Introduction

The multiferroic materials are materials that simultaneously show more than one second-order transition phenomena such as ferroelectricity and ferro/antiferromagnetism and ferroelasticity. If the ordering phenomena are coupled, one type of ordering can influence the parameters of other type of ordering leading to practical applications. For example, if the ferroelectricity can be coupled to ferromagnetism, dielectric properties can be controlled by the application of magnetic fields or the magnetic properties can be controlled by application of electric fields. Although the mechanisms for second-order ferroelectric and magnetic ordering phenomena are very similar in many ways, their coexistence in the same material is infrequent. Rare-earth manganite (RMnO3) compounds (R represents Y and rare-earth ions from Ho to Lu) have been found to show such coexistence of ferroelectricity and ferro/antiferromagnetism in them. In these compounds with hexagonal or orthorhombic crystal structure (i.e., distorted perovskite structure), the spin–spin interactions between Mn3+ ions present within their close-packed basal planes are dominant [1–7]. Rare-earth manganites with different rare-earth ions present at the rare-earth sites show different magnetic phases ranging from ferromagnetic-to-ferrimagnetic-to-antiferromagnetic-to paramagnetic [3, 5, 6] and consequently exhibit different physical properties below their magnetic transition temperature. Among the rare-earth manganites with hexagonal crystal structure, YMnO3 is relatively simple because a single magnetic sublattice of Mn is present and the material has been investigated by several authors [8, 9]. Below 1000 K, they undergo a paraelectric-to-ferroelectric transition to a non-centrosymmetric structure with the space group P63cm [9]. At lower temperatures near 100 K, these manganites order with a non-collinear antiferromagnetic structure.

For technological applications in low temperatures like refrigeration for liquefaction of hydrogen and rocket engines [10–14], materials showing large magnetocaloric effect are important. Study of magnetocaloric effect also leads to better understanding the low temperature magnetism and physics of magnetic refrigeration. RMnO3 materials also show large magnetocaloric effect. However, their practical applications in magnetic refrigeration have not been investigated yet. Here we report the magnetocaloric properties of bulk YMnO3 calculated from specific heat measurements.

Experimental

Polycrystalline bulk YMnO3 sample was prepared by the standard solid-state ceramic route. Considering the hygroscopic nature of the rare-earth material Y2O3 and MnO2, they were given a pre-heat treatment at 1,000 °C for 10 h. The starting materials (of AR grade purity) were taken in the required stoichiometric ratio and were mixed by grinding in a mortar and pestle for five hours. The mixed powdered sample was twice calcined at 1,000 °C for 12 h in air ambient with an intermediate grinding. The calcined powder was subsequently pelletized and the pellets were sintered at 1,350 °C for 24 h in air ambient. The room temperature XRD patterns were recorded using a Rigaku Dmax 300 diffractometer using the CuK α radiation. For microstructural analysis of the sample, a scanning electron microscope (SEM) of ZEISS EVO Series make (Model EVO 50) was used. Magnetization measurements (M-T) were carried out with a SQUID magnetometer (make MPMS XL) under field-cooled (FC) and zero-field-cooled (ZFC) protocols at an applied magnetic field (H) of 0.1 T. Magnetization (M-H) values were measured up to a maximum applied field (H) of 1–2 T at temperatures of 10, 30, and 50 K. Specific heat (C p) measurements were carried out using a PPMS system at various applied magnetic fields in the temperature range 2–300 K.

Results and discussion

Structural characterization

The measured XRD powder diffraction pattern of YMnO3 is shown in Fig. 1a. The Rietveld refinement technique was used to analyze the XRD data assuming YMnO3 to have a hexagonal structure with P63cm space group. XRD peak profiles were calculated using a pseudo-voigt function. Figure 1b shows the calculated Rietveld refined XRD patterns of the sample along with difference in the calculated and measured XRD diffraction patterns. The crystallographic data obtained from this analysis is given in Table 1. Figure 2 shows the SEM micrograph of the fractured surface of the YMnO3 sample. From that figure, it could be concluded that all the grains were uniform and ~1.5 μm in size.

Fig. 1
figure 1

X–ray diffraction measurement of YMnO3 using Rietveld refinement technique assuming hexagonal structure with P63cm space group—a gives the observed XRD peak intensities and b gives the calculated XRD peak intensities from the known structure for YMnO3 and the differences between the observed and calculated values

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Table 1 Lattice parameters and magnetic constants from XRD and magnetic susceptibility data
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Fig. 2
figure 2

SEM micrograph of fractured surface of YMnO3 showing uniform grain size throughout the sample. The black bar at the right bottom corner measures 3 μm in length

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Magnetization measurement

Results of measurements of dc magnetization versus temperature (M-T) performed with application of an external magnetic field (H) of 0.1 T under temperature-dependent zero-field-cooled (ZFC) and field-cooled (FC) protocols are shown in Fig. 3. Temperature-dependent ZFC and FC magnetization values (Fig. 3) showed bifurcation between them at the temperature ~50 K. The ZFC curve displayed a sharp peak at around 42 K, where the irreversibility between ZFC and FC curves became obvious. Such a feature is the hallmark of a spin glass transition. A small amount of excess Mn present in YMnO3 causing a deviation in stoichiometry can bring about the formation of a spin glass state [15]. In contrast to this, there are reports [9, 16] that there is no difference in the ZFC and FC curves of pure YMnO3. However, alternately spin cantering at Mn3+ sites might also happen at low temperature leading to a spin glass like transition. Therefore, for YMnO3 samples cooled under ZFC protocol, it was concluded that for the magnetic force applied later on would not be capable of aligning the spins aligned in random directions due to the viscous behavior of the spins. High applied magnetic fields during FC protocol could align the spin cantering and hence would become responsible for a higher magnetic moment under FC protocol.

Fig. 3
figure 3

ZFC-FC measurement of magnetization (M) at an applied magnetic field of 0.1 T versus temperature (T) for YMnO3 showing divergence of the FC and ZFC curves below a temperature (called irreversibility temperature) of ~42 K. There is a clear indication and signature of a spin glass transition

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For understanding of the nature of magnetic transition of the YMnO3 sample, inverse of magnetic susceptibility (χ −1) was plotted against temperature (T). High temperature (>150 K) M-T data could be fitted to the Curie law χ = C/(T + ӨN) consistent with the paramagnetic (PM) to antiferromagnetic transition (AFM) and the results are shown in the inset of Fig. 3. From the fittings, Neel temperature (ӨN), Curie constant (C), and effective paramagnetic moment (µ) in Bohr magnetons (μ B) have been obtained and are given in Table 1. Low temperature M-T data (Fig. 3) showed a spin glass transition with irreversibility temperature around 42 K that was consistent with observations of Chen et al. [15].

To understand the low temperature transition, M-H measurements were carried out below the transition temperature of 42 K. Figure 4 shows the results of M-H measurements done on YMnO3 below the spin glass transition at temperatures of 10, 30, and 50 K. These measurements showed hysteresis in M-H loops at temperature below 30 K. Remanence (M R), coercivity (H c), and saturation magnetization (M s) were calculated and are shown in Table 2.

Fig. 4
figure 4

Variation of magnetization (M) with applied magnetic field (H) curve for YMnO3 up to a maximum applied magnetic field of 1–2 T at the temperatures of 10, 30, and 50 K showing M-H loops with hysteresis due to ferrimagnetic behavior at 10 and 30 K, but M-H loop at 50 K showing a mixed phase with both ferrimagnetic and paramagnetic phases present

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Table 2 Parameter extracted from M-H measurements
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It was interesting to see that at temperatures less than 50 K, M-H measurement showed a ferrimagnetic behavior with a low value of saturation magnetization, M s and at a temperature of 50 K, it showed a mixed phase consisting of both PM and ferrimagnetic phases. It can be concluded that a phase change from PM to ferrimagnetic occurred at a temperature below 50 K in YMnO3. In the YMnO3 sample, since the magnetic contribution is from Mn3+ ions at B-sites, and since Mn3+ ions would normally have anti-parallel alignment of their magnetic moments due to the B-B interaction, only possible magnetic interaction that could explain for the M-H curves at the low temperature in ferrimagnetic YMnO3 could be arising only from cantering of spins of Mn3+ ions at B-sites.The cantering of the spins giving rise to Y-K angle (\( \alpha_{{\text{y}}{ - }{\text{k}}}\)), were calculated at 10 , 30 , and 50 K for YMnO3 using the formula [17, 18]

$$ n_{\text{B}} = M_{\text{B}} (x)(1 - { \cos }\,\,\alpha_{{\text{y}}{ - }{\text{k}} }), $$
(1)

where M B is the magnetization of Mn3+ ion and \( n_{\text{B }}, \) is the number of Bohr magneton per two YMnO3 molecules and it has been calculated using the relation [19]

$$ n_{\text{B}} = \frac{{2{\text{M}}M_{\text{s}} }}{{N_{\text{A}} \mu_{\text{B}} }}, $$
(2)

where M = molecular weight of YMnO3, M s = saturation magnetization, N A = Avogadro’s number.

The values of \( \alpha_{{\text{Y}}{ - }{\text{K}}}\) and nB for YMnO3 samples at temperature 10, 30, and 50 K are shown in Table 2. It was observed that the saturation magnetization (M s) and magnetic moment per two YMnO3 molecules, n B, decreased with the temperature. The decrease in the \( \alpha_{{\text{y}}{ - }{\text{k}}}\) angles with increasing temperature may be attributed to the presence of triangular spin arrangement on B-site [17, 20]. This would lead to the reduction in the B-B exchange interaction and a consequent decrease in Ms.

Specific heat

Figure 5 shows the variation of specific heat (C p) of YMnO3 sample with temperature (T) under different magnetic fields (H). The specific heat increased with increase in temperature. It can be seen from figure that there was a clear transition at 42 K. This is the hallmark of a spin glass transition. These results are agreement with the magnetization results. The peak that appeared at 42 K in zero magnetic fields got smeared in the magnetic fields and gradually vanished at 10 T. The peak shifted to higher temperatures with wider spreads as the applied magnetic field increased. In fact, this is the primary signature of a ferromagnetic (or ferrimagnetic) material. Kimura et al. [21] also observed similar kind of behavior of the magnetic field dependent peak broadening in specific heat versus temperature data observed for some ferromagnetic materials [22] near the ferromagnetic transition temperature, which was verified from the M-H curves taken below and above the transition temperature. Tomuta et al. [23] suggested that such hump is due to system progressively searching for its true ground state, which can be verified by M-H and M-T graphs showing a constant increase in the susceptibility below the transition.

Fig. 5
figure 5

Specific heat (C p) of the YMnO3 sample with temperature (T) under different magnetic fields. Peak was attributed to spin glass transition and peak broadening was due to ferrimagnetic ordering/cantering of spins. Inset shows how the magnetic contribution to the specific heat (C M) was estimated by taking the lattice specific heat of LaMnO3 from literature [26] and scaling it to fit the YMnO3 data to obtain lattice specific heat of YMnO3 and then taking the difference between the measured C p and lattice specific heat as C M

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Magnetocaloric effect

Magnetocaloric effect (MCE) is studied for examining the possibility of refrigeration by changing the applied magnetic field. Some of the materials examined for their magnetocaloric properties are bulk and/or nanocrystalline Gd5(Si2Ge2) [24], γ-Fe2O3 [25], samarium ferrite [25], gadolinium ferrite [25], PrMnO3 [26], Ca-doped LaMnO3 [27], and Sr-doped LaMnCoO3 [28]. The methods to study MCE can be divided into two methods—direct method and indirect method. In the direct method, the material is subjected to a magnetic field change and its change of temperature is directly measured by different techniques [29]. In the indirect method, the parameters of MCE are determined from the magnetization and/or heat capacity data.

Experimental data of magnetization (M) versus applied magnetic field (H) can be used to calculate magnetic entropy change (ΔS M) by using the equation:

$$ \Delta S_{\text{M}} = \int\limits_{{{\text{H}}1}}^{{{\text{H}}2}} {\left( {\frac{\partial M}{\partial H}} \right) {\text{d}}H} $$
(3)

The C p versus T data measured in different magnetic fields also allows calculation of a complete set of parameters required for magnetic refrigerator design as discussed below. In order to calculate these parameters, entropy is calculated from the specific heat data using the formula given below:

$$ S (T ,H )= \int\limits_{0}^{\text{T}} {\left( {\frac{{C_{\text{p}} }}{T}} \right){\text{d}}T}. $$
(4)

Figure 5 shows the variation of specific heat of our bulk YMnO3 with temperature at different magnetic fields. However, both lattice vibrations and magnetic field changes contributed to the measured specific heat and entropy. The lattice contribution to the specific heat (C lat) was estimated from the C lat values for non-magnetic LaMnO3. For this purpose, the specific heat values were taken from the C lat data of Cheng et al. [26]. To accommodate the difference in lattice contribution for the two different rare-earth compounds, it was assumed that specific heat follows a scaling law. According to this law, the lattice specific heat of a rare-earth compound follows the universal curve if plotted as a function of (T/T R), where T R is characteristic temperature of the compound. This assumption is similar to Debye or Einstein model where lattice specific heat of any material is represented by a single curve if T R is Debye or Einstein temperature. Therefore, specific heat of La compound was made to overlap with that of YMnO3 sample of the present investigation above the magnetic transition temperature (or in the PM region) by multiplying the C p axis for LaMnO3 with a suitable factor as shown in the inset of Fig. 5. The magnetic contribution to the specific heat (C M) in the presence of external magnetic fields and consequent magnetic entropy (S M) were calculated using the formula given below.

$$ C_{\text{M}} = C_{\text{p}} - C_{\text{lat}} $$
(5)
$$ S_{\text{M}} (H )= \int\limits_{0}^{\text{T}} {\left( {\frac{{C_{\text{p}} { - }C_{\text{lat}} }}{\text{T}}} \right){\text{d}}T} $$
(6)

The change in magnetic contribution to entropy, ΔS M, on application of a magnetic field, H, could be calculated as follows:

$$ \Delta S_{\text{M}} = S (H ) { - }S ( 0 ) $$
(7)

Figure 6 displays the entropy change due to magnetic field (ΔS M) as a function of temperature for the various magnetic fields. The curves showed a characteristic broad peak with a maximum in the vicinity of the magnetic transition temperature and the peak width increased as the applied magnetic field increased. The position of the maximum shifted from 43 to 45 K when the magnetic field (H) increased from 1 to 10 T. The maximum peak value of −ΔS M(T) at each value of applied field (H) (ΔS Mmax) increased linearly with increasing magnetic field up to 1.1 J mol−1 K−1 at 10 T. The field-induced magnetic transition contributed to the enhancement of magnitude of ΔS M.

Fig. 6
figure 6

This displays the magnetic contribution to the entropy change (−ΔS M) of YMnO3 as a function of temperature (T) for various applied magnetic fields. Peaks can be seen near the transition temperature of ~42 K with temperature of the peak position shifting to higher temperatures and peak height increasing on increasing the applied magnetic field (H)

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Universal curve

Then phenomenological universal curve for second-order transitions as suggested by Franco and Conde [30] converges the ΔS M versus temperature curves to a single universal curve if (−ΔS M/ΔS Mmax) versus a reduced number (θ) is plotted with

$$ \theta \, = \, \left( {T \, - \, T_{\text{c}} } \right)/\left( {T_{\text{r}} - \, T_{\text{c}} } \right), $$
(8)

where T c is the temperature; ΔS Mmax occurs in −ΔS M versus T curves, and T r is the temperature where −ΔS M is equal to 0.7 ΔS Mmax in −ΔS M versus T curve.

Similar convergence of MCE behavior has been seen for La2/3Ba1/3BaMnO3 [31] and other compounds [32]. In the present case for YMnO3, (−ΔS M/ΔS Mmax) versus the reduced number (θ) was plotted and is shown in Fig. 7. The convergence of all curves of Fig. 6 was seen in Fig. 7 due to scaling discussed above.

Fig. 7
figure 7

The curves of Fig. 6 can be reduced to almost a single universal curve by following the formulism of Franco and Conde [30] using −ΔS M/−ΔS Mmax and θ = (T–T c)/(T r–T c) in the y and x axes, respectively.

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The magnetic field dependence of ΔS M follows a power law [30], \( \varDelta S_{\text{M}} \propto H^{\text{n}} \) with the exponent being temperature dependent. From the slope of the log–log plot of −ΔS M versus H, the exponent (n) was calculated and the plot of ‘n’ versus the reduced number (θ) is shown in Fig. 8. The value of ‘n’ varied between 0.5 and 2.0 in the θ range of −2.5 to +2.5. Within experimental errors (given as error bars in Fig. 8), the magnetic field exponent values compared well with the values (obtained by Franco and Conde [30] for alloys.

Fig. 8
figure 8

Variation in magnetic field exponent (n) of −ΔS M (−ΔS M α H n) has been plotted as a function of the reduced parameter (θ). The vertical bars at each data point give the estimated errors in ‘n’

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Relative cooling power

The adiabatic temperature difference (ΔT ad) could be obtained from the isentropic difference between the entropy curves S(0,T) and S(H,T) [24]. The temperature dependence of ΔT ad is plotted in Fig. 9 for different magnetic fields. The peak of the ΔT ad versus T curve, ΔT admax, occurred at a ΔT ad value of 2.2 K for a magnetic field change of 10 T. In addition to the values of ΔS Mmax and ΔT ad, the relative cooling power (RCP) could also be evaluated to determine the cooling efficiency of a magnetocaloric material. RCP based on the magnetic cooling power is defined as the product of ΔS Mmax and the full width at half maximum, δTFWHM, of ΔS M versus T curve, i.e., RCP = ΔS Mmax × δTFWHM. In Table 3, we have presented RCP values as a function of magnetic field change from 0T. RCP increased with the increase in field. The RCP value at a magnetic field change of 5T was 26 J kg−1. For bulk LaMnO3 and Ca or Ba substituted LaMnO3, Biswas et al. [33] report an RCP value in the range of 22–250 J kg−1 for a magnetic field change of 5T and the value reported for YMnO3 here falls within that range. Therefore, the magnetocaloric properties of YMnO3 satisfies some important criteria for selecting it as a magnetic refrigerants such as exhibition of large magnetic entropy change, large adiabatic temperature change, and high RCP value.

Fig. 9
figure 9

The temperature (T) dependence of the adiabatic temperature difference (ΔT ad) calculated from the magnetic entropy changes have been plotted for different applied magnetic fields

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Table 3 Variation of maximum magnetic entropy change (ΔS Mmax), relative cooling power (RCP), and other relevant parameters with applied magnetic field for bulk YMnO3
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Conclusions

Polycrystalline YMnO3 multiferroic samples with hexagonal crystal structure were prepared by the solid state reaction method and the crystal structure was confirmed by XRD studies. Magnetization and specific heat measurements were carried out under different magnetic fields over a temperature range 2–300 K. The specific heat and magnetization measurements exhibited a PM to ferrimagnetic phase transition at ~42 K that was also a spin glass transition. A large magnetic entropy change of ~1 J mol−1 K−1 was obtained for, under, a magnetic field change of 0–10 T.