Magnon transport in quasi-two-dimensional van der Waals antiferromagnets

The recent emergence of 2D van der Waals magnets down to atomic layer thickness provides an exciting platform for exploring quantum magnetism and spintronics applications. The van der Waals nature stabilizes the long-range ferromagnetic order as a result of magnetic anisotropy. Furthermore, giant tunneling magnetoresistance and electrical control of magnetism have been reported. However, the potential of 2D van der Waals magnets for magnonics, magnon-based spintronics, has not been explored yet. Here, we report the experimental observation of long-distance magnon transport in quasi-twodimensional van der Waals antiferromagnet MnPS3, which demonstrates the 2D magnets as promising material candidates for magnonics. As the 2D MnPS3 thickness decreases, a shorter magnon diffusion length is observed, which could be attributed to the surface-impurity-induced magnon scattering. Our results could pave the way for exploring quantum magnonics phenomena and designing future magnonics devices based on 2D van der Waals magnets.

distance. Recently, the long distance magnon transport has been demonstrated in 3D ferromagnetic and antiferromagnetic insulators, such as YIG, Cr2O3, and Fe2O3 [30][31][32]. Specially, antiferromagnetic Fe2O3 offers an electrically tunable magnon channel that could be used for magnonics devices that operate in the absence of any magnetic field [32]. Different from 3D magnetic insulators, such 2D van der Waals magnets offer special platforms for very intriguing quantum transport phenomena, including the spin Nernst effect, topological and Weyl magnons that have already been intensively studied theoretically [33][34][35]. However, the potential of 2D van der Waals magnets for magnon transport has not been experimentally investigated yet.
Here, we report the magnon transport properties in 2D van der Waals antiferromagnet MnPS3.
The long-distance magnon propagation over several micrometers in 2D MnPS3 has been demonstrated, which is comparable to the 3D ferromagnetic insulator yttrium iron garnet (YIG).
Systematical studies on the spacing dependence of the nonlocal magnon signal reveal a magnon relaxation length of several micrometers. As the temperature decreases, a longer magnon relaxation length is observed, which could be related to longer magnon lifetimes in such a van der Waals antiferromagnet at lower temperatures. As the 2D MnPS3 thickness decreases, a shorter magnon diffusion length is observed, which could be attributed to the surface-impurity-induced magnon scattering. These experimental results have demonstrated 2D van der Waals magnets as a new platform for the magnonics applications [29,36], and could further pave the way for exploring magnon-dependent quantum transport phenomena in 2D van der Waals magnets [33][34][35]37]. MnPS3 devices, where the 2D van der Waals MnPS3 flakes are prepared on the ~300 nm SiO2/Si substrates from bulk MnPS3 single crystals using the mechanical exfoliation method [23]. Bulk MnPS3 single crystals are grown using the chemical vapor transport method. Stoichiometric amounts of high-purity manganese, red phosphorus, and sulfur were sealed into an evacuated quartz tube in a temperature gradient from 780 °C (source region) to 730 °C (growth region) for seven days. Fig. 1(b) shows the crystalline and spin structures of the van der Waals antiferromagnet MnPS3. In each layer of the crystal's ab plane, the spins of the Mn atoms are antiferromagnetic coupled with their nearest neighbors, while the interlayer exchange coupling between the Mn spins is ferromagnetic [38]. The Néel temperature (TN) of MnPS3 bulk single crystals is ~79 K, obtained from temperature-dependent magnetization measurement ( The prepared 2D MnPS3 flakes on ~300 nm SiO2/Si substrates are first identified by a Nikon high-resolution optical microscope, and then fabricated for the nonlocal magnon devices using standard electron-beam lithography and lift-off processes. The electrodes are made of 10 nm thick Pt grown in a magneton sputtering system with a base pressure lower than 8×10 -7 mbar. The width of the Pt electrodes is ~200 nm. Fig. 1(c) shows the opitcal image of a typical magnon device made on 8 nm 2D MnPS3 flake, where the thickness is determined by atomic force microscopy (Fig. S2).

II. EXPERIMENTAL
Raman studies show that the electron-beam lithography and device fabrication processes are not damaging the MnPS3 flakes (Fig. S3).
The magnon transport in the quasi-2D van der Waals antiferromagnet MnPS3 is measured using the nonlocal geometry via standard low-frequency lock-in technique in a Physical Properties Measurement System (PPMS; Quantum Design). During the nonlocal magnon transport measurement, a current source (Keithley K6221) is used to provide the low frequency AC current (f = 7 Hz) in the range from 10 to 150 A in the spin injector Pt electrode, and the nonlocal voltages are measured using lock-in amplifiers (Stanford Research SR830). The voltage probes the magnon-dependent chemical potential due to magnon diffusion in the quasi-2D MnPS3 channel.
During the measurement, low noise voltage preamplifiers (Stanford Research SR560) are used to enhance the signal-to-noise ratio.
The magnons are generated in quasi-2D van der Waals antiferromagnet MnPS3 under the left Pt electrode (magnon injector), and then diffuse towards the right Pt electrode (magnon detector) which detects the magnon-mediated spin current via inverse spin Hall effect of Pt in the nonlocal geometry [30][31][32]39,40]. To perform magnon injection, both electrical means via spin Hall effect of Pt and thermal means via thermal spin injection could be utilized [30], which give rise to the first and second harmonic nonlocal voltages probed at the magnon detector ( and ), respectively. Both means could be used to investigate the magnon transport properties in magnetic insulators, as demonstrated in previous reports [40][41][42][43]. In our experiment with the AC injection curent (Iin in Fig. 1(c)) in the range from 10 to 150 A, only the second harmonic nonlocal voltages could be clearly observed, while no obvious first harmoinc voltrages could be detected (Fig. S4).
This result could be attributed to higer effciencey magnon generation via themral means than via the electrical means due to spin Hall effect of Pt. Hence, to probe the magnon transport in quasi-2D van der Waals MnPS3, thermal means is utilized to generate the magnons arising from the temperature gradient at the MnPS3-Pt interface via Joule heating [30,31,41,44]. As discussed earlier, since the magnons are injected via thermal means and the diffusive magnons are detected via the inverse spin Hall effect of Pt, R2 is expected to be proportional to sin (φ) [30]:

III. RESULTS AND DISCUSSION
where the is the nonlocal spin signal. The red solid lines in Fig. 2 dependence of the nonlocal magnon signals on both devices is shown in Fig. 2(d) (T = 2 K). As in-plane magnetic field increases, the canted magnetic moment increases, giving rise to the enhancement of the second harmonic nonlocal magnon signals [31]. Fig. 2(e) shows the temperature dependence of the nonlocal magnon signals of both devices at B = 9 T. The nonlocal magnon signals are observed when the temperature is lower than ~ 20 K for the 8 nm MnPS3 device and ~ 30 K for the 16 nm MnPS3 device , which could be attributed to lower Néel temperature for thinner MnPS3, a Heisenberg antiferromagnet [45]. These results demonstrate the potential of using a quasi-2D van der Waals antiferromagnet for the magnon transport, which might have advantages compared to ferromagnetic insulator YIG, such as the capability of functioning in the presence of large magnetic fields and the absence of stray fields [46,47].
To investigate the magnon transport properties of quasi-2D van der Waals antiferromagnet MnPS3, the spacing profile of the magnon-dependent chemical potential ( ) is systematically studied. Since the MnPS3 thickness is much smaller than the spacing between the two Pt electrodes, magnon transport is expected to follow the one-dimensional drift-diffusion model [30,48]. As illustrated in Fig. 3(a), is expected to exponentially decay as the magnon-mediated spin current diffuses away from the magnon injector in the presence of magnon scatterings. At the distance of d away from the magnon injector, can be described by the following expression: where is the magnon-dependent chemical potential in MnPS3 under the Pt injector and is the magnon relaxation length. Quantatively, the decrease of the nonlocal magnon resistances as a function of d can be expressed by [40,41]: where C is a constant related to the spin-to-charge conversion effciency of Pt, the magnon injection/detection efficiencies, and the spin-mixing conductances at the interface between MnPS3 and Pt. Fig. 3(b) shows the normalized nonlocal magnon resitance ( * ) as a funtion of d for the 16 nm MnPS3 device measured at B = 9 T and T = 2 K and 15 K, repectively. * is used to take into account of the length effect of the magnon detector, and it is calcualted using the following formula * = × _ , where _ is the length of the magnon detector. During the investigation of the magnon relaxation lengths, the spacings are purposely chosen to be longer than or equal to 2 µm, since there is a magnetic depletion region close to the Pt injector arising from local Joule heating induced spin Seebeck effect (Fig. S9) [42]. The spin signal probed from the local Pt injector is of opposite sign compared to the nonlocal Pt detector which probes the magnon transport across a spacing that is much bigger than the thickness of MnPS3 (Fig. S9).
To quantitatively determine the magnon relaxatton length, the log( * ) vs. d measured at various temperatures are plotted in Fig. 3(c). It is clear that the experimental results at various temperatures are all in good agreement with the exponential decay of magnon-dependent chemical potential expected theoretically (solid lines in Fig. 3(c)). Based on the best fitting results of the experimental data, the magnon relaxation lengths of the 16 nm MnPS3 are obtained to be 2. for these devices are similar to that measured on the 16 nm MnPS3 device (Fig. 3(d)). scattering and lower Néel tempeature for thinner MnPS3, a Heisenberg antiferromagnet [45].

IV. CONCLUSIONS
In conclusion, long-distance magnon transport over several micrometers has been demonstrated in the quasi-two-dimensional van der Waals antiferromagnet MnPS3. Systematical studies on the temperature and MnPS3 thickness dependences of the magnon relaxation lengths have been performed. As the 2D MnPS3 thickness decreases, a shorter magnon diffusion length is observed, which could be attributed to the surface-impurity-induced magnon scattering. Our results demonstrate that van der Waals antiferromagnets provide a 2D platform for magnon spintronics and magnon spin computing [29]. Furthermore, these results could pave the way for the future investigation of novel magnon phenomena in van der Waals 2D magnets, including spin Nernst effect, magnon topological properties, quantum magnon Hall effect, etc [33][34][35]37].