Giant Modulation of the Second Harmonic Generation by Magnetoelectricity in Two‐Dimensional Multiferroic CuCrP2S6

Multiferroic materials have attracted considerable attention owing to their unique magnetoelectric or magnetooptical properties. The recent discovery of few‐layer van der Waals multiferroic crystals provides a new research direction for controlling the multiferroic properties in the atomic layer limit. However, research on few‐layer multiferroic crystals is limited and the effect of thickness‐dependent symmetries on those properties is less explored. In this study, the symmetries and magnetoelectric responses of van der Waals multiferroic CuCrP2S6 are investigated by optical second harmonic generation (SHG). Structural and magnetic phase transitions are successfully probed by the temperature‐dependent SHG signals, revealing significant changes by applying the magnetic field reflecting the magnetoelectric effect. Moreover, it is found that symmetries and resultant magnetoelectric responses can be modulated by the number of layers. These results offer a new principle of controlling the multiferroicity and indicate that 2D van der Waals multiferroic material is a promising building block for functional nanodevices.


Introduction
2D van der Waals magnets are emerging material platforms for realizing physical properties and functionalities, and are an important building block for functional van der Waals interfaces.Among these, van der Waals antiferromagnets have attracted increasing interest because of their versatile magnetic DOI: 10.1002/adma.202312781structures and symmetries.Unique electronic and optical properties can appear because of the complex magnetic symmetries without macroscopic magnetization.[3][4][5][6][7][8] However, the effects of the magnetoelectric properties on SHG, that is, the modulation of SHG signals under a magnetic field and its thickness dependence in 2D antiferromagnets, are not well understood.In this study, we investigated the symmetries and magnetoelectric responses of the van der Waals multiferroic CuCrP 2 S 6 (CCPS).Both the structural phase transition from centrosymmetric to noncentrosymmetric structures and the antiferromagnetic phase transition were detected by enhanced SHG signals along specific polarization directions.The polarization dependence of the SHG signals was significantly modified, and the signal magnitude was enhanced by one order of magnitude under a finite magnetic field, which could be explained by the magnetoelectric effect.
Furthermore, we clarified that these SHG signals showed systematic changes as a function of the thickness, indicating that the symmetries and magnetoelectric responses can be modulated by the number of layers.Our results demonstrate a new aspect of controllability of van der Waals multiferroics and offer a new research direction for 2D magnets.

Crystal and Magnetic Structures of CuCrP 2 S 6
Figure 1a-c shows the schematics of the crystal and magnetic structures of CCPS.It is a layered material composed of the honeycomb lattice of distorted CrS 6 octahedra and CuS 3 triangles and pairs of P ions inside the honeycomb.At T > T C = 190 K, mobile Cu ions occupy either the upper or lower side of the 2D plane with equal probability, leading to a centrosymmetric crystal structure with a C2/c space group (Figure 1a).[11][12] With decreasing the temperature, the movement of Cu ions starts to freeze at T = 190 K and completely settles down at T = 145 K, which causes the Figure 1.Crystal structures and magnetic properties of CuCrP 2 S 6 .a-c) Schematic illustrations of the crystal lattice structures and antiferromagnetic order in CuCrP 2 S 6 .The schematics of the crystal lattices were created using VESTA 3. [36] At high temperatures (T > 190 K), CuCrP 2 S 6 shows the centrosymmetric crystal structure (space group: C2/c), see (a), whereas the structural phase transition from the centrosymmetric to non-centrosymmetric phase (space group: Pc) occurs around T = 190 K (see (b)).Below T = 32 K, an interlayer antiferromagnetic order was observed with the Néel vector parallel to a-axis (see (c)).d) Temperature dependence of the specific heat of the bulk CuCrP 2 S 6 crystal.The kink structures around T = 32, 155, and 185 K correspond to the magnetic and structural phase transitions, respectively.AFM (PM) in the figure means antiferromagnetic (paramagnetic) phase.e) Temperature dependence of the magnetization of the bulk CuCrP 2 S 6 crystals.The red (blue) curve indicates the magnetic moment when a magnetic field is applied in a direction out of (in) the 2D ab-plane.
structural transition to the noncentrosymmetric phase with the Pc space group (Figure 1b).Because neighboring layers are mirror images with respect to the ac plane and glide symmetry exists, electric polarization in the ac plane appears in this phase.With a further decrease in temperature, CCPS shows the A-type antiferromagnetic ordering below T N = 32 K, in which spins of Cr 3+ align along the a-axis (Figure 1c).Because both the spatial inversion symmetry and time-reversal symmetry are broken in the low-temperature phase, bulk CCPS samples show the magnetoelectric effect. [13,14]However, it is unknown how the symmetry, magnetic order, and multiferroicity of CCPS will evolve by changing the sample thickness.
First, the bulk CCPS samples were characterized by measuring their specific heat and magnetization.Figure 1d shows the temperature dependence of the specific heat.Anomalies, which correspond to the antiferromagnetic or structural phase transitions, were observed around T = 32, 150, and 190 K.The antiferromagnetic phase transition at T = 32 K was confirmed by the temperature dependence of the magnetization (Figure 1e).In the figure, the red (blue) curve represents the magnetic moment when an in-plane (out-of-plane) magnetic field is applied.Therefore, the difference between the red and blue data indicates the in-plane magnetic anisotropy of the material.These results are consistent with previous reports on bulk CCPS [9,[15][16][17][18][19][20] (see Section S1, Supporting Information, for other magnetization properties of the CCPS.)

Temperature Dependence of the SHG
To study the symmetry and multiferroicity of the exfoliated CCPS samples, we employed SHG anisotropy (Figure 2a).[23][24][25][26][27][28][29][30] Linearly polarized laser pulses (1.55 eV, 1 μJ) were irradiated normally to the sample and SHG images polarized parallel to the incident light were obtained (see Experimental Section and Section S2, Supporting Information).Figure 2b shows an optical microscopy image of sample 1 with a thickness of 27 nm and Figure 2c shows an example of its SHG image (T = 5 K).Finite SHG signals were observed in the CCPS flakes.Figure 2d-f shows the polarization-resolved SHG intensity in the encircled area of Figure 2c in the low-temperature (T = 5 K, Figure 2d), intermediate-temperature (T = 100 K, Figure 2e), and high-temperature phase (T = 300 K, Figure 2f), respectively.We confirmed that the SHG patterns were similar, regardless of the position in the sample (see Section S3, Supporting Information).At T = 300 K, small sixfold SHG signals were observed (Figure 2f).Because the inversion symmetry is preserved in this phase, a possible origin of this SHG signal is the surface or electric quadrupole term.After the structural phase transition occurs at T = 190 K, the electric dipole (ED) term of the SHG is allowed, which generates an additional contribution to the SHG intensity along the a-axis (Figure 2e).In the multiferroic phase below T = 32 K, another SHG contribution appeared along the b-axis (Figure 2d), which can be interpreted as SHG signals originating from the magnetic dipole (MD) term.[3][4][5] In Section S4, Supporting Information, we argue that the observed polarization-resolved SHG patterns can be explained and reproduced by considering the above-mentioned surface, ED, and MD terms.Notably, these polarization-resolved SHG patterns are almost mirror-symmetric about the a-axis, which indicates that glide symmetry with respect to the ac-plane exists in all phases of bulk CCPS.
To capture precisely the symmetry changes caused by phase transitions, we studied the detailed temperature dependence of the SHG intensity at specific polarization angles (Figure 2g).Red and green data are the temperature variations of the SHG intensities for  = 10 °and 90 °, respectively.SHG intensity for  = 90 °shows a clear anomaly at T = 24 K.The significant enhancement of the SHG signal from a small and nearly constant value suggests that it is related to magnetic phase transition.The slight difference in the transition temperature from that of the bulk crystal may be owing to the heating of the sample (see detailed explanation in the Supporting Information).SHG intensity for  = 10 °gradually decreases with the increase of temperature and shows the anomalies around T = 155 K and T = 210 K, which are considered to reflect the structural transitions.These results indicate that the symmetry changes induced by structural or magnetic phase transitions in exfoliated CCPS can be successfully probed by SHG.

SHG Signals Under Finite Magnetic Field
We further studied the effects of the magnetoelectric properties on the SHG signals in the multiferroic phase.A magnetic field of 1.16 T was applied along the in-plane direction (Voigt configuration) using a permanent magnet set on a rotational mount.Figure 3a shows the polarization-resolved SHG intensities of Sample 1 at T = 5 K without a magnetic field (black) and under a magnetic field along the b-axis (green).The SHG pattern changed considerably, and the signal intensity was significantly enhanced under the magnetic field.Notably, SHG intensity for the light polarization  = 0 °under the magnetic field is an order of magnitude larger than that at zero magnetic field.This giant enhancement of SHG intensity for  = 0 °can be understood by the magnetoelectric effect of CCPS.Magnetic field-induced electric polarization emerges along the a-axis when a magnetic field is applied along the b-axis.The electric polarization induced by the magnetoelectric effect may generate a large SHG in this material (see Supporting Information for a detailed discussion).Such modulation of the SHG signals under a magnetic field that reflects the magnetoelectric effect has been reported in oxide multiferroics. [31]Because the induced polarization direction is sensitive to the direction of the applied magnetic field, a characteristic directional dependence of SHG is expected.In Figure 3b, we compare the polarization-resolved SHG intensities without a magnetic field (black) and with a magnetic field along the positive (blue) or negative (red) directions of the a-axis.Although the enhancement of the SHG intensity is smaller than that when the magnetic field is applied along the b-axis, the SHG pattern for B // +a is different from that for B // −a, which can be explained by the interference between the SHG originating from the original crystallographic polarization and the polarization induced by the above magnetoelectric effect.Because B = 1.16 T (// a) is sufficiently large for the spin-flop transition in the CCPS, the detailed magnetic structure in this phase should be clarified in future experiments.Figure 3c is the summary of the in-plane magnetic field directional dependence of the SHG patterns.The polarization-resolved SHG pattern and its intensity strongly depend on the direction of the magnetic field, further supporting the above scenario.These results demonstrate that the contribution from the electric polarization induced by the magnetoelectric effect is dominant in the SHG of the CCPS, and that magnetic SHG is an excellent probe of magnetoelectric responses.

Thickness-Dependent SHG Signal
Finally, we studied the thickness-dependent symmetry and multiferroicity.][34][35] However, the effect of sample thickness on multiferroic properties, such as the magnetoelectric effect, has not yet been studied.As shown in Figures 1 and 2, the bulk CCPS has glide symmetry with respect to the ac-plane in all phases, and the SHG pattern is almost mirror-symmetric about the a-axis.This glide symmetry disappears when the sample thickness is reduced; thus, the sample cannot be regarded as a bulk crystal.Figure 4a illustrates this situation.The red and blue layers represent mirror images of the ac-plane.In thin samples, translational symmetry along the stacking direction was prohibited because of the boundary.Thus, a thin CCPS does not have any symmetry operation and should show SHG patterns different from those of thick samples.
To verify this symmetry change from bulk crystals to thin films, we acquired the SHG image of sample 2, which contained several regions with different thicknesses (Figure 4b). Figure 4c-e shows the polarization-resolved SHG intensities in region 1 (Figure 4c), 2 (Figure 4d), and 3 (Figure 4e) encircled in Figure 4b.Sample thickness is estimated as 15 nm in region 1, 10 nm in region 2, and 5 nm in region 3, respectively.The SHG signals were measured at T = 100 K (T > T N , top) and 5 K (T < T N ) without (middle) or under a magnetic field along the b-axis (B = 1.16 T, bottom).The SHG patterns in region 1(Figure 4c) are similar to those in the 27-nm-thick sample 1, implying that the symmetry of this region is the same as that of the bulk crystal.However, if we focus on the SHG signals in region 2 (Figure 4d), different SHG patterns can be observed.The polarization direction of the maximum SHG intensity was tilted from the a-axis in the polar paramagnetic phase (Figure 4d top), and the shape of the polarization-dependent pattern changed from a 4-peak structure to a 6-peak structure.Below T < T N , a magnetic SHG signal develops along the b-axis with an antiferromagnetic transition similar to sample 1 and region 1 (Figure 4d middle), but the enhanced SHG signal by the magnetoelectric effect is not parallel to the a-axis but tilted (Figure 4d bottom), possibly reflecting the modulations of magnetoelectric tensors by the crystal symmetry change.Note that the SHG pattern in this region is not mirror-symmetric along the a-axis, which is consistent with the aforementioned argument regarding the absence of glide symmetry in thin films.In the thinner region 3 (Figure 4e), the sixfold SHG pattern becomes more prominent at T > T N (Figure 4e top).Although magnetic SHG from the antiferromagnetic ordering is unclear in this region (Figure 4e middle), the SHG pattern under the magnetic field shows a significant change (Figure 4e bottom), which indicates that both spatial-inversion symmetry and time-reversal symmetry are broken, and the resultant magnetoelectric effect exists even in this thin region.In Sections S7 and S8, Supporting Information, we confirmed that the magnetic ordering remained and the transition temperature did not change up to the 6 nm thick regions from the temperature variation of the SHG intensity.More systematic SHG modulations, as a function of thickness, are shown and discussed in the Supporting Information.

Conclusions
In this study, structural and magnetic phase transitions, which cause symmetry changes in CCPS, were successfully probed by SHG.In particular, in the low-temperature multiferroic phase, SHG signals are effectively modulated by the application of a magnetic field, which can be explained by the magnetic fieldinduced electric polarization that reflects the magnetoelectric effect.Furthermore, thickness-dependent symmetry changes and the resultant modulation of the magnetoelectric responses were observed, clarifying the novel design principle of 2D multiferroics.It is expected that the symmetry and multiferroic properties of CCPS can be further controlled by fabricating interfaces or nanostructures.Owing to its high stability (see Supporting Information), CCPS is a promising building block for van der Waals nanodevices with unique magneto-optical functionalities.

Experimental Section
Specific Heat and Magnetization Measurements: Single crystals of CCPS were purchased from HQ graphene and cut into the size of 3-4 mm square for the bulk sample measurements.The specific heat of the bulk CCPS was measured using a PPMS (Quantum Design Inc.), and the magnetization was measured using an MPMS (Quantum Design Inc.).For magnetization measurements, a magnetic field of B = 0.1 T was applied.

Preparation of Exfoliated Samples:
The CCPS samples were exfoliated onto SiO 2 /Si substrates using the scotch tape method.The thickness of the CCPS was measured using atomic force microscopy (AFM; Hitachi AFM 5100N).The crystal orientations of the CCPS thin flakes were determined from the SHG patterns of thick sample regions.As discussed in the main text, the SHG polarization dependence of the thick CCPS showed a mirror-symmetric pattern along the a-axis and a characteristic temperature evolution reflecting the phase transitions.We used a thin flake of the CCPS to which a thick part was attached, assuming that the crystal orientations of the thin and thick sections were identical.
SHG Measurements: All sample substrates were placed on a pillarshaped copper mount with varnish and inserted into a cryostat (Cryo Industries).A thermometer was placed at the bottom of the copper mount.Fundamental laser pulses at 1.55 eV photon energy were generated using a Ti:Sapphire amplifier (1 kHz, 100 fs) and sent to the sample with pseudo-Kölller geometry, and the SHG images at 3.1 eV reflected from the sample were detected by a cooled CCD camera (PIXIS: 1024B).The linear polarizations of the incident light and the SHG signals were set to be parallel.For the SHG anisotropy measurements, the half-wave plate was rotated from 0°to 90°(see Supporting Information for the detailed optical setup).To apply an in-plane magnetic field (Voigt configuration), a custom-made Halbach array magnet with B = 1.16 T was used at the sample position mounted on a rotational stage covering the cryostat snout.To extract the SHG intensity from the SHG images, the intensity in the encircled regions presented in the figures was averaged, with the background subtracted.

Figure 2 .
Figure 2. Temperature dependence of SHG signals under zero magnetic field.a) Schematic of second-harmonic generation (SHG) measurement.Linearly polarized light (1.55 eV, red) is normally incident on the ab-plane, and reflected light at the second-harmonic frequency (3.1 eV, blue) with a linear polarization parallel to the incident light was detected.b,c) Optical and SHG images of the exfoliated CuCrP 2 S 6 crystal (sample 1 with a thickness of 27 nm).d-f) Polarization dependence of SHG signals at T = 5 K (d, AFM phase), 100 K (e, PM phase with space group Pc), and 300 K (f, PM phase with space group C2/c).g) Temperature dependence of the normalized SHG signals.The green (red) data indicate the SHG intensity at a polarization angle of 90°(10°).The enhancement of the SHG signals corresponded to magnetic and structural phase transitions.

Figure 3 .
Figure 3. Modulation of the SHG signals under the magnetic field.a) Polarization dependence of the SHG pattern when a magnetic field (B = 1.16 T) is applied along the b-axis (green).The original SHG pattern (under a zero magnetic field, black) is shown for comparison.A significant enhancement in the a-axis SHG component was observed.b) Polarization-dependent SHG signals under a magnetic field along the a-axis.Red and blue represent SHG signals under a magnetic field along the 180-degree direction (B // −a) and 0-degree direction (B // +a), respectively.The SHG pattern under zero magnetic field (black) is also shown.c) SHG patterns under various magnetic field directions.The greenarrow indicates the magnetic field direction for each data point, and the inset schematics show thespin order in CuCrP 2 S 6 under a magnetic field.

Figure 4 .
Figure 4. Thickness dependence of SHG signals.a) Crystal symmetry of few-layer CuCrP 2 S 6 .Top (top) and side (bottom) views.Because the neighboring layers of CuCrP 2 S 6 are related to the mirror symmetry operation (M ac ), the glide symmetry with respect to the ac-plane, which exists in the bulk crystal, is lost in the thin films, leading to lower symmetry.b) Optical image of an exfoliated CuCrP 2 S 6 crystal (sample 2) c-e) Thickness-dependent SHG signals.Purple (c), orange (d), and red (e) represent SHG signals in regions 1 (15 nm thickness), 2 (10 nm thickness), and 3 (5 nm thickness), respectively.The SHG signals measured at T = 100 K (T > T N , top) and 5 K (T < T N ) without (middle) or under a magnetic field along the b-axis (B = 1.16T, bottom) are shown.