Jeffrey Quilliam

Fig. 1: ⁵¹V NMR spectra of the kagome antiferromagnet Vesignieite [1].

Solid-state NMR makes use of the nuclear spins within a material to obtain a distribution of internal magnetic fields. A large and homogeneous external magnetic field, H₀, is applied to polarize the nuclear spins. Then, perpendicular field pulses are applied which cause the spins to tip and precess around the static field with a frequency f = H₀γ/2π, where γ is the gyromagnetic ratio of the nucleus in question. The variations in frequency of the resulting free-induction decay (or spin echo) indicate the variations in magnetic field within a material. Furthermore, by looking at the rates at which the precession decays, the relaxation, one can determine how quickly the fields within a material are fluctuating. NMR is a very versatile tool that has applications in virtually all domains of condensed matter physics, from superconductivity to quantum magnetism.

[1] J. A. Quilliam et al. Physical Review B 84, 180401(R) (2011). Work performed in collaboration with P. Mendels at the Laboratoire de Physique des Solides.

Fig. 4: µSR data on Ba₃LuRu₂O₉ at various temperatures. Oscillations at low temperature indicate long range magnetic order.

µSR is a local probe technique which operates on very similar principles to NMR. Instead of using a nuclear spin normally residing in the material, µSR involves implanting a muon inside the sample which will then precess in the internal magnetic fields of a material. Detection of the muons' spin orientation is accomplished by observing the positrons emitted when the muon decays, which travel preferentially along the muon spin direction. Although it requires travelling to one of a handful of user facilities around the world (Vancouver, Switzerland, England and Japan), µSR is a highly sensitive and efficient technique for studying small levels of spin freezing or ordering in materials.

[2] D. Ziat et al. Accepted in Physical Review B (2017).

Fig. 3: Specific heat of Yb₂Ti₂O₇.

Specific heat, the energy required to change the temperature of a material, is possibly the most fundamental and broadly applicable thermodynamic property. At low temperatures this measurement becomes especially difficult, however, requiring very precise thermometry and a detailed attention to heat flows and anomolous heating. On the left are measurements of the low temperature specific heat of Yb₂Ti₂O₇ [3] showing variations between single crystal and powder samples at the possible Higg's transition [4].

[3] K. A. Ross et al. Physical Review B 84, 174442 (2011). Measurements performed in the group of J. Kycia at the University of Waterloo.

[4] L.-J. Chang et al. Nature Communications 3, 992 (2012).

Fig. 2: Dynamics of magnetic monopoles in Ho₂Ti₂O₇, measured with a SQUID.

One of the most effective ways to study magnetic materials is naturally to measure their magnetization, or magnetic susceptibility. In my laboratory we perform susceptibility measurements using conventional susceptomters based on magnetic induction as well as what is known as a SQUID (Superconducting QUantum Interference Device), the most sensitive magnetic field sensor available. SQUID magnetometers can provide an extremely precise measure of the magnetization or susceptibility of a material and can cover a vast range of frequencies from 1 mHz up to several kHz. Such a tool is very useful for studying spin glasses, magnets that freeze randomly at a glass transition T_g, and has also recently foundan important application in studying the motion of magnetic monopoles in frustrated magnetic materials called spin ice (data on Ho₂Ti₂O₇ is shown in the accompanying figure) [2].

[5] J. A. Quilliam et al. Physical Review B 83, 094424 (2011). Work done in collaboration with J. Kycia at the University of Waterloo.

Fig. 5: Field scans of ultrasound velocity in a spin liquid candidate material, SrDy₂O₄.

Precise measurements of the velocity of ultrasonic waves in a single crystal can provide a very sensitive indicator of phase changes of various kinds. In magnetic materials, the sound velocity can be coupled to the magnetization, to magnetic order parameters and to spin fluctuations. We apply rf pulses to a piezoelectric transducer that is glued to a surface of the sample in order to generate sound waves. We detect an electrical signal in another transducer on the other side of the sample or else pick up the reflected signal with the same transducer. By measuring the phase of the received signal (or echo) we can measure tiny relative changes in velocity.

[6] C. Bidaud et al. Phys. Rev. B 93, 060404(R) (2016).

Often my research concentrates on the properties of materials at somewhat to extremely low temperatures. Using ordinary liquid helium, ⁴He, we can reach temperatures nearing 1 degree above absolute zero. However, using a dilution refrigerator, which combines a mixture of the two isotopes of helium (³He and ⁴He), we can obtain temperatures of 20 mK or colder!