Magnetocaloric effect measurements

Magnetocaloric effect (MCE) measurements monitor the temperature of a single- crystal sample of Cu(pyz)(gly)ClO4 with a four-wire ac magnetoresistance measure-

ment of a calibrated bare-chip Cernoxtm thermometer that is directly attached to the sample. In these experiments, a rapidly changing magnetic field is provided by the capacitor-driven short-pulse (SP) or generator-driven long-pulse (LP) magnet at NHMFL (Los Alamos). While the measurements made with each pulsed-field system may have a different degree of adiabaticity to each other, and to the SP magnetometry measurements displayed in Fig. 3.3, the large (∂Smag/∂H)T of this

material and Eq. 1.14 together imply that any experiment that departs from isother- mal conditions ought to exhibit a finite MCE.

For measurements performed with the SP magnet, the field evolution of the Cernoxtm temperatureTCer is recorded on decreasingH [Fig. 3.5(a)] and these

traces exhibits two features that resemble the form of the experimentally determined isentropes of Cu(pyz)(gly)ClO4. Firstly, a kink (or minimum) is observed near µ0H ≈2 T (dark blue arrows). QMC simulations of networks of spin-dimers with

interdimer spin-exchange interactions in two-spatial dimensions [88] predict that a rapid increase Γ =T−1(∂T /∂H) occurs at two stages during an adiabatic H sweep, once when the applied field is sufficient for triplons to first condense and again once the number ofS = 1 bosons saturates. The low-field kink in the measured data is concurrent with a change in sign in the measured parameter Γ =T_Cer−1(∂TCer/∂H),

as determined by a peak in dΓ/dH [Fig. 3.5(b)], and this is therefore taken as the estimate forHc1. A second feature ofTCer(H) measurements is that a linear response

is recorded for applied magnetic fields in excess ofµ0H≈5.5 T. This is indicative of

a field and temperature regime whereSmag is approximately governed by a function

of H/T, as is determined to be the case for Cu(pyz)(gly)ClO4 from an analysis of

the isentropes in the spin-polarized phase (see above). While the measured change in behaviour ofTCeraround 5.5 T is too subtle to induce resolvable peaks in dΓ/dH,

the position of the upper phase boundary is determined from the point at which a linear fit to theTCer(H) traces forµ0H ≥7 T departs the measured data [Fig. 3.5(a),

blue lines]. The linear fit models the data to an accuracy of±0.3% over the fitted temperature range andHc2is estimated from the low-field point at which the linear

fit and measured data diverge by more than 0.3% (light blue arrows).

For MCE measurements performed with the LP magnet, limiting the applied field sweep rateµ0|dH/dt|to approximately 100 Ts−1 is found to increase the sensi-

Figure 3.5: The field evolution of: (a) the Cernoxtm temperature; and (b) dΓ/dH

(red lines), for MCE measurements performed with the capacitor-driven SP magnet recorded on the field down sweeps. In panel (a), data forµ0H ≥7 T are fitted to

straight line (pale blue). Arrows mark estimates ofHc1 (dark blue) andHc2 (pale blue), respectively (see text). (c) Field evolution of the Cernoxtm temperature (lines) for MCE measurements utilizing the generator-driven LP magnet. Data are labelled by the pulse profile from Fig. 2.3(b) and are superimposed on the published [74] quasistatic measurements of the BEC phase boundary. (d) Critical fields from the MCE measurements (triangles) plotted as a function of the initial He bath temperature; phase diagram from panel (c) repeated here.

tivity of the Cernoxtm thermometer to changes in the sampleT compared to the SP experiments. Minima develop atHc1andHc2 in the LPTCer(H) traces [Fig. 3.5(c)]

and, furthermore, these features become more prominent as the initial sample tem- perature is lowered, which suggests that the features of the TCer(H) derive from

changes in the sample temperature. The critical fields determined from the SP and LP MCE experiments are plotted as a function of the initial He bath temperature

T0 in Fig. 3.5(d) (triangles), where both Hc1 and Hc2 in the LP experiments are

extracted from peaks in dΓ/dH (Fig. 3.6). The phase boundaries extracted from the pulsed-field MCE measurements tend to follow the form of the extended dome as per the case of Fig. 3.2(a). This supports the conclusion that a MCE occurred during the pulsed-field magnetometry measurements, whereby the sample is cooled forH >0 even when T0 exceeds the maximum temperature of the BEC dome.

While the features observed in the TCer(H) traces during the MCE experi-

Figure 3.6: Measured values of dΓ/dH, plotted here in arbitrary units (a.u.), for MCE measurements performed with the LP magnet. Using the field profile labelling scheme defined in Fig. 2.3(b), MCE data shown here are measured with profiles: (a)

A;(b)B; and (c)C, respectively. Phase transitions, indicated by peaks in dΓ/dH

(arrows), are checked for consistency against maxima in dΓ/dH [panels (d)₋(f )] that are found by differentiating the isentropes derived from the heat capacity for constant entropy contours beginning at initial temperatures similar to the MCE experiments. Each curve is labelled by the sample temperature atH = 0.

is swept, both the SP and LP MCE measurements are insensitive to the full magni- tude of the MCE that is implied from the results of pulsed-field magnetometry and quasistatic heat capacity experiments. This limits the discussion of the MCE data to the features ofTCer(H) forH≈Hc1,2 where the changes in Γ are greatest. The

apparent increase in sensitivity of the LP measurements to the MCE in the sample (relative to the SP experiments) most likely results from a decrease in the amount of self heating generated by the Cernoxtm_{in these comparatively slow H sweeps. If}

a future study was performed to improve the thermal coupling of the Cernoxtm _to

a polymeric sample in a MCE measurement, the results of the MCE experiments performed on for Cu(pyz)(gly)ClO4 suggest that the LP magnet at NHMFL would

be an advantageous tool in this investigation. However, the form of the isentropes of Cu(pyz)(gly)ClO4, and hence the full extent of the MCE, are derived from the

results of quasistatic heat capacity experiments. It is therefore concluded that heat capacity measurements are likely to be an efficient means to investigate both the isothermal and adiabatic physics of quantum spin systems for which the fullH−T