Finding the Separation Between First-and Second-Order Phase transitions in La(Fe,Ni,Si)13 magnetocaloric materials

Magnetocaloric (MC) materials have the potential to renew the basis of refrigeration technologies for the next years. To date (and since first commercial devices in 1927), refrigerators operate by expansion/compression of gases in a closed circuit where the condensation/evaporation produces wasted heating/the cooling of a load. The main disadvantages of such devices are their usage of non-environmental-friendly gases (e.g. ozone depletion) and low energy efficiency. Conversely, magnetic refrigerator using magnetocaloric materials addresses these issues by utilizing solids of non-contaminating refrigerants and their prototypes show a larger energetic efficiency. In this case, the MC material replaces those gases and the expansion/compression is replaced by the application/removal of a magnetic field. The largest reversible temperature variation of a material submitted to a variable magnetic field in adiabatic conditions (ΔT
S
) occurs near the temperature of a magnetic or magnetostructural phase transition. These phase transitions can be classified as first order (FOPT) or second order ones (SOPT) according to the Ehrenfest classification. Therefore, the MC characterization is not only useful from a technological point of view but can also be used to extract information about the phase transition. It has been demonstrated that assuming a power law expression for the field dependence of the magnetic entropy change (ΔS
T
), taking the form $\Delta S_{T}(T,H)=a(T)\Delta H^{{{n {(}} {T {,}}} {H {)}}}$. The values of the exponent n at the transition temperature (T
trans
) are related with the critical exponents of a SOPT as $n= 1 +(1 -1/ \beta )/ \delta $, where the exponents β and δ give the temperature dependence of M at zero field and the field dependence of M at T
trans
, respectively. For materials with long range interactions the values of $n(T_{trans})$ in SOPT are typically close to those using the critical exponents for mean field model (0.67). On the other hand, for short range interactions, the typical values are close to Heisenberg or 3D-Ising models (0.63 and 0.57, respectively). For the $n(T_{trans})$ of SOPT there exists a lower limit that corresponds to the case where the material transits from a SOPT to a FOPT character, this point is called the critical point of the second order phase transition. The value at that point is 0.4 according to the critical exponents obtained from theoretical considerations. For FOPT, even if there is no critical region, the field dependence of ΔS
T
in the high field range leads to n values lower than 0.4. Therefore, a clear criterion exits to identify the change from SOPT to FOPT according to the values of n(T
trans
). One of the most promising families of magnetocaloric materials are LaFeSi alloys. These alloys show a magnetic FOPT that implies a large magnetocaloric response. Hydrogenation of the samples shifts the transition temperature from ≈ 200 K to temperatures close to room temperature, to facilitate their applications in devices. However, some issues have to be solved before commercialization: its cyclic stability needs to be improved and thermal hysteresis is to be minimized. Different dopants can be used to tune properties such as T
trans
, the MC response and hysteresis. In this work, we study the magnetocaloric properties of LaFeSi alloys doped with Ni (LaFe
11.6-x
Ni
x
Si
1
with x = 0, 0.1, 0.2, 0.3 and 0.4). Microstructural characterization (BSE and XRD) shows a high percentage of LaFe
13
phase in the alloys. EDX analysis confirms the desired nominal compositions. Magnetocaloric characterization has been performed by indirect measurements of ΔS
T
from magnetization measurements) and direct measurements of ΔT
S
dedicated device built in TU Darmstadt). Figure 1 shows how the temperature dependence of ΔT
S
is modified by the addition of Ni. The criterion to distinguish the order of the phase transition from the value of the exponent of the field dependence of ΔS
T
has been applied (Figure 2). This procedure allows us to estimate the composition for which the transition is in the critical point of the second-order phase transition (sample with x = 0.21), also shown in Figure 2. DFT calculations have been performed in order to explain the role of Ni atoms in LaFe
13
phase, showing a good agreement with experimental data. This work was supported by MINECO and EU FEDER (project MAT2013-45165-P), AEI/FEDER-UE (project MAT-2016-77265-R), the PAI of the Regional Government of Andalucía, the Deutscher Akademischer Austauschdienst DAAD (Award A/13/09434). L. M. Moreno-Ramírez acknowledges a FPU fellowship from the Spanish MECD. O.G., I.R., and K.S. would like to acknowledge funding by the DFG in the framework of the priority program “Ferroic Cooling” (SPP1599).