Figure 1

Field dependence of the relative sample-length change parallel and perpendicular to a magnetic field applied along the [111] direction at various temperatures: (a) longitudinal magnetostriction; (b) transversal magnetostriction. The curves are offset for clarity. (c) Model calculation of longitudinal magnetostriction at 0.3 K.

Figure 2

Typical time dependence of the relative sample length of ${\mathrm{Dy}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ in longitudinal geometry $H\parallel \mathrm{\Delta }L/L$ at various temperatures (a) sweeping the field quickly from 1.25 down to $0.75\mathrm{T}$ and (b) sweeping from 0.90 up to $1.00\mathrm{T}$.

Figure 3

Long-time change of the sample length after a quick field sweep from 1.25 to $0.75\mathrm{T}$ and fit lines using different models to describe the data.

Figure 4

Field dependence of the relaxation times of ${\mathrm{Dy}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ at various magnetic fields in longitudinal geometry $H\parallel \mathrm{\Delta }L/L$

after (a) reducing and (b) increasing the magnetic field quickly with 1 T/min. The final external field is shown on the bottom axis. The initial field was always (a) 0.5 T higher and (b) 0.1 T lower than the final field. The internal field after demagnetization correction is labeled on the top axis for the external fields 0.5, 1.0, and 1.5 T.

Figure 5

Contour plot of the relaxation time of ${\mathrm{Dy}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ in the phase space of temperature and internal field with long relaxation times in blue and short relaxation fading to lighter colors. The relaxation times are taken from the quench experiments summarized in Fig. 4. Note the exponential scale of the color code. For comparison, transitions extracted from specific-heat and magnetization data [52] are included as a dashed line.