Origin of Magnetic Anisotropy of Gd Metal

Colarieti-Tosti, Massimiliano; Simak, Sergei I.; Ahuja, Rajeev; Nordström, Lars; Eriksson, Olle; Åberg, Daniel; Edvardsson, Sverker; Brooks, M. S. S.

doi:10.1103/physrevlett.91.157201

Cited by 82 publications

(76 citation statements)

References 37 publications

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“…To obtain knowledge on the mechanism of the b-axis anisotropy, further analysis is required by considering the anisotropy of the conduction electrons due to the spin-orbit interaction, which interacts with the 4f electrons of Gd, as well as the dipole-dipole interaction between the Gd spins. 34) The modification of the cycloidal structure with ϕ = ±0.4π from the ideal one with ϕ = ±π/2 is associated with the non-Bravais lattice of the Gd atoms. Since there is an intersite interaction between the magnetic moments at Gd-1 and Gd-2 sites, the perfect cycloid that should be realized in a single Bravais lattice is modified.…”

Section: Discussionmentioning

confidence: 99%

Temperature-Dependent Cycloidal Magnetic Structure in GdRu₂Al₁₀Studied by Resonant X-ray Diffraction

et al. 2017

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We have performed resonant X-ray diffraction experiments on the antiferromagnet GdRu2Al10 and have clarified that the magnetic structure in the ordered state is cycloidal with the moments lying in the bc plane and propagating along the b axis. The propagation vector shows a similar temperature dependence to the magnetic order parameter, which can be interpreted as being associated with the gap opening in the conduction band and the resultant change in the magnetic exchange interaction. Although the S = 7/2 state of Gd is almost isotropic, the moments show slight preferential ordering along the b axis. The c axis component in the cycloid develops with decreasing temperature through a tiny transition in the ordered phase. We also show that the scattering involves the σ-σ ′ process, which is forbidden in normal E1-E1 resonance of magnetic dipole origin. We discuss the possibility of the E1-E2 resonance originating from a toroidal moment due to the lack of inversion symmetry at the Gd site. The spin-flop transition in a magnetic field is also described in detail.

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Section: Discussionmentioning

confidence: 99%

Temperature-Dependent Cycloidal Magnetic Structure in GdRu₂Al₁₀Studied by Resonant X-ray Diffraction

et al. 2017

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“…This sampling problem severely limits the efficiency and accuracy of ab-initio calculations for many properties. Examples of such difficulties abound even in the recent literature, and include the magnetocrystalline anisotropy of ferromagnets 4 and optical absorption in hot liquid metals, 5 to name just a few. In this paper we describe a widely-applicable WFbased scheme for interpolating both the energy bands E nk and the matrix elements F nm (k).…”

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confidence: 99%

Spectral and Fermi surface properties from Wannier interpolation

et al. 2007

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We present an efficient first-principles approach for calculating Fermi surface averages and spectral properties of solids, and use it to compute the low-field Hall coefficient of several cubic metals and the magnetic circular dichroism of iron. The first step is to perform a conventional first-principles calculation and store the low-lying Bloch functions evaluated on a uniform grid of k-points in the Brillouin zone. We then map those states onto a set of maximally-localized Wannier functions, and evaluate the matrix elements of the Hamiltonian and the other needed operators between the Wannier orbitals, thus setting up an "exact tight-binding model." In this compact representation the k-space quantities are evaluated inexpensively using a generalized Slater-Koster interpolation. Because of the strong localization of the Wannier orbitals in real space, the smoothness and accuracy of the k-space interpolation increases rapidly with the number of grid points originally used to construct the Wannier functions. This allows k-space integrals to be performed with ab-initio accuracy at low cost. In the Wannier representation, band gradients, effective masses, and other k-derivatives needed for transport and optical coefficients can be evaluated analytically, producing numerically stable results even at band crossings and near weak avoided crossings.

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“…1. Such a situation is known in many magnetic systems [17]. Let us now examine the consequences of the spin-orbit coupling for the vortices of S 1 → S 1 map.…”

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Fractional-Flux Vortices and Spin Superfluidity in Triplet Superconductors

Babaev

2005

Phys. Rev. Lett.

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We discuss a novel type of fractional flux vortices along with integer flux vortices in KosterlitzThouless transitions in a triplet superconductor. We show that under certain conditions a spintriplet superconductor should exhibit a novel state of spin superfluidity without superconductivity.Superconductors with triplet pairing allow for a rich variety of topological defects and phase transitions [1,2,3,4,5,6]. For example in p-wave superconductors there exist different realizations of fractional vortices such as: the half-quantum vortex (the Alice string), which is a vortex where phase changes by π and spin is reversed when we go around the vortex core, fractional vortices trapped on a grain boundary, fractional flux trapped by twisted wire and other possibilities (for an excellent review see [1,2]). Another subject which was intensively studied is the split phase transitions in triplet systems (e.g. in the presence of disorder or magnetic field) [2,4,5]. There have also been particularly interesting studies of split transitions in a neutral p-wave superfluid in connection with thin films of liquid 3 He [7,8]. Also the related questions of various partial symmetry breakdowns are relevant and were studied in spin-1 Bose condensates in optical traps [9] and bilayer Quantum Hall systems [10]. In this Letter we discuss the effect of flux fractionalization due to spin-orbit coupling, as well as the appearance of neutral vortices in triplet superconductors and discuss its influence on the Kosterlitz-Thouless (KT) transitions. Based on topological arguments we predict the existence of a novel type of ordering in spin-triplet system -the spin-superfluid nonsuperconducting state.We consider a model spin triplet superconductor similar to one considered in [5] with order parameter Ψ a (r) = √ n(x)ζ a (x) where (a = 1, 0, −1) and ζ is a normalized spinor ζ † · ζ = 1. If one neglects mixed gradient terms, the free energy density can be written as [5,6,11,12]:

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Origin of Magnetic Anisotropy of Gd Metal

Cited by 82 publications

References 37 publications

Temperature-Dependent Cycloidal Magnetic Structure in GdRu₂Al₁₀Studied by Resonant X-ray Diffraction

Temperature-Dependent Cycloidal Magnetic Structure in GdRu₂Al₁₀Studied by Resonant X-ray Diffraction

Spectral and Fermi surface properties from Wannier interpolation

Fractional-Flux Vortices and Spin Superfluidity in Triplet Superconductors

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Origin of Magnetic Anisotropy of Gd Metal

Cited by 82 publications

References 37 publications

Temperature-Dependent Cycloidal Magnetic Structure in GdRu2Al10Studied by Resonant X-ray Diffraction

Temperature-Dependent Cycloidal Magnetic Structure in GdRu2Al10Studied by Resonant X-ray Diffraction

Spectral and Fermi surface properties from Wannier interpolation

Fractional-Flux Vortices and Spin Superfluidity in Triplet Superconductors

Contact Info

Product

Resources

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Temperature-Dependent Cycloidal Magnetic Structure in GdRu₂Al₁₀Studied by Resonant X-ray Diffraction

Temperature-Dependent Cycloidal Magnetic Structure in GdRu₂Al₁₀Studied by Resonant X-ray Diffraction