Topological magnetic textures and long-range orders in terbium-based quasicrystal and approximant

The quasicrystal (QC) possesses a unique lattice structure with rotational symmetry forbidden in periodic crystals. The electric property is far from complete understanding. It has been a long-standing issue whether magnetic long-range order is realized in the QC. Here, we report our theoretical discovery of the ferromagnetic long-range order in the Tb-based QC. The difficulty in past theoretical studies on the QC was lack of the microscopic theory of the crystalline electric field (CEF), which is crucially important in the rare earth systems. By analyzing the CEF in the Tb-based QC, we clarify that magnetic anisotropy plays a key role in realizing unique magnetic textures in the Tb-based QC and approximant crystal (AC). By constructing the minimal model, we show that various magnetic textures on the icosahedron, at whose vertices Tb atoms are located, are realized. We find that the hedgehog state is characterized by the topological charge of one and the whirling-moment state is characterized by an unusually large topological charge of three. The hedgehog and whirling-moment states are shown to be realized as antiferromagnetic orders transcribed as the emergent monopole and antimonopole in the 1/1 AC. We find that these states exhibit the topological Hall effect under applied magnetic field accompanied by the topological as well as metamagnetic transition. Our model and the determined phase diagram are expected to be relevant to the broad range of the rare earth–based QCs and ACs with strong magnetic anisotropy, which are useful not only to understand magnetism but also, to explore topological properties.

Crystal and magnetic structures of R 2Ni1.78In compounds (R = Tb, Ho, Er and Tm)

The crystal and magnetic structures in R 2Ni1.78In (R = Ho, Er and Tm) have been studied by neutron diffraction. The compounds crystallize in a tetragonal crystal structure of the Mo2FeB2 type (space group P4/mbm). At low temperatures, the magnetic moments, localized solely on the rare earth atoms, form antiferromagnetic structures described by the propagation vector k = [kx , kx , ½], with kx equal to ¼ for R = Er and Tm or 0.3074 (4) for R = Ho. The magnetic moments are parallel to the c axis for R = Ho or lie within the (001) plane for R = Er and Tm. The obtained magnetic structures are discussed on the basis of symmetry analysis. The rare earth magnetic moments, determined from neutron diffraction data collected at 1.6 K, are 6.5 (1) μB (Er) and 6.09 (4) μB (Tm), while in the incommensurate modulated magnetic structure in Ho2Ni1.78In the amplitude of modulation of the Ho magnetic moment is 7.93 (8) μB. All these values are smaller than those expected for the respective free R 3+ ions. A symmetry analysis of the magnetic structure in Tb2Ni1.78In is also included, as such information is missing from the original paper [Szytuła, Baran, Hoser, Kalychak, Penc & Tyvanchuk (2013). Acta Phys. Pol. A, 124, 994–997]. In addition, the results of magnetometric measurements are reported for Tm2Ni1.78In. The compound shows antiferromagnetic ordering below the Néel temperature of 4.5 K. Its magnetic properties are found to originate from magnetic moments localized solely on the thulium atoms (the nickel atoms remain non-magnetic in Tm2Ni1.78In). The reduction of rare earth magnetic moments in the ordered state in R 2Ni1.78In (R = Tb, Ho, Er and Tm) and the change in direction of the moments indicate the influence of the crystalline electric field (CEF) on the stability of the magnetic order in the investigated compounds.

Magnetism and topology in Tb-based icosahedral quasicrystal

Quasicrystal (QC) possesses a unique lattice structure with rotational symmetry forbidden in conventional crystals. The electric property is far from complete understanding and it has been a long-standing issue whether the magnetic long-range order is realized in the QC. The main difficulty was lack of microscopic theory to analyze the effect of the crystalline electric field (CEF) at the rare-earth atom in QCs. Here we show the full microscopic analysis of the CEF in Tb-based QCs. We find that magnetic anisotropy arising from the CEF plays a key role in realizing unique magnetic textures on the icosahedron whose vertices Tb atoms are located at. Our analysis of the minimal model based on the magnetic anisotropy suggests that the long-range order of the hedgehog characterized by the topological charge of one is stabilized in the Tb-based QC. We also find that the whirling-moment state is characterized by unusually large topological charge of three. The magnetic textures as well as the topological states are shown to be switched by controlling compositions of the non-rare-earth elements in the ternary compounds. Our model is useful to understand the magnetism as well as the topological property in the rare-earth-based QCs and approximant crystals.

Complex magnetic properties associated with competing local and itinerant magnetism in $${\text {Pr}}_2 {\text {Co}}_{0.86} {\text {Si}}_{2.88}$$

Ternary intermetallic compound $${\text {Pr}}_2 {\text {Co}}_{0.86} {\text {Si}}_{2.88}$$ Pr 2 Co 0.86 Si 2.88 has been synthesized in single phase and characterized by x-ray diffraction, scanning electron microscopy with energy dispersive x-ray spectroscopy (SEM-EDX) analysis, magnetization, heat capacity, neutron diffraction and muon spin rotation/relaxation ($$\mu$$ μ SR) measurements. The polycrystalline compound was synthesized in single phase by introducing necessary vacancies in Co/Si sites. Magnetic, heat capacity, and zero-field neutron diffraction studies reveal that the system undergoes magnetic transition below $$\sim$$ ∼ 4 K. Neutron diffraction measurement further reveals that the magnetic ordering is antiferromagnetic in nature with an weak ordered moment. The high temperature magnetic phase has been attributed to glassy in nature consisting of ferromagnetic clusters of itinerant (3d) Co moments as evident by the development of internal field in zero-field $$\mu$$ μ SR below 50 K. The density-functional theory (DFT) calculations suggest that the low temperature magnetic transition is associated with antiferromagnetic coupling between Pr 4f and Co 3d spins. Pr moments show spin fluctuation along with unconventional orbital moment quenching due to crystal field. The evolution of the symmetry and the crystalline electric field environment of Pr-ions are also studied and compared theoretically between the elemental Pr and when it is coupled with other elements such as Co. The localized moment of Pr 4f and itinerant moment of Co 3d compete with each other below $$\sim$$ ∼ 20 K resulting in an unusual temperature dependence of magnetic coercivity in the system.

Physics of Spin-Orbit-Coupled Oxides

Prior to 2010, most research on the physics and chemistry of transition metal oxides was dominated by compounds of the 3d-transition elements such as Cr, Mn, Fe, Co, Ni, and Cu. These materials exhibited novel, important phenomena that include giant magnetoresistance in manganites, as well as high-temperature superconductivity in doped La2CuO4 and related cuprates. The discovery in 1994 of an exotic superconducting state in Sr2RuO4 shifted some interest toward ruthenates. Moreover, the realization in 2008 that a novel variant of the classic Mott metal-insulator transition was at play in Sr2IrO4 provided the impetus for a burgeoning group of studies of the influence of strong spin-orbit interactions in “heavy” (4d- and 5d-) transition-element oxides. This book reviews recent experimental and theoretical evidence that the physical and structural properties of 4d- and 5d-oxides are decisively influenced by strong spin-orbit interactions that compete or collaborate with comparable Coulomb, magnetic exchange, and crystalline electric field interactions. The combined effect leads to unusual ground states and magnetic frustration that are unique to this class of materials. Novel couplings between the orbital/lattice and spin degrees of freedom, which lead to unusual types of magnetic order and other exotic phenomena, challenge current theoretical models. Of particular interest are recent investigations of iridates and ruthenates focusing on strong spin-orbit interactions that couple the lattice and spin degrees of freedom.

Lattice-Driven Ruthenates

Ruthenates have extended 4d-electron orbitals and comparable Coulomb, crystalline electric field, and spin-orbit interactions, as well as significant p-d orbital hybridization and spin-lattice coupling. The physical properties of ruthenates are highly susceptible to even slight lattice distortions; as a result, external magnetic field, pressure, electrical current, and chemical doping can generate disproportionate responses in structural as well as other physical properties, which can lead to unusual ground states or phenomena. Examples of the unusual, strong coupling of the ruthenates to external stimuli include negative volume thermal expansion via orbital and magnetic order in doped Ca2RuO4, colossal magnetoresistivity via avoiding a spin-polarized state and quantum oscillations in Ca3Ru2O7, and pressure-induced transition from ferromagnetism to antiferromagnetism in Sr4Ru3O10.