Direct Magnetic Evidence, Functionalization, and Low-Temperature Magneto-Electron Transport in Liquid-Phase Exfoliated FePS3

Magnetism and the existence of magnetic order in a material is determined by its dimensionality. In this regard, the recent emergence of magnetic layered van der Waals (vdW) materials provides a wide playground to explore the exotic magnetism arising in the two-dimensional (2D) limit. The magnetism of 2D flakes, especially antiferromagnetic ones, however, cannot be easily probed by conventional magnetometry techniques, being often replaced by indirect methods like Raman spectroscopy. Here, we make use of an alternative approach to provide direct magnetic evidence of few-layer vdW materials, including antiferromagnets. We take advantage of a surfactant-free, liquid-phase exfoliation (LPE) method to obtain thousands of few-layer FePS3 flakes that can be quenched in a solvent and measured in a conventional SQUID magnetometer. We show a direct magnetic evidence of the antiferromagnetic transition in FePS3 few-layer flakes, concomitant with a clear reduction of the Néel temperature with the flake thickness, in contrast with previous Raman reports. The quality of the LPE FePS3 flakes allows the study of electron transport down to cryogenic temperatures. The significant through-flake conductance is sensitive to the antiferromagnetic order transition. Besides, an additional rich spectra of electron transport excitations, including secondary magnetic transitions and potentially magnon-phonon hybrid states, appear at low temperatures. Finally, we show that the LPE is additionally a good starting point for the mass covalent functionalization of 2D magnetic materials with functional molecules. This technique is extensible to any vdW magnetic family.


Determination of the concentration
The concentration of exfoliated material in each sample is calculated from the supernatant collected after the centrifugation process. As indicated in the manuscript, we started from a dispersion of ground FePS3 (10 mg) in iPrOH (10 mL) (Ci = 1 mg·mL -1 ). This initial dispersion is sonicated and centrifuged following a cascade process, where a portion of the supernatant is extracted in each stage, giving rise to the different samples ( 1−4 ).
The collected supernatants were filtered (in PTFE 0.2 um membranes) to determine the mass of exfoliated material and the volume in which it was dispersed, allowing us to know the real concentration of the exfoliated material for each sample, Table S1.             Figure S10 shows the raw magnetic susceptibility measured in a capsule containing the LPE at low temperatures and a small anomaly at around 50K. The susceptibility shown in Figure 3 in the main text results from the subtraction of this component.

Figure S 11. Magnetic susceptibility measured as a function of temperature in a bulk reference sample. A small magnetic transition at T1 = 20 K is observed at low temperatures in addition
to the antiferromagnetic transition at TN = T2 = 118 K.

Additional details of the dielectrophoresis technique
The liquid-phase exfoliated FePS3 flakes can be positioned between metallic electrodes, directly from solution, by dielectrophoresis (DEP). Dielectrophoresis consists in the directed motion of nano-objects in the presence of an ac electrical field. The electrical field polarizes the nano-objects, and exerts a dielectrophoretic force FDEP that, for oblate ellipsoidal particles with large aspect ratios, can be expressed as: 3 where V p is the volume of the particles; ε p * and ε m * are respectively the complex permittivities of the particles and the suspension medium; and E is the non-uniform electric field.
The DEP force is therefore proportional to: (1) The nanoflake volume.
(2) The real part of the Clausius-Mossoti factor: [(ε p * -ε m * )/ε m * ] that is related with the polarizability of the particles and solvent. Besides, the sign of this factor will determine which component becomes polarized. iPrOH has been used before as solvent with other 2D materials due to its relatively weak polarizability. 3 (3) The electrical field distribution and the gradient of the electrical field.
A careful design of the electrodes is therefore required to focus the electric field within the gap between the electrodes and to avoid perturbations to the gradient of the electrical field towards the gap by other parts of the circuit. Figure S14a shows the squared electrical field (E 2 ) distribution for two tip-ended electrodes calculated by finite elements analysis software. See Ref. 3 for details on the simulation. Besides Figure S14b and S14c show the E 2 and ∇|E| 2 profiles taken along the axis perpendicular to the electrodes axis and that crosses the gap area (red dashed line in Figure S14a). The electrical field is maximum within the gap between the electrodes. The gradient is directed towards the gap where it becomes zero. The flakes are therefore trapped once they reach the inter-electrode space. This allows the controlled accumulation of material by graduating the time of dielectrophoresis and concentration of flakes in the liquid phase exfoliation. Figure S15 shows three different examples of this controlled accumulation of material. Figure   S15a shows an SEM image of the electrodes after drop-casting an iPrOH droplet containing LPE FePS3 flakes and in the absence of an electrical field, that is, without dielectrophoresis.
The flakes are randomly distributed over the surface without a preference for the gap between the electrodes. In contrast, Figure S15b shows that by activating the ac electric field, the flakes tend to accumulate in the area predicted in Figure S14. By further increasing the flake concentration in the solvent and/or the intensity of the electrical field (time and voltage) a further accumulation of material between the electrodes can be obtained, as seen in Figure   S15c.   temperatures. Besides a series of wider steps appear below 60 K in the ±150 mV range (green arrows). Figure S 18(a,b) Color plot of the second derivative (d 2 I/dV 2 ) as a function of V and T (2.8 K < T < 180 K), obtained by numerical differentiation of the dI/dV data in Figure 4f of the main text. The wide steps (green arrows in Figure S17) appear as clear peaks below 60 K (marked by the black arrows). The color contrast is adjusted to optimize the visualization of the peaks at a) positive and b) negative bias voltage respectively.