Spin Glass State and Griffiths Phase in van der Waals Ferromagnetic Material Fe₅GeTe₂

Abstract

The discovery of two-dimensional (2D) van der Waals ferromagnetic materials opens up new avenues for making devices with high information storage density, ultra-fast response, high integration, and low power consumption. Fe₅GeTe₂ has attracted much attention because of its ferromagnetic transition temperature near room temperature. However, the investigation of its phase transition is rare until now. Here, we have successfully synthesized a single crystal of the layered ferromagnet Fe₅GeTe₂ by chemical vapor phase transport, soon after characterized by X-ray diffraction (XRD), DC magnetization M(T), and isotherm magnetization M(H) measurements. A paramagnetic to ferromagnetic transition is observed at ≈302 K (T_C) in the temperature dependence of the DC magnetic susceptibility of Fe₅GeTe₂. We found an unconventional potential spin glass state in the low-temperature regime that differs from the conventional spin glass states and Griffiths phase (GP) in the high-temperature regime. The physical mechanisms behind the potential spin glass state of Fe₅GeTe₂ at low temperatures and the Griffith phase at high temperatures need to be further investigated.

1. Introduction

In 2004, Andre Geim et al. reported that graphite can be exfoliated into several layers or even a single layer by mechanical exfoliation processes [1]; this atomic-thick graphite layer is called graphene. The discovery of graphene opened widespread interest in 2D materials and has offered a promising paradigm for the development of low-dimensional spintronic devices [2]. In particular, the spin–orbit coupling of 2D magnetic materials is the basis for potential applications of new low-dimensional spintronic devices, which has made the magnetoelectric coupling of spintronic devices possible [3,4,5]. Subsequent doping of these materials with magnetic elements resulted in the emergence of magnetic properties. Nevertheless, the magnetism observed in these materials is not intrinsic. The Mermin–Wagner theorem states that a one- or two-dimensional isotropic spin-s Heisenberg model with finite exchange interaction can be neither ferromagnetic nor antiferromagnetic at any nonzero temperature [6]. However, large magnetic anisotropy is believed to suppress random spin reorientation induced by thermal fluctuations and provides the existence of two-dimensional magnetism. In 2017, C. Gong et al. reported that 2D van der Waals magnet Cr₂Ge₂Te₆ can maintain long-range magnetic order even at an atomic-scale thickness [7]. B. Huang et al. reported that 2D ferromagnetism in exfoliated monolayer CrI₃ [8]. However, their potential applications remain constrained by the relatively low magnetic transition temperature. Soon, Fe₃GeTe₂, an exfoliable vdW magnet, was discovered, with a reasonably high T_C of about 220–230 K [9]. It exhibits robust 2D ferromagnetism with strong perpendicular anisotropy [10]. Furthermore, by applying an ionic gate, the T_C of thin flakes can be raised to room temperature, much higher than the bulk T_C [11].

Fe_5-xGeTe₂ is a tourmaline ferromagnet with a hexagonal crystal structure [12], which is noteworthy due to its very high Curie temperature (T_C = 270–310 K), and its ferromagnetic behavior persists near room temperature in flakes thinned down to four unit cells thick (12 nm) [13]. The magnetic properties of Fe₅GeTe₂ have received much attention recently. B. W. Casas et al. reported that merons and anti-merons in Fe_5−xGeTe₂ coexist with Néel skyrmionic states over a broad range of temperatures and demonstrated that the topological Hall effect (THE) even at room temperature [14]. C. Zhang et al. reported the unconventional helicity modulation behavior of magnetic sigmoid in Fe_5−xGeTe₂ nanosheets [15]. By employing an electric field modulation technique, M. Tang et al. demonstrated that the magnetic anisotropy properties of Fe₅GeTe₂ display a pronounced dependence on both temperature and sample thickness [16]. However, there is an absence of research in the field of the magnetic phase transition of Fe₅GeTe₂.

The phenomenon of spin-glass (SG) behavior was initially identified and postulated during the investigation of dilute magnetic alloys, later observed in certain chalcogenide oxides [17]. Once the sample has reached the spin-frozen state, the magnetic moments within the system are frozen in a disordered distribution in all directions. Following the random freezing of the spin in the SG, the magnetic moment is kept in a fixed direction and is unable to rotate freely. Furthermore, the ferromagnetic–paramagnetic transition refers to the change in the magnetic state of a material at a specific temperature, known as the Curie temperature (T_C). At temperatures below the Curie temperature, the material displays ferromagnetic behavior, whereby the magnetic moments of the constituent atoms or molecules are parallelly aligned spontaneously. At temperatures above the Curie point, the material undergoes a transition to a paramagnetic state, wherein the magnetic moments are randomly oriented. Both spin-glass states and ferromagnetic–paramagnetic transitions are the fundamental issues for pursuing two-dimensional room-temperature ferromagnetic materials [11].

In this work, we study the magnetic phase transitions in Fe₅GeTe₂ single crystal by utilizing a physical property measurement system (PPMS), revealing two distinct, intriguing magnetic phase transitions: paramagnetic to ferromagnetic at T_C~302 K and potential spin-glass transition at T_f~98 K. In the low-temperature region, Fe₅GeTe₂ crystal is in a potential spin glass state. In the high-temperature region, Fe₅GeTe₂ exhibits non-linear magnetization due to the Griffiths phase. The physical mechanisms behind the potential spin glass state of Fe₅GeTe₂ at low temperatures and the Griffith phase at high temperatures need to be further investigated.

2. Sample Preparation and Characterization

2.1. Single-Crystal Growth

High-quality Fe₅GeTe₂ single crystals were successfully synthesized by the chemical vapor transport method, using iodine as the transporting agent. The mixture of Fe (Aladdin, 99.9%), Ge (Alfa Aesar, 99.999%), and Te (Alfa Aesar, 99.999%) with the ratio of 6:1:2 was sealed into an evacuated quartz ampoule. The ampoule was then heated to create a temperature gradient with 800–1000 °C at the hot end and 600–800 °C at the cold end of the quartz ampoule for 7–20 days to grow the single crystal.

Fe₅GeTe₂ crystallizes in a trigonal structure (space group R3m, No. 160) [18], comprising layered building blocks that are stacked along the c-axis, as illustrated in Figure 1a; each block contains a Fe-Ge slab comprising three distinct Fe atom sites (Fe1, Fe2, and Fe3, as illustrated in Figure 1a), with two layers of Te atoms positioned above and below the Fe-Ge slab, respectively. It is noteworthy that the additional Fe1 and Fe3 layers serve to distinguish the structural and magnetic properties of Fe₅GeTe₂ from those of Fe₃GeTe₂ [19].

2.2. X-ray Diffraction Measurements

The X-ray diffraction (XRD) pattern of as-grown Fe₅GeTe₂ single crystal at room temperature is shown in Figure 1b. During the XRD measurement, the X-rays were incident on a flat surface of the crystal, resulting in diffraction peaks exclusively corresponding to the (00l) planes. It indicates the single-crystalline nature of the material, and the inset of Figure 1b shows the photo of Fe₅GeTe₂, further revealing that the planes of the crystal represent the ab plane. Our XRD results agree well with the theoretical values, as shown in the table (Supplemental Material Table S1). Self-intercalation of the transition metal ion has been reported in vdW materials, for example, in CrTe₂ [20]. Since the c-axis lattice constant of a Fe-intercalated Fe₅GeTe₂ single crystal will be greatly enlarged due to the existence of the intercalated layer, its X-ray diffraction pattern should be dramatically different from the standard Fe₅GeTe₂. Our XRD measurement rules out the existence of self-intercalation of the transition metal.

2.3. Scanning Electron Microscope Measurements

The scanning electron microscopy (SEM) analysis reveals that Fe₅GeTe₂ single crystal exhibits a layered structure with a relatively uniform morphology shown in Figure 1c. Most of the samples present in the form of hexagonal flake materials featured a smooth surface. This characteristic is highly favorable for the subsequent mechanical exfoliation or liquid-phase exfoliation processes to obtain few-layer samples.

2.4. Energy-Dispersive X-ray Spectroscopy Measurements

To investigate the elemental composition and chemical homogeneity of Fe₅GeTe₂, energy-dispersive X-ray (EDX) spectroscopy has been performed on the Fe₅GeTe₂ single crystal. As shown in Figure 1d,e, spots in the area on the surface of the crystal were measured. The values were finally averaged, which are presented in Table S2, showing the compositions as Fe:Ge:Te = 5.14:1.00:2.39 without other impurities and matching the earlier report [19].

3. X-ray Photoemission Spectroscopy Measurements

The surface chemical composition and core-level binding energy of the Fe₅GeTe₂ single crystal were measured by utilizing X-ray photoemission spectroscopy (XPS). The XPS results for Fe, Ge, and Te in the Fe₅GeTe₂ single crystal are presented in Figure 2. As shown in Figure 2, Fe 2p spectra, Fe(III) doublets (Fe 2p_1/2, Fe 2p_3/2), and Fe(II) doublets (Fe 2p_1/2, Fe 2p_3/2) could be observed with their resonance transition (satellite peaks) at their corresponding binding energies. Fe³⁺ with binding energies of Fe 2p_3/2 at 712.10 eV and Fe 2p_1/2 at 725.56 eV is the dominant species in Fe₅GeTe₂, which becomes the clear evidence for the high-spin state of Fe in their ferromagnetic state. Furthermore, the presence of Fe²⁺ 2p_3/2 (710.56 eV) and Fe³⁺ 2p_3/2 (712.10 eV) peaks suggests that Fe exists in ionic form with a mixed valence of +2 and +3 in Fe₅GeTe₂. The analysis of the Ge 3d_5/2 and Ge 3d_3/2 peaks in Figure 2 reveals that Ge is present as both elemental Ge and Ge (IV) species in the Fe₅GeTe₂ single crystal; only the latter is used to determine the composition. Similarly, the Te 3d spectrum exhibits two peaks at a binding energy of 576.42 eV and 586.83 eV, corresponding to the 3d_3/2 and 3d_5/2 levels of the Te⁴⁺ oxidation state, while peaks at approximately 572.98 eV and 583.32 eV are attributed to metallic tellurium (Te⁰) in Figure 2. The oxidation of the surface atoms of Fe₅GeTe₂ upon exposure to air is suggested by the oxide peaks observed in all species [21]. Element Ge is nonmagnetic, which will not affect the measured magnetism, as reported in Fe₄GeTe₂ [21] and Fe₃GeTe₂ [22].

4. Magnetization Measurements

Figure 3 shows the temperature dependence of magnetization, the corresponding derivatives, and inverse magnetic susceptibility for the Fe₅GeTe₂ single crystal under an applied magnetic field of 3000 Oe parallel to the c axis. The temperature dependence of the DC magnetization was investigated for Fe₅GeTe₂ under zero-field-cooling (ZFC) and field-cooling (FC) conditions in a magnetic field of 3000 Oe applied along the crystallographic c-axis within a temperature range of 2–350 K, as shown in Figure 3a. The Fe₅GeTe₂ was initially cooled from 350 K to 2 K in the absence of an applied magnetic field. Subsequently, an applied magnetic field of 3000 Oe was introduced at 2 K, and the DC magnetization data were recorded while the Fe₅GeTe₂ single crystal was warmed up. This resulted in a ZFC magnetization curve. The FC magnetization curve is obtained by lowering the temperature of the Fe₅GeTe₂ single crystal from 350 K to 2 K in the presence of an applied magnetic field of 3000 Oe.

As the temperature decreases from 350 K, the magnetization M(T) rises to a markedly high value of magnetization, as shown in Figure 3a, which indicates the transition of the paramagnetic to ferromagnetic phases. It is evident that a plateau transition is occurring as the cooling process continues. However, at low temperatures, there is an obvious bifurcation between the magnetization curves of the ZFC and the FC along the c-direction, exhibiting an extreme value of approximately 108 K in the ZFC and 103 K in the FC processes. In the magnetically ordered state of ferromagnetic materials, this behavior is very extraordinary. A possible interpretation is that either the samples may undergo a structural phase transition [23] or other magnetic phase transitions in this temperature regime. The crystal structure of Fe₅GeTe₂ was measured at 103 K, 108 K, and 298 K by variable-temperature X-ray diffraction. The results of this measurement demonstrate that Fe₅GeTe₂ does not undergo a structural phase transition around 103 K and 108 K, as shown in Figure 4. Furthermore, this phenomenon may be due to the ferromagnetic domain-wall pinning effect [24], spin-glass freezing behavior [25,26,27,28], the antiferromagnetic correlation between the local spins and itinerant electrons [29], or other kinds of magnetic inhomogeneity.

Spin glasses are magnetic systems in which the interactions between the magnetic moments are ‘in conflict’ with each other due to some frozen-in spin disorder. Therefore, it is impossible to establish any conventional long-range order (neither ferromagnetic nor antiferromagnetic type) [30]. The effect of ‘disorder’ has been employed for the definition and the characteristics of spin glass states. A spin glass system is defined as a system in which the magnetic moments exhibit disordered orientation. In such disordered magnetic systems, the magnetic moments frequently exhibit competing relationships between antiferromagnetic and ferromagnetic interactions. Here, we demonstrated that Fe₅GeTe₂ potentially exists in a spin glass state below the freezing temperature based on the observed correlation between the M_ZFC and M_FC relationships. Two key characteristics of spin glass systems are magnetic frustration and magnetic disorder. The sample was cooled in fields of zero and 3 k Oe, after which magnetization measurements were taken upon warming at 3 k Oe. M_ZFC falls below M_FC below the freezing temperature T_f (~98 K), which is potentially a typical behavior observed in spin-glass materials. The distribution of the magnetic ion concentration in the magnetic system is inhomogeneous, which in turn gives rise to inhomogeneous interactions between the magnetic moment spins. Furthermore, this will result in antiferromagnetic interactions being present in the system at all times, which will cause ferromagnetic frustration. The formation of a ferromagnetic region is initiated by a phase transition occurring first in the region of stronger magnetic interactions. At elevated temperatures, the level of ferromagnetic frustration is relatively minimal. However, as the temperature decreases, the frustration effect gradually increases. When the level of frustration is sufficiently high, the energy required for the system to form a long-range magnetic order is greater than that needed for the formation of a spin-glass state. As a result, the system will gradually evolve into a spin-glass state [31]. It is also noteworthy that the FC and ZFC curves exhibit two intersections in the low-temperature region, at 98 K and 118 K, which differ from the previously reported spin-glass states [27,28]. The anomalous behavior observed between 98 K and 108 K requires further investigation, specifically through the measurement of the AC magnetic susceptibility and the magnetic relaxation effects.

As shown in Figure 3b, the first derivatives of the magnetization with respect to the temperature of Fe₅GeTe₂ under both field-cooled (FC) and zero-field-cooled (ZFC) conditions reveal three distinct extremes. In the case of the FC condition, the temperatures of extremes are 117 K, 276 K, and 302 K, while in the case of the ZFC condition, the corresponding temperatures are 120 K, 310 K, and 334 K. The ferromagnetic transition temperature (T_C) of the current Fe₅GeTe₂ crystal was approximated by examining the first derivative of the magnetization with respect to temperature as a function of temperature. The resulting T_C was determined to be 302 K, as shown in Figure 3b; this is close to the value previously reported [13]. In our system, the T_C of Fe₅GeTe₂ single crystals is 302 K, which is higher than the T_C of the Fe₃GeTe₂ single crystal (T_C = 220 K) [32] and the T_C of the Fe₄GeTe₂ single crystal (T_C = 270 K) [33]. The elevated T_C could be attributed to the enhanced Fe-Fe exchange interaction among neighboring atoms as the consequence of the increased incorporation of Fe into the system, thereby significantly augmenting the number of Fe neighbors [18].

Figure 3c shows the temperature dependence of the inverse susceptibility 1/χ. The data in the high-temperature range were well fitted by the modified Curie–Weiss law:

$$\mathsf{\chi }={\mathsf{\chi }}_0+{\displaystyle \frac{\mathrm{C}}{\mathrm{T}-\mathsf{\theta }}}$$

(1)

In this context, χ₀ represents the temperature-independent susceptibility, C denotes the Curie–Weiss constant, and θ signifies the Weiss temperature. The fitting process yielded the following parameter values: C = 8.32534 emu K/mol, θ = 305.06639 K, and χ₀ = 0.02728 emu/mol for H || c. The results indicate that at elevated temperatures, χ(T) displays a nearly isotropic paramagnetic behavior. The Curie–Weiss temperature (θ = 305.06639 K) was obtained from the Curie–Weiss fit, which is similar to that of the Curie temperature (T_C = 302 K), which was estimated based on the temperature dependence of the first derivative of the magnetization with respect to temperature. A positive θ indicates that the ferromagnetic interaction between the Fe atoms is the dominant interaction between the layers.

The temperature dependence of χ⁻¹ derived from the M(T) curves for the Fe₅GeTe₂ crystal under zero-field-cooled (ZFC) conditions is shown in Figure 3d. The downturn in inverse susceptibility (χ⁻¹) as a function of temperature above T_C is considered to be a signature of Griffiths singularity [33]. In the high-temperature regime, the inverse susceptibility (χ⁻¹) exhibits a linear relationship with temperature, according to the Curie–Weiss (CW) law. The Griffiths phase (GP) is the transitional phase between the FM and PM phases, when inverse susceptibility [χ⁻¹(T)] depicts a decline as a function of temperature. The occurrence of Griffith phases was evaluated for both Tb₅Si₂Ge₂ [34] and La_1−xSr_xMnO₃ [35] based on the observation that the inverse-susceptibility [χ⁻¹(T)] curves exhibit a deviation from linear dependency, characterized by a downward bend. In this work, a pronounced downward bend in χ⁻¹(T) above the critical temperature (T_C) (Inset Figure of Figure 3d) is observed, which indicates the appearance of the Griffiths phase (GP). In addition, the magnetic field plays a significant role in influencing the Griffiths phase, and the presence of an externally applied field can effectively suppress the Griffiths phase [35].

In order to further elucidate the anisotropic magnetic properties of the synthesized Fe₅GeTe₂ crystal, isothermal magnetization measurements were conducted at temperatures of 20, 100, 150, 200, and 300 K, and the resulting field dependences are presented in Figure 5a. In the magnetically ordered state at 20 K, the magnetization of Fe₅GeTe₂ crystals saturates in the c-direction with negligible hysteresis losses, indicating a soft ferromagnetic behavior similar to that of Fe₃GeTe₂ [36]. The inset in Figure 5a presents the isothermal magnetization (M-H) as a function of the magnetic field H at 20 K. From this data, we determine a saturation magnetization (M_sat) of 4.7 μ_B/Fe at 20 K. This saturation magnetization is higher than those of Fe₅GeTe₂ (2.1 μ_B/Fe at 3 K, H//ab) [18], Fe₃GeTe₂ (1.625 μ_B/Fe) [9], and Fe₄GeTe₂ (1.8 μ_B/Fe) [33] single crystals. Furthermore, as the temperature increases, the saturating magnetization demonstrates a gradual decrease.

Based on the Landau mean field theory [37], the M-H in the vicinity of the Curie temperature can be expressed as follows:

$$\mathrm{a}\left(\mathrm{T}\right)+\mathrm{b}\left(\mathrm{T}\right){\mathrm{M}}^2={\mathsf{\mu }}_0{\displaystyle \frac{\mathrm{H}}{\mathrm{M}}}$$

(2)

Consequently, it can be reasonably deduced that the Arrott plot (M²-H/M) should ideally form a straight line with an intercept that approaches zero as the temperature T nears the Curie temperature T_C. Additionally, the Curie temperature (T_C) can be accurately determined from the Arrott plot. The reliability of this methodology has been substantiated in Fe₃GeTe₂ crystal [9] and Ni₃Al [38]. Figure 5b shows the M² vs. H/M plots for Fe₅GeTe₂ at various temperatures for H || c. We find that the positive slope of the M² vs. H/M plots near T_C suggests that the Fe₅GeTe₂ crystal undergoes a second-order magnetic transition at T_C. However, M² does not show a linear relationship with H/M over the whole range of temperatures; instead, it shows a curvature. However, at the high-field region, all the Arrott plots show a linear relation. In this context, the M⁴ vs. H/M plot is very useful to determine T_C. This has been confirmed in Fe_xCo_1−xSi [39] and Fe₃GeTe₂. The linear correlation observed between M⁴ and H/M can be elucidated by Takahashi theory, which incorporates the influence of the critical thermal amplitude of spin fluctuations under the applied magnetic field. Therefore, we replotted the isothermal magnetization curves in the form of M⁴ vs. H/M, as shown in Figure 5c. From the M⁴ vs. H/M plot, T_C is determined to be greater than 300 K for Fe₅GeTe₂, which is consistent with the T_C (=302 K) we obtained earlier.

5. Summary

In summary, this work presents an experimental study of the structure, DC magnetization, and isothermal magnetization data of Fe₅GeTe₂ single crystals grown by chemical vapor phase transport. Fe₅GeTe₂ single crystal has a trigonal crystal structure with space group R3m (No. 160). DC and isothermal magnetization studies of the Fe₅GeTe₂ crystals show that a ferromagnetic (FM) to paramagnetic (PM) transition occurs at 302 K (T_C). In the low-temperature region, Fe₅GeTe₂ crystal has a potential spin glass state with a freezing temperature (T_f) of 98 K. However, there are two intersections in the low-temperature region of the FC and ZFC curves, which differ from the previously reported spin glass states. In the high-temperature region, Fe₅GeTe₂ exhibits non-linear magnetization due to the Griffiths phase.