Hybrid sterility is a major form of postzygotic reproductive isolation. Although reproductive isolation has been a key issue in evolutionary biology for many decades in a wide range of organisms, only very recently a few genes for reproductive isolation were identified. The Asian cultivated rice (Oryza sativa L.) is divided into two subspecies, indica and japonica. Hybrids between indica and japonica varieties are usually highly sterile. A special group of rice germplasm, referred to as wide-compatibility varieties, is able to produce highly fertile hybrids when crossed to both indica and japonica. In this study, we cloned S5, a major locus for indicajaponica hybrid sterility and wide compatibility, using a map-based cloning approach. We show that S5 encodes an aspartic protease conditioning embryo-sac fertility. The indica (S5-i) and japonica (S5-j) alleles differ by two nucleotides. The wide compatibility gene (S5-n) has a large deletion in the N terminus of the predicted S5 protein, causing subcellular mislocalization of the protein, and thus is presumably nonfunctional. This triallelic system has a profound implication in the evolution and artificial breeding of cultivated rice. Genetic differentiation between indica and japonica would have been enforced because of the reproductive barrier caused by S5-i and S5-j, and species coherence would have been maintained by gene flow enabled by the wide compatibility gene.subspecies of rice ͉ hybrid sterility ͉ wide compatibility ͉ aspartic protease

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MER3, a ZMM protein, is required for the formation of crossovers in Saccharomyces cerevisiae and Arabidopsis. Here, MER3, the first identified ZMM gene in a monocot, is characterized by map-based cloning in rice (Oryza sativa). The null mutation of MER3 results in complete sterility without any vegetative defects. Cytological analyses show that chiasma frequency is reduced dramatically in mer3 mutants and the remaining chiasmata distribute randomly among different pollen mother cells, implying possible coexistence of two kinds of crossover in rice. Immunocytological analyses reveal that MER3 only exists as foci in prophase I meiocytes. In addition, MER3 does not colocalize with PAIR2 at the beginning of prophase I, but locates on one end of PAIR2 fragments at later stages, whereas MER3 foci merely locate on one end of REC8 fragments when signals start to be seen in early prophase I. The normal loading of PAIR2 and REC8 in mer3 implies that their loading is independent of MER3. On the contrary, the absence of MER3 signal in pair2 mutants indicates that PAIR2 is essential for the loading and further function of MER3.

A global picture of magnetic domain wall (DW) propagation in a nanowire driven by a magnetic field is obtained: A static DW cannot exist in a homogeneous magnetic nanowire when an external magnetic field is applied. Thus, a DW must vary with time under a static magnetic field. A moving DW must dissipate energy due to the Gilbert damping. As a result, the wire has to release its Zeeman energy through the DW propagation along the field direction. The DW propagation speed is proportional to the energy dissipation rate that is determined by the DW structure. An oscillatory DW motion, either the precession around the wire axis or the breath of DW width, should lead to the speed oscillation.Magnetic domain-wall (DW) propagation in a nanowire due to a magnetic field [1,2,3,4,5] reveals many interesting behaviors of magnetization dynamics. For a tail-to-tail (TT) DW or a head-to-head (HH) DW (shown in Fig. 1) in a nanowire with its easy-axis along the wire axis, the DW will propagate in the wire under an external magnetic field parallel to the wire axis. The propagation speed v of the DW depends on the field strength [3,4]. There exists a so-called Walker's breakdown field H W [6]. v is proportional to the external field H for H < H W and H ≫ H W . The linear regimes are characterized by the DW mobility µ ≡ v/H. Experiments showed that v is sensitive to both DW structures and wire width [1,2,3]. DW velocity v decreases as the field increases between the two linear H-dependent regimes, leading to the so-called negative differential mobility phenomenon. For H ≫ H W , the DW velocity, whose time-average is linear in H, oscillates in fact with time [3,6].Schematic diagram of a HH DW of width ∆ in a magnetic nanowire of cross-section A. The wire consists of three phases, two domains and one DW. The magnetization in domains I and II is along +z-direction (θ = 0) and -zdirection (θ = π), respectively. III is the DW region whose magnetization structure could be very complicate. H is an external field along +z-direction.It has been known for more than fifty years that the magnetization dynamics is govern by the LandauLifshitz-Gilbert (LLG) [7] equation that is nonlinear and can only be solved analytically for some special problems [6,8]. The field induced domain-wall (DW) propagation in a strictly one-dimensional wire has also been known for more than thirty years[6], but its experimental realization in nanowires was only achieved [1,2,3,4,5] in recent years when we are capable of fabricating various nano structures. Although much progress [9,10] has been made in understanding field-induced DW motion, it is still a formidable task to evaluate the DW propagation speed in a realistic magnetic nanowire even when the DW structure is obtained from various means like OOMMF simulator and/or other numerical software packages. A global picture about why and how a DW propagates in a magnetic nanowire is still lacking.In this report, we present a theory that reveals the origin of DW propagation. Firstly, we shall show that no static HH (TT...

A thory of field-induced domain wall (DW) propagation is developed. The theory not only explains why a DW in a defect-free nanowire must propagate at a finite velocity, but also provides a proper definition of DW propagation velocity. This definition, valid for an arbitrary DW structure, allows one to compute the instantaneous DW velocity in a meaningful way even when the DW is not moving as a rigid body. A new velocity-field formula beyond the Walker breakdown field, which is in excellent agreement with both experiments and numerical simulations, is derived.It is a textbook knowledge[1] that a magnetic field can drive a magnetic domain wall (DW) to move. However, our understanding of the field-induced DW motion is far from complete although it has been intensively studied for more than fifty years and many interesting phenomena of magnetization dynamics have been found. Recent development in nanomagnetism[2] demands a deep understanding of DW motion in nanowires, especially how a field affects DW propagation velocity. DW dynamics is governed by the Landau-Lifshtiz-Gilbert (LLG) equation that can only be solved analytically for some special problems [3,4]. A number of theories have been widely accepted and written in books[1], such as kinetic potential approach that assumes zero-damping, Thiele dynamic force equilibrium formulation that is correct for rigid DW propagation, Schryer and Walker analytical solution that is valid only for 1D and exact only for field smaller than a so-called Walker breakdown field H W [3], Slonczewski formulation that simplifies a DW by its center and the cant angle of DW plane. None of these orthodox theories works beyond H W although they have greatly enriched our current understanding of DW dynamics. For example, kinetic potential approach cannot be a correct description of DW propagation because it violates the principle of "no damping, no propagation" that will be explained in this paper. Thiele approach is a good way to describe a rigid DW propagation for small field H < H W , but its assumptions are not valid for H > H W . Schryer and Walker's approach is for 1D and H < H W , and its predictions for H > H W are incorrect. For instance, its prediction that the v − H line for H >> H W passing through the origin differs from both experiments and micromagnetic simulations [6,7,8,9]. Its generalization predicts a saturated velocity[5] (bounded by the velocity at H W ) that does not agree either with experiments or with simulations [6,7,8,9]. Slonczewski formulation is a great simplification of LLG equation that not only replaces partial differential equations by ordinary differential ones, but also is based on Thiele rigid DW approximation although the Slonczewski equations have also been applied to the case of H > H W where it is known that DW deformation cannot be neglected. The problems with both Thiele and Slonczewski formulations can also be seen from their v − H formula[9, 10] that do not capture the trend for H > H W . Even more surprising, none of the existing theories provi...

We present an exact solution of a modifed Dirac equation for topological insulator in the presence of a hole or vacancy to demonstrate that vacancies may induce bound states in the band gap of topological insulators. They arise due to the Z2 classification of time-reversal invariant insulators, thus are also topologically-protected like the edge states in the quantum spin Hall effect and the surface states in three-dimensional topological insulators. Coexistence of the in-gap bound states and the edge or surface states in topological insulators suggests that imperfections may affect transport properties of topological insulators via additional bound states near the system boundary.PACS numbers: 73.20.Hb, Topological insulators are narrow-band semiconductors with band inversion generated by strong spin-orbit coupling [1]. They are distinguished from the ordinary band insulators according to the Z 2 invariant classification of the gapped band insulators due to the time reversal symmetry. The variation of the Z 2 invariant at their boundaries will lead to the topologically protected edge or surface states with the gapless Dirac energy spectrum [2][3][4][5][6][7]. Imperfections, such as impurity, vacancy, and disorder, are inevitably present in topological insulators. Owing to the time-reversal symmetry, an exciting feature of topological insulator is that its boundary states are expected to be topologically protected against weak non-magnetic impurities or disorders [8,9]. This provoked much interest on the single impurity problem on the surface of a topological insulator, starting with gapless Dirac model [10][11][12][13][14]. However, reminding that the boundary state is only a manifestation of the topological nature of bulk bands, it should also start with the examination of the host bulk to know how the imperfections affect the electronic structure. It is well known that single impurity or defect can induce bound states in many systems, such as in the Yu-Shiba state in s-wave superconductor [15,16] and in d-wave superconductors [17]. Topological defects were discussed in the B-phase of 3 He superfluid[18] and topological insulators and superconductors [19]. Here we report that bound states can form around a single vacancy in the bulk energy gap of topological insulators. These bound states are found to have the same origin as boundary states due to the Z 2 classification, thus are also topologically protected.The formation of the topological bound states can be readily illustrated by reviewing the quantum spin Hall effect in two-dimensional (2D) topological insulators [20][21][22], in which strong spin-orbit coupling twists the bulk conduction and valence bands, leading to a nontrivial Z 2 index. As the Z 2 varies across the edge, edge states arise in the gap with the gapless Dirac dispersion. Unlike the quantum Hall effect in a magnetic field, spin-orbit coupling preserves the time reversal symmetry, so the result-

Microwave-assisted magnetization switching was investigated using Fe30Co70∕AlOx∕Ni80Fe20 magnetic tunnel junctions incorporated with a coplanar waveguide. Coercivity field of Ni80Fe20 layer was dramatically reduced in a small amplitude microwave. The authors eliminated the thermal effect in coercivity reduction by comparing two types of measurements which are with and without spin precession in the presence of microwave. It was found that the coercivity reduction depends on both frequency and power of the microwave. The numerical simulation based on Landau-Lifshitz-Gilbert equation reproduced the trend of the experimental data. The results indicate that microwave can be an efficient means to switch the magnetization of a thin film.

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