Room-temperature ferromagnetism via unpaired dopant electrons and $p-p$ coupling in carbon-doped In${}_2$O${}_3$: Experiment and theory

Observations of magnetism in semiconductors doped with nonmagnetic atoms (C, N, etc.) show promise for spintronics applications, but pose an interesting challenge for conventional theories of magnetism. In this work, the magnetic semiconductor carbon-doped In${}_2$O${}_3$ is studied using theoretical and experimental techniques. Density-functional theory calculations predict that ferromagnetism can exist near room temperatures when substitutional carbon atoms have a formally unpaired $2p$ electron that does not participate in bonding. The unpaired $2p$ electrons lead to an impurity band near the Fermi level and consequent enhanced density of states which accommodates a strong $p-p$ coupling between local magnetic moments. The unpaired electrons and ferromagnetic coupling are found to arise from a combination of interstitial and substitutional carbon atoms in close proximity. Finally, experimental measurements on samples with varying magnetic properties verify the importance of both strong C $2p$ character at the Fermi level and strong C $2sp$-In $4d$ hybridization for yielding room-temperature ferromagnetism. These results shed light on the interesting field of nonmagnetic dopants inducing ferromagnetism in semiconductors.

Figure 1

Optimized local defect structures for (a) single substitutional carbon, (b) two substitutional carbons, (c) one substitutional and one interstitial carbon, (d) two substitutional carbons and one interstitial carbon, and (e) three substitutional carbons and one interstitial carbon.

Figure 2

The calculated densities of states per atom for different types of carbon structural defects in In${}_2$O${}_3$.

Figure 3

Partial densities of states (PDOS) for the different substitutional and interstitial configurations. The three columns are for the $1S+I$, $2S+I$, and $3S+I$ cases from left to right, respectively. The three rows show, for each configuration, the spin-projected PDOS for the substitutional [C($S$)] and interstitial carbon atoms [C($I$)] and the PDOS for the In and O atoms (In/O).

Figure 4

The calculated densities of states per atom for different types of carbon structural defects in In${}_2$O${}_3$ which include an oxygen vacancy. For comparison, the C $2p$ states are shown in light shaded gray for the case with no vacancy as well.

Figure 5

Magnetization curves of the In${}_2$O${}_3$:C films studied. Inset: expanded full hysteresis loop for the 4.5$\%$ sample prepared at room temperature.

Figure 6

X-ray spectroscopy results for the In${}_2$O${}_3$:C samples described in the text. Carbon $K$-edge XES, RXES, and XAS are shown in the main lower portion of the figure. Left inset: correction necessary to remove the second-order oxygen signal. Right inset: magnified view of the XAS onset. The upper plot shows the oxygen $K$-edge XES and XAS of one sample to display the similar In $4d$ to anion $2sp$ hybridization seen for both the O and C anions, as well as the host DOS in the band-gap region.

Figure 7

Chemical bonding diagrams for the defect clusters considered in the calculations. (a–e) $1S$, $2S$, $1S+I$, $2S+I$, and $3S+I$ cases, respectively.