Session P24: 3D Frustrated Spin Systems: Pyrochlores and Novel Geometries

Quantum and classical phases of the pyrochlore Heisenberg model with competing interactions

We investigate the Heisenberg model on the pyrochlore lattice for a generic spin-S in the presence of nearest-neighbor J1 and second-nearest-neighbor J2 interactions. Employing the pseudofermion functional renormalization group method we find, for S=1/2 and S=1, an extended quantum spin liquid phase centred around J2=0. At J2=0, the paramagnetic character of this phase is found to be robust against the introduction of breathing anisotropy. The J1-J2 model is shown to host seven different classical magnetic orders, which are also found in the low-spin regime, with no new magnetic orders being stabilized by quantum fluctuations. As a ``material application'', we investigate the low-temperature physics of NaCaNi2F7, a recently synthesized S=1 quantum spin liquid candidate material. Using density functional theory, we find that the compound is well described by a J1-J2 (both antiferromagnetic) Heisenberg model, with J2/J1=0.02, which securely places it deep inside the putative quantum spin liquid phase. A PFFRG analysis of the model Hamiltonian of NaCaNi2F7 reveals paramagnetic behavior down to a temperature of at least T=|\Theta_{\rm CW}|/100, in agreement with the experimental findings, and pointing to a first potential realization of a S=1 quantum spin liquid in three dimensions.   

The spin-1/2 Heisenberg antiferromagnet on the pyrochlore lattice: An exact diagonalisation study

We present exact diagonalisation calculations for the spin-1/2 nearest neighbour
antiferromagnet on the pyrochlore lattice. We study a section of the lattice in the
$[111]$ direction and analyse the Hamiltonian of the breathing pyrochlore system
with two coupling constants $J_1$ and $J_2$ for tetrahedra of different orientation
and investigate the evolution of the system from the limit of disconnected tetrahedra
($J_2 = 0$) to a correlated state at $J_1=J_2$. We evaluate the low energy spectrum,
two and four spin correlations, and spin chirality correlations for a system size of up to
36 sites. The model shows a fast decay of spin correlations and we confirm the presence
of several singlet excitations below the lowest magnetic excitation. We find chirality
correlations near $J_1=J_2$ to be small at the length scales available at this system size.
Evaluation of dimer-dimer correlations and analysis of the nature of the entanglement of
the tetrahedral unit shows that the triplet sector of the tetrahedron contributes significantly
to the ground state entanglement at $J_1 = J_2$.

Reference : V. R. Chandra and J. Sahoo, arXiv:1710.11316   

Competing orders in the spin-one pyrochlore lattice antiferromagnet

We study the physics of the spin-one local moments with a generic interacting spin model on a pyrochlore lattice. We develop a flavor wave theory and combine with a mean-field approach to study the global phase diagram of this model and establish the relation between different phases in the phase diagram. We find the regime of the quantum paramagnetic phase where a degenerate line of the magnetic excitations emerges in the momentum space. We further predict the critical properties of the transition out of the quantum paramagnet to the proximate orders. The presence of quantum order by disorder in the part of the ordered phases is then suggested. We discuss the potential relevance to the fluoride pyrochlore NaCaNi₂F₇ and comment on the role of the spin-orbit coupling in the Ru-based pyrochlore A₂Ru₂O₇, and the Mo-based pyrochlore A₂Mo₂O₇.   

Non-equilibrium control of the effective free energy landscape in a frustrated magnet

Geometrically frustrated magnets often possess accidentally degenerate ground states at zero temperature. At low temperature, thermal fluctuations lift the accidental degeneracy and tend to stabilize ground states with maximal entropy. This phenomenon, known as “order by disorder”, underlines the fluctuation contribution to the free energy landscape in frustrated magnets.

In this talk, I show that one can control such free energy landscape in a non-equilibrium setting [1]. In a frustrated magnet with precessional dynamics, the system’s slow drift motion within the degenerate ground state manifold is governed by the fast modes out of the manifold [2]. Exciting these fast modes can generate a tuneable effective free energy landscape with minima located at thermodynamically unstable portions of the ground state manifold. I demonstrate this phenomenon in pyrochlore XY antiferromagnet, whose effective free energy landscape can be controlled straightforwardly with a magnetic field pulse.

[1] Yuan Wan and Roderich Moessner, Phys. Rev. Lett. 119, 167203 (2017).
[2] Benoit Douçot and Pascal Simon, J. Phys. A: Math. Gen. 31 5855 (1998).   

Single Crystal Growth and Magnetic/Thermal Characterization of Breathing Pyrochlores

Breathing Pyrochlore (BP) has recently become one of the most popular spin frustrated systems, due to its alternating array of different size tetrahedra, which results in breaking inversion symmetry of the lattice sites. Despite great interests, very few real-world BP systems have been reported. Moreover, so far all the reported compounds have been limited to powder samples. Similar to conventional pyrochlore systems, having access to single crystal samples of BP would play a key role in understanding the underlying physics of frustrated magnetism and associated exotic phases. To that end, recently we have successfully grown large high quality single crystals of two different classes of BP systems. In this talk we present the modified and improved floating zone furnace technique developed, and discuss the magnetic and thermal characterization results for single crystals of BP compounds Ba3Yb2Zn5O11 and LiGaCr4O8.   

Investigation of Vibron Bound State in Tb2Ti2O7

After the discovery that the rare earth pyrochore Tb₂Ti₂O₇ supports a cooperative paramagnetic phase down to 50 mK, its ground state remains controversial as antiferromagnetic order was expected from pure spin models. An effect that might contribute greatly to the Hamiltonian is the presence of strong magnetoelastic coupling. Various couplings have been identified in the excitation spectrum of Tb₂Ti₂O₇, including a coupling between the first crystal field excitation (CEF1) and acoustic phonons. In some cerium-based intermetallics, coupling between crystal field excitations and optical phonons produces vibrational bound states or vibrons. A similar vibron formed by the coupling of the third crystal field level (CEF3) and an optical phonon was proposed in Tb₂Ti₂O₇ on the basis of inelastic neutron scattering (INS) experiments. Three distinct peaks are visible, the temperature dependence for which distinguishes the CEF3 from two magnetoelastic optic modes (MEOMs) derived from the optical phonon. We present a detailed investigation of vibron modes in a single crystal of Tb₂Ti₂O₇ using polarized and field dependent INS, which clearly demonstrate the presence of the phonon and the tuning of the coupling by modifying the quadrupolar matrix element of the crystal field transition.

  

Micro-eV neutron spectroscopy in Pr2Zr2O7

Low spin pyrochlores where exchange interactions prevail over dipole-dipole interactions can have substantial quantum fluctuations and perhaps realize quantum spin ice [1-2] with emergent electrodynamics [3]. We have conducted ultra-high-resolution neutron scattering experiment to study the low energy excitation in the quantum spin ice candidate Pr₂Zr₂O₇. The floating zone synthesis procedure was optimized to achieve stoichiometric single crystals with high quality. The local (Q-averaged) response function was mapped versus temperature and energy with a resolution of 3.7 μeV. We observed low energy excitations and a gapless spectrum with temperature dependence into the mK regime that links it to the low temperature thermodynamic properties of Pr₂Zr₂O₇. [1] K. A. Ross et al., Phys. Rev. X 1 (2011) 021002. [2] K. Kimura et al., Nat. Commun. 4 (2013) 1934. [3] M. Hermele et al., Phys. Rev. B 69 (2004) 064404.   

Magnon triple points, topological transitions, and thermal Hall effect in pyrochlore iridates

Triple points, triply degenerate band crossings, have been recently identified as new types of fermions realized in electronic systems. We present a bosonic analog of a triple point topological semimetal. We theoretically show that such triple points can arise in the magnon band structure of pyrochlore iridates with the all-in-all-out antiferromagnetic order. By controlling the strength of Dzyaloshinskii- Moriya (DM) interaction in our spin model, we find three distinct regimes of magnon band topology, distinguished by different configurations of triple points in the Brillouin zone. We calculate the thermal Hall effect as an experimental probe of the magnon band topology of pyrochlore iridates. We find that the three regimes exhibit qualitatively different patterns of magnon thermal Hall effect. Particularly, in a regime relevant for real materials, the system shows a characteristic thermal Hall response that can be used to estimate the size of the DM interaction in experiments.   

Partial Order in Fe3PO4O3

The magnetic frustration brought about by triangular motifs and competing antiferromagnetic interactions in Fe₃PO₄O₃ (spacegroup R3m) have been shown to lead to an unusual magnetic state below T_N = 163 K. Below T_N, antiferromagnetic order is restricted to nanosized needle-like domains oriented along the c-axis, with the correlation length restricted to ξ= 7nm in the ab plane. Here we present single crystal neutron diffraction results, which reveal that this state does not select a preferred ordering wavevector in the ab plane, resulting in continuous rings of scattering rather than well-defined satellite Bragg peaks. The lack of a preferred incommensurate ordering wavevector can be understood in terms of the competition between J₁ (nearest neighbor) and J₂ (next nearest neighbor) interactions in a Heisenberg model, which produces a quasi-degenerate manifold of ordering wavevectors. The inability to form long range coherent structure remains unexplained, however the restriction to small domain sizes in the ab plane implies the presence of a high density of topological defects. Determining the nature of these defects and the mechanism of their formation is an avenue for further research.   

Utilizing Torque Magnetometry to Measure Thin Films of Frustrated Magnets

Capacitive torque magnetometry was used to investigate the effects of strain on the magnetic properties of thin films of pyrochlore titanates. Films with thicknesses ranging from 35 to 200 nm have been measured as a function of temperature and applied field. Sample rotation allowed application of field along various crystallographic directions of the sample. Equivalent measurements on titanate single crystals have been performed to directly compare the effects of strain in a systematic manner. The responses found in the temperature range from 20 mK to 1 K have been compared with measurements done in a Quantum Design MPMS at 1.8 K. An explicit angular dependence has been observed in both thin films and single crystals, indicating the richness of the anisotropy within these systems. This experiment demonstrates the versatility in the usage of torque magnetometry as a method for probing magnetocrystalline anisotropy in strained thin films of frustrated magnetic systems.   

Inelastic neutron scattering study of molecular multiferroic (ND4)2[FeCl5(D2O)]

(ND₄)₂[FeCl₅(D₂O)] was recently discovered to exhibit magnetically induced multiferroicity. At zero field, the system first undergoes a magnetic long-range order transition to an incommensurate (IC) collinear sinusoidal spin state at T_N=7.3 K, followed by a second transition to an IC cycloidal spin state at T_FE=6.8K accompanied by spontaneous ferroelectric polarization. Applying modest magnetic field along a, or c-axis induces transitions to distinct magnetic and ferroelectric phases. Here we report preliminary inelastic neutron scattering results that reveal the spin dynamic in this molecular multiferroic material.
  

Magnetic structure and excitations of the frustrating perovskite oxide PbCoO3

The perovskite oxide PbBO₃ (B: transition metal) shows interesting charge disproportionation of Pb ions. Very recently, it was found that in PbCoO_3, an unusual charge distribution occurs with charge ordering of both Pb (Pb²⁺/ Pb⁴⁺) and Co (Co²⁺/ Co³⁺).[1] The Co³⁺ and Co²⁺ ions are expected to have the low spin (S=0) and the high spin state (S=3/2), respectively. Magnetic succeptibility and specific heat measurements show a two-step transition at 4 K and 7.8 K. Since the Co²⁺ ions form a pyrochlore lattice, the magnetic states are expected to originate from frustrating interactions. The magnetic structure and excitations of PbCoO₃ were investigated using elastic and inelastic neutron scattering experiments and the magnetic propagation vector was found to be q_m = (0.5, 0.5, 0.5). Possible magnetic structures in the two magnetic phases will be discussed. Inelastic neutron scattering experiments show two magnetic excitations centered at 0.9 meV and 1.55 meV. A possible spin Hamiltonian that explains the neutron scattering data will also be presented. [1] J. Am. Chem. Soc. 2017, 139, 4574−4581