Session C24: 3D Frustrated Spin Systems: Pyrochlores and Spinels

NMR investigation of the rare earth pyrochlore Yb2Pt2O7

Until recently, there have been few NMR experiments on the pyrochlores, as many of the well-studied ones (such as Yb₂Ge₂O₇, Dy₂Ti₂O₇ and Yb₂Mo₂O₇ etc.) contain atoms whose nuclei are not suitable for NMR. Recently, however, platinum based pyrochlores have been synthesized. ¹⁹⁵Pt is an excellent nucleus for NMR as it has a large nuclear gyromagnetic ratio, relatively high abundance, and is nuclear spin ½. We present results from a field dependent NMR study of Yb₂Pt₂O₇, from 0.5 T to 8 T. 1/T₁ exponentially decreases as temperature is decreased from ~20 K to ~2 K in 2T and higher. This indicates that the low frequency spin fluctuations freeze out well before the known zero-field transition to a ferromagnet at ~ 0.3 K. Although 1/T₁ continues to decrease with decreasing temperature in the low field cases (1 T and lower), the freezing out of low frequency spin fluctuations is not nearly as dramatic, or definitively exponential, as in the high field case. We attempt to elucidate the behaviour of the low-frequency spin-fluctuations and how they behave with magnetic field.   

Quantum versus classical effects at zero and finite temperature in the quantum pyrochlore Yb2Ti2O7

We study the finite temperature properties of the candidate quantum spin ice material Yb₂Ti₂O₇ within the framework of an anisotropic nearest-neighbor spin 1/2 model on the pyrochlore lattice. Using finite temperature Lanczos and classical Monte Carlo methods, we highlight the importance of quantum mechanical effects for establishing the existence and location of the low-temperature ordering transition [1]. We perform simulations of the 32 site cluster, which capture the essential features of the specific heat curve seen in the cleanest known samples of this material. Focusing on recent experimental findings, we address the question of how the phase boundary between the ferromagnetic and paramagnetic phases changes when subjected to a magnetic field. Quantum mechanical effects explain discrepancies observed with a completely classical treatment and are at the heart of the observed reentrant lobed phase diagram. We also develop a qualitative understanding of the existence of a ferromagnet by relating it to its counterpart that exists in the vicinity of the classical ice manifold.

[1] HJC, arXiv:1710.02234   

The magnetic excitations in the ground state of Yb2Ti2O7

The nature of the zero-field ground state of Yb₂Ti₂O₇ remains an enigma within the pyrochlore titanate series. The disparate results are attributed to subtle changes in the sample stoichiometry, which seems to tune the delicate magnetic order of different samples across a phase boundary. We report a thorough study on the zero-field ground state of a powder sample of the pyrochlore Yb₂Ti₂O₇ [1]. A sharp, heat capacity anomaly at Tc =280 mK is accompanied by a quasi-collinear ferromagnetic order with a magnetic moment of 0.87(2)μ_B. Our high-resolution inelastic neutron scattering measurements show that, at 10 K, a broad quasielastic paramagnetic scattering dominates the observed energy range. Upon cooling, an inelastic continuum of excitations at ~0.6 meV is observed to persist from at least 2.5 K down to the lowest reached temperatures. Below Tc, the coexistence of sharp gapped low-energy magnetic excitations with a remnant quasielastic contribution evidences that spin fluctuations persist despite the long-range magnetic order.
[1] Viviane Peçanha-Antonio et al., arXiv:1709.01013   

The spinon continuum in pyrochlore ice U(1) spin liquid: spectral periodicity and field evolution

Motivated by the rapid experimental progress of quantum spin ice materials, we study the dynamical properties of pyrochlore spin ice in the U(1) spin liquid phases. In particular, we focus on the spinon excitations that appear at high energies and show up as an excitation continuum in the dynamic spin structure factor. The keen connection between the crystal symmetry fractionalization of the spinons and the spectral periodicity of the spinon continuum is emphasized and explicitly demonstrated. When the spinon experiences a background π flux and the spinon continuum exhibits an enhanced spectral periodicity with a folded Brillouin zone, this spectral property can then be used to detect the spin quantum number fractionalization and U(1) spin liquid. Our prediction can be immediately examined by inelastic neutron scattering experiments among quantum spin ice materials with Kramers' doublets. Further application to the non-Kramers' doublets is discussed. We also discuss the evolution of the spinon continuum under magnetic fields in dipole-octupole doublets.   

What does inelastic neutron scattering measure in pyrochlore ice spin liquids?

We study the U(1) quantum spin liquid on the pyrochlore spin ice systems. For the non-Kramers doublets such as Pr³⁺ and Tb³⁺, we point out that the inelastic neutron scattering not only detects the low-energy gauge photon, but also contains the continuum of the "magnetic monopole" excitations. Unlike the spinons, these "magnetic monopoles" are purely of quantum origin and have no classical analogue. We further point out that the ``magnetic monopole" experiences a background dual π flux due to the spin-1/2 nature of the local moment when the "monopole" hops on the dual diamond lattice. We then predict that the "monopole" continuum has an enhanced spectral periodicity. This prediction can be examined among the existing data on the non-Kramers doublet spin liquid candidate materials like Pr₂TM₂O₇ and Tb₂TM₂O₇ (with TM = "transition metal"). The application to the Kramers doublet systems and numerical simulation is further discussed. Finally, we present a general classification of distinct symmetry enriched U(1) quantum spin liquids based on the translation symmetry fractionalization patterns of "monopoles" and "spinons".   

Rich field dependence of thermal transport in quantum spin ice candidate Yb2Ti2O7

Thermal transport can be a very powerful tool for studying magnetic excitations in frustrated quantum systems. One such system whose excitations are of particular interest is Yb₂Ti₂O₇, a quantum spin ice candidate with a pseudospin-1/2 ground state that should give rise to strong quantum fluctuations. Here, we report field dependent (B ‖〈111〉) longitudinal and transverse thermal conductivity measurements made on a highly stoichiometric crystal of Yb₂Ti₂O₇ over a wide range of temperatures. Our results reveal a rich dependence of both κ_xx and κ_xy on temperature and magnetic field that provides new information about the system’s unconventional excitations. While some features are very reminiscent of previously reported measurements on Tb₂Ti₂O₇, another quantum spin ice candidate, others are quite novel. In particular, at very low temperatures, we observe a large positive thermal hall signal followed by a sign inversion at low fields, but features characteristic of conventional magnons at higher ones. These and other results as well as possible explanations will be discussed.   

Ground State Selection in the XY Pyrochlore Magnet Er2Ti2O7 and its Stability to Chemical Pressure and Quenched Impurities

Er₂Ti₂O₇ is a quantum S_eff=1/2 XY pyrochlore magnet that orders into a non-linear, non-coplanar Néel state below T=1.2 K via ground-state selection proposed to originate from an order-by-disorder mechanism [1,2]. As the ground state selection is relatively weak, it is interesting to examine its stability to perturbations such as magnetic dilution and chemical pressure. Indeed, recent theory strongly suggests rich phase diagrams resulting from such instabilities [3,4,5,6]. Magnetic dilution was achieved by substituting a small fraction of the S_eff=1/2 Er³⁺ ions for non-magnetic Y³⁺ ions; while chemical pressure resulted from the replacement of non-magnetic Ti⁴⁺ ions within the pyrochlore structure by other non-magnetic ions such as Pt⁴⁺. I will discuss our recent experimental results [7,8], with a focus on neutron scattering, where these chemical perturbations demonstrate the richness of the phase space in which XY pyrochlore magnets, such as Er₂Ti₂O₇, reside - a consequence of anisotropic exchange and order-by-disorder effects. [1] L. Savary et al., Phys. Rev. Lett. 109, 167201 (2012), [2] M.E. Zhitomirsky et al., Phys. Rev. Lett. 109, 077204 (2012) [3] Maryasin, V. S., and M.E. Zhitomirsky, Phys. Rev. B 90, 094412 (2014), [4] Andreanov, A., and P. A. McClarty, Phys. Rev. B 91, 064401 (2015), [5] H. Yan et al., Phys. Rev. B 95, 094422 (2017) [6] E.C. Andrade et al., arXiv:1710.06658 (2017), [7] J. Gaudet et al., Phys. Rev. B 94, 060407(R) (2016), [8] A. M. Hallas et al., Phys. Rev. Lett. 119, 187201 (2017)   

Phase Competition in the Palmer-Chalker XY Pyrochlore Er2Pt2O7

We report neutron scattering measurements on Er₂Pt₂O₇, a new addition to the XY family of frustrated pyrochlore magnets. Symmetry analysis of our elastic scattering data shows that Er₂Pt₂O₇ orders into the k = 0, Γ₇ magnetic structure (the Palmer-Chalker state), at 0.38 K. This contrasts with its sister XY pyrochlore antiferromagnets Er₂Ti₂O₇ and Er₂Ge₂O₇, both of which order into Γ₅ magnetic structures at much higher temperatures, 1.2 and 1.4 K, respectively. Below T_N = 0.38 K, Er₂Pt₂O₇ displays a gapped spin-wave spectrum with an intense, flat band of excitations at lower energy and a weak, diffusive band of excitations at higher energy. The flat band is well described by classical spin-wave calculations, but these calculations also predict sharp dispersive branches at higher energy, a striking discrepancy with the experimental data. This, in concert with the strong suppression of T_N, is attributable to enhanced quantum fluctuations due to phase competition between the Γ₇ and Γ₅ states that border each other within a classically predicted phase diagram.   

Spin-lattice coupling in quantum spin liquids

We construct phenomenological theories to investigate spin-lattice coupling in quantum spin liquids (QSLs) by using gauge-invariance and strain tensor with lattice symmetries. In deconfined QSLs, it is shown that perturbative approaches are valid, and our theory is applied to U(1) QSLs with gapped fractionalized particles in quantum spin ices, so-called emergent Coulomb phases. We find characteristic decay rates of emergent photons and acoustic phonons under spin-lattice coupling. Namely, the decay rate of the photons contains the Boltzmann factor while the decay rate of the phonons is dominated by temperature independent contributions. The characteristic behaviors of decay rates may affect physical quantities such as thermal conductivity.   

Investigation of Elastic and Magnetic Properties of GeCo2O4

Geometrically frustrated Magnets continue to attract attention due to their inclination towards unconventional ground states at low temperatures. Among these, GeCo₂O₄ a normal spinel, has been recently suggested to undergo a magnetic ordering at 21K accompanied by a cubic-tetragonal distortion. However, its low temperature properties especially the nature and origin of the structural distortion are not clearly understood to date. Therefore we have investigated the elastic and magnetic properties of GeCo₂O₄ single crystal using ultrasound velocity measurements down to 2K. The temperature dependence of the elastic constant C₄₄, at zero magnetic field shows an anomaly at 20.8K consistent with a first order AF phase transition. The elastic instability of C₄₄ implies that, the magnetic ordering might be accompanied by a cubic-tetragonal distortion. When the field is applied along [100], the maximum critical field is 10.5T. For fields B// [111], the maximum critical fields of the first and second phase transition is 11T and 13T, respectively. Whereas for fields B// [110], the maximum critical fields of the first and second phase transition are 4.5T and 9.5T, respectively. The magnetic field anisotropy is probably due to distortion of the crystal lattice at higher magnetic fields.
  

Low-temperature thermal conductivity of the frustrated S=3/2 Heisenberg helimagnet ZnCr2Se4

We report thermal conductivity measurements on single crystals of ZnCr₂Se₄ in the temperature range 5 K ≤ T ≤ 300 K. This compound undergoes^a,b a helical antiferromagnetic transition accompanied by a cubic-tetragonal structural modification at T_N ≈ 21 K. Its magnetic sublattice comprises spin-3/2 Cr³⁺ ions in a geometrically-frustrated pyrochlore structure. We will discuss thermal conductivity measurements along various crystallographic directions, the overall magnitude of which are higher than that of polycrystals^c by a factor of 5.

^a R. Plumier, J. Phys. 27, 213 (1966).
^b V. Felea et al., Phys. Rev. B 86, 104420 (2012).
^c X. Chen and Z. Yang, AIP Advances 6, 056212 (2016).   

Structural and Magnetic Properties of CoV2O4 Thin Films

Spinel vanadates, poster materials for orbital physics in frustrated antiferromagnets, have been intensely studied in recent years to gain a better understanding on how orbital order helps relieve spin degeneracy. CoV2O4 is the most interesting because of its proximity to a localized-itinerant crossover regime. Only recently a weak spin canting and structural transition has been identified at T*= 90 K in powder samples at the edge of detectability, which has been associated with an orbital glass transition. We present xray, magnetization and neutron scattering results on CoV2O4 films grown on SrTiO3 substrates via pulsed laser deposition. In contrast to the weak effects seen in bulk powders and crystals, our films demonstrate clear signatures of spin canting, which can be associated with long-ranged orbital order.   

Unusual Thermal Properties in Magnetic MnFe2O4 and FeMn2O4 Single Crystals

Materials that form the AB₂O₄-type spinel structure are known to exhibit geometric frustration, as the A sublattice forms diamond-like structure and B sublattice is pyrochlore-like. They are thus promising candidates for studying unconventional thermal and magnetic properties. Here, we report thermal conductivity, thermopower, and specific heat in magnetic spinel MnFe₂O₄ and FeMn₂O₄ single crystals. One remarkable feature is their low thermal conductivity in a wide temperature range (2 K and 400 K) with a maximum value of ~ 2.0 W/K-m, which is usual for single crystalline materials. Furthermore, both the low-temperature thermal conductivity and specific heat exhibit T^3/2 dependence instead of T³ behavior. This strongly suggests that heat in these magnetic spinel materials is predominantly carried by magnons, while phonons exhibit glass-like behavior, conducting little heat. The latter should be attributed to geometric frustration inherent in spinel materials.