We find possible superconducting states for tetrahedral (T h ) symmetry crystals with strong spinorbit 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 T h .
It is shown that a k = 0, A2u distortion of the terbium tetrahedral network in Tb2Ti2O7 causes the apparent isolation of single tetrahedra as seen in neutron scattering studies. Single tetrahedron collective spin states, rather than individual spins, account for the main features of the spin liquid state, namely, fluctuating local moments and the absence of long range order. Singlet and doublet collective spin ground states are considered. An effective interaction between tetrahedra on the fcc lattice is derived and found to be weak and anisotropic.PACS numbers: 75.10. Jm, 75.25.+z Tb 2 Ti 2 O 7 is an example of three dimensional geometric frustration because the magnetic Tb 3+ ions are arranged on a corner-sharing tetrahedral network. It has a spin liquid phase, characterised by the absence of long range correlations and rapidly fluctuating local magnetic moments, which persists down to at least 50 mK. 1,2This article is devoted to another mysterious feature of Tb 2 Ti 2 O 7 , namely the apparent isolation of single tetrahedra from the tetrahedral network. Such isolation is suggested by neutron scattering experiments, which find that magnetic correlations beyond the size of a single tetrahedron are absent, 1 and exact calculations of spin eigenstates on single tetrahedra reproduce well diffuse neutron scattering patterns. 4,5A reasonable description of the exchange interaction across the four Tb sites on a single tetrahedron in Tb 2 Ti 2 O 7 has been obtained only recently.4,5 The crystal electric field (CEF) ground state of the Tb ions is a doublet, giving rise to a classical picture of Ising-like spins constrained to point into or out of the four vertices of the tetrahedron. However, mixing with higher CEF levels tends to restore transverse spin components, negating the classical picture. The resulting ground state resembles neither the ferromagnetic "spin ice" states, which have two spins pointing inside the tetrahedron and two pointing out, nor the anti-ferromagnetic "all-in or allout" states. Instead it is a linear combination of various states and with no classical analogue.The issue of how to deal with the entire tetrahedral network, and why the single tetrahedron picture is valid, remains an outstanding problem. Because of the connectivity of the tetrahedral network, eigenstates of a single tetrahedron are not in general eigenstates of the entire tetrahedral network. This article offers a solution to this paradox, which involves symmetry breaking in the form of a lattice distortion.Lattice distortions are often invoked in theory as a way to relieve geometrical frustration and arrive at an ordered state, 6 and usually these involve a change of the crystal system, for example, from cubic to tetragonal. In fact, there is evidence that such a transition occurs in Tb 2 Ti 2 O 7 below any accessible temperature.7 In this article, we propose another kind of lattice distortion, one which lowers the point group symmetry but leaves the crystal system unchanged. This distortion does not remove the frustration c...
We consider the possibility that the discrete long-range ordered states of Er2Ti2O7 are selected energetically at the mean field level as an alternative scenario that suggests selection via thermal fluctuations. We show that nearest neighbour exchange interactions alone are not sufficient for this purpose, but that anisotropies arising from excited single ion crystal field states in Er2Ti2O7, together with appropriate anisotropic exchange interactions, can produce the required long range order. However, the effect of the single ion anisotropies is rather weak so we expect thermal or quantum fluctuations, in some guise, to be ultimately important in this material. We reproduce recent experimental results for the variation of magnetic Bragg peak intensities as a function of magnetic field. arXiv:0810.2483v2 [cond-mat.stat-mech]
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 of materials 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 twofold degenerate mode with E(u) symmetry and that motions of the O ions forming the O octahedra dominate the energetics of the transition.
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.Comment: 5 pages. Submitted to J. Phys. Soc. Jpn. Best quality figures are available at http://www.physics.mun.ca/~isergien/pubs.htm
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