Ultrafast cooling and heating scenarios for the laser-induced phase transition in CuO

The multiferroic compound CuO exhibits low-temperature magnetic properties similar to antiferromagnetic iron oxides, while the electronic properties have much more in common with the high-$T_c$ cuprate superconductors. This suggests novel possibilities for the ultrafast optical excitation of magnetism. On the basis of atomistic spin dynamics simulations, we study the effect of phonon-assisted multimagnon absorption and photodoping on the spin dynamics in the vicinity of the first-order phase transition from collinear to spin-spiral magnetic order. Similar as in recent experiments, we find that for both excitations the phase transition can proceed on the picosecond timescale. Interestingly, however, these excitation mechanisms display very distinct dynamics. Following photodoping, the spin system first cools down on subpicosecond time scales, which we explain as an ultrafast magnetocaloric effect. Opposed to this, following phonon-assisted multimagnon excitation, the spin systems rapidly heats up and subsequently evolves to the noncollinear phase even under the influence of isotropic exchange interactions alone.

Figure 1

The spin configurations of the (a) AF1 and (b) AF2 phases in CuO. Blue and grey spheres are Cu atoms on different $\left(010\right)$ planes [28, 29]. The red arrows show the Cu spin polarization. Entering the AF2 phase, the ${\mathbf{q}}_{\mathrm{AF}1}=(0.5,0,-0.5)$ ordering vector is modulated to the incommensurate ordering vector ${\mathbf{q}}_{\mathrm{AF}2}=(0.506,0,-0.483)$. (c) The static structure factor $S\left(\mathbf{q}\right)$ for ${\mathbf{q}}_{\mathrm{AF}1}$ and ${\mathbf{q}}_{\mathrm{AF}2}$, and the total energy $E$ and heat capacity $C_V$ per spin, obtained in classical Monte Carlo simulations for a $36a\times 4b\times 36c$ supercell using the parameters of Ref. [28]. The structure factor is normalised to unity for the $T=0$ K AF1 spin configuration.

Figure 2

Histogram of energies $\left\{E_i\right\}$ after exciting a system in equilibrium at $T=10$ K (black circles) with a concentration $x=0.02$ of two-magnons flips. The blue arrows indicate the two peaks in the red curve that are corresponding to two and four magnon excitations, respectively. The inset shows the temperature evolution of the spin system. Full (dashed) lines show undamped $\alpha =0$ (damped $\alpha =0.01$) dynamics.

Figure 3

Dynamics following multimagnon excitation. The upper panel shows the trajectory in time of $S({\mathbf{q}}_1,t)$ (red) and $S({\mathbf{q}}_2,t)$ (blue), averaged over 128 replicas, for $\alpha =0$ (full line) and $\alpha =0.01$ (dashed line) dynamics. $t<0$ is before pump and $t>0$ is after pump. The initial temperature is $T=160$ K, and the initial excitation intensity is $x=0.02$. The lower panel shows the evolution of the temperature of the system. The inset shows the first 250 fs of evolution for the normalised order parameters. The dash-dotted lines are for simulations using the isotropic Hamiltonian ${\mathcal{H}}_{\mathrm{iso}}$.

Figure 4

The relative histograms $I\left(t\right)/I(t<0)$ of energies $\left\{E_i\right\}$ evolving in (a) $\alpha =0$ and (b) 0.01 dynamics, respectively, after exciting a system in equilibrium at $T=160$ K (black circles) with a concentration $x=0.02$ of two-magnons flips. The quota $I_n\left(t\right)/I_n(t<0)$ becomes very noisy at energies larger than 35 meV, given the overall low bin counts in this energy range. Therefore $I_n\left(t\right)/I_n(t<0)$ is shown only for the energy interval 0 to 35 meV. The insets show the temperature evolution of the spin system.

Figure 5

The full line shows the energy of the spin system as a function of temperature. The blue and black symbols indicate the initial $T$ and the energy after excitation with strength $x=0.010$ or 0.020, respectively, (the concentration of pairs flipped) of a system which before pump is in thermal equilibrium at $T=160$, 162, or 164 K.

Figure 6

Excitation intensity dependence of dynamics following MM excitation. The trajectories in time of $S({\mathbf{q}}_1,t)$ (top) and $S({\mathbf{q}}_2,t)$ (bottom), averaged over 128 replicas, and with $\alpha =0$. The initial temperature was $T=160$ K, and the initial excitation intensity was in the range $[0.005,0.040]$. The inset shows the evolution of the order parameters during the first 250 fs.

Figure 7

Dynamics following on PD. The upper panel shows the trajectory in time of $S({\mathbf{q}}_1,t)$, averaged over 128 replicas, for $\alpha =0.00$ (full lines) and $\alpha =0.01$ (dashed lines). The initial temperature was $T=160$ K, and the initial excitation intensity of vacancies was $x=0.02$. The lower panel shows the evolution of the temperature of the system. The inset shows the first 250 fs of evolution for the normalised order parameters, using the same range of the axes as in the inset of Fig. 3.

Figure 8

The entropy $S(T,x)$ for CuO as a function of temperature and vacancy concentration $x$ for pure CuO and for CuO with $x=0.02$ and 0.04. The horizontal dashed line indicates the cooling at constant entropy showing rather close quantitative agreement with the temperatures, indicated by vertical arrows with error bars, measured within the spin dynamics simulations.

Figure 9

Excitation intensity dependence of dynamics following on PD. The trajectory in time of $S({\mathbf{q}}_2,t)$, averaged over 128 replicas, and with $\alpha =0.01$. The initial temperature was $T=160$ K, and the initial excitation intensity of vacancies was in the range $[0.005,0.040]$.

Figure 10

Dynamics following on a change of the heat bath temperature. The trajectory in time of $S({\mathbf{q}}_1,t)$ and $S({\mathbf{q}}_2,t)$, averaged over 128 replicas, and with $\alpha =0.01$. The initial temperature was $T=160$ K.

Figure 11

(a) Histograms (symbols) of energies $E_i$ for spin systems in thermal equilibrium. The data for different temperatures have been shifted along the $y$ axis. The full lines show the Boltzmann distribution for the temperature of the heat bath, dashed lines show the fitted temperatures. (b) The measured spin system temperature obtained with the histogram method (blue curve) or the MDSW formula (red curve). The upper inset displays the deviation of the measure temperatures to the bath temperature. The lower inset shows the measured spin system temperature for the bilinear in spin Hamiltonian ${\mathcal{H}}_{\mathrm{bilin}}$.