250\mu \mathrm{J}/{\mathrm{cm}}^2$.

Figure 6

(a) The nonequilibrium DMFT simulations of the light-induced dynamics of the nonequilibrium population of doublons and holons $n$ for various temperatures. The excitation is caused by the ultrashort pulse having the duration of 60 fs. (b) The corresponding light-induced magnetic dynamics in ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ for the same temperatures. The inset shows the temperature dependence of the net magnetization obtained from the Hubbard model solved on the Bethe lattice. (c) The exponential decay time of the magnetic order as a function of the temperature extracted from the time traces obtained within the DMFT simulations. The solid black line is a guide to the eye.

Figure 7

(a) Time-resolved changes in the MOKE rotation caused by the pump pulse as a function of time delay between the pump and the probe pulses. The data are shown for two opposite values of external magnetic field $\pm 3.5\mathrm{kOe}$. The sample temperature is 80 K and the pump fluence is $100\mu \mathrm{J}/{\mathrm{cm}}^2$. (b) Transient changes in the MOKE rotation as a function of time delay between the pump and probe pulses measured at various temperatures. The time-resolved traces are normalized to the maximal value to emphasize the recovery dynamics. The inset shows the corresponding changes in the reflectivity signal. (c) The recovery time for the magnetization (red circles) and reflectivity signal (black squares) as a function of the sample temperature. The solid lines are guides to the eye.

Figure 8

(a) Profile of the magnetic free energy in the form of the Landau expansion containing terms up to fourth order, shown for various temperatures below the Néel point. (b) Numeric simulation of the light-induced magnetization dynamics. The normalized value $\mathrm{\Delta }M/M_0$ is plotted. (c) Black hollow dots: square of the inverse magnetization $M_0^{-2}$ plotted as a function of the temperature. Red dashed line: recovery time of the magnetization as a function of temperature. The same data are presented in Fig. 7. The data are shown for comparison. (d) Numeric simulation of the light-induced dynamics of the net magnetic moment. The normalized value $\mathrm{\Delta }J/J_0$ is plotted. (e) Numeric simulation of the light-induced changes in the concentration of the localized moments. The normalized value $\mathrm{\Delta }l/l_0$ is plotted.