Magnetocaloric properties and nature of magnetic phase transition

expect a large change in entropy around these transitions. Hence, in order to quantify change in entropy we performed M vs. H measurements in the vicinity of the magnetic transitions pertinent to HoFe1-xCrxO3 (0.25 ≤ x ≤ 1) compounds. We have excluded HoFeO3 compound in this study as it consists a secondary iron garnet phase (Ho3Fe5O12).

0 20 40 60 0

10 20 30



T = 5 K

200 K

Magnet iz at ion M ( em u/ g)

100 K



T = 5 K

0 20 40 60

0 10 20

HoCrO

3

Cr

³⁺

ordering Cr

³⁺

ordering

HoFe

0.25

Cr

0.75

O

3

SR transition HoFe

0.50

Cr

0.50

O

3

SR transition HoFe

0.75

Cr

0.25

O

3



T = 10 K

200 K 120 K

0 20 40 60

0 10

20

_{146 K}

136 K



T = 2 K

Magnetic Field (kOe)

0 20 40 60

0 10 20 30 40

(d) (c)

(b)

200 K 100 K

(a)

Figure 4.6: First quadrant magnetization isotherms around (a – b) SR transition related to

x = 0.25 and x = 0.50 compounds, (c – d) Cr³⁺ ordering temperature pertinent to x = 0.75 and x = 1 compounds with an applied field up to 60 kOe for HoFe1-xCrxO3

(0.25 ≤ x ≤ 1) compounds.

below which the material shows AFM behaviour and exhibits ferromagnetic (FM) behaviour above this field. Such a field induced transition in low field region can be ascribed to the onset of a first order metamagnetic transition (from original AFM state to FM state). Evidenced metamagnetic transition may be due to the magnetization reversal of those ions whose magnetic moments are directed opposite to the applied magnetic field and the similar behaviour has been observed in the single crystals of DyCrO3 as the rotation of Dy³⁺ and Cr³⁺ moments [188]. From Fig. 4.5 (c) and Fig. 4.5 (d), it is evident that there is a magnetization crossover around the AFM FM transition, which can be ascribed as a result of the competition between the Zeeman energy due to the applied external field and the strong magneto-crystalline anisotropy energy around the metamagnetic transition [189].

Figure 4.6 (a – b) shows the first quadrant isothermal magnetization curves (M vs.

H) around the spin reorientation transition corresponding x = 0.25 and x = 0.50 compounds, whereas Fig. 4.6 (c – d) represents M vs. H curves around TN (Cr³⁺

ordering) in x = 0.75 and x = 1 compounds. It is evident from the Fig. 4.6 (c – d) that low field nonlinearity is due to weak ferromagnetic (WFM) component which arises due to canting of Cr³⁺ moments. Apart from that, an increase in linearity of M vs. H curves is evident with an increase in temperature from 100 K up to TN

(155 K for x = 0.75 and 142 K for x = 1 compound) due to decrease in strength of WFM component. The disappearance of nonlinearity for M vs. H curves above TN

indicates the paramagnetic phase.

As there are multiple transitions in HoFe1-xCrxO3 (0.25 ≤ x ≤ 1) compounds, we do expect a large change in entropy around these transitions. Hence, we calculated magnetic entropy change (–ΔSM) from isothermal magnetization curves using well

where Hmax is the maximum value of external applied field. From the above equation 4.3, it can be noticed that the value of –ΔSM depends on both the values of magnetization (M) and

H

M T

 

 

   . The larger values of –ΔSM can be obtained when the values of M and

H

M T

 

 

   are large in the magnitude [190].

Quantified values of –ΔSM at various magnetic transitions in HoFe1-xCrxO3

(0.25 ≤ x ≤ 1) compounds and its temperature variation is shown in Fig. 4.7 (a – d) and Fig. 4.8 (a – d). Here, Fig. 4.7 (a – d) depicts the –ΔSM vs. T

around Ho³⁺ ordering for HoFe0.75Cr0.25O3 (–ΔSM ~ 8.63 J/kg-K at 9 K), HoFe0.5Cr0.5O3 (–ΔSM ~ 8.18 J/kg-K at 12.5 K), HoFe0.25Cr0.75O3 (–ΔSM ~ 8. 08 J/kg-K at 11 K) and HoCrO3 (–ΔSM ~ 6.99 J/kg-K at 9 K) compounds respectively with a maximum magnetic field of 60 kOe. Large values of –ΔSM in all the compounds can be ascribed to evidenced metamagnetic transition and the Ho³⁺

ordering. Reason for the enhancement in the value of –ΔSM in HoFe0.75Cr0.25O3

compound compared to that of the HoCrO3 compound can be explained as follows.

Essentially, HoCrO3 is distorted type perovskite material and crystallizes in orthorhombic structure with a space group of Pbnm [191]. For an ideal perovskite Cr-O1-Cr bond angle must be 180°. However, due to the distortion as a result of tilting of CrO6 octahedra in HoCrO3, there would be a change in Cr-O1-Cr bond angle (146.2^o) [in the present study from refinement], which is distinctly different from an ideal perovskite. This distortion decreases the orbital overlap and leads to non collinear antiferromagnetic structure of Cr³⁺ ions with a weak ferromagnetic component. Obtained bond angle value from Rietveld refinement pertinent to Fe(Cr)-O1-Fe(Cr) is smaller for HoFe0.75Cr0.25O3 (144.0^o) in comparison with the HoCrO3 (146.2^o) compound. This indicates an increase in canting of spins and hence an enhancement in –ΔSM value for HoFe0.75Cr0.25O3 compound in comparison with HoCrO3. The increase in canting angle of Fe³⁺/Cr³⁺ sublattice with AFM axis for HoFe0.75Cr0.25O3 has been evident from the neutron diffraction data on HoFe1-xCrxO3

solid solutions [178].

6 9 12 15 18 0 3 6 9

(d)

^{10 kOe} _{20 kOe}

30 kOe 40 kOe 50 kOe 60 kOe

HoCrO

3

HoFe

0.25

Cr

0.75

O

3

HoFe

_0.50

Cr

_0.50

O

₃

HoFe

_0.75

Cr

_0.25

O

₃

3 6 9 12 15 18 21 0

3 6 9 12

-  S M ( J/kg -K ) -  S M ( J/k g-K )

3 6 9 12 15 18 21 -3

0 3 6 9

Temperature T (K)

Ho

³⁺

ordering

3 6 9 -6

-3 0 3 6 (c) 9

(a) (b)

90 120 150 180 210 0.0

0.2 0.4 0.6 0.8 1.0

-  S M ( J/kg-K )

(c) SR transition

-  S M ( J/kg-K )

SR transition

120 140 160 180 200 0.0 0.2 0.4 0.6

(d)

90 120 150 180 0.0

0.2 0.4 0.6 0.8 1.0

(b)

Cr

³⁺

ordering

10 kOe 20 kOe 30 kOe 40 kOe 50 kOe 60 kOe

Cr

³⁺

ordering (a)

136 138 140 142 144 146 0.0 0.2 0.4 0.6 0.8 1.0 HoCrO

₃

1.2

HoFe

_0.25

Cr

_0.75

O

₃

HoFe

_0.50

Cr

_0.50

O

₃

HoFe

_0.75

Cr

_0.25

O

₃

Temperature T(K)

Figure 4.8: (a – d) Temperature dependence of the magnetic entropy –ΔSM obtained from

isothermal M vs. H data corresponding to Fig. 4.6 (a – d) for HoFe1-xCrxO3 (0.25 ≤ x ≤ 1) compounds.

The values of MCE obtained for HoFe1-xCrxO3 (0.25 ≤ x ≤ 1) compounds in the vicinity of Ho³⁺ ordering temperature are large when compared to DyMnO3 (–ΔSM

~ 6.8 J/kg-K at 7 T and 10 K) [192] , SmFe0.5Mn0.5O3 (5.6 J/kg-K at 18 K and with 7 T) [193] and HoFe0.3Cr0.7O3 (6.83 J/kg-K at 20 K and with 7 T) [194]. However, the values of –ΔSM obtained in the present study are smaller compared to giant MCE material such as TmZn [195], ErMn2Si2 [196], Tm2Cu2In [197], HoPdIn [198]

and RE2Cu2O5 (RE = Dy and Ho) [199] in the low temperature region.

From the Fig. 4.7 (a), Fig. 4.7(c) and Fig. 4.7(d), it is evident that –ΔSM values shows both positive and negative values as though there exists re-entrant magnetocaloric effect. Such an unusual nature of re-entrant inverse MCE in HoFe0.3Cr0.7O3 [194] as well as un-doped HoCrO3 [200] compound has been not observed earlier. The reason for such an intriguing phenomenon may be due to the subtle changes in relative orientations of Ho³⁺ and Fe³⁺/Cr³⁺ moments occurs with a variation of temperature and/or magnetic field [201]. Earlier inverse magnetocaloric effect has been observed around SR transition in single crystals of HoFeO3 [128]. We conceive from our observation that magnetization crossover and complex interaction between FM and AFM phases might be a reason for re-entrant MCE behaviour in the present compound.

Figure 4.8 (a) and Fig. 4.8 (b) depicts –ΔSM vs. T around SR transition for HoFe0.75Cr0.25O3 (–ΔSM ~ 0.86 J/kg-K at 102.5 K), HoCr0.5Fe0.5O3 (–ΔSM ~ 0.61 J/kg-K at 125 K) compounds respectively with a magnetic field of 60 kOe. On the other hand, Fig. 4.8 (c) and Fig. 4.8 (d) depicts –ΔSM vs. T around TN (Cr³⁺

ordering) for HoFe0.25Cr0.75O3 (–ΔSM ~ 0.59 J/kg-K at 157.5 K) and HoCrO3 (–ΔSM

~ 1.05 J/kg-K at 141 K) compounds respectively at a maximum magnetic field of 60

0 5000 10000 0.0

0.2 0.4 0.6 0.8

5 K 8 K 11 K 14 K 17 K 20 K

0 4000 8000

0.0 0.2 0.4 0.6

2 K 4 K 5 K 6 K 8 K 10 K

HoCrO HoFe

3

0.25

Cr

0.75

O

3

HoFe

0.50

Cr

0.50

O HoFe

3

0.75

Cr

0.25

O

3

M ² (emu/g) ²

Ho

³⁺

ordering

0 5000 10000

0.0 0.2 0.4 0.6 0.8

(c) (d)

(b)

2.5 K 4 K 6 K 8 K 10 K 12 K 14 K 16 K 18 K 20 K

H/ M (kOe. g/emu )

(a)

0 6000 12000

0.3 0.6

2.5 K 4 K 6 K 8 K 10 K 12 K 14 K 16 K 18 K 20 K

Figure 4.9: (a – d) Arrott plots deduced from magnetization isotherms corresponding to Fig. 4.5 (a – d) for HoFe1-xCrxO3 (0.25 ≤ x ≤ 1) compounds.

0 500 1000 1

2 3 4

100 K 110 K 120 K 130 K 140 K 150 K 160 K 170 K 180 K 190 K 200 K

0 300 600

2 4

Cr

³⁺

ordering HoCrO

Cr

³⁺

ordering

3

HoFe

0.25

Cr

0.75

O

3

SR transition HoFe

0.50

Cr

0.50

O

3

SR transition HoFe

0.75

Cr

0.25

O

3

120 K 130 K 140 K 150 K 160 K 170 K 180 K 190 K 200 K

0 400 800 1200

2 3 4

100 K 110 K 120 K 130 K 140 K 150 K 160 K 170 K 180 K 190 K 200 K

0 200 400

2 3

136 K 138 K 140 K 142 K 144 K 146 K

M ² (emu/g) ²

H/M (kOe. g/ em u)

0 1

1 2

(c) (d) (a) (b)

Figure 4.10: (a – d) Arrott plots deduced from magnetization isotherms corresponding to

molecular field of Cr³⁺ moments will try to order the Ho³⁺ moments and thus the magnetization increases. This leads to an increase in magnetic entropy change up to ordering temperature of Ho³⁺ moments and reaches a maximum value.

It is believed that the magnitude of the magnetic entropy change at a particular magnetic phase transition and its dependence on temperature and magnetic field strongly depend upon the nature of the corresponding phase transition [203], hence, it is essential to determine the nature of magnetic phase transitions in these compounds. To do this, the first quadrant magnetization isotherms are plotted in the form of Arrott plots (H/M vs. M²) [204], which can be deduced from Ginzburg- Landau theory in the close vicinity of the magnetic transition.

The thermodynamic potential with Ginzburg-Landau type expansion which includes the magnetostatic field energy (MH) near the magnetic transition is as follows:

G T M( , )G₀M²M⁴...MH …… (4.4)

where α, β are the Landau coefficients dependent on temperature. In the equilibrium condition, G 0

M

 

 , the equation 4.4 reduces to H M²

M 







. According to Banerjee’s criterion [205], a negative slope of H/M vs. M² at some point indicates the first order magnetic transition. On the other hand a positive slope of H/M vs.

M² indicates the second order magnetic transition.

Figure 4.9 (a – d) and Fig. 4.10 (a – d) shows the Arrott plots corresponding to magnetization isotherms shown in Fig. 4.5 (a – d) and Fig. 4.6 (a – d) respectively.

The negative slope of H/M vs. M² for the Fig. 4.9 (a – d) corresponding to HoFe1-xCrxO3 (0.25 ≤ x ≤ 1) compounds indicates that the Ho³⁺ ordering is a first order magnetic phase transition. The positive slope of H/M vs. M² for Fig. 4.10 (a) and Fig. 4.10 (b) corresponding to x = 0. 25 and x = 0.5 compounds indicates the spin reorientation transition is a second order magnetic phase transition which is in agreement with the literature [206]. On the other hand, the negative slope of Arrott plot for the Fig. 4.10 (c) and Fig. 4.10 (d) related to x = 0.75 and x = 1 compounds

indicating that the Cr³⁺ ordering (AFM transition) is a first order magnetic phase transition.