Light-driven topological and magnetic phase transitions in thin-layer antiferromagnets

We theoretically study the effect of low-frequency light pulses in resonance with phonons in the topological and magnetically ordered two septuple-layer (2-SL) MnBi2Te4 (MBT) and MnSb2Te4 (MST). These materials share symmetry properties and an antiferromagnetic ground state in pristine form but present different magnetic exchange interactions. In both materials, shear and breathing Raman phonons can be excited via non-linear interactions with photo-excited infrared phonons using intense laser pulses attainable in current experimental setups. The light-induced transient lattice distortions lead to a change in the sign of the effective interlayer exchange interaction and magnetic order accompanied by a topological band transition. Furthermore, we show that moderate anti-site disorder, typically present in MBT and MST samples, can facilitate such an effect. Therefore, our work establishes 2-SL MBT and MST as candidate platforms to achieve non-equilibrium magneto-topological phase transitions.

(MBT) and MnSb 2 Te 4 (MST). These materials share symmetry properties and an antiferromagnetic ground state in pristine form but present different magnetic exchange interactions. In both materials, shear and breathing Raman phonons can be excited via non-linear interactions with photo-excited infrared phonons using intense laser pulses attainable in current experimental setups. The light-induced transient lattice distortions lead to a change in the sign of the effective interlayer exchange interaction and magnetic order accompanied by a topological band transition. Furthermore, we show that moderate anti-site disorder, typically present in MBT and MST samples, can facilitate such an effect. Therefore, our work establishes 2-SL MBT and MST as candidate platforms to achieve non-equilibrium magneto-topological phase transitions.

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Antiferromagnetic topological insulators (ATIs) can host exotic phases of matter such as the quantum anomalous Hall (QAH) effect and axion insulators. 1 The search for these topological phases motivated the addition of magnetic dopants in topological insulators, which led to the observation of a QAH effect and candidates for axion insulators at very low temperatures. [2][3][4] However, intrinsic ATIs promise to manifest these phases at higher temperatures, desirable for applications. Indeed, the recent predictions, synthesis and exfoliation of the van der Waals materials MnBi 2 Te 4 , MnBi 2n Te 3n+1 , and MnSb 2 Te 4 5-12 allowed the detection of QAH states in odd septuple layers (SLs), axion states in even SLs , [13][14][15][16][17] and the observation of an electric-field-induced layer Hall effect in six SL samples. 18 The intertwined nature of the magnetic and topological order in ATIs offers the possibility to explore topological transitions induced by changes in the magnetic order and vice-versa.
For example, recent experiments suggest that increasing the distance between the magnetic planes in the MnBi 2n Te 3n+1 family leads to ferromagnetic order. 8 On the other hand, reducing the distance in MnBi 2 Te 4 single crystals via hydrostatic pressure leads to the suppression of the AFM order. 19,20 In contrast, in CrI 3 -a low-dimensional magnetic system with trivial topology -hydrostatic pressure induces an antiferromagnet (AFM) to ferromagnet (FM) transition. 21 However, a suitable mechanism to modify the magnetic order in ATIs without applied external magnetic fields or superlattices remains elusive.
To this end, non-equilibrium approaches provide a possible pathway to achieve magnetotopological transitions in ATIs. 22 Interestingly, the moderate anti-site disorder typically present in these materials reduces the laser intensity threshold to induce the transition.
In MXT materials, the constituent SLs (see Fig. 1(a)) are held together via van der Waals forces, which allows exfoliation in thin samples. 37,38 We will focus on systems with two SLs, since they correspond to the minimal system which can accommodate interlayer AFM order. Now that we have established that the shear and breathing modes are allowed by symmetry, and determined their irreps, we calculate the phonon frequencies at the Γ point. We driving an E u mode allows coupling with the low-frequency shear modes in conjunction with Once an IR mode has been driven with a strong-enough laser pulse, coupling to all Raman modes with compatible irreps is allowed by symmetry. However, in our case, since the solution of the dynamical equations scale with the inverse square of the Raman frequency (∼ Ω −2 R ), we can simplify the calculation and restrict the non-linear interactions to only the low-frequency shear and breathing modes. 27, 48 We now consider a laser pulse optimized to couple with the highest-frequency IR modes, with irrep A 2u . This mode presents the strongest coupling with the laser as shown by the largest Born effective charge Z * 50,51 (see the Supporting Information). In this case, the non-linear potential for 2-SL MBT takes the where γ 3 and β 3 are non-linear coefficients determined from DFT calculations (for the procedure and numerical values, see the Supporting Information), E 0 is the electric field amplitude with Gaussian profile F (t) = exp{−t 2 /(2τ 2 )}, and Ω is the laser frequency, which we choose in resonance with the IR mode Ω = Ω IR = 4.69 THz. Notice that the driven A 2u non-linear potential is much simpler than the one for driven E u modes. This is because the A 2u phonons do not couple to E g modes up to cubic order interactions.
For 2-SL MST, there are two IR modes with A 2u irreps, similar Born effective charge, and frequency. Therefore, we need to consider the simultaneous excitation of the two A 2u IR modes which leads to the potential For 2-SL MST, we consider the laser frequency Ω = (Ω IR(1) +Ω IR(2) )/2 THz. The phonon dynamics are determined by the equations of motion where i runs over the driven IR modes. We solve the differential equations numerically. In this work, we do not consider the phonon lifetime. Recent Raman measurements have shown that the lifetime of the breathing mode is approximately 13.3 ps, 52 which is sufficiently long for the electronic degrees of freedom to respond.
The phonon dynamics for a general laser intensity and pulse duration can be obtained by solving the equations of motion numerically. In Fig. 3(a), we show a sketch of a laser- where the intralayer Hamiltonian can be written as with exchange interaction J ij (up to fourth-neighbor interactions are needed to fit the data correctly with SJ 1 = 0.3 meV, SJ 2 = −0.083 meV, and SJ 4 = 0.023 meV), and SD = 0.12 meV is a single-ion anisotropy. Thus, the effective intralayer coupling is positive and leads to the ferromagnetic order in each Mn layer. The interlayer Hamiltonian is given where experiments suggest a nearest-neighbor AFM interlayer interaction SJ c = −0.055 meV. 56 We obtain the spin Hamiltonian from first-principle calculations, employing a Green's function approach and the magnetic force theorem. 57 We now study the effect of laser-induced transient lattice distortions on the magnetic order. Under a time-dependent lattice deformation, small compared with the equilibrium inter-atomic distances, the spin exchange interaction can be approximated as, 60 where u(t) is the real-space lattice displacement, J 0 is the equilibrium interaction, and δJ is First, we will assume that the anti-site disorder has a negligible effect on the phonon frequencies. This assumption is supported by recent Raman measurements in 2-SL MBT samples with inherent anti-site disorder, since the measured phonon frequencies are in agreement with density functional calculations for pristine samples. 52 Next, we introduce disorder in our calculations for the exchange interactions. The antisite disorder is assumed to be an interchange of Mn with Bi(Sb) elements between the Mn layer and Bi(Sb) layers. This is consistent with recent experiments. 41 Anti-site disorder effects were found to have a quantitatively important effect on the exchange interaction in these materials. Disorder effects are treated using a coherent potential approximation (CPA) as it is implemented within multiple scattering theory. 66 We show our results in Fig.   4, where we consider 5% anti-site disorder, which is a realistic concentration in most of the known MXT samples. 5, 41,63 In general, anti-site disorder favors a ferromagnetic interlayer coupling. The main reason for this is that Mn moments in Bi(Sb) layers favour a longrange ferromagnetic coupling between the septuple layers. 67 Also the reduction of magnetic moments in Mn layers diminishes the antiferromagnetic coupling. At zero displacement, a finite amount of disorder can weaken the effective exchange interaction, leading to weaker electric fields necessary to drive the transition. In Fig. 4, the concentration we consider leads to a disorder-induced ferromagnetic ground state.
In the previous sections, we established theoretically the possibility to tune the interlayer magnetic order from antiferromagnetic to ferromagnetic in 2-SL MXT samples using light in resonance with the phonons. In this section, we demonstrate that a topological transition accompanies such a light-induced magnetic transition.
The topology in MBT is rich. In bulk MBT the magnetic structure is invariant with respect to time-reversal and half a lattice translation symmetries. This leads to a Z 2 topological classification, with Z 2 = 1. 5 In the thin-film limit, the topology depends in the number of SLs. 68 For example, 1-SL MBT is predicted to be a FM trivial insulator, with Chern number