Isothermal magnetization curves up to 23 T have been measured in Gd 5 Si 1.8 Ge 2.2 . We show that the values of the entropy change at the first-order magnetostructural transition, obtained from the Clausius-Clapeyron equation and the Maxwell relation, are coincident, provided the Maxwell relation is evaluated only within the transition region and the maximum applied field is high enough to complete the transition. These values are also in agreement with the entropy change obtained from differential scanning calorimetry. We also show that a simple phenomenological model based on the temperature and field dependence of the magnetization accounts for these results. DOI: 10.1103/PhysRevB.66.100401 PACS number͑s͒: 75.30.Sg, 75.30.Kz, 64.70.Kb The magnetocaloric effect ͑MCE͒ is the adiabatic temperature change that arises from the application or removal of a magnetic field. MCE is associated with the isothermal entropy change due to the field variation. Recently, a great deal of interest has been devoted to searching for systems showing first-order magnetostructural transitions with large entropy change, since they are expected to display giant MCE. Among these materials, Gd 5 (Si x Ge 1Ϫx ) 4 ͑Refs. 1-5͒ and Mn-As-based 6,7 intermetallic alloys are the most promising candidates.The correct evaluation of the entropy change related to the MCE is a controversial issue and has lately aroused much discussion. 1,8 -12 For Gd 5 (Si x Ge 1Ϫx ) 4 , Giguère et al. 8 showed that the use of the Maxwell relation to calculate the entropy change overestimates ͑at least ϳ20%͒ the value obtained from the Clausius-Clapeyron equation that the authors 8,11 claimed to be the correct procedure due to the first-order nature of the transition in these alloys. According to them, the entropy change in the magnetostructural transition is not associated with the continuous change of the magnetization as a function of T and H, but rather with the discontinuous change in the magnetization due to the crystallographic transformation. They claimed that Maxwell relations do not hold since magnetization is not a continuous, derivable function in that case. In contrast, Gschneidner, Jr. et al. 9 argued that the Maxwell relation is applicable even in the occurrence of a first-order transition, except when this transition takes place at a fixed T and H, giving rise to a steplike change of the magnetization ͑ideal case͒. Besides, they claimed that Clausius-Clapeyron equation would imply an H-independent adiabatic temperature change, which however, is not consistent with the experimental observations. 8 Moreover, Sun et al. 10 showed that the entropy change calculated from the Maxwell relation is indeed equivalent to that given by the Clausius-Clapeyron equation, provided the magnetization M is considered T-independent in whichever phase the transition involves, and M is a step function with a finite jump at the transition temperature. They also suggested that the two procedures may yield different results, since the Clausius-Clapeyron meth...

We have analyzed magnetization measurements in a series of composition-related Ni-Mn-Ga shape-memory alloys. It is shown that the magnetocaloric effect in the vicinity of the martensitic transition mainly originates from two different contributions: ͑i͒ magnetostructural coupling on the mesoscopic scale between the magnetic moments and the martensitic variants, which is also responsible for the magnetic shape-memory effect and ͑ii͒ the microscopic spin-phonon coupling which gives rise to the shift of the transition temperature with the applied magnetic field. The relative importance of these two contributions has been shown to vary with composition, which is suitably expressed through the average number of valence electrons per atom e/a. In alloys with a large difference between the Curie and martensitic transition temperatures (e/aӍ7.5), mesoscopic coupling is dominant and a negative giant magnetocaloric effect ͑increase of temperature by adiabatic demagnetization͒ is induced at moderate applied fields. In contrast, in alloys when these temperatures are very close to one another (e/aӍ7.7), the microscopic coupling is the most relevant contribution and gives rise to a positive giant effect.

The magnetocaloric effect that originates from the martensitic transition in the ferromagnetic Ni-Mn-Ga shape-memory alloy is studied. We show that this effect is controlled by the magnetostructural coupling at both the martensitic variant and magnetic domain length scales. A large entropy change induced by moderate magnetic fields is obtained for alloys in which the magnetic moment of the two structural phases is not very different. We also show that this entropy change is not associated with the entropy difference between the martensitic and the parent phase-arising from the change in the crystallographic structure-which has been found to be independent of the magnetic field within this range of fields.

We have developed a differential scanning calorimeter capable of working under applied magnetic fields of up to 5 T. The calorimeter is highly sensitive and operates over the temperature range 10-300 K. It is shown that, after a proper calibration, the system enables determination of the latent heat and entropy changes in first-order solid-solid phase transitions. The system is particularly useful for investigating materials that exhibit the giant magnetocaloric effect arising from a magnetostructural phase transition. Data for Gd 5 (Si 0.1 Ge 0.9 ) 4 are presented.

In this paper, the application of an in situ stress measurement technique to a silicon nitride thin film deposited onto a thick silicon substrate is presented. The method is based on the measurement of the displacement field originated when a slot is milled into the material under study. Displacements are obtained by digital correlation analysis of scanning electron microscope (SEM) images, whereas milling is performed by ion milling in focused ion-beam equipment. Due to the mechanical constraint introduced by the substrate and the small thickness of the tested layer, the displacements generated by the milling process are in the range 0–5 nm, which is one of the smallest displacement ranges measured up to now in a relaxation-based measurement technique. The local stress value determined with this new method is in good agreement with values obtained by a classical method like the wafer bending test.