We use density functional theory to explore the possibility of making the semiconducting transition-metal dichalcogenide MoS2 ferromagnetic by introducing holes into the narrow Mo d band that forms the top of the valence band. In the single impurity limit, the repulsive Coulomb potential of an acceptor atom and intervalley scattering lead to a twofold orbitally degenerate effective-mass like e state being formed from Mo d x 2 −y 2 and dxy states, bound to the K and K valence band maxima. It also leads to a singly degenerate a 1 state with Mo d 3z 2 −r 2 character bound to the slightly lower lying valence band maximum at Γ. Within the accuracy of our calculations, these e and a 1 states are degenerate for MoS2 and accommodate the hole that polarizes fully in the local spin density approximation in the impurity limit. With spin-orbit coupling included, we find a single ion magnetic anisotropy of ∼ 5 meV favouring out-of-plane orientation of the magnetic moment. Pairs of such hole states introduced by V, Nb or Ta doping are found to couple ferromagnetically unless the dopant atoms are too close in which case the magnetic moments are quenched by the formation of spin singlets. Combining these exchange interactions with Monte Carlo calculations allows us to estimate ordering temperatures as a function of x. For x ∼ 9%, Curie temperatures as high as 100K for Nb and Ta and in excess of 160K for V doping are predicted. Factors limiting the ordering temperature are identified and suggestions made to circumvent these limitations. PACS numbers: 75.70.Ak, 73.22.-f, 75.30.Hx, 75.50.Pp FIG. 2. Schematic of the effective mass acceptor states bound to the valence band maxima (VBM): an e state bound to the K-K VBM and an a 1 state to the Γ VBM. n is the principal quantum number and only n = 1, 2, 3 levels of the Rydberg series are sketched at the Γ point.

Density functional theory is used to explore the possibility of inducing impurity band ferromagnetism in monolayers of semiconducting MoS2 by introducing holes into the narrow Mo 4d band that forms the top of the valence band. A large out of plane anisotropy is found for unpaired spins bound to the substitutional acceptor impurities V, Nb and Ta that couple ferromagnetically for all but the shortest separations. Using the separation dependent exchange interactions as input to Monte Carlo calculations, we estimate ordering temperatures as a function of the impurity concentration. For about 9% of V impurities, Curie temperatures in excess of 160 K are predicted. The singlet formation at short separations that limits the ordering temperature is explained and we suggest how it can be circumvented.PACS numbers: 75.70. Ak, 75.30.Hx, 75.50.Pp Introduction.-The extraordinary interest sparked by the discovery of intrinsic ferromagnetism in the two dimensional van der Waals semiconducting crystals CrGeTe 3 1 and CrI 3 2 has led us to examine the possibility of inducing ferromagnetism in monolayers of MoS 2 by doping the narrow Mo d band that forms the top of the valence band with holes. Theoretical analysis of the MX 2 layered transition metal dichalcogenides (M = Mo, W; X = S, Se, Te) more than forty years ago 3,4 revealed the curious electronic structure shown in Fig. 1. The d valence states of the Mo atoms interact with the chalcogen p states to form a substantial band gap leaving a single "nonbonding" Mo d band (lhs, solid red line) in the hybridization gap between bonding states (dashed black lines, with nominal X p character) and antibonding states (dashed red lines, with nominal Mo d character). The projected densities of states (DoS) in Fig. 1(b) show the considerable mixing that actually occurs. The reduced coordination number of metal atoms in twodimensional structures leads to smaller bandwidths and higher state densities than in three dimensions making this system favourable for the occurrence of itinerant ferromagnetism. Motivated by predictions of hightemperature ferromagnetism in narrow impurity bands, 5 we examine the behaviour of single acceptor states in the low concentration regime. We show that Mo 1−x V x S 2 monolayers should become ferromagnetic semiconductors with Curie temperatures much larger than those found for either CrGeTe 3 or CrI 3 .

We report a remarkable photoinduced relaxation process and its dependence of thickness and temperature in mixed-phase BiFeO₃ films grown on (001) LaAlO₃ substrates. When the films are illuminated by the light above the bandgap, their resistances are reduced with the increase of temperature. The photoinduced change of resistance reaches to the maximum of about 2.17 × 10^5% at 300 K. It is noted that the relaxation processes of the resistance are significantly different between T-like phase and T-R mixed phase due to structural strain, symmetry breaking and built-in electric field at the phase boundaries. These results provide more insights into intrinsic mechanisms of mixed-phase multiferroic materials and potential applications in all-oxide photoelectric devices.