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Anisotropic magnetocaloric effect and critical behavior in CrSbSe3

In this work, we report anisotropic magnetocaloric effect and critical behavior in a quasi-one-dimensional ferromagnetic CrSbSe 3 single crystal. The maximum magnetic entropy change - Δ S M max is 2.16 J kg - 1 K - 1 for the easy a axis (2.03 J kg - 1 K - 1 for the hard b axis) and the relative cooling power RCP is 163.1 J kg - 1 for the easy a axis (142.1 J kg - 1 for the hard b axis) near T c with a magnetic field change of 50 kOe. The magnetocrystalline anisotropy constant K u is estimated to be 148.5 kJ m - 3 at 10 K, decreasing to 39.4 kJ m - 3 at 70 K. The rescaled Δ S M ( T , H ) curves along all three axes collapse onto a universal curve, respectively, confirming the second-order ferromagnetic transition. Further critical behavior analysis around T c ~ 70 K gives that the critical exponents β = 0.26 ( 1 ) , γ = 1.32 ( 2 ) , and δ = 6.17 ( 9 ) for H ∥ a , while β = 0.28 ( 2 ) , γ = 1.02 ( 1 ) , and δ = 4.14 ( 16 ) for H ∥ b . The determined critical exponents suggest that the anisotropic magnetic coupling in CrSbSe 3 is strongly dependent on orientations of the applied magnetic field.

2-dimensional systems↗

Three-dimensional Ising ferrimagnetism of Cr-Fe-Cr trimers in FeCr2Te4

We carried out a comprehensive study of magnetic critical behavior in single crystals of ternary chalcogenide Fe Cr 2 Te 4 that undergoes a ferrimagnetic transition below T c ~ 123 K. Detailed critical behavior analysis and scaled magnetic entropy change indicate a second-order ferrimagnetic transition. Critical exponents β = 0.30 ( 1 ) with T c = 122.4 ( 5 ) K , γ = 1.22 ( 1 ) with T c = 122.8 ( 1 ) K , and δ = 4.24 ( 2 ) at T c ~ 123 K suggest that the spins approach the three-dimensional Ising ( β = 0.325 , γ = 1.24 , and δ = 4.82 ) model coupled with attractive long-range interactions between spins that decay as J ( r ) ≈ r - 4.88 . Our results suggest that the ferrimagnetism in Fe Cr 2 Te 4 is due to itinerant ferromagnetism among the antiferromagnetically coupled Cr-Fe-Cr trimers.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Strain-modulated helimagnetism and emergent magnetic phase diagrams in highly crystalline MnP nanorod films

Here, we explore strain-modulated helimagnetism in highly crystalline MnP nanorod films grown on Si(100) substrates using molecular beam epitaxy. The strained MnP film exhibits a paramagnetic to ferromagnetic (FM) phase transition at $T_C$ ~ 279 K, and the FM to helical phase transition at $T_N$ ~ 110 K. The value of $T_N$ is greater than $T_N$ ~ 47K for the MnP single crystal, indicating strong strain-modulated helimagnetic states in the MnP nanorod film. The presence of significant thermal hysteresis in the helical phase indicates the coexistence of competing magnetic interactions, leading to the first-order metamagnetic transition. Similar to its single-crystal counterpart, an anisotropic magnetic effect is observed in the MnP film, which is independently confirmed by magnetic hysteresis loop and radio-frequency transverse susceptibility (TS) measurements. The evolution of the screw to the cone and fan phases is precisely tracked from magnetization vs magnetic field/temperature measurements. The temperature dependence of the anisotropy fields, extracted from the TS spectra, yields further insight into the competing nature of the magnetic phases. Unfolding of the different helical phases at $\textit{T}$ < 120 K (~$T_N$) is analyzed by the temperature- and field-dependent magnetic entropy change. Based on these findings, the comprehensive magnetic phase diagrams of the MnP nanorod film are constructed for both the in-plane and out of plane magnetic field directions, revealing emergent strain/dimensionality-driven helical magnetic features that are absent in the magnetic phase diagram of the MnP single crystal.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Flexocaloric effect near a ferroelastic transition

A Ginzburg-Landau model embedded into a vibrational model is used to study the flexocaloric effect in a beam near a ferroelastic transition. The caloric response upon bending is characterized by the isothermal entropy change and the adiabatic temperature change of the beam. Here, we obtain a larger response relative to the strength of the applied forces at temperatures slightly above the transition temperature. It is also obtained that the maximum caloric response is almost linear with the bending angle of the beam, whereas the relation between the bending angle and the applied forces is highly nonlinear. Small hysteresis associated with the phase transition is obtained for sufficiently large bending forces due to the existence of a critical point in the temperature-stress phase diagram of the ferroelastic material. Finally, the microstructure changes with bending in the beam are consistent with previous experimental observations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Small-moment antiferromagnetic ordering in single-crystalline La 2 Ni 7

Single crystals of La 2 Ni 7 have been grown out of a binary, La-Ni melt. Temperature dependent, zero magnetic field, specific heat, electrical resistivity, and low field magnetization measurements indicate that there is a series of antiferromagnetic phase transitions at T 1 = 61.0 ± 0.2 K, T 2 = 56.5 ± 0.2 K and T 3 = 42.2 ± 0.2 K. The three specific heat anomalies found at these temperatures qualitatively have very small entropy changes associated with them and the anisotropic M(H) data saturate at ~ 0.12 μ B /Ni; both observations strongly suggesting the AFM order is associated with very small, itinerant, moments. Anisotropic, H ||c and H ⟂c , ρ(H) and M(H) isotherms as well as constant field, ρ(T) and M(T) sweeps manifest signatures of multiple phase lines and result in HT phase diagrams that are clearly anisotropic. Analysis of M(T) and M(H) data allow for the identification of the two lower temperature magnetically ordered states as antiferromagnetically ordered, with the moments aligned along the crystallographic c-axis, and the higher temperature, T 2 < T < T 1 , state as having a finite ferromagnetic component. In addition, the metamagnetic transition at low temperatures, for H applied along the crystallographic c-axis (H ||c ) appears to be a near classic example of a spin-flop transition, resulting in a field stabilized antiferromagnetic state with the moments ordered perpendicular to the c-axis. Finally, although the small moment ordering, and existence of multiple phase transitions in field and temperature, suggesting an energetic proximity of these states, could foretell a degree of pressure sensitivity, our measurements of R(T) for applied pressures up to 2.0 GPa indicate that there is very little pressure dependence of T 1 , T 2 and T 3 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Magnetic frustration driven by conduction carrier blocking in Nd 2 Co 0.85 Si 2.88

The intermetallic compound Nd 2 Co 0.85 Si 2.88 having a triangular lattice could be synthesized in single phase only with defect crystal structure. Investigation through different experimental techniques indicate the presence of two magnetic transitions in the system. As verified experimentally and theoretically, the high-temperature transition $T_H$ ~ 140 K is associated with the development of ferromagnetic interaction between itinerant Co moments, whereas the low-temperature transition at $T_L$ ~ 6.5 K is due to the coupling among Nd–4$\textit{f}$ and Co–3$\textit{d}$ moments, which is antiferromagnetic in nature. Detailed studies of temperature-dependent dc magnetic susceptibility, field dependence of isothermal magnetization, nonequilibrium dynamical behavior, viz., magnetic relaxation, aging effect, magnetic-memory effect, and temperature dependence of heat capacity, along with density functional theory (DFT) calculations, suggest that the ground state is magnetically frustrated spin glass in nature, having competing magnetic interactions of equivalent energies. DFT results further reveal that the 3$\textit{d}$/5$\textit{d}$-conduction carriers are blocked in the system and act as a barrier for the 4$\textit{f}$–4$\textit{f}$ RKKY interactions, resulting in spin frustration. Presence of vacancy defects in the crystal are also conducive to the spin frustration. This is an unique mechanism of magnetic frustration, not emphasized so far in any of the ternary $R_2TX_3$ ($\textit{R}$ = rare earth, $\textit{T}$ = transition elements, and $\textit{X}$ = Si, Ge, In) type compounds. Due to the competing character of the itinerant 3$\textit{d}$ and localized 4$\textit{f}$ moments, the compound exhibits anomalous field dependence of magnetic coercivity. Further, the system also exhibits a considerable magnetic entropy change of –Δ$S_M$ ~ 13.3 J/kg K with a relative cooling power (RCP) of 220 J/kg and adiabatic temperature change $ΔT_{\text{ad}}$ of 6 K for magnetic field change of 70 kOe.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Electronic and magnetic phase diagrams of the Kitaev quantum spin liquid candidate Na 2 Co 2 TeO 6

The 3⁢d 7 Co 2+ -based insulating magnet Na 2 ⁢Co 2 ⁢TeO 6 has recently been reported to have strong Kitaev interactions on a honeycomb lattice and is thus being considered as a Kitaev quandum spin liquid candidate. However, due to the existence of other types of interactions, a spontaneous long-range magnetic order occurs. This order is suppressed by applied magnetic fields leading to a succession of phases and ultimately saturation of the magnetic moments. The precise phase diagram, the nature of the phases, and the possibility that one of the field-induced phases is a Kitaev quantum spin liquid phase are still a matter of debate. Here, in this study, we measured an extensive set of physical properties to build the complete temperature-field phase diagrams to magnetic saturation at 10 T for magnetic fields along the a and a* axes, and a partial phase diagram up to 60 T along c. We probe the phases using magnetization, specific heat, magnetocaloric effect, magnetostriction, dielectric constant, and electric polarization, which is a symmetry-sensitive probe. With these measurements, we identify all the previously incomplete phase boundaries and find additional high-field phase boundaries. We find strong magnetoelectric coupling in the dielectric constant and moderate magnetostrictive coupling at several phase boundaries. Furthermore, we detect the symmetry of the magnetic order using electrical polarization measurements under magnetic fields. Based on our analysis, the absence of electric polarization under zero or finite magnetic field in any of the phases or after any combination of magnetic/electric field cooling suggests that a zigzag spin structure is more likely than a triple-Q spin structure at zero field. Finally, we investigate the hysteresis and first- or second-order nature of each phase transition and its entropy changes. With this information, we establish a map of the magnetic phases of this compound and its magnetic, thermodynamic, and magnetoelectric properties, and discuss where spin liquid or other phases may be sought in future studies.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Multiple magnetic interactions and large inverse magnetocaloric effect in TbSi and TbSi 0.6 Ge 0.4

We present a comprehensive investigation of the electronic structure, magnetization, specific heat, and crystallography of TbSi (FeB structure type) and TbSi 0.6 ⁢Ge 0.4 (CrB structure type) compounds. Both TbSi and TbSi 0.6 ⁢Ge 0.4 exhibit two antiferromagnetic (AFM) transitions at T N⁢1 ≈ 58 and 57 K, and T N⁢2 ≈ 36 and 44 K, respectively, along with an onset of weak metamagneticlike transition around 6 T between T N⁢1 and T N⁢2 . High-resolution specific heat (C P ) measurements show the second- and first-order nature of the magnetic transition at T N⁢1 and T N⁢2 , respectively, for both samples. However, in the case of TbSi, the low-temperature (LT) AFM to high-temperature (HT) AFM transition takes place via an additional AFM phase at the intermediate temperature (IT), where both LT to IT AFM and IT to HT AFM phase transitions exhibit a first-order nature. Both TbSi and TbSi 0.6 ⁢Ge 0.4 manifest significant magnetic entropy changes (Δ⁢S M ) of 9.6 and 11.6 J/kg-K, respectively, for Δ⁢μ 0 ⁢H=7 T, at T N⁢2 . The HT AFM phase of TbSi 0.6 ⁢Ge 0.4 is found to be more susceptible to the external magnetic field, causing a significant broadening in the peaks of Δ⁢S M curves at higher magnetic fields. Temperature- and field-dependent specific-heat data have been utilized to construct the complex HT phase diagram of these compounds. As a result, temperature-dependent x-ray diffraction measurements demonstrate substantial magnetostriction and anisotropic thermal expansion of the unit cell in both samples.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Evolution of noncollinear magnetism in magnetocaloric MnPtGa

MnPtGa crystallizes in the hexagonal Ni 2 In structure type in space group P6 3 /mmc and has been reported to display a ferromagnetic Curie temperature near 220K. Here we find a transition near T c = 236 K to a ferromagnetic state, albeit with a reduced moment from what is expected for collinear ordering. The peak magnetocaloric entropy change was determined to be ΔS M = –1.9 J kg –1 K –1 for an applied magnetic field of H = 5 T at the ferromagnetic ordering temperature. Magnetostructural coupling manifests as a change in the slope of the thermal expansion coefficients of the c lattice parameter near T c , with a negative spontaneous volume magnetostriction; ω = –300 ppm at 190K. In this work, neutron powder diffraction studies of the magnetic ground state reveal an evolution in complexity as temperature decreases: from a ferromagnet, to a canted antiferromagnet, to the eventual formation of a spin-density-wave state at low temperatures.

36 MATERIALS SCIENCE↗

Crystal structure and physical properties of Yb 2 In and Eu 2–x Yb x In alloys

While binary R E 2 In , where R E = rare earth , have been reported a few decades ago, recent investigations revealed intriguing new physical insights. For instance, the discovery of a nearly ideal first-order ferromagnetic transition in Eu 2 In calls for further exploration of structures and properties of R E 2 In , in particular for the least-documented R E = Eu and Yb cases. In this work, we investigate Eu 2 – x Yb x In pseudobinaries with nominal values of x = 0.25 , 0.5, 0.75, 1, 1.5, 2 by powder x-ray diffraction (including as function of temperature from 100 to 375 K for Yb 2 In ), magnetization (5–300 K), as well as electrical resistivity (5–300 K) and calorimetric (2–150 K) measurements for Yb 2 In . Compared to other RE , Yb or Eu always raise challenging questions linked to their valence states. From average atomic volume, Yb is anticipated to be divalent in Yb 2 In , at least between 100 and 375 K, which is in line with the absence of 4 f magnetism. In agreement with x-ray diffraction and magnetization data, the resistivity of Yb 2 In is rather featureless and typical of a metal. Establishing Yb 2 In as a nonmagnetic isostructural reference for Eu 2 In allows one to use its heat capacity to revisit that of the latter, and get experimental insights into the exceptional magnetocaloric effect of the compound with Eu. In particular, we show that a third of the total magnetic entropy ( S m ≈ 35.6 J mo l – 1 K – 1 at T = 100 K ) is concentrated in a 3 K temperature window around the T C of Eu 2 In . Starting from the ferromagnetic compound Eu 2 In [ T C = 55.2 ( 5 ) K ] , we show that Yb substitutions in Eu 2 – x Yb x In lead to a decrease in both the Curie temperature [ T C = 41 ( 2 ) and 32(2) K for x = 0.25 and 0.5] and magnetic saturation, while weakening the first-order character of the transition as x increases. A significant isothermal entropy change of 5.1 ( 4 ) J mo l – 1 K – 1 for Δ B = 2 T is found at 44 K in Eu 1.75 Yb 0.25 In , demonstrating that the giant magnetocaloric effect of Eu 2 In can be tuned to lower temperatures by Yb substitutions.

36 MATERIALS SCIENCE↗

Large anisotropic magnetocaloric effect in all-sputtered epitaxial terbium thin films

We present an experimental investigation of the magnetic and magnetocaloric properties of sputtered epitaxial and amorphous Tb thin films. We grew epitaxial Nb (50-nm)/Tb (100-nm) bilayer thin films on Al 2 O 3 $(11\bar{2}0)$ substrate using DC magnetron sputtering at high temperature, with excellent crystalline quality of the hcp Tb(0001) layer. While the amorphous Tb thin film exhibits more isotropic magnetocaloric properties, we show that the epitaxial Tb thin film displays large anisotropic magnetocaloric properties, with a large maximum magnetic entropy change of 6.27 J kg -1 K -1 at the Néel temperature as well as a large relative cooling power of 225 J kg -1 with a magnetic field change ΔH = 20 kOe applied along the in-plane direction. These large and anisotropic magnetocaloric properties are much larger than those measured for the amorphous Tb thin film, or previously reported for Tb-based thin-film structures. Our findings highlight the opportunities for growing epitaxial rare-earth thin films using sputtering techniques and demonstrate the importance of crystallographic control on the magnetocaloric effect in Tb thin films.

36 MATERIALS SCIENCE↗

Tablelike magnetocaloric effect and enhanced refrigerant capacity in EuO 1- δ thin films

The effect of electron doping of EuO 1- δ thin films through oxygen vacancies ( δ = 0, 0.025, and 0.09) upon the magnetocaloric response is presented here. The films each showed a paramagnetic to ferromagnetic transition around 65 K, with an additional magnetic ordering transition at higher temperatures in the oxygen deficient samples. All transitions are observed to be of second order. A maximum magnetic entropy change of 6.4 J/kg K over a field change of 2 T with a refrigerant capacity of 223 J/kg was found in the sample with δ = 0, and in all cases the refrigerant capacities of the thin films under study were found to exceed that reported for bulk EuO. Adjusting the oxygen content was shown to produce tablelike magnetocaloric effects, desirable for ideal Ericsson-cycle magnetic refrigeration. These films are thus excellent candidates for small-scale magnetic cooling technology in the liquid nitrogen temperature range.

36 MATERIALS SCIENCE↗

Magnetoelastic-coupling-assisted first-order antiferromagnetic transitions in the corrugated honeycomb-lattice compounds (Ca, Sr) ⁢Mn 2 ⁢ P 2

Understanding the origin of unconventional magnetic order is a central theme in the research field of functional quantum materials for spin-dependent applications. In general, a paramagnetic (PM) to antiferromagnetic (AFM) transition is of thermodynamically second order in nature in the absence of a magnetic field. In the magnetically frustrated corrugated-honeycomb lattice compounds (Ca, Sr) ⁢Mn 2 ⁢ P 2 , electrical resistivity 𝜌 measurements in the 𝑎⁢𝑏 plane are reported to exhibit sharp discontinuities at the respective PM to AFM ordering temperatures 𝑇 N = 69.5 and 53 K, respectively, signifying the unusual first-order nature of the AFM transition. To reveal the origin of such anomalous transitions, high-resolution linear thermal-expansion measurements are reported for both CaMn 2 ⁢P 2 and SrMn 2 ⁢ P 2 in the 𝑎⁢𝑏 plane and along the 𝑐 axis using capacitance dilatometry. The thermal expansion measurements show a sharp discontinuity in Δ⁢𝐿/𝐿 at 𝑇 N , yielding a diverging behavior in the thermal expansion coefficient 𝛼⁡(𝑇) associated with strong magnetoelastic coupling, driving the first-order AFM transition in CaMn 2 ⁢P 2 . However, this effect is weaker in SrMn 2 ⁢P 2 , consistent with the magnetic entropy changes 𝑆⁡(𝑇) obtained from the heat-capacity measurements. Temperature-dependent 𝑎⁢𝑏-plane x-ray diffraction measurements for CaMn 2 ⁢ P 2 near its 𝑇 N yield a volume thermal expansion coefficient consistent with literature data for other materials. The uniaxial pressure derivatives of 𝑇 N in the two compounds are found to be respectively opposite in sign, presumably due to the different magnetic structures.

Pakhira, Santanu [Maulana Azad National Institute ↗

Verwey transition as evolution from electronic nematicity to trimerons via electron-phonon coupling

Understanding the driving mechanisms behind metal-insulator transitions (MITs) is a critical step toward controlling material’s properties. Since the proposal of charge order–induced MIT in magnetite Fe 3 O 4 in 1939 by Verwey, the nature of the charge order and its role in the transition have remained elusive. Recently, a trimeron order was found in the low-temperature structure of Fe 3 O 4 ; however, the expected transition entropy change in forming trimeron is greater than the observed value, which arises a reexamination of the ground state in the high-temperature phase. Here, we use electron diffraction to unveil that a nematic charge order on particular Fe sites emerges in the high-temperature structure of bulk Fe 3 O 4 and that, upon cooling, a competitive intertwining of charge and lattice orders arouses the Verwey transition. Our findings discover an unconventional type of electronic nematicity in correlated materials and offer innovative insights into the transition mechanism in Fe 3 O 4 via the electron-phonon coupling.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Effect of Temperature and FEC on Silicon Anode Heat Generation Measured by Isothermal Microcalorimetry

Isothermal microcalorimetry (IMC) was used to better understand parasitic reactions and heat generation from Si electrodes in the first 10 cycles using Li/Si half cells. Heat generation from cell polarization (ohmic heat), entropy changes (reversible heat), and parasitic reactions (parasitic heat) are separated and quantified. The effect of temperature and fluoroethylene carbonate (FEC) as an electrolyte additive are also explored. Our results show that at the C/10 cycling rate used here, ohmic heat makes the largest contribution to overall heat generation while reversible heat is the smallest. Ohmic heat generation increases with cycle number due to increasing internal resistance, though the effect is smaller for cells with FEC. Interestingly, capacity-normalized parasitic heat generation is largely unaffected by changes in temperature despite differing reaction kinetics. We show that this is caused by a decrease in average parasitic reaction enthalpy as temperature is increased. Further, cells with FEC display higher average parasitic reaction enthalpy than cells without. The average parasitic reaction enthalpies for all the Si electrodes we tested were lower than previously reported values for graphite, indicating that the SEI formed on Si is less stable.

25 ENERGY STORAGE↗

Isothermal Microcalorimetry Analysis of Li/ β -MnO 2 Discharge

Despite widespread use over several decades, the lithium/manganese dioxide (Li/MnO 2 ) discharge mechanism is not completely understood owing to the structural complexity of the material. However, an improved understanding could lead to broader adoption as a primary and even secondary cathode material. Here, we examine the discharge of single-phaseβ-MnO 2 using isothermal microcalorimetry for the first time. Equilibrium voltage and entropy changes are characterized over the entire discharge range and used to rationalize the results. These measurements are supplemented by electrochemical impedance and X-ray diffraction data that give the clearest picture of theβ-MnO 2 lithiation process to date. We find that the first half of discharge is dominated by a two-phase reaction to form Li 0.5 MnO 2 followed by single-phase insertion to a composition of Li 1.0 MnO 2 , which confirms prior first-principles calculations. The tetragonalβ-MnO 2 lattice undergoes asymmetric expansion from Jahn-Teller distorted Mn 3+ to form an orthorhombic LiMnO 2 phase which retains the 1 × 1 tunnel structure. Microcalorimetry results suggest the presence of parasitic reactions occurring during the second half of discharge, which could arise from decomposition of electrolyte or release and reaction of residual water retained in the structure.

Electrochemistry↗

External-Field-Induced Phase Transformation and Associated Properties in a Ni 50 Mn 34 Fe 3 In 13 Metamagnetic Shape Memory Wire

Metamagnetic shape memory alloys exhibit a series of intriguing multifunctional properties and have great potential for applications in magnetic actuation, sensing and magnetic refrigeration. However, the poor mechanical properties of these alloys with hardly any tensile deformability seriously limit their practical application. In the present work, we developed a Ni-Fe-Mn-In microwire that exhibits both a giant, tensile superelasticity and a magnetic-field-induced first-order phase transformation. The recoverable strain of superelasticity is more than 20% in the temperature range of 233–283 K, which is the highest recoverable strain reported heretofore in Ni-Mn-based shape memory alloys (SMAs). Moreover, the present microwire exhibits a large shape memory effect with a recoverable strain of up to 13.9% under the constant tensile stress of 225 MPa. As a result of the magnetic-field-induced first-order phase transformation, a large reversible magnetocaloric effect with an isothermal entropy change ΔS m of 15.1 J kg –1 K –1 for a field change from 0.2 T to 5 T was achieved in this microwire. The realization of both magnetic-field and tensile-stress-induced transformations confers on this microwire great potential for application in miniature multi-functional devices and provides an opportunity for multi-functional property optimization under coupled multiple fields.

36 MATERIALS SCIENCE↗

A Robust Protocol for Entropy Measurement in Mesoscopic Circuits

Previous measurements utilizing Maxwell relations to measure change in entropy, S, demonstrated remarkable accuracy in measuring the spin-1/2 entropy of electrons in a weakly coupled quantum dot. However, these previous measurements relied upon prior knowledge of the charge transition lineshape. This had the benefit of making the quantitative determination of entropy independent of scale factors in the measurement itself but at the cost of limiting the applicability of the approach to simple systems. To measure the entropy of more exotic mesoscopic systems, a more flexible analysis technique may be employed; however, doing so requires a precise calibration of the measurement. Here, we give details on the necessary improvements made to the original experimental approach and highlight some of the common challenges (along with strategies to overcome them) that other groups may face when attempting this type of measurement.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗