Percolative magnetic correlation and competing-antiferromagnetism in highly oriented pyrolytic graphite with hexagonal Moiré superlattices at the magic-angle

Occurrence of magnetic-correlation-phenomena in multi-layered carbon-materials has recently attracted an important attention for applications in magnetic devices and spintronics. In this study, exfoliated highly-oriented-pyrolytic-graphite (HOPG) lamellae exhibiting hexagonal-Moiré-superlattices, with periodicity of ∼13 nm (1st category, θ rot ∼ 1.09° ) and ∼36 nm (2nd category, θ rot ∼ 0.39°) were investigated. Raman-spectroscopy evidenced weak D, D’ and intense G bands. In 1st category, magnetization versus field, ZFC- FC magnetic-curves from 2 K to 300 K and T-ESR revealed presence of uncorrelated and correlated ferromagnetic clusters at T* ∼ 150 K together with a critical transition at Tc ∼ 50 K, compatible with percolative-ferromagnetic-correlation. Comparative measurements on the 2nd category, revealed an analogue trend, with at T* ∼ 50–60 K together with an irreversibility at Tc ∼ 40 K, indicative of competing ferromagnetic/antiferromagnetic-correlations.

Theoretical analyses have also predicted the occurrence of antiferromagnetic and superconducting instabilities in presence of topological disorder [17]. In particular, the concept of ferromagnetic correlation was described on the basis of the percolative theory of ferromagnetism [18].
Despite these important findings reported in literature, additional work is needed in order to elucidate the physical mechanism that induces magnetic ordering in graphite. A significant role of local-graphene-layer rotation in such a magnetic correlation process can not be excluded. Interestingly a recent work by Seo et al has shown the existence of an exotic ferromagnetic state for θ rot ∼1.8°in TGBs [15]. The latter finding opens new directions towards the possible existence of multiple magnetic ordering features, controllable by graphene layer rotation.
In this letter we report a novel study on exfoliated HOPG lamellae exhibiting two categories of hexagonal Moiré superlattices with periodicity of∼13 nm (1st category, θ rot ∼1.09°) and∼36 nm (2nd category, θ rot ∼0.39°). By applying the equation a/2D=sin(θ /2) [21] where a is the basal lattice constant of HOPG (∼0.247 nm), D is the period of the Moiré pattern and θ is the rotational angle, rotational angles θ rot of 1.09°and 0.39°could be identified. The observed super-periodicities have analogy with those reported by Kuwabara et al [21], Patil et al [22] and Brihuega et al [24]. Raman spectroscopy evidenced presence of weak D and D' bands compatible with those expected for graphene layer rotation [25], together with an intense G band. Magnetization versus field measurements at 2 K, revealed unsaturated and progressively saturated ferromagnetic signals from 50 Oe to 150 Oe in the 1st category. Further, magnetization versus field, zero field cooled (ZFC) and field cooled (FC) measurements of the magnetization from 2 K to 300 K and T-electron spin resonance (ESR) revealed presence of uncorrelated and correlated ferromagnetic clusters at T * ∼ 150 K together with a critical transition at T c ∼50 K, compatible with percolative-ferromagnetic-correlation, in agreement with the percolative theory reported by Kopelevich et al [18].
Comparative measurements on the 2nd category, revealed an analogue trend, with at T * ∼50-60 K together with an irreversibility at T c ∼40 K; this latter observation provides evidence of a spin-glass-like behaviour, which we ascribed to the existence of additional competing antiferromagnetic correlations arising at low temperature (T∼59 K). No superconductive-transition was found in the analysed temperature range [26][27][28].

Experimental
HOPG samples with dimensions of 5×5×1 mm and mosaic angle of 0.5°,±0.2°(grade A) were purchased from XFNANO, INC China. TEM measurements were performed with a 200 kV American FEI Tecnai G2F20. Note that the topmost surface layers of the as purchased HOPG samples were removed in order to exclude contribution from surface impurities. See ESI figures S.3-5 (available online at stacks.iop.org/MRX/7/125602/ mmedia) for energy dispersive x-rays (EDX) measurements revealing also presence of minor Ca-based impurities in some of the as exfoliated lamellae. SQUID magnetometry measurements were performed with a Quantum design instrument. Raman Spectroscopy were collected in a custom-built Raman system using a triple grating monochromator (Andor Shamrock SR-303i-B, EU) with an attached EMCCD (ANDOR Newton DU970P-UVB, EU), excitation by a solid-state laser at 532 nm (RGB lasersystem, NovaPro 300 mW, Germany) and collection by a 100×, 0.90 NA objective (Olympus, Japan). Additional characterization can be found in the electronic supplementary information (ESI).

Results and discussion
Examples of the 1st and 2nd categories of Moiré superlattices are shown in figures 1-2 by high resolution transmission electron microscopy (HRTEM). As shown in figures 1, 2(A)-(D) with an increasing magnification, hexagonal Moiré superlattices with periodicity of∼13 nm (θ rot of∼1.09°) and∼36 nm (θ rot of∼0.39°) were found in two separate exfoliated lamellae. The observed superlattice resembles those reported by Kuwabara et al [21], Patil et al [22] and Brihuega et al [24]. In figure 1(E) Raman spectroscopy analyses performed in multiple areas of the lamella revealed presence of weak D and D' bands and intense G bands. Comparable D, D' bands and intense G bands were found in the 2nd category sample, as shown in figure 2(E). See also ESI figure S.1 for typical deconvolution analyses of these signals.
Magnetization versus field signals were then acquired by employing superconducting quantum interference device (SQUID) magnetometry. A typical example of magnetization signal obtained at 2 K in 1st category, is shown in figure 3(A), in conditions of maximum applied fields of ∼50 Oe. Interestingly an unsaturated signal was found. Field dependent zero field cooled (ZFC) and field cooled (FC) measurements of the magnetization were considered in order to elucidate the type of magnetic ordering in the sample. The signals were acquired from 2 K to 300 K at the fields of 10 Oe, 30 Oe and 50 Oe. According to the percolation-type picture outlined above and reported in ref. [18], uncorrelated ferromagnetic clusters can be formed below a certain temperature T * , leading to finite values of M s (T,H), M rem (T,H), and ΔM(T,H) [18][19][20]. As the temperature decreases, ferromagnetic correlations develop on a larger scale, and eventually a long-range ferromagnetic order emerges. It is possible to identify T∼50 K as a transition temperature below which an enlargement of pre-existing ferromagnetic cluster contribution takes place [18][19][20]. The ZFC-FC magnetization irreversibility shown in figures 3(B)-(D) evidences an enlargement of pre-existing ferromagnetic clusters below 50 K. This interpretation was further supported by additional analyses involving the subtraction of the magnetic moment of the ZFC signal to the magnetic moment of the FC signal (i.e. mFC-mZFC analytical method) as shown in figure S6. Note in figures 3(A)-(C) the presence of a field dependent percolative ferromagnetic correlation effect, with the ZFC and FC magnetic curves that converge and approximately overlap at 50 Oe. The observed trend can be explained by the existence of progressively saturated correlated ferromagnetic clusters in agreement with the percolative theory outlined in ref. [18]. In order to validate this interpretation and verify possible existence of superconductive components arising from graphene-layer rotation [13,14,26,27], additional characterization was sought through field dependent magnetization versus field measurements at T∼2 K. The signals were acquired at maximum applied fields of 50 Oe, 100 Oe and 150 Oe. As shown in figures 3(E), (F) no superconductive signals could be detected. A transition from an unsaturated hysteresis-like signal to a ferromagnetic hysteresis was found from 50 Oe to 150 Oe, for lamellae-layers orientation perpendicular and parallel to the applied field (figures 3(E), (F)). The evolution of the magnetization versus field signals with the temperature is then shown in figure 4. In figure 4(A) the signals observed at 2 K and 3 K, with the lamella layers respectively oriented perpendicular and parallel to the applied field, are evidenced. The evolution of the signal at higher temperatures is further shown in figures 4(B)-(E) before and after diamagnetic subtraction. Note the significant weakening of the ferromagnetic signal at T∼150 K (above the T c temperature and in proximity of T * temperature [18]) in figure 4(D), E, implying the existence of mixed correlated and uncorrelated ferromagnetic clusters at this temperature as predicted by the percolative theory [18]. This  [18]. By analysing the ZFC and FC signal it appears evident the presence of a ferromagnetic correlation effect, with the ZFC and FC magnetic curves that converge and approximately overlap as the field is increased to 50 Oe. The observed trend can be explained on the basis of the percolative theory of ferromagnetism [18]. In figures 3(E), (F) field dependent magnetization versus field measurements acquired from 1st sample category, at T∼2 K. The signals were acquired at maximum applied fields of 50 Oe, 100 Oe and 150 Oe. As shown in figures 3(E), (F) a transition from an unsaturated signal to a ferromagnetic hysteresis was found as the field was increased from 50 Oe to 150 Oe. observation was further confirmed by T-ESR in figure 4(F), where a significant shift in the differential absorption peak was found at ∼150 K from g ∼1.99 to g∼1.98 (as the temperature was increased from ∼77 K to ∼300 K).
Comparative measurements were then sought in the 2nd sample-category exhibiting Moiré superlattices with period D∼36 nm, θ rot of ∼0.39°.
As shown in figures 5(A)-(B) (see also ESI figure S2), ZFC and FC magnetization versus temperature measurements revealed an analogue T * ∼50-60 K, together with a magnetization irreversibility at∼40 K. The latter being compatible with a spin-glass-like behaviour induced by competing ferromagnetic and antiferromagnetic electron-correlation events [18]. It is possible to identify the T c ∼40 K as a critical irreversibility temperature below which coexistence of multiple competing components may take place. In order to better analyse this aspect, the mFC-mZFC subtraction method was applied to the signal in figure 5(A). Interestingly, as shown in figure S7 a ferromagnetic transition could be probed at ∼40 K. The presence of a ferromagnetic transition was further confirmed by orientation-dependent magnetization versus field measurements in figures 5(C)-(F) (before and after diamagnetic background subtraction). Note the presence of a possible T * ∼50-60 K, while no superconductive-transition could be detected in the analysed temperature range [26][27][28]. This observation implies that superconductivity in graphite may originate from other unknown defect features (as recently suggested by Arnold et al [28]) or may require different experimental conditions in order to be detected [14]. By comparing the mFC-mZFC subtraction-signals shown in figures S-6, 7 for the type 1 and 2 lamellae (see figure S8) it is also important to highlight an additional magnetic contribution arising below 17 K only for the lamella containing the θ rot ∼1.09°(D∼13 nm, figure S6).
The possible presence of variable periodic stacking between twisted layers may play also a role in inducing shifts in the expected value of the magic angle required for observation of orbital ferromagnetic ordering (expected value for TBG θ rot ∼1.2° [29]) or for superconductivity (expected value for TBG θ rot ∼1.09° [13]). This interesting aspect was computed by Khalaf et al in ref. [30]. It was shown that significant shifts in the value of the magic-angle may exist with the increase of sample thickness, especially for systems characterized by an alternate stacking of twisted multilayer graphene components. For n e sequences, a shift by a factor of 2cos (π * k/ n+1) with k=1,K..,n e was found with respect to the original value of the magic angle [13,24]. temperature measurements from 2nd sample category, revealing a magnetic irreversibility compatible with a spin-glass-like behaviour at∼40 K. It is possible to identify the irreversibility at T∼40 K as a critical transition point below which the coexistence of multiple competing components is established. The ZFC-FC magnetization curves shown in figures 5(A)-(B) provide evidence of a spin-glass-like behaviour at T∼40 K, possibly induced by competing antiferromagnetic correlations able to stabilize the random orientation of the ferromagnetic clusters. No superconductive-transition was found in the analysed temperature range. In figures 5(C)-(F) temperature dependent magnetization versus field measurements evidencing the ferromagnetic signal for sample-layers orientation parallel and perpendicular to the applied field, before (figures 5(C), (D)) and after (figures 5(E), (F)) diamagnetic subtraction.

Conclusion
In conclusion. we have reported a novel investigation on the magnetic ordering in exfoliated HOPG lamellae exhibiting hexagonal Moiré superlattices with periodicity of∼13 nm, θ rot ∼1.09°and∼36 nm, θ rot ∼0.39°. Raman Spectroscopy evidenced presence of weak D and D' bands compatible with those expected for rotated graphene layers, together with an intense G band in both sample-categories.
Magnetization versus field at 2 K, revealed unsaturated and saturated ferromagnetic signals in the 1st category. Field dependent, ZFC and FC magnetization versus temperature from 2 K to 300 K at the fields of 10 Oe, 30 Oe and 50 Oe revealed a transition at T c ∼50 K, compatible with ferromagnetic correlation. Comparative magnetometry measurements on the 2nd sample category revealed an analogue critical ferromagnetic transition at T c ∼40 K together with a spin-glass-like behaviour indicating existence of competing antiferromagnetic correlations at∼59 K.