Specific heat measurements were performed using a Quantum Design PPMS calorimeter as described in Section 4.2.2. The temperature dependence of the specific heat of SrHo2O4
in zero applied field is shown in Fig. 5.15. The lattice contribution to the specific heat of SrHo2O4was estimated by measuring the heat capacity of two single crystal non-magnetic
isostructural compounds: SrY2O4and SrLu2O4, and is also shown in Fig. 5.15.
At low temperature, and especially for temperatures below 10 K, the lattice contri- bution to the specific heat of SrHo2O4is negligible, but a broad peak centred around 3 K is
observed. This type of feature could potentially be caused by a low-lying crystal field level, but is more likely to be associated with the onset of low-dimensional magnetic correlations seen in the powder neutron diffraction data, which were discussed in Section 5.1.2. Above
∼10 K the heat capacity begins to rise again, but only some of this rise is likely to be the result of the lattice contribution, and to try and estimate this the differences in specific heat
CSrHo2O4 −CSrLu2O4 andCSrHo2O4 −CSrY2O4, are plotted in the inset to the top panel
of Fig. 5.15. Unlike the broad peak at low temperatures, it is likely that this additional contribution toC(T) is probably caused by the low-lying crystalline electric field levels present in SrHo2O4. A more detailed analysis of the crystal field levels will be discussed in
Section 5.5.
Fig. 5.16 shows the temperature dependence of the specific heat divided by tem- perature (in zero applied field) in the region of 0.4 to 1.6 K for three different samples of SrHo2O4. These measurements were taken using the 3He insert for the PPMS (see Sec-
tion 4.2.2). No immediately obvious sharpλ-type anomalies, which correspond to a mag- netic phase transitions are observed, and the specific heat steadily rises due to the nuclear contribution from the Ho3+ions. The first dataset had too large a step size in temperature to try and observe the transition at 0.62 K, which was seen as a cusp in single crystal magnetic susceptibility measurements. Subsequent attempts to look at the temperature region of in-
0 50 100 150 200 250 300 0 20 40 60 80 T (K) Ho Lu Y Ho-Lu Ho-Y C ( J / m o l K ) T (K) 0 H = 0 T 4 6 8 0 25 50 75 C ( J / m o l K ) 0 5 10 15 20 0 2 4 6 0 H = 0 T Ho Lu Y C ( J / m o l K ) T (K) ~3 K
Figure 5.15: Temperature dependence of the specific heat of SrHo2O4and of the nonmag-
netic isostructural compounds SrLu2O4 and SrY2O4 measured on single-crystal samples for the full temperature range (top) and the low temperature range (bottom). A broad peak in the specific heat at∼3 K is associated with short-range magnetic correlations.
0.4 0.8 1.2 1.6 3 4 5 6 7 0 H = 0 T 070910a 150311a 250811a C / T ( J / m o l H o K 2 ) T (K)
Figure 5.16: Temperature dependence of the specific heat divided by temperature for several single crystal samples of SrHo2O4. Due to the large contribution to the heat capacity from
the nuclear Schottky anomaly of Ho3+ it is difficult to tell whether there is a transition in the specific heat at 0.62 K (the temperature at which a cusp is observed in the single crystal susceptibility measurements).
terest were plagued by temperature instabilities, but even with a good dataset, it is still very hard to tell whether a phase transition is happening because the nuclear contribution com- pletely overwhelms any magnetic signal. The temperature dependence of entropy, which is usually calculated as an area under theC/T(T)curve which has been extended linearly down toT = 0 K, cannot be calculated as there is not enough data to accurately subtract the nuclear Schottky anomaly. Thus any integration performed on the data presented is likely to be misleading like the data presented in the inset to Fig. 3 in Ref. [104].
Due to the problems of the nuclear contribution, the specific heat in an applied field was measured only for the fields applied along thecaxis for SrHo2O4, and the data is shown
in the top panel of Fig. 5.17. The broad peak due to the short range correlations seems to be suppressed with the application of higher fields. Measurements in fields higher than∼2 T could not be completed as the sample tended to come off from the sample holder, due to the
0 5 10 15 20 2.5 3.0 3.5 4.0 4.5 H || c 0 H (T) 0.0 1.0 2.0 C ( J / m o l H o K ) T (K) 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 2.50 2.75 3.00 3.25 3.50 3.75 T (K) 2 15 C ( J / m o l H o K ) 0 H (T) H || c
Figure 5.17: (Top) Temperature dependence of the specific heat of SrHo2O4in several fields
applied along thecaxis of a single-crystal sample. The broad peak associated with short- range magnetic correlations seen in the specific heat at ∼3 K in zero field is suppressed with increasing values of the applied field. (Bottom) Field dependence of the specific heat at two temperatures for a single crystal sample of SrHo2O4, when the field is applied along
thecaxis. The differences in specific heatCSrHo2O4−CSrLu2O4 andCSrHo2O4−CSrY2O4,
significant torque generated by the large moment of the Ho3+ions as the easiest axis rapidly changes fromctobabove 1 T, see Fig. 5.14. The specific heat measured as a function of field was also measured forH ∥ c, and this is shown in the bottom panel of Fig. 5.17. The high temperatures theC(H)curve is pretty featureless, but at 2 K there seems to be a change in the specific heat above 0.75 T, but which does not look like a phase transition.