Ultrafast laser-induced spin–lattice dynamics in the van der Waals antiferromagnet CoPS₃

Since the seminal discovery of ultrafast demagnetization in Ni,¹ the ultrafast manipulation of magnetism with ultrashort pulses of light has evolved into a fascinating research topic of nonequilibrium magnetism, with examples ranging from excitation of collective magnetic modes^2–6 to light-driven magnetic phase transitions^7–9 and switching of spin orientation.^10–12 The recent resurgence of interest in two-dimensional (2D) van der Waals (vdW) materials hosting intrinsic long-range magnetic orders has offered a novel playground for investigating these phenomena in systems where the interplay between structural and magnetic orders plays a pivotal role.^13–17 Understanding the nonequilibrium dynamics in vdW magnets particularly promises to provide important insights into the fundamental physics of spin–lattice interactions and spin relaxation in ultimately thin magnets. Moreover, the inherently strong light–matter interactions, typical of vdW materials,^13,18–24 open up exciting possibilities for efficient manipulation of magnetism on the ultrafast timescale, promising novel energy-efficient data processing devices for future spintronics and magnonics applications.^25,26

Among the various vdW magnets, transition metal thiophosphates, XPS₃ (X = Fe, Ni, Mn, and Co), form a unique class of 2D antiferromagnets (AFMs) with intralayer AFM order on a honeycomb lattice. In addition to the 2D AFM order, previous studies of XPS₃ have uncovered strongly coupled spin and charge orders,^27,28 highly anisotropic excitons,²⁹ magneto-electric coupling,^30,31 signatures of the Berezinskii–Kosterlitz–Thouless (BKT) transition,³² and strong electron correlations.^33,34 The family has also recently attracted a lot of attention for its ultrafast control of magnetism. In particular, it has been shown that a sudden perturbation of electron orbital momentum via resonant pumping of specific electronic transitions opens up new ways to control spins and lattice at an ultrafast timescale.^19,20,34,35 CoPS₃ stands out in the XPS₃ family due to the Co²⁺ ions, characterized by the large spin and unquenched orbital momentum. The presence of such ions in magnetic materials usually results in a strong coupling of the spins to the lattice,^36,37 large magnetocrystalline anisotropy,³⁸ high frequencies of magnetic resonance,³⁹ and strong photomagnetic effects.^11,36,37 Furthermore, it has (not sure about “been”)recently suggested that the high-spin d⁷ configuration of Co²⁺-based compounds may host a dominant Kitaev interaction.^40–42 However, despite intense studies of the XPS₃ family, the ultrafast optical control of magnetism and lattice in CoPS₃ remains unexplored.

Here, we address these shortcomings by first introducing optical magnetic linear dichroism (MLD) as an efficient means to probe the AFM order in CoPS₃ and then employing time-resolved magneto-optical pump–probe spectroscopy to detect the ultrafast light-induced dynamics of spins and lattice in this AFM compound. Comparison of the results with earlier studies for MnPS₃ and FePS₃ reveals that the presence of the large unquenched orbital momentum in CoPS₃ results in a substantially higher MLD and much faster laser-induced melting of the spin order. Moreover, the unquenched momentum leads to exceptionally strong spin–lattice coupling and provides an opportunity for highly efficient optical control of the lattice dynamics by the selective pumping of specific orbital transitions in magnetic Co²⁺ ions.

CoPS₃ is a layered van der Waals AFM, characterized by a weak coupling between the adjacent crystal and magnetic layers, which can be viewed approximately as a quasi-2D antiferromagnet.⁴³ The intralayer spin ordering below T_N = 120 K results in the formation of ferromagnetic “zigzag” chains along the a-axis, while the adjacent chains in the direction of the b-axis are AFM coupled (see Fig. 1(a). Introducing individual magnetizations of the adjacent chains as M₁ and M₂, the AFM order in CoPS₃ can be naturally characterized by a Néel vector L, such that L = M₂ − M₁. Inelastic neutron scattering shows that CoPS₃ has sizable easy-axis single-ion anisotropy, which defines the orientation of the spins and the resultant Néel vector along the crystallographic a-axis.⁴⁰ The formation of spin chains, combined with a strong spin–lattice interaction of Co²⁺ ions, leads to a reduction of the crystal symmetry, such that the point group of a single CoPS₃ layer changes from D_3d to C_2h.¹⁶ Above T_N in the paramagnetic (PM) phase, the crystal lattice is characterized by a six-fold rotational symmetry. Below T_N, the ordering of spins in chains leads to a compression of a and an elongation of b lattice parameters, effectively elongating the hexagons formed by the Co²⁺ ions in the direction perpendicular to the spin chains. The structural changes that accompany the magnetic transition strongly affect the vibrational (phonon) spectrum of CoPS₃. Recent Raman studies show that upon spin ordering, several otherwise double degenerate E_g phonon modes lose their degeneracy and split into a pair of nondegenerate A_g and B_g ones, of which the frequencies demonstrate an anomalous behavior below T_N.¹⁶ 

Although MLD, in general, strongly depends on the probe photon energy, already in our experiment its value reaches 30%. This is almost an order of magnitude larger than the largest MLD reported for FePS₃.¹³ To define the origin of the MLD in CoPS₃, we studied the effect as a function of the probe photon energy. As shown in the supplementary material Fig. S1, two well-pronounced MLD bands appear with the maxima centered at the photon energies of about 1.69 and 2.34 eV. These energies closely match the energies of the so-called d–d transitions of Co²⁺ ions that are responsible for the change of the orbital state of the magnetic ion.⁴⁵ This observation, thus, indicates that the d–d transitions are the origin of MLD in CoPS₃, in agreement with previous studies.^13,19,20,35

Figure 1(d) shows MLD in CoPS₃ as a function of temperature T. It is seen that α_MLD reduces significantly when approaching T_N from below. To quantify the critical behavior of α_MLD, we fitted the temperature dependence of α_MLD in the AFM phase using a power law α_MLD∝|T_N − T|^2β. The results, shown in Fig. 1(d), yield 2β = 0.60 ± 0.01. This value agrees well with the critical exponent characterizing a temperature scaling of the decay in the intensity of the neutron Bragg diffraction peak from the underlying AFM order in CoPS₃ which was found to be 2β = 0.60.⁴³ As the Bragg intensity scales with the Néel order as L², its comparison with our results suggests that α_MLD also scales as L². In theory, MLD should be quadratic concerning L, but experimentally, this is not always the case, especially in AFMs with strong piezomagnetism.⁴⁶ At the same time, MLD is known to be one of the most universal effects to probe the AFM order using light in a broad spectral range, including THz,⁴⁷ visible,^48,49 and x-rays.⁵⁰ Yielding β ≈ 0.30 for the critical exponent characterizing the temperature dependence of the AFM order parameter, our results further confirm that the spin order in CoPS₃ is best described by the 3D Ising model.⁵¹ Note, the dichroism, as defined in this work, does not depend on the sample thickness and, thus, can be potentially employed to probe AFM spin order in CoPS₃ down to a single layer. At the same time, we observed that in the finite size CoPS₃ samples studied in our experiments, the linear dichroism does not completely vanish above T_N; see Fig. 1(d). This is because the ideal six-fold rotational symmetry of the honeycomb lattice, present in a single-layer form, vanishes in bulk crystals due to the displacement of the stacked layers along the a-axis.³¹ 

In our experiments, to probe the anisotropy of the optical properties induced by the spin order, we employ the fact that if the polarization of the incoming light does not orient along and/or perpendicularly to the Néel vector (the a- and b-axes, respectively), the MLD will result in rotation of the polarization plane for light propagating through the sample. In our case, the light, initially polarized at 45° with respect to both the a- and b-axes, upon propagation through a 4 µm thick sample experiences a net polarization rotation for an angle reaching about 13° [Fig. 1(e)]. We note that, although the value of the angle is large, it is by far less than expected for an MLD as large as 30%. This difference can be explained by the fact that according to the Kramers–Kronig relations,^52,53 linear dichroism is always accompanied by linear birefringence. The latter can modify the polarization state of light from linear to elliptical and even circular and, thus, substantially hampers the measurements of the polarization rotation.⁵⁴ 

To study the light-induced ultrafast dynamics of spins and lattice in CoPS₃, we carried out an all-optical pump–probe experiment; see Fig. 2(a). To excite the dynamics, we employed ultrashort (∼50 fs) linearly polarized pulses of light with the photon energy hv tunable in a range from 0.7 to 2.5 eV. This energy range covers the vast majority of the orbital d–d transitions in Co²⁺ ions.⁴⁵ To probe the light-driven spin dynamics, we relied on measuring the transient polarization rotation Δθ providing, as we have already shown, access to the Néel order. The polarization rotation was also employed to detect the lattice vibrations (phonons), of which the dynamics are intrinsically highly anisotropic and, thus, contribute to the linear birefringence.^18,55 Figure 2(b) shows an example of the light-induced dynamics triggered by the pump pulse at a temperature of T = 77 K when the sample is in the AFM phase. It is seen that, after the excitation, the signal of the transient rotation Δθ suddenly drops, indicating a suppression of the AFM order. Note, that the suppression does not occur instantaneously within the duration of the pump pulse but rather proceeds on a longer timescale τ_s of about 1.5 ps [Fig. 2(b)]. The quenching of the AFM order is concomitant with a set of coherent high-frequency phonon oscillations featuring frequencies from 3 to 10 THz and dominated by a phonon mode at 4.74 THz; see the inset in Fig. 2(b) and the supplementary material in Fig. S2.

Figure 3(a) shows the dynamics of the pump-induced polarization rotation Δθ, demonstrating the evolution of the light-induced quenching as a function of the temperature T. We fit the time-resolved traces to a single exponential function from which we extract amplitude and quenching time; see the supplementary material S3. It is seen [Fig. 3(b)] that upon approaching T_N the amplitude of the quenching is gradually growing and peaks right below T_N. Above T_N, no significant light-induced magnetic dynamics is seen; the small residual signal is likely of non-magnetic origin and caused by pump-induced changes to the electronic part of the dielectric function.⁵⁶ The growth of the quenching amplitude is accompanied by the growth of the quenching time τ_s. Upon approaching T_N [Fig. 3(c)], this time increases from 1.6 ps at T = 10 K to a maximum detected time of 5 ps at about T = 118 K. We note that qualitatively similar behavior was also observed when the probing was performed in the reflection geometry; see the supplementary material Fig. S4.

To establish the origin of the AFM quenching, we varied the photon energy of the pump pulse in the range of several d–d transitions of Co²⁺ ions. We find that the amplitude of the quenching scales with the absorption does not depend on the origin of the optical transition. The quenching is defined by the amount of heat deposited into CoPS₃ by a laser pulse. The origin of the laser-induced quenching of AFM order is, thus, similar to that reported earlier for other materials from the XPS₃ family.¹⁸ Although laser-induced demagnetization is often described using a three-temperature 3T-model,¹ CoPS₃ lacks free electrons and the model is not adequate in this case. Instead, the quenching of the AFM order in CoPS₃ can be described by a two-temperature 2T model, where the pump photons increase the potential energy of the excited electrons without making them hot. Upon non-radiative recombination of the excited electrons, the latter promptly (<1 ps) transfer the gained photon energy to the lattice.⁵⁷ The subsequent heat exchange via spin–lattice interaction leads to an increase in the effective spin temperature and consequently to the melting of the spin order.⁵⁸ This mechanism can explain a substantial increase in the magnitude of the quenching as the temperature approaches T_N. Indeed, at higher temperatures, the derivative of the Néel order parameter L with respect to the temperature increases, and the spins become more susceptible to temperature variations; see Fig. 1(d). Remarkably, not only the amplitude of the quenching goes up, but the quenching time τ_s also experiences a substantial increase in the vicinity of T_N. Such a critical slowing down of the transient spin dynamics induced by light is seen in many AFM compounds, including in recently published results on MnPS₃ and FePS₃.^19,35 It has been shown¹⁸ that in magnetic insulators the rate of the spin–lattice coupling defining τ_s scales with the spin-specific heat C_s, such that τ_s = C_s/g_sl, where g_sl is the spin–lattice relaxation rate representing the strength of the spin–lattice interaction. As the heat capacity near the Néel temperature is expected to diverge, assuming a weak temperature dependence of g_sl near T_N, the characteristic time τ_s is expected to follow the divergence of C_s. Indeed, our experiment shows that τ_s ∝ |T_N − T|^−α with a critical exponent α ∼ 0.1. Remarkably, this value closely matches the theoretical one of α = 0.1 characterizing the critical scaling of the heat capacity in the 3D Ising model.^51,59

We would like to emphasize that the characteristic time for the quenching of the AFM order in CoPS₃ (τ_s = 2 ps) is much shorter than the one reported for other XPS₃ compounds and MnPS₃, in particular (τ_s = 30 ps).¹⁹ It is well known that the heat capacity C_s scales with the strength of the exchange interaction, which is proportional to the Néel temperature. As CoPS₃ and MnPS₃ are characterized by similar values of T_N, the difference in the quenching time can only be explained by a difference in the magnitude of the spin–lattice relaxation rate g_sl. Using the available data for the specific heat capacity,^16,60 we estimate g_sl to be about 1 × 10¹⁴ Wm⁻³ K⁻¹ and 5 × 10¹¹ Wm⁻³ K⁻¹ for CoPS₃ and MnPS₃, respectively. Our experiment, thus, shows that the strength of the coupling can be effectively changed by more than two orders of magnitude by inducing an orbital momentum at the ground state of the magnetic ion. We note that, although the obtained values of the spin–lattice relaxation rates in CoPS₃ due to the unquenched momentum of the Co²⁺ ions are high, this is only in comparison with electronically similar materials lacking mobile electrons (dielectrics and semiconductors). In metals, free electrons serve as an additional reservoir of energy that can increase the rate of laser-induced demagnetization by another two orders of magnitude.⁶¹ 

To further understand the nature and excitation mechanism of the light-driven coherent phonon mode that dominates the Δθ signal, we studied its dynamics as a function of both temperature and photon energy. Figure 4(a) shows the oscillations measured at various T. It is seen that the excitation is the most efficient below T_N, where both the amplitude and the frequency of the oscillations are strongly dependent on T. Using the Fourier transform, we retrieved the frequency and amplitude of the oscillations and plotted them as functions of T in Figs. 4(b) and 4(c), respectively. As the temperature increases, the phonon frequency f softens until it reaches T_N, where it stabilizes at f₀ = 4.64 THz. Fitting the temperature evolution of the frequency shift Δf = f − f₀ to a critical law similar to the one used for α_MLD, we find that their critical exponents closely match each other, thus indicating that Δf also follows L². In accordance with Ref. 16, we assign the oscillations to the B_g phonon mode that involves antiphase motions of the magnetic Co²⁺ ions in the direction parallel to the orientation of their spins [Fig. 5(b)]. The comparison of the temperature behavior of the amplitude of the phonon mode in AFM and PM phases shows that, in PM (T > T_N), there is no significant temperature dependence, but in AFM (T ≤ T_N), the amplitude rises linearly as temperature decreases. The rise, concomitant with the onset of the AFM order, clearly indicates that the establishment of the Néel order facilitates the excitation of the lattice dynamics.

Figure 5(a) shows the amplitude of the B_g phonon mode as a function of the pump photon energy hv. Unlike the light-induced spin quenching, the laser-induced lattice dynamics does not correlate with the absorption coefficient but, instead, is most efficient if the photon energy is in resonance with the d–d transition ⁴T_1g → ⁴T_2g in the Co²⁺ ions at 0.87 eV.⁴⁵ We have also found that the efficiency of the excitation is strongly dependent on the incoming pump polarization. The inset in Fig. 5(a) shows how the amplitude of the phonon oscillations depends on the angle γ the pump polarization plane forms with the a-axis along which the spins chains are formed. It is seen that the excitation is most efficient if the pump is polarized at 45° with respect to the spins, while no oscillations are excited if the polarization is oriented either along or perpendicularly.

To conclude, we have shown that in the vdW AFM CoPS₃, characterized by a strong spin–lattice coupling, the AFM order can be effectively probed with MLD. Using MLD, we detected the ultrafast dynamics of spins and lattice induced by ultrashort pulses of light. We showed that light can suddenly heat the magnetic system, leading to a substantial loss (∼1%) of the spin ordering within nearly a single picosecond. Resonantly pumping d–d transitions in magnetic Co²⁺ ions, we effectively change the orbital momentum of Co²⁺ ions and show that this excitation, mediated by the spin–lattice coupling, brings Co²⁺ ions in a coherent motion in the direction of the AFM Néel vector. Our experiments not only elucidate the nature of the ultrafast spin–lattice coupling in 2D vdW AFMs but also lay the ground for future ultrafast pump–probe experiments, particularly those aimed at resonant pumping of infrared-active structural phonon modes.^7,66

The supplementary material includes five individual sections. Section I shows the spectral dependence of the MLD in CoPS3. Section II demonstrates the time-resolved traces of the pump-excited coherent phonon modes and their corresponding Fast Fourier Transform (FFT) spectra. Section III describes the fitting procedure for the time-resolved dynamics of the pump-induced quenching of the AFM order. Section IV shows the time-resolved traces of the pump-induced polarization rotation reflection in the reflection geometry. Section V demonstrates the temperature dependence of the spin–lattice coupling constant gsl. The phenomenological theory of the spin–phonon coupling mechanism is described in Sec. VI.

The authors are grateful to M. Matthiessen, J. R. Hortensius, A. D. Caviglia and M. I. Katsnelson for their fruitful discussions and to S. Semin, K. Saeedi, and C. Berkhout for their technical support. This work was funded by the Netherlands Organization for Scientific Research (NWO), the European Union Horizon 2020 and innovation program under the European Research Council ERC Grant Agreement No. 856538 (3D-MAGiC), the European Union Horizon 2020 innovation program under the Marie Skłodowska-Curie Grant Agreement No. 861300 (COMRAD), the National Research Fund of Ukraine within Project No. 2020.02/026, the Gravitation program of the Dutch Ministry of Education, Culture and Science (OCW) under the research program “Materials for the Quantum Age” (QuMat) registration number 024.005.006, and the ERC (Grant Nos. 1010 78206, ASTRAL). S.M.V. acknowledges the Generalitat Valenciana for the postdoctoral fellow APOSTD-CIAPOS2021/215, and S.A. was supported by the Computational Chemical Sciences program within the Office of Basic Energy Sciences, U.S. Department of Energy under Contract No. DE-AC36-08GO28308.

The authors have no conflicts to disclose.

D. Khusyainov: Data curation (lead); Formal analysis (lead); Investigation (lead); Methodology (lead); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). T. Gareev: Data curation (supporting); Formal analysis (supporting); Investigation (supporting); Methodology (supporting); Visualization (supporting). V. Radovskaia: Data curation (supporting); Formal analysis (supporting); Investigation (supporting); Methodology (supporting); Visualization (supporting). K. Sampathkumar: Data curation (supporting); Formal analysis (supporting); Investigation (supporting); Methodology (supporting); Writing – original draft (supporting); Writing – review & editing (supporting). S. Acharya: Conceptualization (supporting); Formal analysis (supporting); Writing – review & editing (supporting). M. Šiškins: Conceptualization (supporting); Resources (equal); Writing – review & editing (supporting). S. Mañas-Valero: Resources (equal); Writing – review & editing (equal). B. A. Ivanov: Conceptualization (equal); Investigation (equal); Methodology (equal); Writing – review & editing (equal). E. Coronado: Resources (equal); Supervision (equal). Th. Rasing: Funding acquisition (equal); Project administration (equal); Supervision (equal); Writing – original draft (equal); Writing – review & editing (equal). A. V. Kimel: Conceptualization (equal); Formal analysis (equal); Funding acquisition (equal); Project administration (equal); Supervision (equal); Validation (equal); Writing – review & editing (equal). D. Afanasiev: Conceptualization (lead); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (lead); Resources (equal); Supervision (lead); Validation (equal); Visualization (equal); Writing – original draft (lead); Writing – review & editing (lead).

The data that support the findings of this study are available from the corresponding author upon reasonable request.