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Thickness dependence of antiferromagnetic phase transition in Heisenberg-type MnPS3

The behavior of 2-dimensional (2D) van der Waals (vdW) layered magnetic materials in the 2D limit of the few-layer thickness is an important fundamental issue for the understanding of the magnetic ordering in lower dimensions. The antiferromagnetic transition temperature TN of the Heisenberg-type 2D magnetic vdW material MnPS3 was estimated as a function of the number of layers. The antiferromagnetic transition was identified by temperature-dependent Raman spectroscopy, from the broadening of a phonon peak at 155 cm-1, accompanied by an abrupt redshift and an increase of its spectral weight. TN is found to decrease only slightly from ~78 K for bulk to ~ 66 K for 3L. The small reduction of TN in thin MnPS3 approaching the 2D limit implies that the interlayer vdW interaction is playing an important role in stabilizing magnetic ordering in layered magnetic materials.


Introduction
2-dimensional (2D) van der Waals (vdW) magnetic materials have recently attracted much interest owing to interesting physical properties depending on magnetic phases and structures [1] as well as potential applications in flexible or nanoscale spintronic devices. From the studies of 2D ferromagnetic materials such as CrI3 [2] and CrBr3 [3], interesting effects of the interlayer interaction on the magnetic transition have been reported. For example, bulk CrI3 is known to be an Ising-type ferromagnet, but few-layer CrI3 exhibits interesting layer-number-dependence: ferromagnetic for odd number of layers and antiferromagnetic for even number of layers [2]. On the other hand, bilayer (2L) CrBr3 exhibits ferromagnetic ordering for 2H stacking and antiferromagnetic ordering for 3R stacking whereas monolayer (1L) CrBr3 is ferromagnetic [3].
Furthermore, the Curie temperature (TC) of few-layer Cr2Ge2Te6 is suppressed as the number of layers decreases although exact determination of TC was difficult in the initial magneto-optic measurements [4] . For 2D vdW antiferromagnetic materials, direct measurements of the magnetic ordering are not easy because of the lack of net magnetization and the small sample volume.
Raman spectroscopy can be used when a certain phonon mode couples with the magnetic ordering to show abrupt changes in the line shape, the frequency, or the intensity [5][6][7][8][9][10][11][12]. Sometimes, the magnon signals that reflect the magnetic structure are observed in the Raman spectrum and can be correlated with the magnetic ordering [7,13].
Transition-metal phosphorus trisulfides (TMPS3; TM= Fe, Ni, and Mn) are one of 2D vdW antiferromagnet families with the bandgap energies in the range of 1.5 to 3.0 eV [14]. Although the crystal structure is identical, the type of magnetic ordering depends on the transition metal element: Ising type for FePS3, XXZ type for NiPS3, and Heisenberg type for MnPS3 [14][15][16]. Isingtype FePS3 exhibits antiferromagnetic ordering down to the 1L limit with almost no change in the Néel temperature (TN) [5,6]. For XXZ-type NiPS3, which behaves like an XY-system [17,18] at low temperatures, exhibit antiferromagnetic ordering down to 2L with a slight decrease of TN as the thickness is decreased, but the magnetic ordering is suppressed in 1L [7]. These behaviors are consistent with the XY (XXZ) system being more prone to fluctuations than the Ising system in the 2D limit. Heisenberg-type MnPS3 also shows antiferromagnetic ordering at low temperatures, and an indication of the ordering was observed down to 2L. However, the dependence of TN on the number of layers has not been studied systematically due to the very weak signal of the Raman mode that reflects the magnetic ordering. Because a Heisenberg system is more susceptible to fluctuations, in a simple picture, it is expected that TN will decrease rapidly as the number of layers decreases. However, we found that TN decreases as the number of layers decreases, but the decrease is modest, not more than the case of XXZ-type NiPS3.

Methods
Single crystals of MnPS3 were grown by a self-flux chemical vapor transport method in a quartz tube ampoule evacuated to high vacuum. The details of the crystal growth have been published previously [9]. Few-layer MnPS3 samples were mechanically exfoliated from the single crystal onto SiO2/Si substrates with 90 nm oxide layer. The samples on substrates were kept in vacuum to avoid degradation from air exposure.
We carried out Raman scattering measurements with an Ar-ion laser with the wavelength of 488 nm (2.54 eV) and the power of ~50 μW. A 40× objective lens (N.A.=0.6) was used to focus the laser on the samples with a spot of ~1 μm in diameter and to collect Raman scattered photons from the samples. A substrate with exfoliated samples was loaded into a He-flow optical cryostat (Oxford MicrostatHe2). The scattered light from the sample was dispersed with a Jobin-Yvon Horiba iHR550 spectrometer (2400 grooves/mm) and was detected with a CCD using liquid nitrogen for cooling. A spike filter was used to removed unwanted plasma lines from the laser, and a long-pass edge filter was used to block the Rayleigh scattered light from entering the spectrometer. The cutoff of the edge filter was ~100 cm -1 . Polarized Raman measurements were performed with polarizers and λ/2 wave plates to obtain Raman signals selectively in appropriate polarization configurations of incident and scattered light. The sample was kept in vacuum during Raman measurements to avoid photochemical degradation due to laser exposure.  Figure 1(b) shows the spin alignment of Mn ions when the temperature is below TN. Each Mn ion is coupled to its three nearest neighbors antiferromagnetically, leading to antiferromagnetic ordering within the monolayer unit.   Fig. 1(c), one can clearly recognize the 1L MnPS3 flake in the AFM topography image of Fig. 1(d). The thickness of 1L MnPS3 was measured from AFM to be ~ 1 nm, which is consistent with the layer spacing of ~0.7 nm measured by X-ray diffraction [19].  as the layer number decreases as shown in Fig. 2 (b). Although the sample was kept in vacuum at all times, we noticed that some degradation occurred during Raman measurements even with the low excitation laser power of ~50 μW if the laser illuminates the same spot for an extended period of 500 s or longer (See Fig. S1 for details). In order to avoid such degradation, we obtained Raman spectra from multiple points within an area of ~10×8 μm 2 with a short integration time (50 or 100 s) at each point and used the average of such spectra for better signal-to-noise ratios. The AFM topography image and Raman mapping

Raman spectra of layered MnPS3 at room temperature
show that the sample is highly uniform over the measured area. (See Fig. S2 and Fig. S3).

Temperature dependence of P2 in few-layer MnPS3
The antiferromagnetic transition temperature TN was estimated from the temperature dependence of the Raman spectra. In previous work, it was found that the peak P2, which comes from vibrations of Mn ions [20], can be used as the indicator of antiferromagnetic ordering; the peak redshifts abruptly as the temperature is lowered through TN and the linewidth increases near TN [9]. The red shift is attributed to the coupling of the phonon vibration modes with the ordered magnetic moments below the TN. Furthermore, large fluctuations near the phase transition temperature should disrupt the coherence of the lattice vibration modes, shortening the phonon lifetime, which in turn causes broadening of the Raman peak near TN [9]. Figure 3 shows the Raman spectra of 3-, 4-, 5-, 7-, 8L and bulk MnPS3 measured at several representative temperatures. Unfortunately, the P2 signal from 1L and 2L samples were too weak to be resolved at low temperatures. We used the cross polarization configuration [ ( ) z z xy ] for this set of measurements to better resolve P2; the weak luminescent background can be suppressed with the cross polarization whereas P2 has the same intensity in parallel and cross polarizations. As the temperature is lowered toward the magnetic transition temperature, the P2 peak broadens and becomes weak. As the temperature is lowered even more, this peak re-emerges at a lower frequency with a sharper line shape.
This trend is common to all the thicknesses measured. For example, the linewidth of P2 for exfoliated bulk MnPS3 has a maximum near ~ 78 K, which is the TN of single crystal MnPS3 [9,10]. In order to estimate TN for each sample, we analyzed the line shape by fitting each spectrum with a Lorentzian function. Figure 4  In order to crosscheck the estimated TN, we analyzed other spectral parameters. Figure 5 shows the relative peak shift (Δω) and the spectral weight of P2 for each sample. The peak position is adjusted for the overall shift of phonon frequencies due to the anharmonicity [21]. The transition temperature TN and its uncertainty from Fig. 4 are also shown. One can clearly see that the peak abruptly redshifts as the temperature is lowered through TN whereas other peaks blueshift (see Fig.   S4), and the spectral weight is increased near TN. These results are compatible with the estimate of TN in Fig. 4.

Néel temperature of few-layer MnPS3
Our results are consistent with another work in which TN was estimated to be independent of the number of layers down to 5L [8]: the shift in TN between bulk and 5L is less than 5 K in our data. The ~12 K shift of TN between bulk and 3L is of the same order as in the case of XXZ-type NiPS3 [7], which is somewhat surprising. In a Heisenberg-type system, the magnetic ordering should not exist in the 1L limit according to the Mermin-Wagner theorem [22], and TN is expected to approach 0 K rapidly as the thickness is reduced. Our results indicate that 3L MnPS3 is closer to bulk than to the 2D limit of 1L. This implies that the interlayer interaction is playing an important role in stabilizing the magnetic ordering although the overall dimensionality is close to the 2D limit. In this respect we should note on a recent report in which TN of MnPS3 was estimated from the temperature dependence of the magnetoresistance [23]. Although this estimate was rather indirect, the authors claimed that TN does not change down to 1L and that the Mermin-Wagner theorem does not apply to MnPS3 due to long-range interactions. More follow-up studies are needed to elucidate the intricate interplay of dimensionality and interlayer interactions in Heisenberg-type layered vdW magnetic materials.

Conclusions
The thickness dependence of the antiferromagnetic transition temperature TN of the Heisenberg-type 2D magnetic vdW material MnPS3 was estimated from temperature dependence of the Raman spectra. The antiferromagnetic transition was identified by the broadening of a phonon peak P2, accompanied by an abrupt redshift and an increase of the spectral weight. We found that TN decreases only slightly from ~78 K for bulk to ~ 66 K for 3L. The unexpected small reduction of TN in thin MnPS3 implies that the interlayer vdW interaction is playing an important role in stabilizing magnetic ordering in layered magnetic materials.

Declaration of competing interest
The authors declare no competing financial interest.