IEEE TRANSACTIONS ON MAGNETICS, VOL. 51, NO. 11, NOVEMBER 2015
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Magnetism in Cr2O3 Thin Films: An Ab Initio Study Renu Choudhary1, Ralph Skomski2 , and Arti Kashyap1 1 School
2 Department
of Basic Sciences, IIT Mandi, Mandi 175005, India of Physics and Astronomy, Nebraska Center for Materials and Nanoscience, Lincoln, NE 68588 USA
The magnetism of Cr2 O3 thin films on α-Al2 O3 is investigated using first-principle calculations by considering three Cr2 O3 films having thicknesses of 4.1 Å (I), 6.7 Å (II), and 10.9 Å (III) and comparing the spin structures of free films with those on the substrate. For the free films, we find that I is ferromagnetic (FM), while II and III are antiferromagnetic (AFM). On the substrate, the Cr2 O3 film I is also FM. Films II and III remain basically AFM, although the spins of the top Cr layers change sign in both films, creating a ferrimagnet with a small uncompensated net moment. Index Terms— Cr2 O3 film, local moment, spin structure and ferrimagnetism.
I. I NTRODUCTION
A
NTIFERROMAGNETIC (AFM) Cr2 O3 has attracted much attention due to its room-temperature magnetoelectric and piezomagnetic behavior and has been proposed for data-storage applications [1]–[5], [10]. The physics of thin films of Cr2 O3 is very complex and involves a variety of mechanical, electric, and magnetic phenomena. Bulk Cr2 O3 is an AFM Mott insulator with TN = 307 K, but films of Cr2 O3 have been reported to exhibit hysteresis loops with a moderate saturation of 33 emu/cm3 [33 kA/m] and significant coercivity up to 400 K (7.5 mT at 300 K) by Punugupati et al. [4]. The magnetic moment in [4] was attributed to oxygen-related defects whose concentration is controlled by strain present in the films. Electric and magnetoelectric properties of Cr2 O3 film on Pt have also been studied experimentally [6], and ferromagnetic (FM) behavior was found in the film. According to [6], compressive stress at the Cr2 O3 /Pt interface induces a small net moment and it could be possible to modify the magneto-electric effect by changing substrate stress. The magnetic structure of oxygenterminated Cr2 O3 surface was studied using the ab initio density functional theory [7]. Thin films of α-Cr2 O3 (0001) have a more stable structure with a single Cr3+ -terminated surface, compared with double Cr3+ and oxygen terminated surfaces. The surface Cr3+ atoms move inward by 50% of their original positions because of very large surface relaxation. The magnetism of bulk Cr2 O3 is well understood in terms of first-principle calculations, including local spin density approximation (LSDA) + U [2], [3]. The structure of α-Cr2 O3 (0001) thin films with Cr and oxygen terminated surfaces has been studied using LSDA correlation functional by Rehbein et al. [8], who have found that Cr-terminated thin films form the most stable structure. A particular feature of the AFM spin structure of Cr2 O3 is the presence of antiferromagnetically coupled layers in the c-direction of the rhombohedral unit cell [9]. Manuscript received March 22, 2015; revised April 26, 2015; accepted May 11, 2015. Date of publication May 25, 2015; date of current version October 22, 2015. Corresponding author: R. Choudhary (e-mail:
[email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMAG.2015.2435035
Fig. 1. Cr2 O3 films having (I) 4 Cr layers, (II) 6 Cr layers, and 10 Cr layers.
Our focus is on the effect of substrate effects on the magnetism of Cr2 O3 thin films, wondering whether there are alternative sources of ferromagnetism in Cr2 O3 . We use ab initio calculations to investigate free Cr-terminated Cr2 O3 films and Cr2 O3 films deposited on an Al2 O3 substrate. The Cr2 O3 films have thicknesses of four, six, and ten Cr layers, and we show that the spin structure changes from ferromagnetism to antiferromagnetism as the layer thickness increases. II. C OMPUTATIONAL M ETHOD Fig. 1 shows the structure of investigated Cr-terminated Cr2 O3 (0001) thin films. Sapphire, α-Al2 O3 (0001), is taken as a substrate, because it has a corundum structure similar to that of α-Cr2 O3 , with a 4.21% lattice mismatch. We have studied Cr2 O3 thicknesses of 4.10 Å, 6.70 Å, and 10.90 Å, which are denoted as structures I, II and III, respectively. We have studied both free-standing (ii) Cr2 O3 films and Cr2 O3 films deposited on α-Al2 O3 (0001). The thickness of the Al2 O3 substrate layer is 6.80 Å, having six Al layers (isostructural with film II), and the surface is terminated with Al. The lattice parameters are taken as a = b = 4.951 Å and c = 13.599 Å [10]. The first principle calculations are performed using the Vienna ab initio simulation package, which employs the LSDA for the exchange and correlation functional. We studied the films with both the LSDA and LSDA + U approaches, but the results were the same. Only a small energy difference
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IEEE TRANSACTIONS ON MAGNETICS, VOL. 51, NO. 11, NOVEMBER 2015
Fig. 2. Total DOS for the Cr2 O3 film III. (a) Without substrate. (b) On the α-Al2 O3 substrate. Fermi level is at E = 0 eV. TABLE I GSE AND M AGNETIC M OMENT PER Cr ATOM FOR FM AND AFM S PIN S TRUCTURE OF THE Cr2 O 3 T HIN F ILMS ON Al2 O 3 S UBSTRATE
Fig. 3. Ground-state spin structures of the films described in Fig. 1. (a) Free-standing Cr2 O3 films and (b) Cr2 O3 films on Al2 O3 . The spin configuration (b) was obtained using (a) as the starting point and then converging the spin structure. The corresponding moments are listed in Table II.
(approx. 0.05 meV) in ground state was observed, and moments on the atoms were the same in both the cases. This is also reported in [7] and [8], where the structures of Cr2 O3 films have been studied with the LSDA approach. We have used 9 × 9 × 1 -centered k-point grid for the self-consistent calculations. We have taken the energy cutoff as 520 eV for the plane wave basis set. III. R ESULTS AND D ISCUSSION We have performed FM and AFM calculations for thin-film Cr2 O3 , focusing on local density of states (DOS), local moments, magnetization, and energy differences between the FM and AFM states. Both free-standing Cr2 O3 films and films deposited on Al2 O3 have been considered for all three thicknesses. The Cr2 O3 thin films II and III, without substrate are AFM, whereas the AFM configuration of Cr2 O3 films II and III on α-Al2 O3 gain some magnetic moment due to FM coupling of the outermost two Cr layers after convergence. Fig. 2 compares the total DOS for the free-standing Cr2 O3 film III [see Fig. 2(a)] with that on α-Al2 O3 [Fig. 2(b)]. We have performed ground-state energy (GSE) calculations for both FM and AFM starting configurations. Table I shows the results, listing ground-state energies, and magnetic moments per atom of the films (I, II and III) for both FM and AFM spin structures. Fig. 3(b) shows the ground-state spin structures we have obtained in our calculations for the Cr2 O3 thin films on the substrate, and Table II lists the ground-state and some excitedstate Cr moments. Fig. 3(a) shows the spin structure for the free-standing layers.
This spin structure has also been used as the starting spin configuration for Cr2 O3 on the substrate. Fig. 3(b) shows the outcome of the latter calculation. From Fig. 3 and from Tables I and II, we see that the thinnest film (I) has an FM ground state and the other two films, i.e., II and III, are basically AFM but exhibit an FM alignment in the topmost two Cr layers (red spin arrows). A more accurate description of the spin structure in Fig. 3(b) (II–III) is therefore ferrimagnetism with a small uncompensated moment at the surface. The thinnest film (I) is FM with an average moment of 2.82 μ B per Cr atom. In the AFM configuration, Film II has an average moment of 2.6 μ B per Cr atom and the thickest film (III) has an average moment of 2.32 μ B per Cr atom. The coupling between the topmost two Cr layers in the II and III films is FM, similar to the O-terminated Cr2 O3 film [7]. The main reason for the disagreement is the low moment of the Cr atoms at the interface compared with the moment of the Cr atoms at the surface. Unconstrained (free-standing) stable FM Cr2 O3 film I has an average moment of 2.88 μ B per Cr atom and stable AFM Cr2 O3 films II and III have average moments of 2.56 μ B and 2.55 μ B per Cr atom, respectively. The magnetic moment of Cr atom is not symmetric for the films. This may be because of the uncompensated spin structures of the films. The spin structures may have a symmetry lower than that of the lattice. Fig. 4 compares the partial densities of d-states for two nonequivalent Cr atoms and p-states of two nonequivalent O atoms in the thickest Cr2 O3 film (III) on Al2 O3 substrate.
CHOUDHARY et al.: MAGNETISM IN Cr2 O3 THIN FILMS: AN AB INITIO STUDY
TABLE II L OCAL M AGNETIC M OMENTS m Cr , M EASURED IN μ B AND L ISTED F ROM THE B OTTOM (I NTERFACE ) TO THE T OP (S URFACE ) IN
F IG . 3. A N A STERISK (∗) D ENOTES THE E XCITED AFM S TATES
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The oxygen moments are between −0.037 and +0.03 μ B per atom. The occurrence of FM order in Cr oxide systems is not surprising. For example, bulk CrO2 is a ferromagnet. This trend is easily understood in terms of the charge state of Cr3+ and Cr4+ , which leads to respective moments of 3 and 2 μ B per atom. The trend toward ferromagnetism is most pronounced for ions with half-filled shells (5 μ B ) [11], as exemplified by Mn2+ , Fe2+ , and Fe3+ , which have 4–5 μ B per atom. Of course, the charge state is not the only consideration, and the atomic environment plays an important role. Our calculations indicate that the Cr surface and interface atoms trigger a transition from AFM to FM in very thin films. IV. C ONCLUSION In conclusion, we have performed studies to understand the recently suggested FM in Cr2 O3 thin films. Without substrateinduced strain, Cr2 O3 thin film I is FM while films II and III are AFM. Investigating Cr2 O3 thin films on Al2 O3 , we have found that the energy differences between FM and AFM configurations are very small: The thinnest film (4.1 Å) is FM, while the other two films have more complex spin structures, with FM interactions near the surface and an uncompensated net moment. ACKNOWLEDGMENT This work was supported by Army Research Office under Grant W911NF-10-2-0099. R EFERENCES
Fig. 4. AFM DOS for the d-states of Cr and p-states of O in the thickest Cr2 O3 film (10.9 Å). (a) and (c) At the Cr2 O3 /Al2 O3 interface. (b) and (d) On the surface of the film. Fermi level is at E = 0 eV.
The moment contribution of the surface Cr atoms is larger than that of the interface Cr atoms at the Cr2 O3 /Al2 O3 interface, in agreement with Table II. The net moment of O is not zero.
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