Session Q34: Focus Session: Frustrated and Low-D Magnetism -- Spins, Orbitals, and Phonons

Probing spin correlations in the frustrated magnets CdCr$_2$O$_4$ and ZnCr$_2$O$_4$

We performed optical, magnetic susceptibility, and specific heat measurements on CdCr$_2$O$_4$ and ZnCr$_2$O$_4$ single crystals. We estimate the nearest-neighbor and next-nearest neighbor exchange constants from the magnetic susceptibility and extract the spin-spin correlation functions obtained from the magnetic susceptibility and the magnetic contribution to the specific heat. In comparison with the frequency shift of the infrared optical phonons above $T_N$, we can obtain estimates for the spin-phonon coupling in both systems. Moreover, we will discuss optical signatures of the magnetic excitation spectrum which are found to persist up to room temperature in ZnCr$_2$O$_4$.   

Model for frustrated spin-orbital chains: application to CaV2O4

Motivated by recent interest in quasi-one-dimensional compound CaV2O4, we investigate the physics of frustrated vanadium chains in which the interplay of geometrical frustration, spin-orbital couplings, Jahn-Teller effect, and enhanced quantum fluctuations leads to a rich phase diagram. Contrary to its spinel cousins, V ions in CaV2O4 are arranged in zigzag chains of edge-sharing VO6 octahedra. Antiferromagnetic interaction on zigzag chains consisting of triangular loops is subject to geometrical frustration as well. The rather weak and frustrated inter-chain couplings make the vanadium chains quasi-1D systems susceptible to quantum fluctuations. To make progress toward an understanding of the ground-state structure and the nature of phase transitions in CaV2O4, we study the zero-temperature phase diagram of its building blocks, i.e. zigzag chains with S=1 spins and Ising orbital variables. We find that while orbital interaction governed by an Ising-like Hamiltonian favors an antiferro-orbital order, on-site coupling of orbitals to spins and phonons tends to destroy the long-range order. Depending on the underlying orbital configuration, magnetic properties of the zigzag chain is equivalent either to those of two weakly coupled S=1 chains, or of an unfrustrated spin-1 ladder. In the presence of large spin-orbit coupling, the zigzag chain can be viewed as a spin-2 chain with anisotropic interaction.   

Magneto-elastics of a spin liquid: X-ray studies of Tb2Ti2O7 in pulsed magnetic fields

At low temperatures, the pyrochlore antiferromagnet Tb$_2$Ti$_2$O$_7$ exhibits a dynamically short-range ordered magnetic state. No credible evidence for long range order has been reported in the literature down to temperatures as low as 20 mK, despite the fact that the material displays a Curie-Weiss temperature roughly a thousand times larger than this. Intriguingly, under application of magnetic field at these low temperatures the system displays giant magnetostriction (as large as that of the best commercial materials), and a non-trivial long-range ordered magnetic state. Both effects appear to be strongly sensitive to the direction of the applied magnetic field. We have performed high-resolution pulsed-field x-ray scattering measurements, which constitute the first successful experiment commissioning the mini-coil magnet at Argonne National Lab. This new instrument facilitates single crystal x-ray scattering experiments at temperatures as low as 4.5 K, and in applied magnetic fields as large as 30 Tesla. Our measurements reveal rich magnetoelastic effects in the spin liquid pyrochlore terbium titanate.   

Frustration in antiferromagnets and spin liquids

Correlated electronic systems with an additional complexity of a geometrically frustrated lattice provide an exciting ground for the study of several competing interactions among spin, orbital and lattice degrees of freedom. In this talk we shall discuss the role of frustration in prototypical 3D-networks like the spinels ZnV$_2$O$_4$ and MnV$_2$O$_4$ and in 2D-networks like the $\kappa$-(BEDT-TTF)$_2$X family. By performing density functional calculations we analyze the nature of the structural, orbital and magnetic transitions in the Mott insulators ZnV$_2$O$_4$ [1] and MnV$_2$O$_4$ [2] and outline the importance of correlation effects and spin-orbit coupling on the behavior of these systems. The 2D triangular networks described by the $\kappa$-(BEDT-TTF)2X family show a complex phase diagram with magnetic, superconducting, Mott insulating and even spin liquid phases. With extensive density functional theory calculations we refresh the link between many-body theory and experiment by determining hopping parameters of the underlying Hubbard model [3]. This leads us to revise the widely used semi-empirical parameters for these systems in the direction of less frustrated, more anisotropic triangular lattices. The implications of these results on the systems' description will be discussed and comparison to other Mott-Hubbard insulators will be shown. [1] T. Maitra and R. Valenti, Phys. Rev. Lett. {\bf 99}, 126401 (2007). [2] S. Sarkar {\it et al.}, Phys. Rev. Lett. {\bf 102}, 216405 (2009). [3] H. C. Kandpal {\it et al.}, Phys. Rev. Lett. {\bf 103}, 067007 (2009).   

Low energy excitations in multiferroic hexa-YMnO3

In spite of many years of research, hexa-manganites continue to surprise us with their unusual magnetic and lattice properties which includes multiferroicity (antiferromagnetic + ferroelectric). The triangular arrangement of magnetic Mn ions gives rise to a highly frustrated magnetic interactions and allows coupling to the phonons. The recent discovery of a Gamma- point hybrid magnon-lattice mode in h-YMnO3 by polarized inelastic neutron scattering (Pailhes et al, PRB 79, 134409 (2009)) rises a question about the identity of the coupled phonons. To answer that question, we have combine infrared and Raman spectra with symmetry analysis of magnons and phonons.   

Spin-orbital physics for $t_{2g}$ electron in FCC lattice with application to ordered double perovskites

Ordered double perovskites A$_2$BB$'$O$_6$ are derived compounds from the usual perovskites ABO$_3$ by selectively replacing half of the B ions with magnetic ions B$'$ so that the B$'$ ions form an FCC lattice structure with a lattice constant twice the original cubic lattice of the B ions. Motivated by recent experiments on ordered double perovskites, we started from a microscopic nearest neighbor exchange Hamiltonian and relativistic spin-orbit interaction, and analyzed the spin-orbital physics for different regimes of coupling parameters. We found that when the spin-orbit coupling is weak compared to the exchange, the system develops real orbital order and weakly-coupled layered spin order primarily driven by the exchange. When the spin-orbit coupling is strong, we suggested three different candidate ground states. They are ferromagnetic state, complex orbital order with ordering wavevector ${\bf p} = 2\pi(001)$ and the spin-orbital liquid state. Realization of these states in different double perovskites are discussed.   

Spin-lattice interactions through the quantum critical transition in Cu(pyz)(NO$_3$)$_2$

We measured the magneto-infrared response of the quasi-one-dimensional quantum Heisenberg antiferromagnet Cu(pyz)(NO$_3$)$_2$ to investigate local lattice distortions through the field-driven transition to the fully polarized magnetic state. This magnetic quantum critical transition involves changes in the out-of-plane N and C-H bending modes of pyrazine with field that directly track the magnetization. We discuss our results in terms of calculated spin densities, scaling laws, and extracted spin-phonon coupling constants, the latter of which are remarkably large due to the softness of the pyrazine ligand.   

Magneto-elastic properties of frustrated triangular magnetic structure: flexomagnetic effect

We report results of ab-initio calculations on the magneto-elastic properties of the Mn$_{3}$AN (A=Ga, Zn). We show that these materials exhibit rich array of magneto-elastic phenomena, i.e. change in magnetization due to the mechanical deformation of the crystal lattice, - linear piezomagnetic, non-linear magneto-elastic, and linear flexomagnetic effects. These effects are due to the complex symmetry which combines perovskite crystal and the frustrated triangular magnetic structures. We demonstrate from first-principles calculations of the Mn$_{3}$AN that the external strain gradient induces the magnetization in these systems and it depends linearly on the strain gradient. We applied a classical Heisenberg model to simulate the effect of the strain on the frustrated triangular lattice at zero temperature. We assume antiferromagnetic interactions between nearest neighbors. Using Monte Carlo simulation of the triangular lattice we observe the induction of magnetization upon application of strain gradient. Thus, we conclude that the mechanism behind flexomagnetism is the dependence of the exchange interaction on inter-atomic distances. In particular, when external strain gradient is applied these distances become inequivalent, which results in ``out-of-plane'' rotations of local magnetic moments and appearance of net magnetization. We estimate the flexomagnetic coefficient to be $\sim $2$\mu _{B}${\AA}.   

Low-temperature orbital ordering and dynamical frustration of spins in KCuF$_{3 }$: Theoretical model

A prototypical orbital ordering material, the charge transfer insulator KCuF$_{3}$ is believed to undergo orbital ordering at a temperature $T_{OO}$~$\sim $ 800~K. Recent Raman and X-ray measurements reveal a low-temperature structural transition just preceding the onset of three-dimensional magnetic ordering at $T_{N}$~$\sim $ 40~K. We present a model of how orbital, structural and magnetic fluctuations are coupled at temperatures between $T_{OO}$ and $T_{N}$, leading to the dynamical frustration of in-plane spin order. The low-temperature structural transition quenches the orbital fluctuations, stabilising A-type N\'{e}el spin order. A striking implication of our results is that the ground state of KCuF$_{3}$ lies near a quantum critical point associated with an orbital/spin liquid phase that is obscured by emergent N\'{e}el ordering of the spins. This exotic liquid phase might be accessible with the application of pressure.   

Synthesis and characterization of the charge-transfer insulator KCuF$_{3}$

KCuF$_{3}$ is thought to be a prototypical orbital ordering material, with interesting properties that include a highly anistotropic superexchange ratio and one-dimensional spin dynamics down to a very low energy and temperature scale. High-quality single crystals of KCuF$_{3}$---with a typical size of roughly 3.6$\times $3.6$\times $2.5mm$^{3}$---were grown using an aqueous solution precipitation method. Room temperature x-ray powder diffraction measurements using Cu K$_{\alpha }$ radiation showed that the samples consisted of $>$90{\%} volume fractions of polytype a. Temperature-dependent Raman measurements provide evidence for structural instabilities between 50K and 300K in KCuF$_{3}$, including a decrease with decreasing temperatures (``softening'') of several phonon mode frequencies, and phonon mode splitting near 50K consistent with a tetragonal-to-orthorhombic (TO) transition that precedes the N\'{e}el transition at 40K. We argue that the TO structural transition is associated with rigid GdFeO$_{3}$-type rotations of the CuF$_{6}$ octahedra.   

Low-temperature orbital ordering and dynamical frustration of spins in KCuF$_3$: Experimental

We present new Raman and x-ray scattering evidence for the existence of a structural phase transition at 50 K in KCuF$_3$. Phonon modes associated with the F-ions in CuF$_{6}$ octahedra soften with decreasing temperature down to 50 K, at which temperature there is a splitting of the E$_g$ phonon. Above T$_{N}$ = 40 K, diffuse resonant magnetic scattering from critical fluctuations was observed at the Cu L$_{3}$ edge. Below T$_{N}$, orbital reflections seen by 8.8 keV x-ray scattering exhibit diffuse scattering that is hysteretic with temperature, indicating glassy orbital disorder. The phase behavior of KCuF$_{3}$ above T$_{N}$ is dominated by coupled orbital/lattice fluctuations that are likely associated with dynamical rotations of the CuF$_{6}$ octahedra. A model with interactions between orbital, spin and lattice degrees of freedom explain these observations.   

Elastic Order by Disorder in an Ising Antiferromagnet

By exactly calculating the elastic deformations of the anti-ferromagnetic Ising model on a deformable triangular lattice, we show that the ground state, missed in previous studies [1], has a sub-extensive degeneracy with entropy proportional to the square root of the number or sites. A sample configuration can be visualized as randomly zigzagging stripes [2]. We study the low-temperature behavior of the system by calculating the entropic contributions of phonon excitations to the free energy. Examining several fixed spin configurations, we argue that straight stripes are preferred at low temperature. In other words, the disordered ground-state at zero temperature is converted to an ordered striped state at nonzero temperature via thermal phonon fluctuations: a classic order-from-disorder effect. We use Monte Carlo simulations to back up our analytical results and examine the dynamics of relaxation. Because of large energy barriers between the degenerate ground states, the systems first falls into a glassy randomly zigzagging configuration, which then slowly relaxes to the thermodynamically stable straight stripes. [1] Z.Y. Chen and M. Kardar, J. Phys. C: Solid State Phys. {\bf 19}, 6825 (1986). L. Gu {\em et al.}, Phys. Rev. B {\bf 53}, 11985 (1996). [2] Y. Han {\em et al.}, Nature {\bf 456}, 898 (2008). Y. Shokef and T.C. Lubensky, Phys. Rev. Lett. {\bf 102}, 048303 (2009).   

Phonon drag in thermal conductivity of antiferromagnets

We use Boltzmann equation approach to the thermal transport in low-dimensional antiferromagnets with spin-lattice coupling. We consider the limit of fast spin excitations, relevant to many compounds with $J>>\Theta_D$, where $\Theta_D$ is the Debye energy. We discuss the ``off-diagonal'' contribution to the heat current due to the drag of spin excitations on phonons. We calculate this effect for the one-dimensional spin chain materials.