Magnetic frustration of graphite oxide

Delocalized π electrons in aromatic ring structures generally induce diamagnetism. In graphite oxide, however, π electrons develop ferromagnetism due to the unique structure of the material. The π electrons are only mobile in the graphitic regions of graphite oxide, which are dispersed and surrounded by sp3-hybridized carbon atoms. The spin-glass behavior of graphite oxide is corroborated by the frequency dependence of its AC susceptibility. The magnetic susceptibility data exhibit a negative Curie temperature, field irreversibility, and slow relaxation. The overall results indicate that magnetic moments in graphite oxide slowly interact and develop magnetic frustration.

and 193.25 ppm demonstrate similar behavior. The peak at 193.25 ppm does not change with the modes. However, the peak at 187.94 ppm increased in the CP/MAS mode. Therefore, we conclude that the peak at 58.92 ppm is due to the epoxy groups, the peak at 70.04 ppm is due to the hydroxyl groups, the peak at 130 ppm is due to the stable double bonds 41 , the peak at 193.25 ppm is due to the ketone groups 26,43 , and the peak at 187.94 ppm might be a result of the chemical groups containing carbon and hydrogen atoms such as -COOH. The broad peak around 130 ppm is due to graphitic rings. The NMR data indicate that GO is composed of graphitic and non-graphitic regions. Figure 2(a) compares the Raman spectra of GO and H-GO. GO exhibits two high peaks at 1440 (D) and 1660 (G) cm −1 . It also exhibits characteristic peaks at 2750 (2D), 2930 (D + G), and 3150 (2G) cm −1 . After thermal treatment, the characteristic peaks of GO at the above positions were diminished. The diminished 2D peak indicates that the graphitic regions in GO were damaged. In addition, the D peak at 1440 cm −1 increased and grew broader, implying that more defects were produced during the heat treatment. Figure 2(b) illustrates the C K-edge X-ray absorption near-edge structure (XANES) spectra of GO, H-GO, and polycrystalline graphite acquired in the total electron yield (TEY) mode at 298 K. The spectrum of graphite has two main peaks; the first peak at 285 eV is due to the π* state of C= C [44][45][46] and the second at 292 eV is assigned to C= C σ* antibonding [44][45][46] . The spectrum also includes the peak from the core-exciton, a sharp peak at 291.6 eV. The spectrum of GO is different from that of graphite; peak A is due to unoccupied π* states 44 , peak B at 287 eV results from aliphatic C-OH 47 , peak C at 289 eV is due to C-O-C bonding, and peak D at 291.8 eV indicates unoccupied σ* states 44 . The peaks in the H-GO spectrum of H-GO differ from those in the other samples. Here, peak A (the π* state of C= C) is suppressed because the graphitic structure in GO was damaged during the heat treatment, which is consistent with the Raman results in Fig. 2(a). The height of peak B' at 288 eV near peak B increases due to the generation of aliphatic C-H such as cyclohexane 47 . Peak C is nearly eliminated because epoxy groups decomposed during the thermal treatment and peak D shifts to 293 eV.
DC magnetic susceptibility measurements were performed using a superconducting quantum interference device (SQUID) magnetometer in zero-field-cooled (ZFC) and field-cooled (FC) modes with various applied magnetic fields. Figure 3(a) shows the susceptibilities of GO as a function of temperature. The susceptibility curves in ZFC mode exhibit a characteristic maximum and a thermal hysteresis (multiple paths) below it. As the temperature decreases, the FC curves become saturated. As the field increases from 100 to 800 Oe, the peaks become broader and shift from 25 to 15 K. This feature often appears in relaxors such as spin-glass materials [48][49][50][51][52][53] . The inset in Fig. 3(a) depicts the curves across a wide temperature range. The curves were fitted by the Curie-Weiss law, and the Curie temperatures θ c at different magnetic fields are given in Table 1   In H-GO, the Bohr magneton number n B is below the order of 10 −4 , i.e., negligible compared to that of GO. In addition, H-GO exhibits a linear curve in the M-H measurements in Fig. 3(c), unlike GO, which has an S-shaped curve. The above data indicate that there are ferromagnetic as well as antiferromagnetic interactions in GO and the magnetic properties of GO were destroyed during the heat treatment.
Further investigation of the magnetic behavior of GO was carried out using the Almeida-Thouless (AT) law and critical scaling analysis. The irreversibility temperatures (T ir ) identified by the splitting of the ZFC and FC curves in Fig. 3(a) are plotted as a function of the applied field in Fig. 4(a), and they follow the AT line (H 2/3 ) ( Fig. 4(a) (inset)) 54 . By extrapolating the AT line to H = 0, we determine a freezing temperature T f = 24.5 ± 0.05 K. The order parameters of the spin glass were obtained using critical scaling analysis 55 . Normalized q(T) values, i.e., the deviation of the observed susceptibility from paramagnetic behavior, were extracted from both FC and ZFC data and plotted at various fields, as shown in Fig. 4(b). The FC data was fitted to q = |t| β as t → 0, yielding q = H 2/ (1+γ/β) near T f 52 with β = 0.5 ± 0.1 and γ = 9 ± 1. These parameters vary from those associated with a spin-glass in that β = 0.2 ± 0.1 and γ = 4.5 ± 0.5 in 2D spin-glass and β = 0.5 ± 0.2 and γ = 4.0 ± 0.4 in 3D spin-glass 56 . This variation implies that GO may exhibit both 2D and 3D spin-glass behavior, i.e., both 2D and 3D glass behaviors are present in GO. Figure 4(c) shows the in-phase component χ'(T, ω) of the AC susceptibility of GO between 15 and 35 K in the frequency range 10 ≤ ω ≤ 1000 Hz. The measurements were taken in zero field cooling (ZFC) conditions with a 10 Oe AC field at different frequencies. The χ'(T, ω) curve exhibits a characteristic pronounced maximum with amplitude and position, depending on the frequency. As ω increases, the χ' exhibits a maximum with amplitude and position, which is similar to the AC susceptibility behavior of glassy systems [57][58][59] . The AC susceptibility's dependence on the frequency is a sign of slowing in the magnetization dynamics. The maximum of the peak shifts towards higher temperatures with increasing frequencies, which is a common feature for spin glasses 57,58,60 . The inset shows that the freezing temperature depends on the frequency. However, H-GO does not show any characteristic peak in the AC susceptibility curve (Fig. 4(d)).
To determine whether the GO sample has a slow relaxation, its FC relaxation effects were examined. First, a magnetic field of 100 Oe was applied to the samples at room temperature and then cooled to 7 K. The measurements were performed just after the magnetic field was removed. In Fig. 4(e), the magnetization of GO decreases exponentially with time, whereas H-GO magnetization exhibits no time dependence. The magnetization curve of

GO was fitted as
, where n ~ 0.56 is similar to that of a dilute spin system 52 . Unlike GO, H-GO does not show slow relaxation.
In the previous letter, we demonstrated that the spin densities are mainly localized in the graphitic domains in GO, as shown in Fig. 4(f). When the distance between the graphitic domains becomes short enough, the spins in the domains can be coupled ferromagnetically and/or antiferromagnetically. According to our EDX analysis results, the C:O ratio of the sample is 6:2.3 and the ratio of sp 2 -carbon to sp 3 -carbon is 1.4. The graphitic domains are small because the oxygen coverage is so high. Thus, the interaction among the graphitic domains may be ferromagnetic and/or antiferromagnetic. However, the graphitic and non-graphitic regions in GO depends on the preparation method and the degree of oxidation 27 . The magnetic spin densities might be also influenced by the degree of oxidation and the preparation methods, which also determine the area and distribution of graphitic domains. In addition, the graphitic domains, which are hydrophobic, are different from hydrophilic reacted regions in GO. Thus, the amphiphilicity of GO might make the magnetic properties of GO more complex.
GO exhibits field irreversibility and slow relaxation. The DC susceptibility data show that the sample has a negative Curie temperature and exhibits field irreversibility in addition to slow relaxation. The frequency-dependence of AC susceptibility corroborates the spin-glass behavior. The destruction of epoxy groups gets rid of the magnetic properties of GO. Although the origin of this magnetism is not clear, it is apparent that the epoxy group plays a fundamental role in the observed magnetism. The overall results suggest that the magnetic moments in GO slowly interact and exhibit glass-like behavior.

Method
The GO samples were prepared by the Staudenmaier process 27 . GO was heated at 250 °C for 24 h (H-GO). The structural properties of the sample were characterized using solid-state nuclear magnetic resonance (NMR). The 13 C spectra were obtained at 9.4 Tesla using a Bruker AVANCE 400 MHz spectrometer and 4 mm zirconia MAS rotors spun in air at 6 kHz. 13 C MAS spectra with HPDEC were acquired at 100 MHz with 100-kHz, 90 °C pulses with a duration of 1.25 μs. 1 H-13 C CP/MAS spectra were recorded at different contact times (50-5050 μs) with increases of 500 μs. The peaks were most intense at 3550 μs. Raman spectra were collected at an excitation wavelength of 514 nm (Renishaw, RM-1000Invia, 2400 l/mm). X-ray absorption near edge structure (XANES) measurements were performed on the BACH beamline at ELLETRA in Italy. The magnetic properties of the samples were characterized with a Quantum Design MPMS 1802 magnetometer and a Lakeshore 7000 Series AC Susceptometer.