Reentrant Phase Diagram of ${\mathrm{Yb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ in a $⟨111⟩$ Magnetic Field

We present a magnetic phase diagram of rare-earth pyrochlore ${\mathrm{Yb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ in a $⟨111⟩$ magnetic field. Using heat capacity, magnetization, and neutron scattering data, we show an unusual field dependence of a first-order phase boundary, wherein a small applied field increases the ordering temperature. The zero-field ground state has ferromagnetic domains, while the spins polarize along $⟨111⟩$ above 0.65 T. A classical Monte Carlo analysis of published Hamiltonians does account for the critical field in the low $T$ limit. However, this analysis fails to account for the large bulge in the reentrant phase diagram, suggesting that either long-range interactions or quantum fluctuations govern low field properties.

Figure 1

Heat capacity data for ${\mathrm{Yb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ with magnetic field along $⟨111⟩$. (a) $C$ vs $T$ at various fields. Solid traces indicate long-pulse data, while discrete symbols indicate adiabatic short-pulse data. The fields in the legend are external fields. [(a), inset] Isothermal field scans of heat capacity using the short-pulse method. (b) Color map of long-pulse heat capacity data vs temperature and internal magnetic field. [(b), inset] Relationship between ${\mu }_0{H}_{\mathrm{int}}$ and ${\mu }_0{H}_{\mathrm{ext}}$.

Figure 2

Magnetization of ${\mathrm{Yb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ in applied magnetic fields along $⟨111⟩$. (a)–(c) Temperature dependence of the magnetization where we distinguish between data recorded according to procedure (i) zero-field-cooled or field-heated (zfc-fh), (ii) field-cooled (fc), and (iii) field-cooled or field-heated (fc-fh). (d) Magnetization and (e) numerical derivative of the experimental data of ${\mathrm{Yb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ as a function of internal magnetic field after correction for demagnetization fields. The inset in (d) shows the spontaneous magnetization as a function of temperature obtained from magnetization field sweeps [protocol (A1); see the Supplemental Material [25] ]. (f)–(k) Magnetization in field cycles of sweep types protocol (A2) and (A3) (see Supplemental Material [25]).

Figure 3

Field and temperature dependence of the $(2\overline{2}0)$ Bragg peak intensity. (a) Magnetic field scan going up ($+B$) and down ($-B$) in field. Note the lack of hysteresis. (b)–(d) Temperature scans at external magnetic fields of 550, 300, and 0 mT (internal fields of 473, 239, and 0 mT). Red indicates increasing temperature, blue indicates decreasing temperature. Error bars indicate 1 standard deviation above and 1 standard deviation below the measured value.

Figure 4

(a) Phase diagram of ${\mathrm{Yb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ in a $⟨111⟩$ oriented field, built from heat capacity, magnetization, and neutron scattering. Heat capacity points denote peak location (see Fig. 1), magnetization points denote inflection points (see Fig. 2), and neutron scattering points denote where intensity begins increasing (see Fig. 3). Error bars indicate the difference in transition temperature upon heating vs cooling. Theoretically predicted phase boundaries are shown with the small data points that denote the location of simulated heat capacity peaks. The colored lines are guides to the eye. (b) Change in entropy ($\mathrm{\Delta }S$) extracted from heat capacity compared to $\mathrm{\Delta }S$ computed from the Clapeyron relation. The green line is a guide to the eye.