Based upon ab initio electronic structure calculations by the Korringa -Kohn -Rostoker coherentpotential approximation (KKR-CPA) method within the local-density approximation (LDA), we propose a unified physical picture of magnetism and an accurate calculation method of Curie temperature (T C ) in dilute magnetic semiconductors (DMSs) in II -VI and III -V compound semiconductors. We also propose the unified physical picture of magnetism in the DMS, where ferromagnetic Zener's double-exchange mechanism (or Zener's p -d exchange mechanism) caused by the partially occupied impurity band and anti-ferromagnetic super-exchange mechanism (or ferromagnetic super-exchange mechanism) is competing to determine the magnetic states in the DMS. We propose that the three-dimensional 3D Dairisekiphase and one-dimensional 1D Konbu-phase caused by spinodal nano-decomposition are responsible for high-T C phase in the inhomogeneous system. We propose the new methodology to go beyond LDA to describe the highly correlated electron system by taking into account the self-interaction correction (SIC) to the LDA. the quantal phase (or Berry's phase) and nano-dynamics of spin, charge and atoms in the nano-structures of semiconductors.In order to boost the research on semiconductor nano-spintronics dramatically, we need to realize the high-temperature ferromagnetism (a few times higher-T C than the room temperature) with dilute magnetic semiconductor (DMS) nano-structures for the application of high-density (Tera-bit density per inch 2 ), high-speed (Tera-Hz switching), and low-power consumption (non-volatile memory) electronics. In spintronics application, magnetic properties may be carried by conventional metallic ferromagnets (Fe, Co and Ni) or dilute magnetic semiconductors (DMS) such as (Ga,Mn)As or (In,Mn)Sb. These materials are metallic or bad-metallic systems, therefore, we cannot control the magnetic properties by an electric field through the application of gate voltage. We need to develop the new control method of spin by electric field in semiconductors, carrier controlled ferromagnetism, spin injection into nanostructures, spin correction, spin manipulations, and spin detection, if we seriously want to develop a new class of electronics by semiconductor nano-spintronics to go beyond the silicon CMOS nanotechnology. To do so, self-controlled growth-positioning by the seeding, self-assembled and self-organized fabrication method of nano-scale-size ferromagnets (nano-magnets) in semiconductor matrix is absolutely necessary. This is the only method to control the spin by electric field in order to realize the new class of electronics by controlling the spin and charge degrees of freedom of electrons in the semiconductors. These new fabrication method of nano-magnets in semiconductor matrix permit the real application of semiconductor nano-spintronics [1], such as colossal or giant magneto-resistant memory, high sensitive field sensors, spin transistors, reconfigurable logic and quantum information and communication processing. In t...

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In vortex-like spin arrangements, multiple spins can combine into emergent multipole moments. Such multipole moments have broken space-inversion and time-reversal symmetries, and can therefore exhibit linear magnetoelectric (ME) activity. Three types of such multipole moments are known: toroidal; monopole; and quadrupole moments. So far, however, the ME activity of these multipole moments has only been established experimentally for the toroidal moment. Here we propose a magnetic square cupola cluster, in which four corner-sharing square-coordinated metal-ligand fragments form a noncoplanar buckled structure, as a promising structural unit that carries an ME-active multipole moment. We substantiate this idea by observing clear magnetodielectric signals associated with an antiferroic ME-active magnetic quadrupole order in the real material Ba(TiO)Cu 4 (PO 4 ) 4 . The present result serves as a useful guide for exploring and designing new ME-active materials based on vortex-like spin arrangements.

Ferroic magnetic quadrupole order exhibiting macroscopic magnetoelectric activity is discovered in the novel compound A(TiO)Cu4(PO4)4 with A = Pb, which is in contrast with antiferroic quadrupole order observed in the isostructural compounds with A = Ba and Sr. Unlike the famous lone-pair stereochemical activity which often triggers ferroelectricity as in PbTiO3, the Pb 2+ cation in Pb(TiO)Cu4(PO4)4 is stereochemically inactive but dramatically alters specific magnetic interactions and consequently switches the quadrupole order from antiferroic to ferroic. Our firstprinciples calculations uncover a positive correlation between the degree of A-O bond covalency and a stability of the ferroic quadrupole order. I. INTORODUCTIONEarlier works demonstrated that the usage of specific elements with characteristic chemical properties is effective to realize desired ferroic order. For example, lonepair stereochemical activity of a heavier post-transition metal cation with an s 2 electron configuration such as Pb 2+ and Bi 3+ , which we call an s 2 -cation, is known as a driving force for ferroelectric order [1,2], as discussed in perovskite oxides PbTiO 3 [3], BiMnO 3 [4], and BiFeO 3 [5]. The stereochemically active s 2 -cations are surrounded by "hemidirected" local coordination, in which there is a void in the distribution of bonds to the ligands [1]. The origin for this directional bonding is explained by the hybridization between nominally empty metal p states with anti-bonding states formed by filled metal s states and ligand p states [2]. Such a hybridization is possible only when the inversion-symmetry at the cation site is broken. This is a driving force for off-center distortion and thus ferroelectric order.Another potential role of s 2 -cations is an impact on magnetism in insulating magnetic oxides. There, dominant magnetic superexchange interactions are usually mediated by O 2p orbitals near Fermi energy (E F ) [6]. As exemplified by the comparison between PbTiO 3 and BaTiO 3 [3], s 2 -cations tend to exhibit strong orbital hybridization with O ions, which should significantly affects superexchange interactions. Note that s 2 -cations are not necessarily stereochemically active; there are comparable number of compounds containing such cations located in "holodirected" local environment without a void in the * kentakimura@edu.k.u-tokyo.ac.jp ligand bond distribution [1]. In this case, substituting s 2 -cations can be a promising way of fine-tuning magnetic interactions without large distortion of the original structure.Among various ferroic orders, a particular class of magnetic order with broken space-inversion and time-reversal symmetries has recently attracted considerable interest because it can exhibit symmetry-dependent unique phenomena, such as magnetoelectric (ME) effects [7][8][9][10][11][12][13][14][15] and unconventional nonreciprocal electromagnetic responses [16][17][18]. From a symmetry point of view, it is known that ferroic order of magnetic multipole moments (toroidal, monopole, and quadrupole m...