Jeffrey Quilliam

The low-temperature phase diagram of Yb₂Si₂O₇, as determined with specific heat and sound velocity measurements.

Our project to study the new material Yb₂Si₂O₇ is soon to appear in Physical Review Letters. This system is a new rare-earth dimer magnet. In zero-field it has a singlet ground state, but the application of magnetic field closes the gap to triplet excitations and eventually induces antiferromagnetic order, which is related to Bose-Einstein condensation. Usually such physics is demonstrated using transition-metal ions (for example cuprates). Here, the use of a rare-earth ion with the potential for a complicated single-ion Hamiltonian is a first. One major advantage of this material is the very low critical fields as compared to many transition-metal ion systems.

This project was carried out in collaboratoin with the group of Kate Ross at Colorado State University. Our group contributed some low-temperature specific heat measurements (Djamel Ziat) and the ultrasound velocity measurements (Léo Berges).

[1] G. Hester et al. Phys. Rev. Lett. 123, 027201 (2019).

Specific heat and neutron diffraction intensity showing a clear phase transition at 350 mK.

Our work on the pyrochlore magnet Sm₂Ti₂O₇ has been published in PRB Rapid. This material is found to exhibit all-in all-out magnetism (as opposed to the two-in two-out state observed in spin ice, for example). Djamel Ziat's low-temperature specific heat measurements showed clear evidence of a phase transition at around 350 mK, providing an important contribution to this paper.

[1] C. Mauws et al. Phys. Rev. B 98, 100401(R) (2018).

Magnetic phase diagram of Li₂In_1-xSc_xMo₃O₈, showing antiferromagnetic, spin liquid and mixed phases.

In this work [1] we studied a series of materials, Li₂In_1-xSc_xMo₃O₈, which can be described as a 1/6th filled breathing kagome lattice. A kagome lattice is a corner-sharing network of triangles that is considered to be one of the most highly frustrated lattices. In a "breathing" kagome lattice, the triangles that point upwards have one size and the triangles that point downwards have a different size. The ratio of these sizes is known as the breathing ratio. In these particular materials, only 1 in 3 sites of the kagome lattice is occupied by an electron and this adds a charge degree of freedom to the system.

The phase diagram that we have elucidated using µSR experiments suggests that the In / Sc ratio (x) tunes the system between frozen or ordered magnetism and a quantum spin liquid state. At critical values of x, the system appears to have a smaller breathing ratio (so is therefore closer to a perfectly symmetric kagome lattice) and has a spin liquid-like ground state. From susceptibility measurements, we infer that the change in breathing ratio causes charge ordering to occur. Specifically, for small breathing ratio, it is expected that the system can form a plquette charge order (PCO) where 3 electrons form a resonance on some of the hexagons of the kagome lattice [2]. This charge ordering appears to increase the furstration of the electron spins and thereby generate a quantum spin liquid.

[1] A. Akbari-Sharbaf et al. Phys. Rev. Lett. 120, 227201 (2018).

[2] G. Chen et al. Phys. Rev. B 93, 245134 (2016).

Researchers from the Institut Quantique have obtained a $13 million grant from the Canadian Foundation for Innovation! This project will allow for the construction of a new wing on the faculty of sciences which will host many of the theoretical and experimental activities of the Institut Quantique. It will also allow us to purchase a number of experimental platforms which will be used as shared infrastructure, accessible to all members of the Institut Quantique. Click here for more information.

Phase diagram of GGG for H//[110] given by sound velocity measurements at very low temperature.

The garnet material Gd₃Ga₅O₁₂, otherwise known as GGG, is a long-standing problem in the field of frustrated magnetism. The Gd spins in this material cover what is known as a hyper-kagome lattice – a 3d network of corner-sharing triangles, analogous to the true kagome lattice in 2-dimensions. In zero field, this material has an unconventional spin glass phase which also incorporates extended short range order and persisitent spin fluctuations. Hence it has been at times referred to as a "spin slush". With a small applied field GGG becomes a spin liquid and at higher fields there is a "bubble" of antiferrromagnetism. The origin and nature of these exotic glass and liquid phases is still not understood despite more than 20 years of research. In this paper [1], we have clarified the anisotropy of the material's phase diagram. Notably, we have demonstrated that depending on the orientation of the field, one can obtain either one or two distinct antiferromagnetic phases. Our measurements in low field (in the spin liquid phase) have also hinted at the existence of a gap in the excitation spectrum. This gap may be associated with emergent objects that consist of loops of 10 spins, that were recently discovered with neutron scattering measurements [2].

[1] A. Rousseau, J.-M. Parent and J. A. Quilliam, Physical Review B 96, 060411(R) (2017).

[2] J. A. M. Paddison et al., Science 350,179 (2015)

Band structure of a Weyl semimetal.

A team of researchers at the Institut Quantique (Jeffrey Quilliam, Ion Garate, Louis Taillefer, André-Marie Tremblay and David Sénéchal) as well as Andrea Bianchi at the Université de Montréal, has received $162,000 for 3 years to study Weyl semimetals. These materials are 3-dimensional equivalents of graphene in which the electrons behave as relativistic particles with definite chirality known as Weyl Fermions. Their unusual band structure gives rise to remarkable topological properties in the bulk and on the surface. They hold promise for applications based on their magnetoelectric properties and currently represent one of the hottest topics in condensed matter physics.

Energy level diagram of the Ru-dimers in Ba₃MRu₂O₉.

Combining muon spin rotation measurements, with thermodynamic probes (susceptibility and specific heat) and neutron scattering experiments (in collaboration with Adam Aczel at Oak Ridge National Laboratory), we have shown that the materials Ba₃MRu₂O₉ can be described by molecular magnets interacting antiferromagnetically on a triangular lattice. These systems consist of mixed-valence Ru dimers. That is, one has an 7 valence electrons per Ru dimer. Our measurements indicate that the right way to think of these dimers is as molecular units with orbitals shared between the two Ru sites. Depending on the relative strength of bonding energy and Hunds coupling, these dimers may either have a spin-3/2 ground state (likely the case for M=La) or else a spin-1/2 ground state (as is the case for M=Y, In and Lu). The energy levels in the latter case are shown here. This realization provides a novel way to generate new frustrated quantum magnets. These results were recently published in PRB.

D. Ziat et al., Physical Review B 95, 184424 (2017)

µSR measurements showing that 6HB-Ba₃NiSb₂O₉ does not order or freeze down to very low temperatures, making it a good candidate for quantum spin liquid physics.

6HB-Ba₃NiSb₂O₉ is a new frustrated antiferromagnetic material that has S=1 moments. While this, in principle, makes it more classical than S=1/2 materials, it nevertheless appears to be a good candidate for quantum spin liquid physics. Our µSR measurements have shown that there is no sign of ordering or spin freezing down to as low as 20 mK, despite a Weiss constant of roughly 80 K. NMR shift measurements show that it has a constant Pauli-like susceptibility and relaxation measurements show that T₁ is indep-endant of temperature, suggesting gapless excitations. This material'ss complicated structure means that it may be best described by a J₁-J₂ honeycomb model leading to the possiblity of deconfined quantum criticality in between a plaquette valence bond crystal and Néel order.

J. A. Quilliam et al., Physical Review B 93, 214432 (2016)

Phase diagram of the spin liquid material SrDy₂O₄.

In this work we studied the frustrated spin liquid material SrDy₂O₄ as a function of magnetic field and temperature. A complex phase diagram is revealed that depends heavily on the direction of the applied field. Whereas a dome of 3-dimensional, long-range magnetic order is induced for magnetic field applied along the b-axis, no finite temperature magnetic order is observed for other field directions. When passing between spin liquid and the magnetically ordered phase, significant irreversibility is observed. “Solidification” of the spin liquid (through applied field) proceeds via three distinct steps while melting of the magnetic order into the spin liquid phase is a more continuous process. Our paper has been accepted in PRB Rapid Communications as an editor's selection.

C. Bidaud et al., Physical Review B 93, 060404(R) (2016)

The physics department at the Université de Sherbrooke has been awarded a 33.5 million dollar grant – the largest in the university's history! This grant, headed up by Alexandre Blais, will enable our department to combine our quantum materials and quantum information research efforts, with the ultimate goal of developing quantum technologies.

Phase diagrams of Ba₃CoSb₂O₉ for magnetic fields pointing in and out of the triangular planes.

Ultrasound velocity measurements performed by Maxime Lapointe-Major, Guy Quirion, Jeff Quilliam and Mario Poirier on the first spin-1/2 triangular lattice antiferromagnet, Ba₃CoSb₂O₉, have been published in Physical Review B! Our measurements have provided an extremely precise diagram of the diverse field-induced phases found in this model material. At low temperatures, the spin-1/2 triangular lattice is predicted to order in a magnetic structure wherein a 120 degree angle is found between adjacent spins, as seems to be the case for this material. In this system the slight easy-plane anisotropy plays an important role and depending on how the field is applied, one obtains a different series of phases. Those obtained for H parallel to a and c are shown here. In particular, when H is parallel to a the phase diagram includes an up-up-down 1/3-magnetization plateau which is stabilized by quantum fluctuations.

Furthermore, we have discovered an unusual softening of the lattice at low temperatures (well below the magnetic ordering transitions). This behaviour is quite suprising and is reminiscent of the residual spin dynamics that are often encountered in µSR measurements of frustrated magnetic materials.

[1] G. Quirion, M. Lapointe-Major, M. Poirier, J. A. Quilliam, Z. L. Dun et H. D. Zhou. Physical Review B 92, 014414 (2015).

Djamel changing samples on the M20 beamline at TRIUMF.

Djamel, Aimé and Jeff are in Vancouver, BC at TRIUMF, one of the only facilities in the world at which one can perform muon spin rotation (µSR) experiments. We are studying systems consiting of mixed-valence dimers on a triangular lattice to see what happens with the magnetic and charge degrees of freedom at low temperatures. We are collaborating with Adam Aczel (ONRL) and Haidong Zhou (UTK) on this project.

The µSR research technique requires a cyclotron which is otherwise used for particle physics experiments. The high-energy protons provided by the cyclotron are collided with a target producing pions which then decay and emit muons. The muons thus created are perfectly spin-polarized, with the spin pointing opposite their direction of motion. The muons travel down the beamline and are implanted in our samples. On arrival of a muon in the sample, a very fast clock is started and just microseconds later when the muon decays and an emitted positron is detected, the clock stops. The key to making µSR useful is that the positron is preferentially emitted along the direction of the muon's spin and this means that with more than one positron detector (usually one behind the sample and one in front of the sample), we can get an idea of how the muons are precessing inside the material. If there are no magnetic fields whatsoever, the muon's polarization will not change in time and we will get more counts on the backward detector. But if there are even tiny static fields within the material, the muon polarization will precess leading to an oscillating positron count rate.

This technique is quite powerful in that it works even without applying a large external field (unlike NMR) and can detect extremely small magnetic moments, essential when studying frustrated and quantum magnets.