Magnetic properties of graphite irradiated with MeV ions

We have studied the change in the magnetic properties produced on highly oriented pyrolytic graphite samples by irradiation of H, C, and N ions in the mega-electron-volt energy range. The use of specially made sample holders for the magnetic measurements provided high reproducibility allowing us to obtain directly the irradiation effects without any corrections or subtractions. Our results show that three magnetic phenomena are triggered by the defects produced by the irradiation, namely, Curie-type paramagnetism, ferromagnetism and an anomalous paramagnetic state that appears as precursor of the magnetic ordered state. Using SRIM simulations to estimate the amount of vacancies produced by the irradiation, the Curie-type paramagnetic response indicates an effective Bohr magneton number per nominally produced vacancy $p=0.27\pm 0.02{\mu }_B$. Direct measurements of the surface sample temperature during irradiation and the decrease in the (as-received) paramagnetic as well as ferromagnetic contributions after irradiation indicate that self-heating is one of the causes for small yield of ferromagnetism. Taking into account the hydrogen distribution in the virgin samples, the obtained results indicate that the induced ferromagnetism appears when the average vacancy distance is $\sim 2\text{nm}$ in the near surface region.

Figure 1

SRIM calculation of the distribution of vacancies produced in graphite as a function of depth by protons of 2.5 MeV, around the vacancy peak and also close to the surface. The values of vacancy density at 50 nm from the surface, at the peak $P$ and that of its FWHM used in the text are graphically indicated. Contrary to the narrow ion implantation range, there is a rather flat distribution of vacancies produced in the ion track from the surface to the peak region.

Figure 2

(Color online) Left photo: sample holder ready for being mounted into the irradiation chamber. Graphite sample is fixed to the specially designed sample holder made of golden quartz for the SQUID, that in turn is attached to a setup made of MACOR designed to fit into the irradiation chamber. Right photo: quartz (foreground) and graphite sample (background) already mounted in the irradiation chamber. A rotary feedthrough allows placing them at the irradiation position from outside of the chamber without breaking vacuum.

Figure 3

(Color online) (a) Quartz sample used as reference when irradiated by a proton beam of 8.5 MeV. Light produced due to ion luminescence is used to determine size ($4\text{mm}\times 4\text{mm}$ in this case) and homogeneity of the ion beam prior to graphite irradiation. (b) Thermal image from the sample S12 obtained with an infrared camera, taken through a diagonal viewing port, monitoring in real time the temperature of the sample surface during irradiation (8.5 MeV protons, in this case). Note the inhomogeneous temperature distribution on the sample surface during irradiation, here typically ranging from $70°\text{C}$ to $95°\text{C}$. The other sample holder with the reference quartz sample [still slightly warm after its previous irradiation shown in (a)] can also be seen on the left.

Figure 4

(Color online) (a) Difference in magnetic moment $m_{diff}\left(H\right)$ as a function of field at three different fixed temperatures. Note the absence of any nonlinear behavior. (b) The same but as a function of temperature at a fixed field of 1 T. The dotted curve follows the paramagnetic Curie-law $C/T$ with $C=25\mu \text{emu}\text{K}$. The dashed curve follows the Langevin function [Eq. (7)] with $h=0.01,m_0=17\mu \text{emu}$ and $T^{\star }=350\text{K}$. The continuous line is the sum of the Curie contribution and that given by Eq. (7) with $h=0.03$, instead of 0.01. The dashed dotted (red) line was obtained with similar parameters but with $C$ 15% larger. The difference between the two fits is at low temperatures larger than the error bar of the data, which is $\pm 0.2\mu \text{emu}$.

Figure 5

(Color online) Standard deviation between the fits and the experimental data from sample S1 shown in Fig. 4b as a function of the two free parameters used, namely, $C$ from Eq. (4) and $m_0$ from Eq. (7). The other parameter $h$ does influence only the fit near $T^{\star }$ and it is not shown in this correlation matrix for clarity.

Figure 6

(Color online) (a) The difference in magnetic moment $m_{diff}\left(T\right)$ at 1 T for samples S2a and S2b. The continuous lines were calculated using Eq. (7) as in Fig. 4 and with the parameters $C=60\left(90\right)\mu \text{emu}\text{K}$, $m_0=8\mu \text{emu}$, $h=0.01$, and $T^{\star }=490\left(473\right)\text{K}$ for the sample S2a (S2b). (b) The same as in (a) but for sample S5. The dashed line was calculated following Eq. (6) with the parameters $\Delta =850\text{K}$, $g_1^{\star }=1,g_2^{\star }=10$, the weights $x_1=0.9$ and $x_2=0.1$ for the first and second contributions and $N{\mu }_B=2.3\times {10}^{-4}\text{emu}$. The dotted line follows Eq. (7) with $m_0=2\mu \text{emu}$ with a $T^{\star }=1000\text{K}$. The small deviation between the simple model used and the data can be easily diminished by taking a distribution of the parameter $\Delta$ instead of a fixed one. This has sense physically since the magnetic defects that contribute to the excited multiplet, such as multivacancies, are not all exactly the same in the irradiated matrix. The inset shows the same data but on a linear temperature scale.

Figure 7

(a) Field dependence of the difference in magnetic moment $m_{diff}\left(H\right)$ at three fixed temperatures for sample S10. Note the clear nonlinear behavior at low fields indicating the existence of ferromagnetic behavior induced by proton irradiation. (b) The difference in magnetic moment $m_{diff}\left(T\right)$ at 1 T for sample S10. The dashed line follows the Curie law with $C=35\mu \text{emu}\text{K}$ and the dotted line the approximation for the magnetic order in the quasi-two-dimensional case of Eq. (9) with the parameters $m_{\text{FM}}=\left(3.8–7\times {10}^{-3}\text{T}\right)\mu \text{emu}$ (with $T$ in K). The continuous line is the sum of these two contributions.

Figure 8

(Color online) Magnetic moment before and after irradiation (at 1 T field) without any subtraction for sample S10(a) and sample S11 (b).

Figure 9

(Color online) (a) Field dependence of the difference in magnetic moment $m_{diff}\left(H\right)$ at two fixed temperatures for sample S11. (b) The difference in magnetic moment $m_{diff}\left(T\right)$ at 1 T for sample S11. The continuous line is the sum of these two contributions, namely, the Curie law with $C=17\mu \text{emu}$ (dashed line) and the approximation for the magnetic order in the quasi-two-dimensional magnetic order with the parameters $\left(3.9–12\times {10}^{-3}\text{T}\right)\mu \text{emu}$ (with $T$ in K) (dotted line). The inset shows the measured magnetic moment before and after irradiation (at 1 T field) without any subtraction.

Figure 10

Room-temperature magnetic moment vs field applied parallel to the graphene planes for a virgin HOPG sample from the same batch as those used for irradiation (◼). (○): the same sample after annealing 12 h at 700 K. The hysteresis measurements as well as the annealing were done in the SQUID without taking the sample out of it.

Figure 11

(a) Field dependence of the difference in magnetic moment $m_{diff}\left(H\right)$ at three fixed temperatures for sample S8. Note that the $s$-like form of the curve at 300 K due to the induced ferromagnetic contribution is nearly parallel to the $x$ axis because of the counter balance coming from a decrease in the paramagnetic response. (b) The difference in magnetic moment $m_{diff}\left(T\right)$ at 1 T for sample S8. The continuous line is the sum of two contributions, namely, the Curie law with $C=23.6\mu \text{emu}\text{K}$ and the approximation for the magnetic order in the quasi-two-dimensional case, which follows $\left(1–5\times {10}^{-9}\text{T}\right)\mu \text{emu}$ (with $T$ in K). Note that above 200 K the difference is negative indicating a decrease mainly in the anomalous paramagnetic contribution due to the annealing during irradiation.

Figure 12

(Color online) (a) Field dependence of the difference in magnetic moment $m_{diff}\left(H\right)$ at 1 T and at three fixed temperatures for sample S7. Note that the inverse $s$-like form of the curve at 300 K due to the decrease in the ferromagnetic contribution. (b) The same difference in magnetic moment for sample S12. The inset shows the data between $-0.75$ and 0.75 T and for 100 and 300 K.

Figure 13

Paramagnetic parameter $C$, see Eq. (4), obtained from the fits to the magnetic moment difference data as a function of the nominal vacancy number produced by the irradiation for all measured samples. The labels show the sample number and the label “FM” in brackets means that sample shows induced ferromagnetism by the irradiation. The point with the label “V” refers to the samples in virgin, nonirradiated state, with similar volumes. The points from the samples S13–S15 have a larger error in the $C$ values because of the different misalignment in the SQUID holder since the samples were taken out of the holders for the lower temperature irradiation. The continuous line is the function $C=0.075\times 2.08\times {10}^{-15}\left(N_V+6\times {10}^{16}\right)$. The dashed and dotted lines follow the same function but with the first numerical coefficient equal to 0.085 and 0.065, respectively.

Figure 14

Ferromagnetic moment at saturation as a function of the nominal distance between induced vacancies calculated at 50 nm from the HOPG surface for most of the samples prepared in this work. The errors bars are the maximum estimated ones considering the sensitivity and reproducibility of the SQUID measurements as well as the range of parameters needed to estimate through SRIM the average vacancy distance within a graphene layer at 50 nm from the sample surface. The continuous line follows a Gaussian function and should be taken only as a guide to the eye.