Session F28: Focus Session: Pyrochlores and Spinels

From Spin Glass to Spin Liquid Ground States in Molybdate Pyrochlores

The rare earth molybdate pyrochlores are a well-studied family of geometrically frustrated magnetic materials and in particular, the spin glass ground state in Y$_2$Mo$_2$O$_7$ in the absence of disorder continues to be of interest. Here we will present a study of the Lu-based analogue Lu$_2$Mo$_2$O$_7$, which displays a transition to a spin glass state at $T_f=16$ K and an unusual $T^2$ dependence of low temperature heat capacity. Our neutron scattering studies reveal a build-up of diffuse elastic magnetic scattering and the collapse of the inelastic scattering intensity into the elastic line at $T_f$. Furthermore, we will show that the O$^{2-}$ anions within Lu$_2$Mo$_2$O$_7$ can be topochemically substituted for N$^{3-}$, which consequently oxidizes the molybdenum cations and drives down their spin quantum number from Mo$^{4+}$ $S=1$ to Mo$^{5+}$ $S={\frac{1}{2}}$. This new oxynitride phase shows an absence of magnetic order despite strong antiferromagnetic exchange and the persistence of inelastic neutron scattering down to low energy scales. Our results on the oxynitride Lu$_2$Mo$_2$O$_5$N$_2$ are consistent with a gapless spin liquid, which highlights the significant role of quantum fluctuations [1]. [1] L. Clark et al., Phys. Rev. Lett. $113$, $117201$ ($2014$)   

Partially ordered state in stoichiometric Yb2Ti2O7

The nature of the magnetic state below a first order transition at $T_c = 265$ mK in the Quantum Spin Ice Yb$_2$Ti$_2$O$_7$ is hotly debated. It has been proposed as a Quantum Spin Liquid (QSL) ground state, but some studies find evidence for long range ferromagnetic order; results seemingly vary from sample to sample. We will present low temperature neutron measurements on a polycrystalline sample of Yb$_2$Ti$_2$O$_7$ that is known to be stoichiometric. Our measurements reveal 1) there is a change of intensity at nuclear Bragg positions upon warming which does not occur sharply at $T_c$, and which involves an ordered moment size of $\sim$1.1muB (58\% of the saturation moment) and 2) the inelastic excitations below $T_c$ suggest the presence of dispersive modes coexisting with incoherent low energy fluctuations.  The data will be compared to Yb$_2$Sn$_2$O$_7$, which shows nearly identical behavior via inelastic neutron scattering.  Our results suggest that the ground state in nominally pure Yb$_2$Ti$_2$O$_7$ and Yb$_2$Sn$_2$O$_7$ is not a conventionally ordered ferromagnet, but instead involves only partial polarization of the magnetic moments coexisting with a disordered component, a situation reminiscent of the partially polarized QSL called the Coulomb Ferromagnetic phase.   

Neutron spectroscopic study of Crystal-field excitation in $Yb_{2}(Ti_{2-x}Yb_{x})O_{7-\frac{x}{2}}$

Among the rare-earth titanate pyrochlores, $Yb_2Ti_2O_7$ has attracted much attention as a potential realization of a quantum spin ice [1]. While strong quantum effects are absent in classical spin ice compounds, they are thought to be significant in $Yb_2Ti_2O_7$ because of its effective spin S=1/2 and its XY spin anisotropy, quantities both determined by the Crystal-Electric Field (CEF) levels. However, a thorough neutron spectroscopy study of the CEF levels is still lacking. Here, we report time-of-flight inelastic neutron scattering measurements on $Yb_2Ti_2O_7$. Our results lead to the unambiguous determination of the CEF levels, the ground-state wavefunction and therefore the nature of the spin anisotropy of the J=7/2 $Yb^{3+}$. A significant sample dependence in the low temperature heat capacity has been reported and attributed to an excess of $Yb^{3+}$ (''stuffing'') in the structure [2]. Our measurements, carried out on two well-characterized samples with different levels of stuffing, allow us to discuss the impact of such disorder on the CEF levels. [1] K.A. Ross, L. Savary, B.D. Gaulin, L. Balents,Physical Review X, 1(2), 021002, (2011). [2] K.A. Ross, Th. Proffen, H.A. Dabkowska, J.A. Quilliam, L.R. Yaraskavitch, J.B. Kycia and B.D. Gaulin, Phys. Rev. B 86, 17442   

What is going on in Yb$_2$Ti$_2$O$_7$ ?

Yb$_2$Ti$_2$O$_7$ has become an excellent example of the complexity of frustrated magnets, showing properties of a spin liquid, dimensional reduction, ferromagnetism and multiple phase transitions. In this talk, we shall bring together many of these aspects into one general theoretical framework, showing how competing orderings are able to explain several experimental features observed in bulk measurements (Lhotel et al. PRB 2014) and neutron scattering (Chang et al. Nature Comm. 2012).   

Frozen Spin Ice Ground States in the Pyrochlore Magnet Tb$_2$Ti$_2$O$_7$

The ground state nature of the candidate spin liquid pyrochlore magnet Tb$_2$Ti$_2$O$_7$ has remained a puzzle for over 15 years. Despite theoretical expectations of magnetic order below $\sim$ 1 K based on classical Ising-like Tb${3+}$ spins, early $\mu$SR and neutron scattering experiments showed no long range order down to 50 mK [1,2]. This motivated two theoretical scenarios to account for the apparently disordered ground state: a quantum spin ice scenario in which the classical spin order is suppressed by virtual crystal field excitations that renormalize the antiferromagnetic exchange [3], or a scenario arising from a yet to be observed structural distortion creating a non-magnetic singlet ground state [4]. I will discuss our time-of-flight neutron scattering measurements on Tb$_2$Ti$_2$O$_7$ that reveal a glassy spin ice ground state, characterized by frozen antiferromagnetic short range order and the formation of a $\sim$ 0.08 meV energy gap in its spin excitation spectrum at the (1/2,1/2,1/2) quasi-ordering wave vectors [5]. A new $H-T$ phase diagram for Tb$_2$Ti$_2$O$_7$ in [110] magnetic field will be presented[6]. I will further discuss recent experiments on slightly off-stoichiometric Tb$_{2+x}$Ti$_{2-x}$O$_{7-y}$ samples, which also display the same gapped spin ice correlations at (1/2,1/2,1/2) wave vectors.\\[4pt] [1] Gardner et al., PRL 82, 1012 (1999)\\[0pt] [2] Gingras et al., PRB 62, 6496 (2000) \\[0pt] [3] Molavian et al., PRL 98, 157204 (2007)\\[0pt] [4] Bonville et al., PRB 84, 184409 (2011) \\[0pt] [5] Fritsch et al., PRB 87, 094410 (2013)\\[0pt] [6] Fritsch et al., PRB 90, 014429 (2014)   

Magnetoelastic excitations in Tb2Ti2O7 in applied magnetic field

The key puzzle in Tb$_2$Ti$_2$O$_7$ is how the expected long-range magnetic order and/or structural phase transition are suppressed, resulting in the stabilization of the spin liquid phase [1]. This spin liquid phase supports spin ice-like powerlaw correlations [2,3,4], and an array of anomalous magnetoelastic properties (see e.g. [5]). Recently we have discovered a microscopic coupling between the magnetic and lattice fluctuations, which form a hybrid propagating excitation with both spin and phonon components [6,7]. Using inelastic neutron scattering, we have now explored the effect of an applied magnetic field on the magnetoelastic coupling. I will show how these experiments cast light not only on the coupling between spins and phonons in Tb$_2$Ti$_2$O$_7$, but also on other unexplained phenomena in Tb$_2$Ti$_2$O$_7$, such as the field induced long-range antiferromagnetic order [8]. [1] Gardner et al., Rev. Mod. Phys. 82, 53 (2010); [2] Fennell et al., PRL 109, 017201 (2012); [3] Petit et al., PRB 86, 174403 (2012); [4] Fritsch et al., PRB 87, 094410 (2013); [5] Ruff et al., PRL 99, 237202 (2007); [6] Fennell et al., PRL 112, 017203 (2014); [7] Guitteny et al., PRL 111, 087201 (2013); [8] Rule et al., PRL 96, 177201 (2006);   

The ground state of the Er$_2$Ti$_2$O$_7$ pyrochlore XY antiferromagnet: Energetic vs. order-by-disorder selection

Conclusive evidence of order by disorder is rare in real materials. One of the strongest cases presented has been for the pyrochlore antiferromagnet Er$_2$Ti$_2$O$_7$, with the ground state selection proceeding not only through order by disorder, but induced through the effects of quantum fluctuations. This identification relies on the smallness of higher spin interaction terms that could provide an alternate route to picking the ground state. Here we re-evaluate the arguments that lead to this conclusion. We show that classical effects are much more competitive than has been previously reported and must be considered in detail to establish the mechanism of ground state selection in Er$_2$Ti$_2$O$_7$. From a realistic model of the crystal field excitations we explicitly compute these terms using strong coupling perturbation theory. From these higher-spin interactions, we calculate the effects on the excitation spectrum and ground state energy at the purely classical level. Implications for the interpretation of recent experiments on Er$_2$Ti$_2$O$_7$ will be discussed.   

Inelastic light scattering measurements of structural phase coexistence in ferrimagnetic spinel Mn$_3$O$_4$

The ferrimagnetic spinel Mn$_3$O$_4$ has a number of functional properties, e.g., magnetodielectricity, that are ascribed to a coupling between the spins and lattice of this material. Such a coupling is manifested in the symmetry-lowering structural distortion that occurs when Mn$_3$O$_4$ magnetically orders at $T=33$~K. A recent x-ray diffraction study$^2$ of polycrystalline Mn$_3$O$_4$ found that this distortion is not fully realized, i.e., the high-symmetry and low-symmetry structures coexist below $T=33$~K due to strains from lattice mismatch. To extend this work, we use variable-pressure and variable-magnetic-field inelastic light scattering spectroscopy to study structural phase coexistence in single crystals of Mn$_3$O$_4$. We confirm the coexistence of tetragonal (high-symmetry) and orthorhombic (low-symmetry) phases below $T=33$~K. Furthermore, we demonstrate that the application of hydrostatic pressure suppresses the remnant tetragonal phase, while the application of magnetic field can bolster this phase. These results indicate that microscopic descriptions of functional behavior in Mn$_3$O$_4$ should consider effects due to structural phase coexistence. [2]~M.~C. Kemei, {\it et~al.\/}, {\it Phys. Rev. B\/} {\bf 89}, 174410 (2014).   

Neutron scattering investigation of magnetic phases in Mn$_3$O$_4$ with field applied away from the easy axis

Mn$_3$O$_4$ is an orbitally ordered, magnetically frustrated spinel with strong spin-lattice coupling, which exhibits a series of low temperature magnetic and structural transitions. Recent data shows that the structural phases are radically different with \textbf{H} applied perpendicular to the easy-axis. With the current understanding of the magneto-structural coupling in this material, this data suggests the possibility of a field-tuned quantum phase transition into a tetragonal spin-disordered phase with T=0 spin frustration. In order to probe the field-direction dependence of the magnetic phase, we have performed elastic neutron scattering measurements of the magnetic properties of Mn$_3$O$_4$ with applied field at several different angles to the easy axis. We will present data suggesting that the field-temperature phase diagram of this material is radically altered by varying the applied field direction.   

$\mu$SR study of real space magnetic phase separation in Mn$_3$O$_4$

The material Mn$_{3}$O$_{4}$ is a magnetically frustrated spinel which exhibits three distinct magnetic transitions below ~42 K. Recent work has shown that the lowest of these is accompanied by an orthorhombic structural distortion, implying strong magneto-elastic coupling. Magnetic force microscopy (MFM) measurements indicate a substantial region of phase coexistence below this transition, with domain walls that order on the mesoscale. It is further suggested that a tradeoff in ordered volume with field may play a role in the recent quantum phase transition reported in this material. To follow up on these ideas, we have performed a series of zero- and transverse-field muon spin rotation measurements on single-crystal Mn$_{3}$O$_{4}$. The zero-field data clearly show the co-existence of ordered and disorder volumes, consistent with MFM results. Here we report these data, and further attempts to vary the ordered volume with applied field. We will discuss both zero- and transverse-field results within the context of the current understanding of the material.   

Quantum Criticality in FeSc$_2$S$_4$

Despite possessing a local spin $2$ moment on the iron site and a Curie-Weiss temperature of $45K$, the A site spinel FeSc$_2$S$_4$ does not magnetically order down to 50mK. Previous theoretical work by Chen and Balents advanced an explanation for this observation in the form of the ``$J_2$-$\lambda$'' model which places FeSc$_2$S$_4$ close to a quantum critical point on the disordered side of a quantum phase transition between a N\'{e}el ordered phase and a ``Spin-Orbital Liquid'' in which spins and orbitals are entangled, quenching the magnetization. We present new theoretical studies of the optical properties of the $J_2$-$\lambda$ model, including a computation of the dispersion relation for the quasiparticle excitations and the form of the collective response to electric field. We argue that the latter directly probes a low energy excitation continuum characteristic of quantum criticality, and that our results reinforce the consistency of this model with experiment.   

Competition between the inter- and intra-sublattice interactions in Yb$_{2}$V$_{2}$O$_{7}$

We studied single crystals of Yb$_{2}$V$_{2}$O$_{7}$ using dc and ac susceptibility measurements, elastic and inelastic neutron scattering measurements, and linear spin wave theory. The experimental data shows a ferromagnetic ordering of V$^{4+}$ ions at 70 K, a short-range ordering of Yb$^{3+}$ ions below 40 K, and finally a long-range non-collinear ordering of Yb$^{3+}$ ions below 15 K. With external magnetic field oriented along the [111] axis, the Yb-sublattice experiences a spin flop transition related to the ``three-in one-out'' spin structure. By modeling the spin wave excitations, we extract the Hamiltonian parameters. Our results confirm that although the extra inter-sublattice Yb-V interactions dramatically increases the Yb ordering temperature to 15 K, the intra-sublattice Yb-Yb interactions, based on the pyrochlore lattice, still stabilize the Yb ions' non-collinear spin structure and spin flop transition.   

Quantum spin state in a spin-1/2 breathing pyrochlore antiferromagnet

A pyrochlore lattice antiferromagnet consisting of corner-sharing tetrahedra of magnetic ions has attracted much attention because the inherent geometrical frustration often leads to exotic magnetism such as quantum spin liquid [1]. The key building unit of pyrochlore magnet is a single spin tetrahedron. Thus, a material composed of a spin-tetrahedral unit is expected to provide important insights on physics of full pyrochlore lattice. Moreover, it may show exotic magnetism based on the unique properties of the single tetrahedron associated with the spin chirality. However, no spin-1/2 regular tetrahedral system has been reported to date. In this study, we report the characterization of a new Yb-based material Ba3Yb2Zn5O11 [2]. This material is identified as a model system of a pseudospin-1/2 quantum antiferromagnet on breathing pyrochlore lattice characterized by an alternating array of small and large Yb tetrahedra. Despite antiferromagnetic interactions J $\sim$ 7 K, a large amount of magnetic entropy (25{\%}) remains at 0.38 K, indicating that each small Yb tetrahedron forms a unique doubly degenerate singlet state.\\[4pt] [1] B. Canals and C. Lacroix, Phys. Rev. Lett., 80, 2933 (1998)\\[0pt] [2] K. Kimura, S. Nakatsuji, and T. Kimura, Phys. Rev. B, 90, 060414(R) (2014).