Effects of Fe deficiency and Co substitution in polycrystalline and single crystals of Fe$_{3}$GeTe$_{2}$

Fe$_{3}$GeTe$_{2}$ is a two-dimensional van der Waals material with a ferromagnetic ground state and a maximum transition temperature $T_{\mathrm{c}}\sim225$ K. However, when Fe$_{3}$GeTe$_{2}$ is synthesized lower values of $T_{\mathrm{c}}$ are often reported. This is attributed to a deficiency in the Fe at the 2c site in the crystal structure. Here we investigate the effect of Fe deficiency and the substitution of Co for Fe on the magnetic properties of this system. We have synthesized both polycrystalline material and single crystals by chemical vapor transport and the flux method, with the largest crystals obtained using the flux method. Cobalt substitution at the Fe site is found to significantly reduce the magnetic transition temperature. Crystals of Fe$_{3}$GeTe$_{2}$ grown by chemical vapor transport with $\sim 8\%$ excess Fe in the starting materials display an optimum Fe content and magnetic transition temperature.

Fe 3 GeTe 2 is a 2D magnetic material which has been generating significant attention as it was the first vdW material found to be both magnetic and metallic. It also offers a significant step up in Curie temperature (T c ∼ 225 K) from previous magnetic vdW materials. [16][17][18] Much research has been directed towards tuning the magnetic properties of this material by layer-thickness dependence studies, 19 varying the Fe content, 20 Co substitution, 21,22 and the investigation of the anomalous Hall effect, 23 planar topological Hall effect, 24 Kondo lattice physics, 25 anisotropy magnetostriction effect 26 and ionic liquid voltage gating. 27 In bulk Fe 3 GeTe 2 there have been some conflicting reports over whether the ground state of Fe 3 GeTe 2 should be antiferromagnetic or ferromagnetic. [28][29][30] In its stoichiometric form, there should be inter-layer antiferromagnetism in Fe 3 GeTe 2 , however, Fe vacancies in this system, which correspond to more hole charge carriers, produce a ferromagnetic ground state. 30 This observation agrees with the majority of the literature, in which samples are frequently reported to be Fe deficient and ferromagnetic. 20 It has also been suggested that a antiferromagnetic to ferromagnetic transition in Fe 3 GeTe 2 can be induced by electron doping. 30 In addition to the highly tunable nature of the magnetic properties of Fe 3 GeTe 2 , there have been several studies concentrating on skyrmions and the spin textures which have been observed in this material. Magnetic bubble-like formations were first observed in Fe 3 GeTe 2 when a magnetic Ni tip of a scanning tunneling microscope (STM) was held close to a freshly cleaved surface of Fe 3 GeTe 2 . 31 Lorentz transmission electron microscopy (TEM) measurements further revealed magnetic bubble-like textures in Fe 3 GeTe 2 which were claimed to be skyrmions. 32 These bubbles could be tuned in size with applied magnetic field. The presence of a topological Hall effect has recently been observed in Fe 3 GeTe 2 , this signal is frequently take as the hallmark of skyrmions. 24,33 Since Fe 3 GeTe 2 crystallizes in the centrosymmetric hexagonal space group P 6 3 /mmc (No. 194) as shown in Figure 1, the mechanism for the stabilization of skyrmions in bulk Fe 3 GeTe 2 is currently unclear. Skyrmion-like magnetic bubbles have only been observed in Fe 3 GeTe 2 in a thin film regime or at the interface of the material, as is the case for the STM study, where it is conceivable that inversion symmetry can be broken leading to a Dzyaloshinskii-Moriya (DM) interaction. 34 The observation of Néel type skyrmions at an oxide interface in Fe 3 GeTe 2 gives further confirmation that the DM interaction is allowing the stabilization of skyrmions in this material. 35 Should skyrmions be realized in bulk Fe 3 GeTe 2 , the interactions stabilizing them cannot include the DM interaction due to the centrosymmetric nature of the crystal structure.
We have undertaken a detailed investigation into the dependence of the magnetic properties on the Fe content in the Fe 3 GeTe 2 materials. We have synthesized both polycrystalline and single crystals of Fe 3 GeTe 2 and Co substituted materials, Fe 3−y Co y GeTe 2 for y = 0.3, 0.6, 0.9, 1.2 and 1.5. Investigations of the structure and properties of the polycrystalline and single crystals produced have been undertaken using x-ray diffraction and magnetic measurement techniques. Composition analysis, including estimates of the Fe content in these materials, reveal a direct correlation with the observed magnetic transitions.
We also find that an excess of Fe is necessary in the synthesis of Fe 3 GeTe 2 to optimize the Fe content and therefore achieve the highest T c .

Experimental details
Polycrystalline materials were synthesized by solid state reaction. Single crystal growths were carried out by either chemical vapor transport (CVT) or the flux method using Te flux. All the sample preparation techniques are discussed in more detail in the following section. To determine the phase purity and crystal structure of the synthesized polycrystalline materials, powder x-ray diffraction was performed at room temperature using a Panalytical Empyrean diffractometer (Bragg-Brentano geometry) with a Cu K α1 and K α2 source and a solid state PIXcel detector. Rietveld refinements were carried out on the observed diffraction patterns using the TOPAS academic v6.0 software suite. 36 The quality of the single crystals obtained was investigated by Laue x-ray imaging using a Photonic Science Laue camera.
The chemical composition was determined using a ZEISS GeminiSEM 500 which was used to perform energy dispersive x-ray spectroscopy (EDX). The magnetic properties of both the single crystals and the polycrystalline materials were measured using a Quantum Design Magnetic Property Measurement System (MPMS), superconducting quantum interference device (SQUID) magnetometer. Measurements were made in the temperature range 2-300 K in various applied magnetic fields in the zero-field-cooled (ZFC) and field-cooled (FC) modes.

Material Synthesis
Polycrystalline synthesis

Single crystal growth
Two different techniques were employed to obtain single crystals of the various compositions listed, chemical vapor transport, and the flux method using excess Te.
For the CVT process, growths using two different transport agents, I 2 and TeCl 4 , were attempted. Quantities of Fe, Ge, Co and Te powders (see Table 1) along with 5 mg/cm 3 of the transport agent were sealed in quartz ampoules. The growth of crystals was carried out by holding the source and the sink ends of each tube at different temperatures in a two zone furnace for two weeks, before cooling to room temperature. Several different temperature profiles were used, 750-675 • C for the hot end and 700-650 • C for the cold end. In some of the CVT growths, in addition to the platelets which have been identified as corresponding to the desired Fe 3 GeTe 2 crystals, other needle-like and pyramidal-shaped structures corresponding to other phases of Fe-Ge-Te were also obtained. A photograph of a typical crystal platelet obtained from a CVT growth is shown in Figure 2(a).
For the crystal growth by the flux method, using excess Te (powder) as the flux, mixtures of varying nominal compositions, (see Table 1), were used. The mixtures were placed in an alumina crucible which was then sealed in a quartz ampoule under vacuum. To enable the capture of the crystals during a subsequent centrifuging process, a small amount of quartz wool was placed over the alumina crucible inside the ampoule. The tubes were heated to 1000 • C and cooled at the rate of 3 • C/h to 675 • C, at which temperature the tubes were removed from the furnace and centrifuged to remove the excess Te flux. 20,32 An example of a crystal grown by the flux method is shown in Figure 2(b).
In general the thickness and size of the crystals grown by the flux method were found to be larger than those obtained by CVT. The average size of the CVT grown crystals is 2 × 2 mm 2 while those obtained by the flux method are typically 7 × 5 mm 2 .

Results and discussion
Laue diffraction X-ray back reflection Laue patterns were taken on the crystals to check for crystalline quality.
Typical Laue photographs of isolated platelets of Fe 3 GeTe 2 and Fe 3−y Co y GeTe 2 , mounted with the ab plane perpendicular to the x-ray beam are shown in Figures 2(a) and 2(b). These display the 6-fold symmetry expected observing along the c axis of the crystals.

Powder x-ray diffraction
Phase purity and structural analysis were carried out using powder x-ray diffraction on the polycrystalline materials synthesized. The diffraction patterns obtained could be indexed to the hexagonal space group P 6 3 /mmc (No. 194). Figure 3 shows the observed diffraction patterns for the various nominal starting compositions of the Fe-Ge-Te and Fe-Co-Ge-Te powders and the Rietveld refinements of the observed patterns obtained using the TOPAS software suite. The typical physical and crystallographic parameters obtained for one of the compositions synthesized, Fe 3 GeTe 2 , are given in Table 2 along with the R wp values indicating the quality of the fits. The lattice parameters obtained from the fits to the powder diffraction patterns are also shown in Figure 3. The lattice parameters obtained are largely in agreement with those reported for these materials. 16 The variations in the lattice parameters in the Co substituted powders can be seen to follow a clear trend by tracking the (103) and (006) diffraction peaks as shown in Figure 4.
This gradual shift in the positions of the peaks indicates a decrease in both the a and c lattice parameters, as the level of Co substitution is increased in these materials.
The dependence of the lattice parameters with Fe composition in Fe 3−δ GeTe 2 has been examined. We show that an Fe deficiency results in a decrease in a, while c increases. We find that both the a and c lattice parameters decrease with increasing Co substitution at the Fe site, consistent with what has been reported earlier. 21 It was not possible to determine the actual occupancy levels of the Fe/Co in the Co substituted samples using x-ray diffraction, due to the similar atomic numbers and hence x-ray scattering factors of the Fe and Co atoms.
Therefore, the decrease observed in the lattice parameters can only be indirectly attributed to the preferential substitution of Co at the 2c (Fe2) sites.
X-ray diffraction patterns were also obtained on single crystal platelets mounted with the ab plane parallel to the x-ray beam when the scattering angle is zero, to obtain a series of (00l) reflections. Figure 5 shows the diffraction patterns obtained from two different crystal platelets, exhibiting the (00l) reflections typical of the Fe 3 GeTe 2 structure.

Energy dispersive x-ray analysis
Composition analysis of the crystals obtained was carried out by EDX analysis. Estimates of the relative Fe, Co, Ge and Te content in the crystals are given in Table 1. Examples of the EDX spectra and scanning electron microscope images of two crystals are shown in  Table 1. These resulting compositions are further affirmed by the correlation with the T c measured on these crystals through magnetic susceptibility measurements as discussed in the next section.

Magnetic susceptibility versus temperature
The Curie temperature, T c , of a polycrystalline sample with a nominal composition Fe 3 GeTe 2 was determined from the temperature dependent dc magnetic susceptibility χ (T ) as shown in Figure 8 and gave a T c = 223 (1) Table. 2. Impurity peaks are denoted by a red asterisk.    Intensity peaks for each element are labeled. Oxygen peaks are indicated by a red asterisk. On the right is a scanning electron microscope image of the surface of each single crystal studied. EDX spectra were collected over the entire area of each crystal. The elemental stoichiometry at each numbered site and across the bulk are given in Table. 3      (1)