Role of charge carriers for ferromagnetism in cobalt-doped rutile TiO2

Electric and magnetic properties of a high temperature ferromagnetic oxide semiconductor, cobalt-doped rutile TiO2, are summarized. The cobalt-doped rutile TiO2 epitaxial thin films with different electron densities and cobalt contents were grown on r-sapphire substrates with laser molecular beam epitaxy. Results of magnetization, magnetic circular dichroism, and anomalous Hall effect measurements were examined for samples with systematically varied electron densities and cobalt contents. The samples with high electron densities and cobalt contents show the high temperature ferromagnetism, suggesting that charge carriers induce the ferromagnetism.

grown on r-sapphire substrates. All the sapphire substrates were subject to ultrasonic cleaning in organic solvents followed by annealing in a furnace to have atomically flat step and terrace surface prior to the film growth. TiO 2 buffer layers with 5 nm thick were grown on the substrates at 400 º C in 1 × 10 -4 Torr of oxygen followed by post-annealing at 600 º C in 1 × 10 -2 Torr of oxygen for an hour.
Oxygen pressures during growth (P O2 ) of Ti 1-x Co x O 2-δ films grown at 400 º C on the buffer layers were varied from 1 × 10 -7 Torr to 1 × 10 -4 Torr in order to control the amount of δ. The reflection high energy electron diffraction (RHEED) intensity was in-situ monitored during the film growth. The film thicknesses were typically 70-120 nm. From X-ray diffraction, scanning electron microscopy, transmission electron microscopy, RHEED, and atomic force microscopy, neither impurity phase nor segregation of secondary phase was observed. Photolithographically patterned Hall bars (220 μm long × 60 μm wide) were used for electronic transport measurements. Electron density n e was evaluated from linear slope of normal part of Hall resistance vs. magnetic field curve. Table 1 shows correspondence between x, P O2 , and n e at 300 K for Ti 1-x Co x O 2-δ in this study.  2-δ film is due to the relatively low growth temperature for the Ti 0.95 Co 0.05 O 2-δ film. The clear RHEED streak pattern, as well as atomically flat atomic force microscope image, reflects high crystallinity of the films without any surface segregation. As described in section 5, various spectroscopies were also performed to represent that Co ions in TiO 2 are Co 2+ (d 7 ) state with high spin configuration, thus possible segregation of Co metal is ruled out again.
It is emphasized that optimization of various growth conditions such as pre-treatment of the substrate, deposition rate, and growth temperature was indispensable to obtain high quality films reproducibly. Such films show systematic properties as described in this article hereafter.

Electric properties
In TiO 2-δ , δ yields in charge carriers. Varying P O2 enables to control an amount of δ leading to a systematic change in resistivity with several decades. Figure 2 shows temperature dependence of resistivity for Ti 0.97 Co 0.03 O 2-δ grown in different P O2 . By decreasing P O2 , the resistivity decreases monotonically due to increase in δ. The decrease in resistivity is synchronized with the increase in the lattice constant as shown in inset of Figure 2.
The mobility at 300 K is kept to be ~10 -1 cm 2 /Vs for different x as shown in Figure 3, being comparable with that of bulk rutile TiO 2 , implying that negligible effect of x on the film quality. The small dependence of the mobility on n e in inset of Figure 3 represents that the change in resistivity with δ is mainly caused by the change in n e . Hereafter, we examine various experimental data as a functions of n e and x. Figure 4 shows magnetization curves at 300 K for Ti 1-x Co x O 2-δ with different x and n e . In Figure   4 as well as that in Figure 4(b). Therefore, the magnitude of saturation magnetization and the magnetic anisotropy depends on both n e and x.

Magnetic circular dichroism
Magnetization measurements provide indispensable information of magnetic properties such as the magnetization value and the magnetic anisotropy. However, magnetometer is not able to distinguish extrinsic signals such as a magnetic segregation from intrinsic magnetization. Hence, comprehensive measurements are necessary in order to investigate magnetism of new compounds like Ti 1-x Co x O 2-δ . For this purpose, magnetic circular dichroism is a useful method since intrinsic and extrinsic origins can be distinguished as well as anomalous Hall effect [7]. In several ferromagnetic semiconductors, the absorption and MCD spectra were observed to have an intimate relation, where energy derivative of absorption coefficient is proportional to MCD [19]. Also, effect of substrate, that is usually not negligible due to its much larger volume than ferromagnetic film in case of magnetization measurement, can be completely excluded when using magneto-optically inactive substrate. Figure 5 shows the absorption and magnetic circular dichroism spectra at 300 K for Ti 0.97 Co 0.03 O 2-δ with different n e . The absorption spectra represent almost transparency against visible light, and the absorption increases over 3 eV. For n e ≤ 4 × 10 19 cm -3 , MCD is negligible, and MCD develops with increasing n e . Below the absorption edge, MCD is negative with broad spectral feature probably originated from d-d transition [20]. At the higher photon energy, the MCD changes its sign.
These ferromagnetic MCD spectra have the same magnetic field dependence at any photon energy (not shown), thus the MCD is originated from Ti 1-x Co x O 2-δ without any magnetic sources [21]. For n e ≥ 4 × 10 22 cm -3 , the absorption edge shifts toward higher energy side with small increase in the absorption below 2 eV, that was observed in a reduced TiO 2 [22]. It is noted that nearly the same amount of blue shift is seen in the MCD spectrum as well as absorption spectrum for n e = 4 × 10 22 cm -3 , reflecting a close relation between the absorption and MCD spectra.
For MCD measurement, effect of the substrate on MCD signal is negligible, thus it is useful to study magnetic anisotropy in spite of a lack of the quantitative magnetization value. Figure 6 shows magnetic field dependence of normalized MCD for different n e and x. It is noted that the dependence of the MCD magnitude on n e and x is consistent with that of the magnetization in Fig. 4. For n e = 2 × 10 20 cm -3 (Figure 6(a)), onset of MCD at low magnetic field is steeper for the higher x. For n e ≥ 4 × 10 21 cm -3 ( Figure 6(b)), on the other hand, the onset of MCD is nearly independent on x and the saturation needs higher magnetic field. These results suggest that the moderate n e and higher x lead to the steeper and larger out-of-plane magnetization taking result of Figure 4 into account, although further compilation of data is needed to investigate detail behaviours of the magnetization properties.

Anomalous Hall effect
For thin film of dilute ferromagnetic systems, anomalous Hall effect is a good measure of the ferromagnetism because of its high sensitivity to the magnetization. Also, the anomalous Hall effect will not be affected by small amount of segregation, hence bulk magnetic property can be probed.   Figure 7 because of the higher x leading to increase in the volume magnetization. In this case, the decrease in n e also leads to steeper slope of the normal Hall effect. Figure 9 shows magnetic field dependence of Hall resistivity for different x at 300 K. With increasing x, anomalous Hall resistivity monotonously increases mainly due to the increase in the volume magnetization as described above.
The Hall effect of ferromagnetic Ti 1-x Co x O 2-δ can be simply regarded as the sum of normal and anomalous Hall effects, hence it is straightforward to extract the anomalous Hall part. Study on the anomalous Hall effect is recently revived because of its quantal nature and relevance to spin Hall effect [23]. From the viewpoint of semiconductor spintronics, it is important to confirm whether the anomalous Hall effect can be controlled by external perturbation such as electric field or not, some of which have been demonstrated in (Ga,Mn)As [24]. Figure 10 shows magnitude of anomalous Hall conductivity vs. conductivity plots for various ferromagnetic compounds having metallic or semiconducting conduction. It can be seen that each class of compounds such as Mn-doped III-V semiconductors, transition metal oxides, and Ti 1-x Co x O 2-δ shows a scaling relation: magnitude of anomalous Hall conductivity is proportional to (σ xx ) 1.6 , where σ xx is conductivity [10,16,25], where underlying physics is described elsewhere [26,27]. This relation represents that the magnitude of anomalous Hall conductivity can be evaluated from the conductivity. In case of ferromagnetic semiconductors, the conductivity in single substance can be varied via field effect and so on, thus leading to control of anomalous Hall effect, so that it will be useful for implementation of spintronics devices.

Discussion
Hall resistivity, magnetic circular dichroism, and magnetization for Ti 1-x Co x O 2-δ with different n e and x show the same magnetic field dependence, except unimportant deviation in the Hall resistivity at high magnetic field due to the normal Hall effect as shown in Figure 11. This result rules out a possibility that magneto-optically inactive and/or insulating substance produces the ferromagnetism.
The resultant magnetic phase diagram shows that the higher n e and x induce the ferromagnetic phase ( Figure 12).
In addition to the above magnetic measurements, various types of characterization were performed using the systematic series of our samples. From x-ray photoemission spectroscopy (XPS) and x-ray magnetic circular dichroism (XMCD), electronic state of Co ions was Co 2+ (d 7 ) high spin state although the magnetization values in Figure 4 is smaller than the d 7 state ideally that yields in 3 μ B /Co [28,29]. In order to keep charge neutrality in Ti 1-x Co x O 2-δ , δ is equal to x assuming that valences of Ti and Co ions are 4+ and 2+, respectively. For electrically conductive Ti 1-x Co x O 2-δ , 3d state of Ti ions should be partially filled so that the valence is less than 4+, hence δ > x. Such significant amount of oxygen vacancies will be energetically favourable for the high spin state of Co 2+ ions due to the decrease in the crystal field assuming that oxygen vacancies are adjacent to Co 2+ ions. The presence of Co 2+ ions and oxygen vacancies in the TiO 2 may cause local charge imbalance and lattice distortion.
The local lattice distortion was evidenced by x-ray anomalous scattering of both rutile and anatase Ti 1-x Co x O 2-δ , where Co ions deviate from exact location of Ti sites [30]. Nevertheless, this result does not rule out the substitutional occupation of Co ions since the x-ray absorption and XMCD spectra suggest Co 2+ high spin state in the D 2h -symmetry crystal field at Ti site [29]. The local charge imbalance and the lattice distortion as well as high spin state of Co ions might cause large exchange coupling between localized spins and overlapping electron wave function leading to the high Curie temperature [31].

Summary
Various types of magnetic and electronic characterizations using a systematic series of high quality samples gradually unveil origin of the ferromagnetism in Ti 1-x Co x O 2-δ . The present results suggest an important role of charge carriers to induce the high temperature ferromagnetism.
Nevertheless, high temperature ferromagnetism was also observed for insulating cobalt-doped TiO 2 [32]. It is worth investigating whether such ferromagnetism in the insulating specimens is caused by a local exchange mechanism without presence of charge carriers. Table 1. Correspondence between x, P O2 , and n e (300 K) for Ti 1-x Co x O 2-δ in this study.