Electric-field switchable magnetization via the Dzyaloshinskii-Moriya interaction: FeTiO_3 versus BiFeO_3

In this article we review and discuss a mechanism for coupling between electric polarization and magnetization that can ultimately lead to electric-field switchable magnetization. The basic idea is that a ferroelectric distortion in an antiferromagnetic material can "switch on" the Dzyaloshinskii-Moriya interaction which leads to a canting of the antiferromagnetic sublattice magnetizations, and thus to a net magnetization. This magnetization M is coupled to the polarization P via a trilinear free energy contribution of the form P(M x L), where L is the antiferromagnetic order parameter. In particular, we discuss why such an invariant is present in R3c FeTiO_3 but not in the isostructural multiferroic BiFeO_3. Finally, we construct symmetry groups that in general allow for this kind of ferroelectrically-induced weak ferromagnetism.Comment: 15 pages, 3 images, to appear in J. Phys: Condens. Matter Focus Issue on Multiferroic

Molecular formations in ultracold mixtures of interacting and noninteracting atomic gases

Atom-molecule equilibrium for molecular formation processes is discussed for boson-fermion, fermion-fermion, and boson-boson mixtures of ultracold atomic gases in the framework of quasichemical equilibrium theory. After presentation of the general formulation, zero-temperature phase diagrams of the atom-molecule equilibrium states are calculated analytically; molecular, mixed, and dissociated phases are shown to appear for the change of the binding energy of the molecules. The temperature dependences of the atom or molecule densities are calculated numerically, and finite-temperature phase structures are obtained of the atom-molecule equilibrium in the mixtures. The transition temperatures of the atom or molecule Bose-Einstein condensations are also evaluated from these results. Quantum-statistical deviations of the law of mass action in atom-molecule equilibrium, which should be satisfied in mixtures of classical Maxwell-Boltzmann gases, are calculated, and the difference in the different types of quantum-statistical effects is clarified. Mean-field calculations with interparticle interactions (atom-atom, atom-molecule, and molecule-molecule) are formulated, where interaction effects are found to give the linear density-dependent term in the effective molecular binding energies. This method is applied to calculations of zero-temperature phase diagrams, where new phases with coexisting local-equilibrium states are shown to appear in the case of strongly repulsive interactions.Comment: 35 pages, 14 figure

Symmetry of Magnetically Ordered Quasicrystals

The notion of magnetic symmetry is reexamined in light of the recent observation of long range magnetic order in icosahedral quasicrystals [Charrier et al., Phys. Rev. Lett. 78, 4637 (1997)]. The relation between the symmetry of a magnetically-ordered (periodic or quasiperiodic) crystal, given in terms of a ``spin space group,'' and its neutron diffraction diagram is established. In doing so, an outline of a symmetry classification scheme for magnetically ordered quasiperiodic crystals is provided. Predictions are given for the expected diffraction patterns of magnetically ordered icosahedral crystals, provided their symmetry is well described by icosahedral spin space groups.Comment: 5 pages. Accepted for publication in Phys. Rev. Letter

What is Minimal Model of 3He Adsorbed on Graphite? -Importance of Density Fluctuations in 4/7 Registered Solid -

We show theoretically that the second layer of 3He adsorbed on graphite and solidified at 4/7 of the first-layer density is close to the fluid-solid boundary with substantial density fluctuations on the third layer. The solid shows a translational symmetry breaking as in charge-ordered insulators of electronic systems. We construct a minimal model beyond the multiple-exchange Heisenberg model. An unexpectedly large magnetic field required for the measured saturation of magnetization is well explained by the density fluctuations. The emergence of quantum spin liquid is understood from the same mechanism as in the Hubbard model and in \kappa-(ET)_2Cu_2(CN)_3 near the Mott transitions.Comment: 9 pages, 5 figure

New Symmetries in Crystals and Handed Structures

For over a century, the structure of materials has been described by a combination of rotations, rotation-inversions and translational symmetries. By recognizing the reversal of static structural rotations between clockwise and counterclockwise directions as a distinct symmetry operation, here we show that there are many more structural symmetries than are currently recognized in right- or left-handed handed helices, spirals, and in antidistorted structures composed equally of rotations of both handedness. For example, though a helix or spiral cannot possess conventional mirror or inversion symmetries, they can possess them in combination with the rotation reversal symmetry. Similarly, we show that many antidistorted perovskites possess twice the number of symmetry elements as conventionally identified. These new symmetries predict new forms for "roto" properties that relate to static rotations, such as rotoelectricity, piezorotation, and rotomagnetism. They also enable symmetry-based search for new phenomena, such as multiferroicity involving a coupling of spins, electric polarization and static rotations. This work is relevant to structure-property relationships in all material structures with static rotations such as minerals, polymers, proteins, and engineered structures.Comment: 15 Pages, 4 figures, 3 Tables; Fig. 2b has error

Periodic Vortex Structures in Superfluid 3He-A

We discuss the general properties of periodic vortex arrangements in rotating superfluids. The different possible structures are classified according to the symmetry space-groups and the circulation number. We calculate numerically several types of vortex structures in superfluid 3He-A. The calculations are done in the Ginzburg-Landau region, but the method is applicable at all temperatures. A phase diagram of vortices is constructed in the plane formed by the magnetic field and the rotation velocity. The characteristics of the six equilibrium vortex solutions are discussed. One of these, the locked vortex 3, has not been considered in the literature before. The vortex sheet forms the equilibrium state of rotating 3He-A at rotation velocities exceeding 2.6 rad/s. The results are in qualitative agreement with experiments.Comment: 13 pages, 7 figures, http://boojum.hut.fi/research/theory/diagram.htm

Spontaneous Magnetization of the O(3) Ferromagnet at Low Temperatures

We investigate the low-temperature behavior of ferromagnets with a spontaneously broken symmetry O(3) $\to$ O(2). The analysis is performed within the perspective of nonrelativistic effective Lagrangians, where the dynamics of the system is formulated in terms of Goldstone bosons. Unlike in a Lorentz-invariant framework (chiral perturbation theory), where loop graphs are suppressed by two powers of momentum, loops involving ferromagnetic spin waves are suppressed by three momentum powers. The leading coefficients of the low-temperature expansion for the partition function are calculated up to order $p^{10}$. In agreement with Dyson's pioneering microscopic analysis of the cubic ferromagnet, we find that, in the spontaneous magnetization, the magnon-magnon interaction starts manifesting itself only at order $T^4$. The striking difference with respect to the low-temperature properties of the O(3) antiferromagnet is discussed from a unified point of view, relying on the effective Lagrangian technique.Comment: 23 pages, 4 figure

The Free Energy of the Quantum Heisenberg Ferromagnet at Large Spin

We consider the spin-S ferromagnetic Heisenberg model in three dimensions, in the absence of an external field. Spin wave theory suggests that in a suitable temperature regime the system behaves effectively as a system of non-interacting bosons (magnons). We prove this fact at the level of the specific free energy: if $S \to \infty$ and the inverse temperature $\beta \to 0$ in such a way that $\beta S$ stays constant, we rigorously show that the free energy per unit volume converges to the one suggested by spin wave theory. The proof is based on the localization of the system in small boxes and on upper and lower bounds on the local free energy, and it also provides explicit error bounds on the remainder.Comment: 11 pages, pdfLate