Low-temperature muon spin rotation studies of the monopole charges and currents in Y doped Ho2Ti2O7

In the ground state of Ho2Ti2O7 spin ice, the disorder of the magnetic moments follows the same rules as the proton disorder in water ice. Excitations take the form of magnetic monopoles that interact via a magnetic Coulomb interaction. Muon spin rotation has been used to probe the low-temperature magnetic behaviour in single crystal Ho2−xYxTi2O7 (x = 0, 0.1, 1, 1.6 and 2). At very low temperatures, a linear field dependence for the relaxation rate of the muon precession λ(B), that in some previous experiments on Dy2Ti2O7 spin ice has been associated with monopole currents, is observed in samples with x = 0, and 0.1. A signal from the magnetic fields penetrating into the silver sample plate due to the magnetization of the crystals is observed for all the samples containing Ho allowing us to study the unusual magnetic dynamics of Y doped spin ice.

Single crystals of Ho 2−x Y x Ti 2 O 7 (x = 0, 0.1, 1, 1.6 and 2) were grown in an image furnace using the floating zone technique [1]. The cylindrical crystals were cut into circular disks ∼ 6 mm in diameter and ∼ 1 mm thick. These disks were oriented using the Laue x-ray diffraction technique and then glued, using GE varnish, in a circular pattern on to a silver sample plate as shown in Fig. 1. The samples were covered with a thin (0.01 mm) sheet of silver foil to improve thermal conductivity and mounted on the cold stage of an Oxford Instruments 3 He/ 4 He dilution refrigerator.

µSR Experiments
Muon spin rotation (µSR) experiments were performed using the MuSR spectrometer at the ISIS pulsed muon facility, Rutherford Appleton Laboratory, United Kingdom.
For the magnetic field sweeps at fixed temperature the samples were zero-field cooled to a temperature well below the eventual measuring temperature, thermalised, and then slowly warmed in zero field to the required measuring temperature. A transverse external field was then applied. For these measurements each field point took approximately 15 minutes to collect. At the end of each field sweep the magnetic field was reduced to zero and the sample warmed to 4 K. Note, during zero-field cooling, the stray fields at the sample position were cancelled to less than 3 µT by three pairs of coils forming an active compensation system.
The temperature sweeps were always made following a field sweep measurement at base temperature. This means that in practice the samples were zero-field-cooled to the base temperature of the cryostat, thermalised and a field of 2 mT was applied in steps of 0.25 mT over a period of at least two hours. Data were then collected in zero-field-cooled warming (ZFCW) mode by warming the sample to each measuring temperature up to maximum of 4 K and then in field-cooled cooling (FCC) mode on subsequent cooling to each measuring temperature. Each point in these temperature scans took around 15 minutes to collect. Due to the large low-temperature hyperfine contribution to the specific heat for the samples containing holmium, the effective base temperature of the dilution refrigerator for these samples was limited to 100 mK.
Ho 2 Ti 2 O 7 covered in thick silver foil Muon spin rotation spectra for a sample of pure Ho 2 Ti 2 O 7 covered with a silver foil 0.25 mm thick were collected at fixed temperature in 2 mT. The temperature dependence of the muon relaxation rate λ(T ) extracted from fits to this data are shown in Fig. 2.
For the low-temperature data (T < T CR ) the data were fit using where A 0 is the initial muon asymmetry, υ = γ µ B/2π is the frequency of the oscillations, and γ µ is the gyromagnetic ratio. In order to obtain satisfactory fits to the data above T CR the modified expression.
A(t) = A 0 cos(2πυt) exp(−λt) + A 2 exp(−λ 2 t) (2) was used. The additional A 2 exp(−λ 2 t) term is required to take account of the larger range stray fields within the thick silver foil. This is because the muon facility at ISIS has a significant momentum bite and so the implantation distance for the lower energy muons will be less than those with a higher energy.