The difference in total energy (ΔE; meV) between the FM and AFM configurations for the Zn46O48Gd2 nanowires, without vacancies (second column), with electron injection (third column) and with VO (fourth column).
The magnetic properties of Gd-doped ZnO films and nanostructures are important to the development of next-generation spintronic devices. Here, we elucidate the significant role played by Gd-oxygen-deficiency defects in mediating/inducing ferromagnetic coupling in in situ Gd-doped ZnO thin films deposited at low oxygen pressure by pulsed laser deposition (PLD). Samples deposited at higher oxygen pressures exhibited diamagnetic responses. Vacuum annealing was used on these diamagnetic samples (grown at a relatively high oxygen pressures) to create oxygen-deficiency defects with the aim of demonstrating reproducibility of room-temperature ferromagnetism (RTFM). Samples annealed at oxygen environment exhibited superparamagnetism and blocking-temperature effects. The samples possessed secondary phases; Gd segregation led to superparamagnetism. Theoretical studies showed a shift of the 4f level of Gd to the conduction band minimum (CBM) in Gd-doped ZnO nanowires, which led to an overlap with the Fermi level, resulting in strong exchange coupling and consequently RTFM.
- rare earth
New generations of electronic devices will likely be developed using spintronics technologies . However, generating reproducible long-range ferromagnetism in wide bandgap (WBG)-diluted magnetic semiconductor (DMS) materials remains a major obstacle to the fabrication of spintronic devices operating above room temperature . This obstacle has prompted significant research efforts on WBG-DMSs, particularly doped ZnO . Rare earth (RE) dopants have emerged as promising candidates in the search for room-temperature ferromagnetism (RTFM) in ZnO and have been the subject of intense investigations. Doping ZnO with gadolinium (Gd) should produce stronger ferromagnetism compared with doping ZnO with transition metals due to partially filled
Ferromagnetism was observed in Gd-doped ZnO films and nanostructures prepared by different methods [15–20], which can be further improved by annealing [17, 18]. ZnO single crystals implanted with Gd atoms exhibited saturation moments of up to 1.8
2. Experimental studies on Gd-doped ZnO thin films
In this section, we describe the ferromagnetic behavior of Gd-doped ZnO thin films as observed experimentally and posited theoretically. We then determine the origin of the ferromagnetism in these materials.
2.1. Sample preparation
All in situ Gd-doped wurtzite ZnO thin films were grown by pulsed laser deposition (PLD) on lattice-matched a-sapphire (Al2O3) substrate (0.08% lattice mismatch between [11–21] a-Al2O3 and (0 0 0 1) c-ZnO). When the lattice mismatch was minimized, good quality films could be produced as structural defects in which line defects were substantially reduced. The Gd-doped ZnO and Gd targets were synthesized using 99.99% pure ZnO powder mixed with 0.1–2 wt% Gd2O3 powder. The films were deposited at different oxygen deposition pressures (
2.2. Structural properties
Understanding the structural properties of the materials is crucial to identifying the origin of their magnetic properties. In this respect, in DMS materials, the film orientation, dopant concentrations, crystal quality, defects, and secondary phase inclusions should be identified clearly. The growth direction, the crystal quality, and the lattice parameters can be studied by X-ray diffraction measurements. A long-range scan (shown in Figure 1) of Gd-doped ZnO thin films reveals that they are single crystal and were grown along the
We used high-resolution transmission electron microscopy (HR-TEM) to study crystal distortion and to investigate structural defects. The samples did not exhibit any line defects, as shown in Figure 2. In addition, no secondary phases were observed near the interface, indicating that the diluted Gd concentration was sufficiently low to prevent the formation of clusters and secondary phases .
Materials with secondary phases and segregations are not suitable for practical spintronic applications. Near-edge X-ray absorption fine structure (NEXAFS) spectra can be used to investigate the existence of secondary phases. Because a ZnO matrix cannot be fully polarized and because ferromagnetic signals coming from phase segregation do not contribute to long-range reproducible ferromagnetism, we ran NEXAFS scans to confirm that no secondary phases and segregations were present in the DMS samples. NEXAFS spectra at the O K-edge and Gd
2.3. Optical properties
The study of optical properties allows the investigation of defects that may affect the magnetic properties of materials. We preformed low-temperature photoluminescence (PL) measurements to study the role of defects. In Figure 3(a), the peak at ~369.1 nm represents the ZnO band edge emission. Moreover, the undoped ZnO spectrum shows an orange-red defect band at 587 nm, which we attributed to oxygen interstitials (Oi) using deep-level transient spectroscopy (DLTS) . The spectra pertaining to the Gd-doped ZnO films grown at low
2.4. Magnetic properties
2.4.1. The effect of oxygen deficiency
We measured the magnetization using a superconducting quantum interference device (SQUID) magnetometer (MPMS, Quantum Design, USA) and a SQUID vibrating sample magnetometer (SVSM, Quantum Design, USA). The samples were initially cooled from room temperature to 5 K without application of any magnetic field (zero-field-cooled, ZFC). A field of 100 Oe was then applied and the magnetic data were recorded as a function of temperature as the sample was heated to 300 K and then cooled to 5 K under the same applied field (field-cooled, FC). All undoped ZnO thin films prepared under high or low
Measurements of the dependence of magnetism on temperature were also conducted. Results are shown in the ZFC and FC curves in Figure 6 and Figure 7. Figure 6(e–h) and Figure 7(d) show the ZFC-FC curves without magnetic phase transitions or blocking temperatures. Furthermore, nonzero coercivity was observed in both sets of samples at room temperature, as shown in Figure 6 and Figure 7. The magnetism as a function of the field strength/temperature (H/T) in the samples is shown in Figure 9, indicating that there is no superimposing universality at 5 K and 300 K, excluding the possibility of superparamagnetism . In addition, the Gd-doped ZnO sample (Figure 7(a)) grown with 0.04 at% Gd concentration shows the maximum coercivity (HC) and the highest magnetic moment of 12.35
To confirm the effect of oxygen defects, a ferromagnetic sample of Gd-doped ZnO (0.08 at% Gd) grown at low
Extant studies have confirmed that Gd3+ ions exhibit magneto-crystalline anisotropy due to the
2.4.2. The effect of secondary phases
Finding ferromagnetism in samples annealed at high temperatures (380 K) (described in Sections 2.4.1. and 2.4.2.) suggests that the ferromagnetism does not originate from separation or secondary phases. Figure 11(a) shows FC-ZFC curve for a Gd-doped ZnO sample with secondary phases as well as the Curie temperature (TC) of the Gd clusters. GdZn2 segregation is clearly shown in the curve (TC at ~70 K as shown in Figure 11), whereas the TC of Gd is very close to room temperature, as shown in Figure 11(a). In addition, paramagnetic signals are observed from Gd metals above room temperature, as shown in Figure 11(b). The other expected phase is Gd2O3, which is an antiferromagnetic material.
In highly Gd-doped samples (~2.5 at%) grown at 50 mTorr on c-sapphire substrates, segregation of the secondary phase was observed near the film-substrate interface, as indicated by the HR-TEM results (Figure 12(a)). The M-H loop (Figure 12(b)) at 5 K is dominated by superparamagnetic behavior, as there is no magnetic saturation. Such behavior was reported by Murmu et al.  for (2.5 at%) Gd-implanted ZnO films.
3. Theoretical studies on Gd-doped ZnO
3.1. The origin of the ferromagnetism in Gd-doped ZnO films
All Gd-doped ZnO samples showed n-type conductivity with about 1018 cm−3 carrier concentration. RTFM was observed in all samples grown at low
The theoretical analysis performed in this work focuses on the effect of the Gd complexes with intrinsic defects that introduce donor electrons . First-principles simulations were performed using the Vienna Ab-initio Simulation Package (VASP) [48, 49] with projector-augmented wave potentials (PAW) and a plane-wave expansion of 400 eV on 2 × 2 × 2 k-meshes for structural relaxation. The exchange and correlations were treated in the Perdew-Burke-Ernzerhof generalized gradient approximation (GGA) and a little higher accuracy for the energy calculation. All configurations were fully relaxed until the forces per atom were less than 0.02 eV/Å. For the localized Zn
Ferromagnetism occurs when the Fermi level (EF) is located near the band edge and overlaps with the impurity level. As a result, it can be partially occupied by the donor electrons and magnetic exchange coupling can take place . Figure 13 shows that introducing VO does not shift the Fermi level to the band edge, which, however, moves above the conduction band minimum (CBM) with the introduction of Gd impurities. However, the presence of Gd dopants in defect-free ZnO is not sufficient to induce exchange coupling, as the magnetic results pertaining to Gd:ZnO reveal predominantly paramagnetic behavior . Figure 13 shows a 2-Gd complex with VO and Zni, respectively, suggesting three possibilities of magnetic coupling that lead to the observed RTFM in Gd-doped ZnO deposited at different oxygen-deficiency conditions. First, Gd induces FM through
3.2. The origin of the ferromagnetism in Gd-doped ZnO nanowires
First-principles DFT calculations were carried out within the GGA to elucidate the magnetic phenomena in the Gd-doped ZnO nanowires. A wurtzite ZnO nanowire grown along the [0 0 0 1] direction doped with Gd was considered. The presence of point defects in the nanowire along with the Gd dopant is discussed in the context of magnetic and electronic properties. The possibility of carrier-mediated ferromagnetism originating from the
The Zn48O48 nanowire was modeled by employing super cell approximation in which a vacuum of 15 Å is created along the X and Y directions and infinite periodicity is maintained along the Z direction. Since a comparison of the results obtained with and without the Hubbard U parameter did not alter the qualitative picture, we adopted the GGA approximation as implemented in the plane-wave-based code VASP [48, 49]. Projected augmented wave (PAW) pseudopotentials were considered with a plane-wave cutoff of 400 eV. A Monkhorst-Pack K grid of 1 × 1 × 8 was used for the Brillouin zone integration. With the abovementioned input settings, we were able to achieve energy and force tolerances of 0.0001 eV and 0.004 eV/Å, respectively.
The formation energy was calculated by incorporating the Gd atoms in all possible non-equivalent sites in the ZnO nanowire encompassing the surface, subsurface, and bulk-like regions (Figure 14) using the following equation:
The optimization of a pristine nanowire resulted in a reduction of bond length along the c-axis (1.89 Å), while the ab-plane underwent extension, compared to bulk ZnO (1.99 Å). Substitution of a Gd atom resulted in slight elongation along c-axis, to 2.08 Å, whereas the change within the a-b plane was almost negligible, indicating that the Zn47O48Gd nanowires reached structural stability with minimal lattice distortion. The Gd atoms preferred to occupy the surface sites in agreement with the in situ deposition experiments.
|Configuration||∆E (meV)||∆E(e) (meV)||∆E(VO) (meV)|
The energetic preference of the clustering of Gd atoms was analyzed by putting a pair of Gd atoms in the host ZnO matrix and the lowest formation energies for widely separated Gd atoms were obtained. This is an important result indicating that segregation of Gd atoms in ZnO nanowires is unlikely to occur and that the magnetism does not originate from the Gd clusters. Our findings support the homogeneous distribution of RE atoms during implantation in ZnO. The Gd atoms, when placed in near vicinity, exhibited ferromagnetic exchange coupling in the neutral state with exchange energies (ΔE) as large as 21 meV. The introduction of additional charge to the nanowire by the injection of an electron further enhanced ΔE, indicating that the presence of O vacancies may stabilize ferromagnetic coupling in the nanowire, given that a single O vacancy can release two electrons into the system. The ΔE increased to 200 meV in the presence of O vacancies, supporting the possibility of an increased
The density of states (DOS) of Gd-doped ZnO nanowires with and without O vacancies provided further insight into the exchange mechanism. A pristine ZnO nanowire is semiconducting with nonmagnetic characteristics (Figure 15) . Doping with Gd atom causes a significant shift of the Fermi level to the conduction band close to the Gd
The origin of RTFM in Gd-doped ZnO is intrinsic due to exchange coupling mediated or introduced by a defect band related to the Gd-defect complex. Quantum confinement of the nanowire structure can strengthen the RTFM, as O vacancies play a key role in stabilizing ferromagnetic exchange in Gd-doped ZnO nanowires.
The authors would like to thank the team involved in this study. In particular, we thank Zhenkui Zhank, Shamima Hussain, Tahani H. Flemban, and Ioannis Bantounas from our group at KAUST. We thank J.B. Franklin, B. Zou, P.K. Petrov, M.P. Ryan, and N.M. Alford from Imperial College London and J-S. Lee from the Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory. We thank P. Edwards, K.P. O’Donnell, and R.W. Martin for providing access to the EPMA for WDX measurements at the University of Strathclyde. We thank Ratnamal Chatterjees’s group at IIT Delhi, India, for conducting the SQUID experiments.
G. A. Prinz. Magnetoelectronics. Science. 1998; 282:1660–1663.
S. Chambers. Is it really intrinsic ferromagnetism? Nat. Mater. 2010; 9:956–957.
P. Sharma, A. Gupta, K. V. Rao, F. J. Owens, R. Sharma, R. Ahuja, J. M. O. Guillen, B. Johansson, G. A. Gehring. Ferromagnetism above room temperature in bulk and transparent thin films of Mn-doped ZnO. Nat. Mater. 2003; 2:673–677.
H. Shi, P. Zhang, S. S. Li, J. B. Xia. Magnetic coupling properties of rare-earth metals (Gd, Nd) doped ZnO: first-principles calculations. J. Appl. Phys. 2009; 106:023910.
G. M. Dalpian, S.-H. Wei. Electron-induced stabilization of ferromagnetism in Ga1− xGd xN. Phys. Rev. B. 2005; 72:115201.
P. Dev, P. Zhang. Unconventional magnetism in semiconductors: role of localized acceptor states. Phys. Rev. B. 2010; 81:085207.
X.-L. Li, J.-F. Guo, Z.-Y. Quan, X.-H. Xu, G. A. Gehring. Defects inducing ferromagnetism in carbon-doped ZnO films. IEEE Trans. Magn. 2010; 46:1382–1384.
J. B. Yi, C. C. Lim, G. Z. Xing, H. M. Fan, L. H. Van, S. L. Huang, K. S. Yang, X. L. Huang, X. B. Qin, B. Y. Wang, T. Wu, L. Wang, H. T. Zhang, X. Y. Gao, T. Liu, A. T. S. Wee, Y. P. Feng, J. Ding. Ferromagnetism in dilute magnetic semiconductors through defect engineering: Li-doped ZnO. Phys. Rev. Lett. 2010; 104:137201.
C. D. Pemmaraju, R. Hanafin, T. Archer, H. B. Braun, S. Sanvito. Impurity-ion pair induced high-temperature ferromagnetism in Co-doped ZnO. Phys. Rev. B. 2008; 78:054428.
H. Gu, Y. Jiang, Y. Xu, M. Yan. Evidence of the defect-induced ferromagnetism in Na and Co codoped ZnO. Appl. Phys. Lett. 2011; 98:012502.
A. Khodorov, A. G. Rolo, E. K. Hlil, J. Ayres de Campos, O. Karzazi, S. Levichev, M. R. Correia, A. Chahboun, M. J. M. Gomes. Effect of oxygen pressure on the structural and magnetic properties of thin Zn0.98Mn0.02O films. Eur. Phys. J. Appl. Phys. 2012; 57:10301.
Y. Belghazi, G. Schmerber, S. Colis, J. L. Rehspringer, A. Dinia, A. Berrada. Extrinsic origin of ferromagnetism in ZnO and Zn0.9Co0.1O magnetic semiconductor films prepared by sol–gel technique. Appl. Phys. Lett. 2006; 89:122504.
M. H. N. Assadi, Y. Zhang, R. Zheng, S. P. Ringer, S. Li. Structural and electronic properties of Eu- and Pd-doped ZnO. Nanoscale Res. Lett. 2011; 6:357.
I. Bantounas, S. Goumri-Said, M. B. Kanoun, A. Manchon, I. Roqan, U. Schwingenschlogl. Ab initio investigation on the magnetic ordering in Gd doped ZnO. J. Appl. Phys. 2011; 109:083929.
K. Potzger, S. Zhou, F. Eichhorn, M. Helm, W. Skorupa, A. Mücklich1, J. Fassbender, T. Herrmannsdörfer, A. Bianchi. Ferromagnetic Gd-implanted ZnO single crystals. J. Appl. Phys. 2006; 99:063906.
M. Subramanian, P. Thakur, M. Tanemura, T. Hihara, V. Ganesan, T. Soga, K. H. Chae, R. Jayavel, T. Jimbo. Intrinsic ferromagnetism and magnetic anisotropy in Gd-doped ZnO thin films synthesized by pulsed spray pyrolysis method. J. Appl. Phys. 2010; 108:053904.
P. P. Murmu, J. Kennedy, B. J. Ruck, G. V. M. Williams, A. Markwitz, S. Rubanov, A. A. Suvorova. Effect of annealing on the structural, electrical and magnetic properties of Gd-implanted ZnO thin films. J. Mater. Sci. 2012; 47:1119.
P. P. Murmu, R. J. Mendelsberg, J. Kennedy, D. A. Carder, B. J. Ruck, A. Markwitz, R. J. Reeves, P. Malar, T. Osipowicz. Structural and photoluminescence properties of Gd implanted ZnO single crystal. J. Appl. Phys. 2011; 110:033534.
P. P. Murmu, J. Kennedy, G. V. M. Williams, B. J. Ruck, S. Granville, S. V. Chong. Observation of magnetism, low resistivity and magnetoresistance in the near-surface region of Gd implanted ZnO. Appl. Phys. Lett. 2012; 101:082408.
A. A. Dakhel, M. El-Hilo. Ferromagnetic nanocrystalline Gd-doped ZnO powder synthesized by coprecipitation. J. Appl. Phys.. 2010; 107:123905.
V. Ney, S. Ye, T. Kammermeier, K. Ollefs, F. Wilhelm, A. Rogalev, S. Lebègue, A. L. da Rosa, A. Ney. Structural and magnetic analysis of epitaxial films of Gd-doped ZnO. Phys. Rev. B. 2012; 85:235203.
I. S. Roqan, S. Venkatesh, Z. Zhang, S. Hussain, I. Bantounas, J. B. Franklin, T. H. Flemban, B. Zou, J.-S. Lee, U. Schwingenschlogl, P. K. Petrov, M. P. Ryan, N. M. Alford. Obtaining strong ferromagnetism in diluted Gd-doped ZnO thin films through controlled Gd-defect complexes. J. Appl. Phys. 2015; 117:073904.
S. Venkatesh, J. B. Franklin, M. P. Ryan, J-S. Lee, H. Ohldag, M. A. McLachlan, N. M. Alford, I. S. Roqan. Defect-band mediated ferromagnetism in Gd-doped ZnO thin films. J. Appl. Phys. 2015; 117:013913.
N. Herres, L. Kirste, H. Obloh, K. Kohler, J. Wagner, P. Koidl. X-ray determination of the composition of partially strained group-III nitride layers using the Extended Bond Method. Mater. Sci. Eng. B. 2002; 91–92:425–432.
T. H. Flemban, M. C. Sequeira, Z. Zhang, S. Venkatesh, E. Alves, K. Lorenz, I. S. Roqan. Identifying the influence of the intrinsic defects in Gd-doped ZnO thin-films. J. Appl. Phys..2016; 119:065301.
L. Armelao, F. Heigl, A. Jurgensen, R. I. R. Blyth, T. Regier, X.-T. Zhou, T. K. Sham. X-ray excited optical luminescence studies of ZnO and Eu-doped ZnO nanostructures. J. Phys. Chem. C. 2007; 111:10194.
R. A. Rosenberg, G. K. Shenoy, L. C. Tien, D. Norton, S. Pearton, X. H. Sun, T. K. Sham. Anisotropic X-ray absorption effects in the optical luminescence yield of ZnO nanostructures. Appl. Phys. Lett. 2006; 89:093118.
L. A. Grunes, R. D. Leapman, C. N. Wilker, R. Hoffmann, A. B. Kunz. Oxygen K near-edge fine structure: an electron-energy-loss investigation with comparisons to new theory for selected 3d transition-metal oxides. Phys. Rev. B. 1982; 25:7157–7173.
J. G. Chen, B. Frühberger, M. L. Colaianni. Near edge X-ray absorption fine structure characterization of compositions and reactivities of transition metal oxides. J. Vac. Sci. Technol. A. 1996; 14:1668–1673.
G. Kaindl, G. Kalkowski, W. D. Brewer, B. Perscheid. M-edge X-ray absorption spectroscopy of 4f instabilities in rare earth systems. J. Appl. Phys.. 1984; 55:1910–1915.
B. T. Thole, G. van der Laan, J. C. Fuggle, G. A. Sawatzky, R. C. Karnatak, J.-M. Esteva. 3d X-ray-absorption lines and the 3d9 4fn + 1 multiplets of the lanthanides. Phys. Rev. B. 1985; 32:5107–5118.
C. H. Ahn, Y. K. Young, C. K. Dong, S. K. Mohanta, H. K. Cho. A comparative analysis of deep level emission in ZnO layers deposited by various methods. J. Appl. Phys. 2009; 105:013502.
D. M. Hofmann, D. Pfisterer, J. Sann, B.K. Meyer, R. Tena-Zaera, V. Munoz-Sanjose, T. Frank, G. Pensl. Properties of the oxygen vacancy in ZnO. Appl. Phys. A. 2007; 88:147–151.
L. S. Vlasenko, G. D. Watkins. Optical detection of electron paramagnetic resonance in room-temperature electron-irradiated ZnO. Phys. Rev. B. 2005; 71:125210.
K. Vanheusden, W. L. Warren, C. H. Seager, D. R. Tallant, J. A. Voigt, B. E. Gnade. Mechanisms behind green photoluminescence in ZnO phosphor powders. J. Appl. Phys. 1996; 79:7983–7990.
X. J. Wang, L. S. Vlasenko, S. J. Pearton, W. M. Chen, I. A. Buyanova. Oxygen and zinc vacancies in as-grown ZnO single crystals. J. Phys. D: Appl. Phys.. 2009; 42:175411.
J. Ji, L. A. Boatner, F. A. Selim. Donor characterization in ZnO by thermally stimulated luminescence. Appl. Phys. Lett. 2014; 105:041102.
N. O. Korsunska, L. V. Borkovska, B. M. Bulakh, L. Y. Khomenkova, V. I. Kushnirenko, I. V. Markevich. The influence of defect drift in external electric field on green luminescence of ZnO single crystals. J. Lumin. 2003; 102:733–736.
B. X. Lin, Z. X. Fu, Y. B. Jia.Green luminescent center in undoped zinc oxide films deposited on silicon substrates. Appl. Phys. Lett. 2001; 79:943.
S. Bedanta, W. Kleemann. Supermagnetism. J. Phys. D: Appl. Phys. 2009; 42:013001.
J. P. Bucher, D. C. Douglass, L. A. Bloomfield. Magnetic properties of free cobalt clusters. Phys. Rev. Lett. 1991; 66:3052–3055.
R. H. Kodama, Salah A. Makhlouf, A. E. Berkowitz. Finite size effects in antiferromagnetic NiO nanoparticles. Phys. Rev. Lett. 1997; 79:1393–1396.
S. Mørup, B. R. Hansen. Uniform magnetic excitations in nanoparticles. Phys. Rev. B. 2005; 72:024418.
D. C. Douglass, J. P. Bucher, L. A. Bloomfield. Magnetic properties of free cobalt and gadolinium clusters. Phys. Rev. B. 1993; 47:12874–12889.
Y. E. Kitaev, P. Tronc. Ferromagnetic and antiferromagnetic ordering in the wurtzite-type diluted magnetic semiconductors. Phys. Sol. State. 2012; 54:520–530.
A. Łusakowski. Ground state splitting of S 8 rare earth ions in semiconductors. Phys. Rev. B. 2005; 72:094429.
R. Skomski, D. J. Sellmyer. Anisotropy of rare earth magnets. J. Rare Earths. 2009; 27:675.
G. Kresse, D. Joubert. Ab initio molecular dynamics for liquid metals. Phys. Rev. B. 1993; 47:558
G. Kresse, J. Furthmuller. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B. 1996; 54:11169.
L. Liu, P. Y. Yu, Z. Ma, S. S. Mao. Ferromagnetism in GaN:Gd: a density functional theory study. Phys. Rev. Lett. 2008; 100:127203.
I. Bantounas, V. Singaravelu, I. S. Roqan, U. Schwingenschlogl. Structural and magnetic properties of Gd-doped ZnO. J. Mater. Chem. C. 2014; 2:10331.
Y. Gohda, A. Oshiyama. Intrinsic ferromagnetism due to cation vacancies in Gd-doped GaN: first-principles calculations. Phys. Rev. B. 2008; 78:161201(R).
S. Assa Aravindh, U. Schwingenschoel, I. S. Roqan. Ferromagnetism in Gd doped ZnO nanowires: a first principles study. J. Appl. Phys. 2014; 116:233906.
T. Dietl, H. Ohno, F. Matsukura, J. Cibert, D. Ferrand. Zener model description of ferromagnetism in zinc-blende magnetic semiconductors. Science. 2000; 287:1091.
P. M. Krstajic, F.M. Peters, A. Ivanov, V. Fleurov, K. Kikoin. Double-exchange mechanisms for Mn-doped III–V ferromagnetic semiconductors. Phys. Rev. B. 2004; 70:195215.