The order of magnetic phase transitions in disordered double perovskite oxides Sm₂FeCoO₆ and Dy₂FeCoO₆

Magnetic double perovskite oxides have gained their importance in material science due to their efficiency in exhibiting different tunable physical properties such as magnetoresistance (MR), magnetocaloric effect (MCE), multiferroicity, etc.^1–3 The rare earth based transition metal perovskites of the form R₂MM’O₆, where R is the rare earth cation and M and M’ are transition metal cations, are one of the afore mentioned category which usually exhibit interesting magnetic phenomena due to oxygen mediated cationic exchange interactions.^2,3

The spin re-orientation is commonly observed in Fe, Cr and Mn based magnetic alloys, rare earth perovskites, etc. in which the transition ion spin changes its orientation from one crystallographic direction to the other influenced by temperature, magnetic field, internal pressure, external irradiation etc.^4–6 In general, it can be of a first order abrupt transition or a slower broad transition.⁵ The order of the magnetic phase transition can be preliminarily determined by means of Arrott plots,^7,8 which include modified isotherms with M² and H/M on the axes.

The magnetoresistive double perovskite Sr₂FeMoO₆ geared up the material research in double perovskites due to technology related reasons.¹ The disordered double perovskites Dy₂FeCoO₆ (DFCO) and Sm₂FeCoO₆ (SFCO) are found to exhibit re-entrant magnetization, thermal hysteresis, ZFC-FC bifurcation, spin re-orientation with an antiferromagnetic ground state.⁹ The transition temperatures are found to be lower than that of the corresponding orthoferrite end members.^10,11 The origin of spin re-orientation in these samples are assumed to be the R³⁺ - Fe³⁺ interactions. The occurrence of multiple magnetic transitions in the samples with change in temperature and magnetic field leads us to think about the application of Arrott plot method at the spin re-orientation region to see the behaviour of the order of transition. In this work, we present the characterization of the order of transition around the spin re-orientation region using Arrott plot method for the above referred samples.

The sol-gel synthesized samples⁹ were subjected to DC magnetization measurements in a commercial SQUID based vibrating sample magnetometer (SVSM, MPMS 3, QD USA). The temperature variation of magnetization was taken up to 320 K from 5 K in zero field cooled (ZFC) mode with a magnetic field of 100 Oe. One quadrant isothermal curves were recorded up to a maximum magnetic field of 70 kOe for temperatures close to the observed transitions for the Arrott analysis.

The Fig. 1(a) and (b) show the temperature variation of magnetization for the samples Dy₂FeCoO₆ (DFCO) and Sm₂FeCoO₆ (SmFCO). The different transition temperatures observed were: Neel temperature for the samples around ∼250 K (248 K for DFCO, 246 K for SmFCO), the spin re-orientation temperature around ∼86 K for DFCO and around ∼210 K for SmFCO. The double peaks observed at ∼86 K (for DFCO) and ∼210 K (for SmFCO) in comparison with the orthoferrite counter parts indicate the spin re-orientation feature in the samples.^9–11 

The derivative curves indicate that the transition around 250 K has a ferromagnetic-like behaviour, while those at spin re-orientation temperatures show a double peak behaviour. From the first observation the spin re-orientation of DFCO, which is sharp, can be of first order. While the one for SmFCO with a broadened peak appears to be that of a second order phase transition due to the broad nature.

In order to classify the order of different magnetic transitions nearer to spin re-orientation in the samples, Arrott plot method is adapted.^7,8,12,13 For this purpose, one quadrant M vs H curves were recorded around the respective transitions observed for the samples in a magnetic field range of 0 Oe – 70 kOe. The unsaturated nature of the M vs H curves (not shown here), even at a magnetic field of 70 kOe, point towards the AFM/Weak ferromagnetic nature of the samples.

For DFCO, the spin re-orientation temperature is found to be around ∼86 K, so the M vs H curves were recorded from 75 K to 91 K with an interval of 2 K, where M vs T exhibited a sharp transition. For SmFCO, the spin re-orientation is around 210 K and the M vs H curves were recorded from 175 K to 277 K with an interval of 3 K, and this appeared as a broad transition.

From the equation of state, $HM=a+bM2$⁠, where M is the magnetization, H is the applied magnetic field in Oe, a and b are the coefficients. If the slope of the H/M vs M² curve is negative then the transition is considered to be of first order and for positive slopes it is of second order.^12,13

Figures 2 and 3 represent the Arrott plots for DFCO and SmFCO respectively. The insets are the enlarged view of low field regions. The linear fits were utilized for finding out the intercept values to distinguish the order of phase transitions. The value of intercept at 211 K, for high field region is found to be negative for SmFCO, which indicates the possibility of a first order magnetic transition.

In view of the slopes, it is found that the curves for the low temperature region of Dy₂FeCoO₆ show a negative slope (‘S- shape behaviour’) which is considered as a first order phase transition below the spin re-orientation temperature 86 K (refer Fig. 2), while the high temperature region has positive slope inferring a second order phase transition (not shown).^12,13 For the sample Sm₂FeCoO₆, the one nearer to spin reorientation (∼210 K) has a first order behaviour (refer Fig. 3). From the Arrott plot analysis it can be inferred that the first order spin re-orientation results in a FM-AFM transition in the samples. The presence of disordered B-sites with the magnetic ions of Fe and Co in mixed valence states may be the cause for the complicated magnetic structure observed in these compounds.

The disordered double perovskites Dy₂FeCoO₆ and Sm₂FeCoO₆ show spin re-orientation transition around ∼86 K and ∼210 K respectively. The Arrott plot analysis showed that both the samples have a first order spin re-orientation. Detailed analysis and measurements are yet to be performed for getting more information on the complicated magnetism exhibited by the samples.

Authors acknowledge IITM for funding SVSM. HGR thank Mr. Seenivasan (IIT Madras) for extended experimental support.