Multicaloric Effect in 0–3-Type MnAs/PMN–PT Composites

: The new xMnAs/(1 − x)PMN–PT (x = 0.2, 0.3) multicaloric composites, consisting of the modiﬁed PMN–PT-based relaxor-type ferroelectric ceramics and ferromagnetic compound of MnAs were fabricated, and their structure, magnetic, dielectric properties, and caloric effects were studied. Both components of the multicaloric composite have phase transition temperatures around 315 K, and large electrocaloric (~0.27 K at 20 kV/cm) and magnetocaloric (~13 K at 5 T) effects around this temperature were observed. As expected, composite samples exhibit a decrease in magnetocaloric effect (<1.4 K at 4 T) in comparison with an initial MnAs magnetic component (6.7 K at 4 T), but some interesting phenomena associated with magnetoelectric interaction between ferromagnetic and ferroelectric components were observed. Thus, a composite with x = 0.2 exhibits a double maximum in isothermal magnetic entropy changes, while a composite with x = 0.3 demonstrates behavior more similar to MnAs. Based on the results of experiments, the model of the multicaloric effect in an MnAs/PMN–PT composite was developed and different scenario observations of multicaloric response were modeled. In the framework of the proposed model, it was shown that boosting of caloric effect could be achieved by (1) compilation of ferromagnetic and ferroelectric components with large caloric effects in selected mass ratio and phase transition temperature; and (2) choosing of magnetic and electric ﬁeld coapplying protocol. The 0.3MnAs/0.7PMN–PT composite was concluded to be the optimal multicaloric composite and a phase shift ∆ ϕ = − π /4 between applied manetic ﬁelds can provide a synergetic caloric effect at a working point of 316 K.


Introduction
Recently, new materials exhibiting giant caloric effects of various nature have been actively investigated, due to their prospective applications as energy-efficient and environmentally friendly cooling systems based on solid-state cooling technologies [1][2][3][4][5][6][7][8].In these materials, known as caloric, the adiabatic temperature change (∆T AD ) (isothermal entropy change (∆S) is observed at applied external stimuli (magnetic field, electric field, mechanical (uniaxial, isotropic) load).These phenomena refer to the single caloric effects and are known as magnetocaloric (MCE), electrocaloric (ECE), and mechanocaloric (MechCE) effects, which have potential applications in solid-state cooling technologies.The novel concept based on the coexistence of caloric effects was recently proposed, and phenomena concluded in the observation of combined caloric effects with different external stimuli were noted as multicaloric [9][10][11][12].Materials that exhibit more than two caloric effects are named multicalorics, and are actively studied as advanced objects for energy applications and straintronics [13,14].From another point of view, it is well known that multiferroics materials coexistence with various types of ferro (magnetic, electric, elastics) ordering [15,16].Thus, multicalorics can be classified as multiferroics and generally can be divided into natural and composite.The prospects for applications of composite technologies in the design of multicaloric materials with magnetoelectric (ME) coupling were discussed and the approaches based on composite technologies were proposed as possible ways to control caloric effects [17][18][19][20].
A frontal idea proposed in our work is aimed at the design of multicaloric composites, which consist of two phases: ferroelectric (FE) and ferromagnetic (FM) components with large caloric performance.As the simplest model object of multicaloric material, the ME composite with a 0-3-type connection scheme can be used (Figure 1).A multicaloric composite with a 0-3-type connection consists of FM microparticles with large MCE embedded in an FE matrix of material with large ECE.FM microparticles have random shapes and are randomly distributed in the FE matrix.In the proposed model, both FM and FE components have phase transition (PT) temperatures in the same temperature range.
and are known as magnetocaloric (MCE), electrocaloric (ECE), and mechano (MechCE) effects, which have potential applications in solid-state cooling techno The novel concept based on the coexistence of caloric effects was recently propose phenomena concluded in the observation of combined caloric effects with differen nal stimuli were noted as multicaloric [9][10][11][12].Materials that exhibit more than two effects are named multicalorics, and are actively studied as advanced objects for applications and straintronics [13,14].From another point of view, it is well know multiferroics materials coexistence with various types of ferro (magnetic, electric, e ordering [15,16].Thus, multicalorics can be classified as multiferroics and genera be divided into natural and composite.The prospects for applications of composit nologies in the design of multicaloric materials with magnetoelectric (ME) couplin discussed and the approaches based on composite technologies were proposed as p ways to control caloric effects [17][18][19][20].
A frontal idea proposed in our work is aimed at the design of multicaloric c sites, which consist of two phases: ferroelectric (FE) and ferromagnetic (FM) comp with large caloric performance.As the simplest model object of multicaloric mater ME composite with a 0-3-type connection scheme can be used (Figure 1).A multi composite with a 0-3-type connection consists of FM microparticles with large MC bedded in an FE matrix of material with large ECE.FM microparticles have ra shapes and are randomly distributed in the FE matrix.In the proposed model, bo and FE components have phase transition (PT) temperatures in the same tempe range.This research is devoted to the design, fabrication, and study of caloric effects proposed 0-3 type of multicaloric composite.The cross-caloric effects due to the M pling between FM and FE at PT temperatures are expected.An FM with giant MCE component and a modified solid solution of PMN-PT ferroelectric ceramic with P room temperature was proposed for the design and study of a new 0-3-type multi composite.

Experimental Details
The 0-3-type multiferroic composites (x)MnAs/(1 − x)PMN-PT (x = 0.2; 0.3), c ing of the modified PMN-PT relaxor-type ferroelectric ceramics with formula z)Baz(Mg1/3Nb2/3)m(Zn1/3Nb2/3)y(Ni1/3Nb2/3)nTixO3 (z = 0.10, m = 0.4541, y = 0.098 0.1477, x = 0.3), and ferromagnetic compound of MnAs, were fabricated by a cold-pr method of powders in selected mass ratio.For this procedure, powders of FE a components were milled, sieved, and mixed in a selected ratio for 4 h.Then, the ob final powder was pressed under 3 GPa hydrostatic pressure at room temperature w exposure time of 12 h.This research is devoted to the design, fabrication, and study of caloric effects in the proposed 0-3 type of multicaloric composite.The cross-caloric effects due to the ME coupling between FM and FE at PT temperatures are expected.An FM with giant MCE as FM component and a modified solid solution of PMN-PT ferroelectric ceramic with PT near room temperature was proposed for the design and study of a new 0-3-type multicaloric composite.
The FE component of composite Pb 0.9 Ba 0.1 (Mg 1/3 Nb 2/3 ) 0.4541 (Zn 1/3 Nb 2/3 ) 0.0982 (Ni 1/3 Nb 2/3 ) 0.1477 Ti 0.3 O 3 was prepared by conventional solid-state synthesis using a columbite precursor route [21].The choice of this composition is due to the desire to combine low temperature (close to room temperature) of transition into the ferroelectric state with high piezoelectric parameters [22].Synthesis of the columbite-like compositions MgNb 2 O 6 , NiNb 2 O 6 , and ZnNb 2 O 6 from the oxides MgO, NiO, ZnO, and Nb 2 O 5 included two stages: ZnNb 2 O 6 and MgNb 2 O 6 were synthesized at temperatures of T 1 = 1273 K and T 2 = 1373 K for 6 and 4 h, respectively; for NiNb 2 O 6 , the synthesis temperatures were T 1 = 1273 K and T 2 = 1513 K for 6 and 2 h, respectively.Solid solutions of the final composition were produced by single-phase synthesis of the columbite compositions that had been obtained earlier and also by the synthesis of PbO, TiO 2 , and BaCO 3 at T = 1223 K for 4 h.Sintering was carried out using conventional ceramic technology at a temperature of 1453 K. X-ray diffraction analysis confirmed the absence of traces of impurity phases on the XRD patterns [22].The relative density of the sintered ceramics was ~95% of the theoretical value.
Both components have the temperature of FE and FM phase transition (PT) around room temperature and this was the reason why these components were selected as components of the designed composite [22,26].In total, for further studies, two samples used as pristine FE and FM components of composite and two samples of multicaloric composites with 20 wt.% (0.2MnAs/0.8PMN-PT)and 30 wt.% (0.3MnAs/0.7PMN-PT) of FM component were selected.
The chemical composition and the microstructure of the samples were examined using a JSM F7600 scanning electron microscope (SEM) (JEOL Ltd., Akishima, Japan) equipped with an X-max energy dispersive spectroscopy (EDS) detector (Oxford Instruments, Abingdon, UK).The structure was characterized by X-ray diffraction (XRD) using Cu Kα radiation at room temperature.
The magnetic measurements were carried out using the VSM technique (LakeShore 7400).The MCE was measured by direct method on a homemade setup using a superconducting 8 T magnetic field source [27].The adiabatic temperature change of the sample in a varying magnetic field was measured using a differential thermocouple (type T), fabricated by electric welding of the flattened to plate with a thickness of 3 µm copper and constantan wires (Ø 25 µm).The thermocouple signal that passed through the SR554 transformer preamplifier was measured by the SR830 Lock-in.A cryogen-free superconducting magnet system with a maximum field of 8 T served as a source of the magnetic field.The heating rate of the samples in MCE experiments was about 1 K/min.
The ECE effect was measured using the direct method as adiabatic temperature change ∆T AD ECE under varied electric fields.The control of the initial temperature during measurements was carried out using a liquid thermostat Julabo FP32-ME.The electric field on the sample was applied using a high-voltage amplifier Trek 609E-6 and a pulse generator Agilent 33522A.The temperature change due to the ECE was measured by the contact method using a platinum thermistor connected to a nanovoltmeter Agilent 34420A.Rectangular voltage pulses with a duty cycle of 50% were applied to the sample.The duration of the pulse period was twice as long as the thermal relaxation time of the sample and was 120 seconds.The experimental setup and measurement procedure are described elsewhere [28,29].Polarization hysteresis P(E) measurements were carried out using the Sawyer-Tower method in a quasistatic mode.
Dielectric measurements were performed using test stands fitted with an Agilent E4980A LCR meter (at temperatures ranging from 298 to 873 K) and a Wayne Kerr 6500B impedance analyzer (in the temperature interval of 10-325 K) [22].For dielectric measurements, a disk-shaped sample with a diameter of 10 mm and a thickness of 1 mm was formed.Electric contacts were made by deposition of Ag paste with further curing.The small-signal piezoelectric coefficient d 33 was measured using a Berlincourt-type d 33 meter APC YE2730A.The main electrophysical parameters (dielectric constant of polarized samples, ε 33 T , the dielectric loss tangent, tan δ, the planar electromechanical coupling coefficient, K p , the mechanical quality factor, Q m , the sound velocity, V E 1 , and Young's modulus, Y E 11 ) were determined on polarized samples (polarized at E = 30 kV/cm) by the resonance-antiresonance method using an impedance analyzer (Wayne Kerr 6500B).

Results and Discussion
The normalized XRD patterns of the fabricated composites (x)MnAs/(1 − x)PMN-PT (x = 0.2; 0.3) and their initial FM and FE components of MnAs and modified PMN-PT at room temperature are shown in Figure 2. Observed XRD spectra for initial components confirm the hexagonal NiAs-type structure for MnAs and pseudocubic for Pb 0.9 Ba 0.1 (Mg 1/3 Nb 2/3 ) 0.45 (Zn 1/3 Nb 2/3 ) 0.098 (Ni 1/3 Nb 2/3 ) 0.14 Ti 0.3 O 3 , which is in agreement with data from the literature [22,30].The composite fabrication process does not lead to the appearance of the impurity phases and, as seen, only intensity peaks corresponding to the FM (MnAs) and FE (PMN-PT) components of composites are observed.Some intensity peaks for MnAs and PMN-PT overlapped, and a reduction of unique for MnAs intensity peaks in composite samples was observed.
. Compos.Sci.2023, 7, x FOR PEER REVIEW 4 APC YE2730A.The main electrophysical parameters (dielectric constant of polarized ples, ε33 T , the dielectric loss tangent, tan δ, the planar electromechanical coupling c cient, Kp, the mechanical quality factor, Qm, the sound velocity, V E 1, and Young's mod Y E 11) were determined on polarized samples (polarized at E = 30 kV/cm) by the reson antiresonance method using an impedance analyzer (Wayne Kerr 6500B).

Results and Discussion
The normalized XRD patterns of the fabricated composites (x)MnAs/(1 − x)PMN (x = 0.2; 0.3) and their initial FM and FE components of MnAs and modified PMNroom temperature are shown in Figure 2. Observed XRD spectra for initial compo confirm the hexagonal NiAs-type structure for MnAs and pseudocubic Pb0.9Ba0.1(Mg1/3Nb2/3)0.45(Zn1/3Nb2/3)0.098(Ni1/3Nb2/3)0.14Ti0.3O3,which is in agreement with from the literature [22,30].The composite fabrication process does not lead to the ap ance of the impurity phases and, as seen, only intensity peaks corresponding to th (MnAs) and FE (PMN-PT) components of composites are observed.Some intensity p for MnAs and PMN-PT overlapped, and a reduction of unique for MnAs intensity p in composite samples was observed.The SEM images of the fabricated composites (x)MnAs-(1 − x)PMN-PT (x = 0.2; 0.3) and their initial FM and FE components of MnAs and modified PMN-PT are shown in Figure 3.
Both 0.2MnAs/0.8PMN-PTand 0.3MnAs/0.7PMN-PTsamples have a composite microstructure, and agglomerates of MnAs microparticles (some big agglomerates in Figure 3c,d are circled in red) dispersed in PMN-PT matrix are observed.All inclusions of MnAs particle agglomerates have random shapes and the increase in the concentration of MnAs is observed on SEM images of 0.2MnAs/0.8PMN-PTand 0.3MnAs/0.7PMN-PTsamples.Figure 4 shows the temperature dependence of the dielectric constant (ε) of the studied pristine FE sample of modified PMN-PT ceramics, measured at various frequencies (f ) of an AC electric field on cooling.It is seen that the ε(T) behavior is typical of relaxor ferroelectrics: temperature of the dielectric maximum (T m ) shifts towards high temperature with increasing f and its shape is smoothed.Both 0.2MnAs/0.8PMN-PTand 0.3MnAs/0.7PMN-PTsamples have a composite microstructure, and agglomerates of MnAs microparticles (some big agglomerates in Figure 3c,d are circled in red) dispersed in PMN-PT matrix are observed.All inclusions of MnAs particle agglomerates have random shapes and the increase in the concentration of MnAs is observed on SEM images of 0.2MnAs/0.8PMN-PTand 0.3MnAs/0.7PMN-PTsamples.Figure 4 shows the temperature dependence of the dielectric constant (ε) of the studied pristine FE sample of modified PMN-PT ceramics, measured at various frequencies (f) of an AC electric field on cooling.It is seen that the ε(T) behavior is typical of relaxor ferroelectrics: temperature of the dielectric maximum (Tm) shifts towards high temperature with increasing f and its shape is smoothed.Both 0.2MnAs/0.8PMN-PTand 0.3MnAs/0.7PMN-PTsample crostructure, and agglomerates of MnAs microparticles (some big 3c,d are circled in red) dispersed in PMN-PT matrix are observed.particle agglomerates have random shapes and the increase in the is observed on SEM images of 0.2MnAs/0.8PMN-PTand 0.3MnA Figure 4 shows the temperature dependence of the dielectric con pristine FE sample of modified PMN-PT ceramics, measured at va an AC electric field on cooling.It is seen that the ε(T) behavior is ty lectrics: temperature of the dielectric maximum (Tm) shifts towards increasing f and its shape is smoothed.The frequency dependence of T m for the ceramics studied is well described by the empirical Vogel-Fulcher law: where (for classical relaxors like PbMg 1/3 Nb 2/3 O 3 ) f 0 is the frequency of attempts to overcome the potential barrier, E a is the activation energy, k is the Boltzmann constant, and T VF corresponds to the freezing temperature of the dipole dynamics and the transition from ergodic to nonergodic relaxor state.For the studied ceramic, T VF = 293 K, which means that it is in an intermediate state between the ergodic relaxor and nonergodic (or ferroelectric) at room temperature.
In addition, other features of relaxor ferroelectrics are observed.In particular, the parameter ∆ (∆ = T m2 − T m1 , where T m1 , T m2 , the temperatures of the maxima of ε(T) dependence obtained at f 1 = 1 kHz and f 2 = 100 kHz) is large enough (9 K).Also, the diffuseness parameters of the ε(T) dependence take the typical values for relaxor ferroelectrics: δ = 52.2K and γ = 1.75 (this parameter ranges from 1 for normal ferroelectrics to 2 for ideal relaxor ferroelectrics [31]).The Burns temperature (T B ) was determined from the deviation of the ε(T) dependence from the Curie-Weiss law during cooling and amounted to about 555 K.This is more than 200 K higher than T m , which is also characteristic of relaxor ferroelectrics (like PbMg 1/3 Nb 2/3 O 3 ) [32].All of the above allows us to attribute the investigated solid section to the relaxor ferroelectrics.
At sufficiently large values of the external electric field, the ferroelectric state can be stabilized.The measured electrophysical (dielectric constant of polarized samples ε 33 T , the dielectric loss tangent, tan δ, the planar electromechanical coupling coefficient K p , the mechanical quality factor Q m , the sound velocity, V E 1 , Young's modulus Y E 11 ) and piezoelectric (piezoelectric coefficient d 33 ) parameters are collected in Table 1.Table 1 shows that the sample is characterized by relatively high values of dielectric (ε and ε 33 T > 10,000) and mechanical (Q m > 350) parameters while maintaining the average values of the piezoelectric coefficients.The listed features, as well as high dielectric and electromechanical responses to external electric fields, allow us to consider the studied composition as a component of a magnetoelectric composite.The normalized magnetization M/M s (M s -magnetization in 1 T at 300 K) curves as a function of temperature at 1 T magnetic fields for pristine MnAs and its composites in heating protocol are shown in Figure 5.As seen from the graphs, by increasing the temperature, an abrupt decrement of the magnetization is observed in the 310-320 K temperature region.This behavior corresponds to the first-order magnetic phase transition (FOMPT) from ferromagnetic to paramagnetic and is accompanied by a structural transition from hexagonal NiAs-type to an orthorhombic MnP-type structure (α (B81) → β (B31)).The FOMPT temperature for MnAs at the selected magnetic field is in agreement with the data from the literature [26,33].
With increasing of the applied magnetic field, the FOMPT temperature shifts toward a high-temperature region.In MnAs, a magnetic field shifts the transition toward high temperatures with the rate of dT t /µ 0 dH = ~3.3K/T according to the reported data [33,34].As seen from Figure 4a, for both composites, the FOMPT temperatures (~313 K for x = 0.3 and ~316.5 K for x = 0.3) are shifted to high-temperature regions in comparison with pristine MnAs (~312 K).The transition temperatures were estimated from M(T) curves by calculation of their temperature derivative dM/dT.M(T) depen-dence for 0.3MnAs/0.7PMN-PTlooks more like MnAs, while a more broadened transition is observed for the 0.2MnAs/0.8PMN-PTsample.As is known, the MnAs are very pressure-sensitive and the effect of pressure on FOMPT temperature detail was studied by Goodenough and Kafalas [35].They found that increasing pressure decreases the FOMPT temperature of MnAs with a rate dT t /dp~−9 K/kbar (p is changed from 0.001 kbar to 1.12 kbar).In our case, we do not observe the effect typical of applying isotropic pressure, which can be induced as a result of intergranular mechanical stresses forced on the FM component from the FE matrix.Moreover, both FM and FE components have PT temperatures around the same temperature, where maximal volume changes are typical, and it is complicated to explain the total pressure effect as a result of FM and PM phase interaction.Broadening of FOMPT and some shifting of transition temperature to the high-temperature region may be related to intergranular mechanical interactions between FM and FE microparticles when the matrix of FE particles inhibits the FOMPT.
ponent of a magnetoelectric composite.The normalized magnetization M/Ms (Ms-magnetization in 1 T at 300 K) cu function of temperature at 1 T magnetic fields for pristine MnAs and its comp heating protocol are shown in Figure 5.As seen from the graphs, by increasing perature, an abrupt decrement of the magnetization is observed in the 310-320 K ature region.This behavior corresponds to the first-order magnetic phase tr (FOMPT) from ferromagnetic to paramagnetic and is accompanied by a structura tion from hexagonal NiAs-type to an orthorhombic MnP-type structure (α (B (B31)).The FOMPT temperature for MnAs at the selected magnetic field is in ag with the data from the literature [26,33].
For this purpose, the series of isothermal magnetization curves M(µ 0 H) at different temperatures in the interval from 296 to 330 K were measured.∆S m was calculated using the numerical approximation in Equation (3).To define the integral, the trapezoidal rule was considered, while the numerical derivative was performed assuming the two-point method according to Equation (2): temperatures in the interval from 296 to 330 K were measured.∆Sm was calculated using the numerical approximation in Equation (3).To define the integral, the trapezoidal rule was considered, while the numerical derivative was performed assuming the two-point method according to Equation (2): The temperature dependences of the isothermal magnetic entropy change ∆Sm, calculated from the Maxwell relations, are shown in Figure 7.For all samples, as expected, a maximum of ∆Sm is observed in the region of the magnetic phase transition temperature of MnAs.The maximum value of the ∆Sm for pristine MnAs is about ~10.8 J kg −1 K −1 (1 T); large ∆Sm ~ 25 J kg −1 K −1 (2 T) were reported elsewhere [36].For composite samples, the maximum values of ∆Sm decrease significantly to ~0.12 J kg −1 K −1 for 0.2MnAs/0.8PMN-PTand ~1.56 J kg −1 K −1 for the 0.3MnAs/0.7PMN-PT.It is related to the mass ratio of MnAs, which responded to MCE, while the FE component of the composite is nonmagnetic and does not directly contribute to the MCE.The largest changes in ∆Sm maximum at ∆µ0H = 5 T from 47 J kg −1 K −1 under 0 kbar to 267 J kg −1 K −1 under 2.23 kbar applied hydrostatic pressure were observed by S. Gama et al. [37].
The temperature dependence of the magnetic entropy changes ∆Sm for the 0.2MnAs/0.8PMN-PTcomposite sample shows two broad maxima: the first in the region The temperature dependences of the isothermal magnetic entropy change ∆S m , calculated from the Maxwell relations, are shown in Figure 7.For all samples, as expected, a maximum of ∆S m is observed in the region of the magnetic phase transition temperature of MnAs.The maximum value of the ∆S m for pristine MnAs is about ~10.8 J kg −1 K −1 (1 T); large ∆S m ~25 J kg −1 K −1 (2 T) were reported elsewhere [36].For composite samples, the maximum values of ∆S m decrease significantly to ~0.12 J kg −1 K −1 for 0.2MnAs/0.8PMN-PTand ~1.56 J kg −1 K −1 for the 0.3MnAs/0.7PMN-PT.It is related to the mass ratio of MnAs, which responded to MCE, while the FE component of the composite is nonmagnetic and does not directly contribute to the MCE.The largest changes in ∆S m maximum at ∆µ 0 H = 5 T from 47 J kg −1 K −1 under 0 kbar to 267 J kg −1 K −1 under 2.23 kbar applied hydrostatic pressure were observed by S. Gama et al. [37].MnAs Figure 8 shows the temperature dependences of the adiabatic temperature changes ∆TAD MCE at different applied magnetic fields for pristine MnAs samples and both composites.As expected, the largest value of MCE is observed in pristine MnAs (Figure 8c), and reaches ∆TAD MCE = 13.06K at a field change of 5 T, which is in agreement with the data from the literature [36].For all samples, the behavior remains typical for materials with magnetostructural phase transitions, and a maximum of ∆TMCE is observed around FOMPT temperature.With the field increasing, the area of the MCE extends only toward high temperatures.In the field of 3 T, there is a sharp increase in the value of MCE, which can be explained by the fact that, in addition to changing the magnetic entropy, there is an additional mechanism that contributes to the total MCE.It can be assumed that in this case, that is due to a structural transition from the orthorhombic structure of the MnP type to the low-temperature hexagonal structure of the NiAs type, which is accompanied by a sharp change in the volume of the crystal lattice.The temperature dependence of the magnetic entropy changes ∆S m for the 0.2MnAs/ 0.8PMN-PT composite sample shows two broad maxima: the first in the region of 306 K, and the second in the region of 320 K.The larger maximum is associated with the magnetic phase transition of MnAs, which is shifted towards a high-temperature region compared with a pristine MnAs sample.The nature of small maximum may be related to the intergranular interaction of the FM and FE components of the composite, which can be considered as a multicaloric response as a result of the combination of external stimuli of different natures (magnetic and mechanical).
Figure 8 shows the temperature dependences of the adiabatic temperature changes ∆T AD MCE at different applied magnetic fields for pristine MnAs samples and both composites.As expected, the largest value of MCE is observed in pristine MnAs (Figure 8c), and reaches ∆T AD MCE = 13.06K at a field change of 5 T, which is in agreement with the data from the literature [36].For all samples, the behavior remains typical for materials with magnetostructural phase transitions, and a maximum of ∆T MCE is observed around FOMPT temperature.With the field increasing, the area of the MCE extends only toward high temperatures.In the field of 3 T, there is a sharp increase in the value of MCE, which can be explained by the fact that, in addition to changing the magnetic entropy, there is an additional mechanism that contributes to the total MCE.It can be assumed that in this case, that is due to a structural transition from the orthorhombic structure of the MnP type to the low-temperature hexagonal structure of the NiAs type, which is accompanied by a sharp change in the volume of the crystal lattice.
sites.As expected, the largest value of MCE is observed in pristine MnAs (Figure 8c), and reaches ∆TAD MCE = 13.06K at a field change of 5 T, which is in agreement with the data from the literature [36].For all samples, the behavior remains typical for materials with magnetostructural phase transitions, and a maximum of ∆TMCE is observed around FOMPT temperature.With the field increasing, the area of the MCE extends only toward high temperatures.In the field of 3 T, there is a sharp increase in the value of MCE, which can be explained by the fact that, in addition to changing the magnetic entropy, there is an additional mechanism that contributes to the total MCE.It can be assumed that in this case, that is due to a structural transition from the orthorhombic structure of the MnP type to the low-temperature hexagonal structure of the NiAs type, which is accompanied by a sharp change in the volume of the crystal lattice.It is worth paying attention to the fact that the magnitudes of the ∆TAD MCE shows unusual behavior for composites: for 0.2MnAs/0.8PMN-PTand 0.3MnAs/0.7PMN-PTsamples at 1 T the magnitudes of the MCE are approximately the same (~0.4K), then with increasing of the magnetic field there is an increase in the gap in the magnitude of the MCE in favor of 0.2MnAs/0.8PMN-PT,although this sample contains a smaller amount of magnetic phase than 0.3MnAs/0.7PMN-PT.This behavior may be associated with intergranular mechanical interactions between the FM and FE phases, which are most pronounced in the region of the phase transition temperature and in strong magnetic fields, including an additional contribution to the interaction mechanisms.

Electrocaloric Effect
The P(E) hysteresis loops measured at different temperatures for the pristine FE component are shown in Figure 9a.Due to high leakage currents and problems with the stabilization of temperature, the P(E) measurements for composite samples failed.As seen from Figure 9, the P(E) hysteresis loops have a slim shape typical of relaxor ferroelectrics.Both the remnant polarization and coercive field are gradually decreased when temperature rises (T > TVF).The temperature dependences of polarization at different electric fields are demonstrated as the behavior typical for relaxor-type ferroelectrics (Figure 9b).
Figure 10 shows the temperature dependencies of the adiabatic temperature changes ∆TAD FE at different applied electric fields for the pristine FE component of the modified PMN-PT ceramic.As seen, ∆TAD FE (T) shows a broad maximum around Tm and the maximum of the effect becomes more noticeable at ~0.27 K with an increase in the applied electric field up to 20 kV/cm.Observed temperature dependencies of ∆TAD FE (T) and values of ∆TAD FE are comparable with relaxor ferroelectric (1 − x)Pb(Mg 1/3Nb2/3)O3-xPbTiO3 solid- It is worth paying attention to the fact that the magnitudes of the ∆T AD MCE shows unusual behavior for composites: for 0.2MnAs/0.8PMN-PTand 0.3MnAs/0.7PMN-PTsamples at 1 T the magnitudes of the MCE are approximately the same (~0.4K), then with increasing of the magnetic field there is an increase in the gap in the magnitude of the MCE in favor of 0.2MnAs/0.8PMN-PT,although this sample contains a smaller amount of magnetic phase than 0.3MnAs/0.7PMN-PT.This behavior may be associated with intergranular mechanical interactions between the FM and FE phases, which are most pronounced in the region of the phase transition temperature and in strong magnetic fields, including an additional contribution to the interaction mechanisms.

Electrocaloric Effect
The P(E) hysteresis loops measured at different temperatures for the pristine FE component are shown in Figure 9a.Due to high leakage currents and problems with the stabilization of temperature, the P(E) measurements for composite samples failed.As seen from Figure 9, the P(E) hysteresis loops have a slim shape typical of relaxor ferroelectrics.Both the remnant polarization and coercive field are gradually decreased when temperature rises (T > T VF ).The temperature dependences of polarization at different electric fields are demonstrated as the behavior typical for relaxor-type ferroelectrics (Figure 9b).Due to the leakage currents and Joule heating, it was complicated to provide stable and correct measurements of the direct ECE in composite samples in the full 280-400 K temperature range.Moreover, high electric fields increase the risk of the electrical breakdown of the composite samples.Test measurements of the ∆TAD FE around 340 K for the 0.2MnAs/0.8PMN-PTsample show the value to be ~0.1 K.

Model of Multicaloric Effect
In a thermodynamic cycle based on a multicaloric effect (multiCE), two general scenarios for the application of external stimuli can be used: (1) simultaneous and (2) sequential.The central goal of the simultaneous application of external stimuli is to obtain a synergistic effect in which there is an increase in the total caloric effect due to its occurrence in each of the subsystems.However, in practice, the implementation of this scenario is problematic both from the point of view of the experimental setup and the choice of a material with suitable phase transition temperatures.Sequential application of external fields is used to improve the efficiency of systems based on the ordinary caloric effect in which the second field plays an assisted role.For example, the possibility of using a sequential application of a magnetic field and uniaxial compression to minimize the negative consequences of hysteresis effects was demonstrated in the example of Heulser alloys [12,43].The concept proposed in our work is based on the design of a multicaloric com- Figure 10 shows the temperature dependencies of the adiabatic temperature changes ∆T AD FE at different applied electric fields for the pristine FE component of the modified PMN-PT ceramic.As seen, ∆T AD FE (T) shows a broad maximum around T m and the maximum of the effect becomes more noticeable at ~0.27 K with an increase in the applied electric field up to 20 kV/cm.Observed temperature dependencies of ∆T AD FE (T) and values of ∆T AD FE are comparable with relaxor ferroelectric (1 − x)Pb(Mg 1/3 Nb 2/3 )O 3 -xPbTiO 3 solidsolution systems [38].These systems are one of the promising electrocaloric materials with large ECE in room-temperature regions [39][40][41].As a magnetic material with FOMPT, the ferroelectric relaxor solid solution also has a sensitivity to mechanical stress [42].Therefore, in the case of our 0-3 multicaloric composite, the reverse scenario can be observed when stress-mediated tuning of ECE as a result of magnetostriction or anomalous volume changes around the FOMPT temperature are observed.Due to the leakage currents and Joule heating, it was complicated to provid and correct measurements of the direct ECE in composite samples in the full 280 temperature range.Moreover, high electric fields increase the risk of the electrica down of the composite samples.Test measurements of the ∆TAD FE around 340 K 0.2MnAs/0.8PMN-PTsample show the value to be ~0.1 K. Due to the leakage currents and Joule heating, it was complicated to provide stable and correct measurements of the direct ECE in composite samples in the full 280-400 K temperature range.Moreover, high electric fields increase the risk of the electrical break-down of the composite samples.Test measurements of the ∆T AD FE around 340 K for the 0.2MnAs/0.8PMN-PTsample show the value to be ~0.1 K.

Model of Multicaloric Effect
In a thermodynamic cycle based on a multicaloric effect (multiCE), two general scenarios for the application of external stimuli can be used: (1) simultaneous and ( 2) sequential.The central goal of the simultaneous application of external stimuli is to obtain a synergistic effect in which there is an increase in the total caloric effect due to its occurrence in each of the subsystems.However, in practice, the implementation of this scenario is problematic both from the point of view of the experimental setup and the choice of a material with suitable phase transition temperatures.Sequential application of external fields is used to improve the efficiency of systems based on the ordinary caloric effect in which the second field plays an assisted role.For example, the possibility of using a sequential application of a magnetic field and uniaxial compression to minimize the negative consequences of hysteresis effects was demonstrated in the example of Heulser alloys [12,43].The concept proposed in our work is based on the design of a multicaloric composite material with magnetic and ferroelectric phase transitions close to each other, which is suitable for both scenarios of application of external fields.In the proposed model, we consider the dynamics of the multiCE, when a time-resolved adiabatic temperature change is observed as a result of applying magnetic and electric fields.In our model, we consider MCE as a primary caloric effect, while ECE plays an assisted role.The mechanical interactions between phases are problematic for modeling in multicaloric composites and require the measurement of ME coefficients [44][45][46].Moreover, ME coefficients are sensitive to boundary effects between FM and FE components of composite, and the ratio of mechanical coupling depends on the fabrication protocol.Thus, taking into account this fact, our model was simplified and mechanical interactions between FM and FE components were not considered in the model.For this purpose, we consider a model of a multicaloric composite with 0.3/0.7 composition corresponding to a 0.3MnAs/0.7PMN-PTsample.This composition better matches the proposed model because this sample shows less dependence on the FE matrix pressure than the 0.2MnAs/0.8PMN-PTsample and its MCE behavior looks more like that for pristine MnAs.The adiabatic temperature changes induced by ECE and MCE for initial FE and FM components and their thermophysical parameters collected from the literature data are summarized in Table 2.
For this purpose, a three-dimensional model of a multicaloric compo connectivity type was created.The model considered in the simulation has sional structure consisting of a set of cubic continuously connected cells continuous ferroelectric medium with spherical ferromagnetic inclusions i (Figure 11).Modeling was conducted to solve the thermal conductivity (Equations ( 4) and ( 5)): The equation was solved numerically by the finite element method (FEM).The thermal contact between the FM particles and the FE matrix was considered ideal, that is, the usual condition of continuity of the heat flow was observed.Ideal thermal insulation was provided at the boundaries of the extreme cells, i.e., the structure as a whole was in adiabatic conditions.Heat capacities of materials (C E (T,E), C H (T,H)) and thermal conductivity k(T) were estimated from the literature data, and magneto-and electrocaloric effects (∆T MCE , ∆µ 0 H = const (T), ∆T ECE , ∆E = const (T)) were obtained by direct study of experimental samples.The geometric dimensions of the cell correlate with microstructural studies and the composition of the composite is 0.3/0.7.Thus, the side of the cubic cell is 45.5 µm and the diameter of the FM sphere is 30 µm, which is comparable with sizes of the FM clusters observed in SEM images for 0.3MnAs/0.7PMN-PTsamples.Taking into account the small size of the cell and moderate values of the thermal conductivity of the components (units of W/m•K), the changes in thermal energy associated with the FM and FE were almost instantly distributed evenly throughout the structure, which, taking into account the timescales during modeling (0.1-10 s), allowed us to neglect the effects of lag.Calculations show that in the result of MCE in the FM component, when magnetics are applied, heat is almost instantly distributed through the ferroelectric matrix, as a result of which the MCE in the composite is significantly reduced.The values of changes in the electric and magnetic field strengths were 20 kV/cm and 4 T, respectively.
When the electric and magnetic fields change together, the mutual influence of the FM and FE components of the composite is detected due to heat exchange through thermal conductivity.When modeling the MCE in the composite, it was found that the temperature dependence of the MCE in shape corresponds to the MCE in pure material, and the maximum value of the MCE in the composite was about 1.5 K at 4 T, which is comparable to the value of the MCE with the same magnitude change in the magnetic field strength in the experiment (1.4 K) (Figure 12).The difference in the form of the temperature dependence of MCE is because in the model we did not take into account intergranular interaction between FM and FE components of composites when the broad FOMPT was observed for composite samples.
FM and FE components of the composite is detected due to heat exchange throug mal conductivity.When modeling the MCE in the composite, it was found that t perature dependence of the MCE in shape corresponds to the MCE in pure mater the maximum value of the MCE in the composite was about 1.5 K at 4 T, which is rable to the value of the MCE with the same magnitude change in the magne strength in the experiment (1.4 K) (Figure 12).The difference in the form of the te ture dependence of MCE is because in the model we did not take into account int ular interaction between FM and FE components of composites when the broad F was observed for composite samples.Two scenarios (Case 1 and Case 2) were considered in modeling: 1.
The magnetic field varies according to a sinusoidal law, the diagram of the change in electric intensity corresponds to a meander (the duty cycle is 0.5, the duration of the front/decline is 10%), and the frequency of electric field pulses is 20 times higher than the frequency of the magnetic field (4 Hz and 0.2 Hz, respectively).The case was considered in which the ECE was equal to zero and was equal to that experimentally obtained at a field of 20 kV/cm (100%) and 500% of the experimental (which can be obtained by increasing the intensity).

2.
The diagram of changes in electric and magnetic strengths corresponds to a meander (with the same parameters as in the first case).The pulse frequencies of the electric and magnetic fields were 4 Hz, while the phase shift between the change in the electric and magnetic fields varied.
For the second case, the initial temperature was selected at points slightly above and slightly below the maximum MCE in the magnetic phase.As a result, the temperature change of the composite was mainly determined by the MCE due to its order of magnitude greater in comparison with the ECE in the ferroelectric matrix.
In the first case, it was found that due to the periodic release and absorption of heat associated with the ECE, the amount of heat released and absorbed due to the MCE changed due to the periodic displacement of the initial temperature of FM component of the composite, which manifests itself in a change in the temperature averaged by the ECE pulse and in a change in the envelopes of the temperature diagram of the FM component (Figure 13).
The time profiles for MCE, ECE, and multiCE for Case 2 are shown in Figure 14, and it is demonstrated that the phase shift ∆ϕ = −π/4 between applied magnetic and electric fields can provide a synergetic effect and enhance the multiCE at a working point of 316 K, which is above FOMPT (Figure 14).
In the first case, it was found that due to the periodic release and absorption associated with the ECE, the amount of heat released and absorbed due to th changed due to the periodic displacement of the initial temperature of FM compo the composite, which manifests itself in a change in the temperature averaged by t pulse and in a change in the envelopes of the temperature diagram of the FM com (Figure 13).The time profiles for MCE, ECE, and multiCE for Case 2 are shown in Figure it is demonstrated that the phase shift ∆φ = −π/4 between applied magnetic and fields can provide a synergetic effect and enhance the multiCE at a working poin K, which is above FOMPT (Figure 14).In the second case, it was found that with a small phase shift (up to π change in the average temperature of the entire structure occurs, and the si perature change is associated with both the sign of the phase shift and the ature of the composite (Figure 15).This result is due to a shift in the startin point of the FM component due to the ECE in the result of heat release and  In the second case, it was found that with a small phase shift (up to π/2), a smooth change in the average temperature of the entire structure occurs, and the sign of the temperature change is associated with both the sign of the phase shift and the initial temperature of the composite (Figure 15).This result is due to a shift in the starting temperature point of the FM component due to the ECE in the result of heat release and absorption.
In the second case, it was found that with a small phase shift (up to π/2), a smooth change in the average temperature of the entire structure occurs, and the sign of the temperature change is associated with both the sign of the phase shift and the initial temperature of the composite (Figure 15).This result is due to a shift in the starting temperature point of the FM component due to the ECE in the result of heat release and absorption.Briefly, as a conclusion, based on the results of experiments and calculations, we can assume that the boosting of caloric effect in ME composite systems can be achieved by: 1. Compilation of FM and FE components with large caloric effects in selected mass ratio and PT temperature (sample with x = 0.3 more suitable for proposed concept).2. Choosing of magnetic and electric field coapplying protocol (phase shifted of coapplied external fields).3. Mechanical interactions between components should be taken into account in the design and research of new composite systems with a large multicaloric response.
The proposed concept can be used in the design of solid-state cooling devices used on multicaloric materials with coapplied external fields, where MCE is used as the primary effect while ECE plays an assisted role and is used for tuning and control of the working temperature point.Briefly, as a conclusion, based on the results of experiments and calculations, we can assume that the boosting of caloric effect in ME composite systems can be achieved by: 1.
Compilation of FM and FE components with large caloric effects in selected mass ratio and PT temperature (sample with x = 0.3 more suitable for proposed concept).2.
Choosing of magnetic and electric field coapplying protocol (phase shifted of coapplied external fields).

3.
Mechanical interactions between components should be taken into account in the design and research of new composite systems with a large multicaloric response.
The proposed concept can be used in the design of solid-state cooling devices used on multicaloric materials with coapplied external fields, where MCE is used as the primary effect while ECE plays an assisted role and is used for tuning and control of the working temperature point.

Figure 5 .
Figure 5.The normalized magnetization M/Ms (Ms-magnetization in 1 T at 300 K) curves tion of temperature at 1 T magnetic fields for pristine MnAs and its composites in heating (insert image) The temperature derivatives dM/dT as a function of temperature, calcula normalized magnetization vs. temperature curves.

Figure 5 .
Figure 5.The normalized magnetization M/M s (M s -magnetization in 1 T at 300 K) curves as a function of temperature at 1 T magnetic fields for pristine MnAs and its composites in heating protocol.(insert image) The temperature derivatives dM/dT as a function of temperature, calculated from normalized magnetization vs. temperature curves.

Figure 6
Figure 6 shows the magnetization isotherms used to estimate the MCE by indirect method for pristine MnAs (a) and composite 0.2MnAs/0.8PMN-PT(b), 0.3MnAs/ 0.7PMN-PT (c) samples.To estimate indirectly MCE, the well-known Maxwell relation µ 0 (∂M/ ∂T)H = (∂S/∂H)T was used, which yields the formula for magnetic entropy change ∆S m at applied field change from 0 to H:

Figure 9 .Figure 10 .
Figure 9.The P(E) hysteresis loops measured at different temperatures (a) and temperature dependences of polarization at different applied electric fields (b) for pristine FE component of modified PMN-PT ceramics.

Figure 9 .
Figure 9.The P(E) hysteresis loops measured at different temperatures (a) and temperature dependences of polarization at different applied electric fields (b) for pristine FE component of modified PMN-PT ceramics.

Figure 9 .Figure 10 .
Figure 9.The P(E) hysteresis loops measured at different temperatures (a) and temperature ences of polarization at different applied electric fields (b) for pristine FE component of m PMN-PT ceramics.

Figure 10 .
Figure 10.Temperature dependencies of adiabatic temperature change ∆T AD FE at different applied electric fields (ECE) for pristine FE components of modified PMN-PT ceramics.

Figure 14 .
Figure 14.The time profile for MCE, ECE, and multiCE for Case 2 at working point magnetic phase transition temperature.

Figure 15 .
Figure 15.Temperature dependences of multiCE with different regimes of phase-shifted applications of magnetic and electric fields at working points up to (a) and above (b) magnetic phase transition temperatures (calculations for Case 2).

Figure 15 .
Figure 15.Temperature dependences of multiCE with different regimes of phase-shifted applications of magnetic and electric fields at working points up to (a) and above (b) magnetic phase transition temperatures (calculations for Case 2).

Table 2 .
Thermophysical C p -specific heat capacity; λ-thermal conductivity) of FM and FE components used in multicaloric MnAs/PMN-PT composites (*-for C p and λ, the corresponding parameters for a basic solid solution system PMN-PT are used).