arXiv subjects
Publications and source records attributed to S. H. Curnoe.
Low energy collective angular momentum states of the Tb3+ ions in Tb2Ti2O7 are classified according to the irreducible representations of the octahedral point group. Degeneracy lifting due to the exchange interaction is discussed. Diffuse neutron scattering intensity patterns are calculated for each collective angular momentum state and the ground state is inferred by comparing to experiment.
We examine the superconducting gap nodes in crystals with tetrahedral (T_h) symmetry. The (0,0,1) phase of the three dimensional order parameter in the triplet channel has nodes in the [001] directions. Following a second order phase transition to the state (0,i|eta_2|,|eta_1|), each node lifts away from the Fermi surface and splits into two deep dips. We discuss this scenario in the context of multiple superconducting phases in PrOs4Sb12.
The magnetic phases of hexagonal perovskites RMnO_3 (R=Ho, Er, Tm, Yb, Sc, Y) are analysed using group theory and the Landau theory of phase transitions. The competition between various magnetic order parameters is discussed in the context of antiferromagnetic interactions. A phenomenological model based on four one-dimensional magnetic order parameters is developed and studied numerically. It is shown that coupling of the various order parameters leads to a complex magnetic field-temperature phase diagram and the results are compared to experiment.
We describe the magnetic phases of hexagonal rare earth manganites RMnO3 using Landau theory. A minimal model based on four one-dimensional magnetic order parameters is developed.
In noncentrosymmetric metals, the spin degeneracy of the electronic bands is lifted by spin-orbit coupling. We consider general symmetry properties of the pairing function Delta(k) in noncentrosymmetric superconductors with spin-orbit coupling (NSC), including CePt3Si, UIr and Cd2Re2O7. We find that Delta(k) = chi(k) t(k), where chi(k) is an even function which transforms according to the irreducible representations of the crystallographic point group and t(k) is a model dependent phase factor. We consider tunnelling between a NSC and a conventional superconductor. It is found that, in terms of thermodynamical properties as well as the Josephson effect, the state of NSC resembles a singlet superconducting state with gap function chi(k).
We consider the Landau theory of phase transitions for multiple superconducting phases in T_h crystals. All possible phase transition sequences involving a single superconducting order parameter are found. These results may be applicable to PrOs4Sb12.
All symmetry allowed couplings between the 4f^2-electron ground state doublet of trivalent praseodymium in PrRu4P12 and PrFe4P12 and displacements of the phosphorus, iron or ruthenium ions are considered. Two types of displacements can change the crystal lattice from body-centred cubic to simple orthorhombic or to simple cubic. The first type lowers the point group symmetry from tetrahedral to orthorhombic, while the second type leaves it unchanged, with corresponding space group reductions Im3 --> Pmmm and Im3 --> Pm3 respectively. In former case, the lower point-group symmetry splits the degeneracy of the 4f^2 doublet into states with opposite quadrupole moment, which then leads to anti-quadrupolar ordering, as in PrFe4P12. Either kind of displacement may conspire with nesting of the Fermi surface to cause the metal-insulator or partial metal-insulator transition observed in PrFe4P12 and PrRu4P12. We investigate this scenario using band-structure calculations, and it is found that displacements of the phosphorus ions in PrRu4P12 (with space group reduction Im3 --> Pm3) open a gap everywhere on the Fermi surface.
We find possible superconducting states for tetrahedral (Th) symmetry crystals with strong spin-orbit coupling using Landau theory. Additional symmetry breaking within the superconducting state is considered. We discuss nodes of the gap functions for the different states, secondary superconducting order parameters and coupling to the elastic strain. By comparing our results to experiments, we find that superconductivity in PrOs4Sb12 is best described by the three-dimensional representations of point group Th.
A class of materials known as ``ferroelectric metals'' was discussed theoretically by Anderson and Blount in 1965 [Phys. Rev. Lett. 14, 217 (1965)], but to date no examples of this class have been reported. Here we present measurements of the elastic moduli of Cd2Re2O7 through the 200 K cubic-to-tetragonal phase transition. A Landau analysis of the moduli reveals that the transition is consistent with Cd2Re2O7 being classified as a ``ferroelectric metal'' in the weaker sense described by Anderson and Blount (loss of a center of symmetry). First-principles calculations of the lattice instabilities indicate that the dominant lattice instability corresponds to a two-fold degenerate mode with Eu symmetry, and that motions of the O ions forming the O octahedra dominate the energetics of the transition.
We study domain patterns in cubic-tetragonal ferroelastics by solving numerically equations of motion derived from a Landau model of the phase transition, including dissipative stresses. Our system sizes, of up to 256^3 points, are large enough to reveal many structures observed experimentally. Most patterns found at late stages in the relaxation are multiply banded; all three tetragonal variants appear, but inequivalently. Two of the variants form broad primary bands; the third intrudes into the others to form narrow secondary bands with the hosts. On colliding with walls between the primary variants, the third either terminates or forms a chevron. The multipy banded patterns, with the two domain sizes, the chevrons and the terminations, are seen in the microscopy of zirconia and other cubic-tetragonal ferroelastics. We examine also transient structures obtained much earlier in the relaxation; these show the above features and others also observed in experiment.
We describe the low temperature behaviour of the magnetic susceptibility of Cd2Re2O7 in terms of a Landau theory of structural phase transitions. We calculate the zero temperature Pauli susceptibility using a tight-binding approach to reveal the mechanism of coupling between the structural order parameter and itinerant magnetism.
It is shown that both structural phase transitions in Cd2Re2O7, which occur at T_{s1}=200 K and T_{s2}=120 K, are due to an instability of the Re tetrahedral network with respect to the same doubly degenerate long-wavelength phonon mode. The primary structural order parameter transforms according to the irreducible representation E_u of the point group O_h. We argue that the transition at T_{s1} may be of second order, in accordance with experimental data. We obtain the phase diagram in the space of phenomenological parameters and propose a thermodynamic path that Cd2Re2O7 follows upon cooling. Couplings of the itinerant electronic system and localized spin states in pyrochlores and spinels to atomic displacements are discussed.
We study numerically the time evolution of two-dimensional (2D) domain patterns in proper tetragonal-orthorhombic (T-O) ferroelastics. Our results, found by solving equations of motion derived from classical elasticity theory, disagree with those found by other methods. We study first the growth of the 2D nucleus resulting from homogeneous nucleation events. The later shape of the nucleus is largely independent of how it was nucleated. In soft systems, the nucleus forms a flower-like pattern. In stiff systems, which seem to be more realistic, it forms an X shape with twinned arms in the 110 and \110 directions. Second, we study the relaxation that follows completion of the phase transition; at these times, the T phase has disappeared and both O variants are present, segregated into domains separated by domain walls. We observe a variety of coarsening mechanisms, most of them counterintuitive.
We study the statics and the dynamics of domain patterns in proper hexagonal-orthorhombic ferroelastics; these patterns are of particular interest because they provide a rare physical realization of disclinations in crystals. Both our static and dynamical theories are based entirely on classical, nonlinear elasticity theory; we use the minimal theory consistent with stability, symmetry and ability to explain qualitatively the observed patterns. After scaling, the only parameters of the static theory are a temperature variable and a stiffness variable. For moderate to large stiffness, our static results show nested stars, unnested stars, fans and other nodes, triangular and trapezoidal regions of trapped hexagonal phase, etc observed in electron microscopy of Ta4N and Mg-Cd alloys, and also in lead orthovanadate (which is trigonal-monoclinic); we even find imperfections in some nodes, like those observed. For small stiffness, we find patterns like those observed in the mineral Mg-cordierite. Our dynamical studies of growth and relaxation show the formation of these static patterns, and also transitory structures such as 12-armed bursts, streamers and striations which are also seen experimentally. The major aspects of the growth-relaxation process are quite unlike those in systems with conventional order parameters, for it is inherently nonlocal; for example, the changes from one snapshot to the next are not predictable by inspection.
We derive solutions for the twin wall linking two tetragonal variants of the cubic-tetragonal ferroelastic transformation, including for the first time the dilatational and shear energies and strains. Our solutions satisfy the compatibility relations exactly and are obtained at all temperatures. They require four non-vanishing strains except at the Barsch-Krumhansl temperature TBK (where only the two deviatoric strains are needed). Between the critical temperature and TBK, material in the wall region is dilated, while below TBK it is compressed. In agreement with experiment and more general theory, the twin wall lies in a cubic 110-type plane. We obtain the wall energy numerically as a function of temperature and we derive a simple estimate which agrees well with these values.