The temperature-dependent ac susceptibility studies of in-phase component (χ′ac) and out of phase component (χac″) was done on a single phase polycrystalline NdMn0.6Co0.4O3 sample. The measurements were conducted in 4 Oe ac field and 0 Oe dc field at frequencies of 111, 311, 1011, and 1311 Hz. As the frequency increases, the magnitude of χ′ac decreases, and its peak position, corresponding to Tf, moves towards higher temperatures. This strongly suggests the presence of a spin glass (SG) state and the absence of long-range ferromagnetic ordering. The value of relative shift in freezing temperature (δTf) is found to be δTf = 0.0089, which suggests the existence of canonical SG state in NdMn0.6Co0.4O3 sample. To confirm it the ac susceptibility data was further analyzed using Arrhenius, Vogel Fulcher, and Power–law.

The rare earth-based perovskite manganites RMnO3 (R = La, Nd, Pr, etc.) have been comprehensively studied because of their fascinating properties which owe their origin to the intricate competition between electronic, magnetic, and structural phases. The doping of alkaline earth metal like Ca at the R site or substitution of Mn by Co establishes various properties like ferromagnetism (FM), anti ferromagnetism (AFM), colossal magnetoresistance,1–3 and metal-insulator transition in perovskite manganites. Similarly, doping Sr at the La site induces FM in LaMnO3 associated with the sharp decline in resistivity,4 though the low-temperature ground state of RMnO3 oxides is AFM established long back.4,5 The sharp decrease in the resistivity was also seen in Nd0.5Sr0.5MnO3 on the application of a magnetic field.6 

NdMnO3 is an exciting rare earth manganite showing A-type AFM with ordering of Mn ions at the Néel temperature of TN = 82 K and FM ordering of Nd sublattice at Tl = 20 K.7,8 At room temperature, it possesses an orthorhombic crystal structure with space group Pnma or comparable space group Pbnm.8,9 The ratio Mn3+/Mn4+ significantly makes the magnetic and transport properties of Nd-based manganites more exciting and complex10,11 than the La-based manganites.12 Moreover, the magnetic complexity seen in Nd-based manganites because of the Nd–Mn exchange interaction13 has yet to be witnessed in La-based manganites. It has been observed that the Nd-based compounds like (Nd0.65Y0.35)0.7MnO3 demonstrate SG behavior because of the competing FM- and AFM interactions leading to magnetic frustration.14 Phan et al.15 found that the ionic disordering in Nd2CoMnO6.12 was observed to enhance the component similar to SG.

To investigate its magnetic properties, we performed the temperature-dependent magnetic measurements of 40% Co doped NdMnO3 (NdMn0.6Co0.4O3). The magnetization vs temperature (M vs T) measurement was carried out in zero field cooled (ZFC) and field cooled (FC) mode by applying fields of 0.05 and 1.0 T. The M vs T curves reveal the presence of SG state in the above mentioned sample. These findings were substantiated by conducting ac susceptibility measurements at the frequencies of 111, 311, 1011, and 1311 Hz under the applied field of 4 Oe. The ac susceptibility data was further analyzed employing Arrhenius, Vogel–Fulcher (VF), and Power-law.

A solid-state reaction process was used to obtain the single phase form of the NdMn0.6Co0.4O3 (NMCO4) sample. The high purity Nd2O3, MnO2, and Co3O4 oxides were used in stoichiometric amounts to obtain a homogenous form through extensive grinding using agate mortar. After calcination of this homogenous mixture, the sintering was done at 900 °C for ∼20 h. The pellets of 10 mm diameter were prepared from sintered powder and sintered once again at 1150 °C for 24 h. The sample’s X-ray diffraction (XRD) spectra were acquired at room temperature using a Bruker D8 diffractometer having Cu-Kα radiation source. The magnetization versus temperature measurements were conducted employing a Quantum Design commercial 7T SQUID-vibrating sample magnetometer, and an ac susceptibility study was carried out under an ac field of 4× 10−4 T at 111, 311, 1011, and 1311 Hz using a commercial Physical Quantity Measurement System.

The Rietveld refined XRD pattern of the NMCO4 sample reveals its single phase orthorhombic perovskite structure with a space group of Pbnm (Fig. 1). The experimental patterns are seen to be in good agreement with the fitted spectra.

FIG. 1.

Rietveld refinement of XRD diffraction patterns of NdMn0.6Co0.4O3 sample at room temperature. Bars in green colour represent the Bragg positions and the curves in blue colour display the difference between observed and calculated patterns.

FIG. 1.

Rietveld refinement of XRD diffraction patterns of NdMn0.6Co0.4O3 sample at room temperature. Bars in green colour represent the Bragg positions and the curves in blue colour display the difference between observed and calculated patterns.

Close modal
The refined structural parameters are given below:
a(Å)=5.4218,b(Å)=5.5490, c(Å)=7.6885,Volume(Å3)=231.31χ2=1.9

It is observed that a<c/√2<b, thus making NMCO4 an O-type orthorhombic structure.

The ZFC and FC variation of magnetization with temperature for the NMCO4 sample at the external field of 0.05 and 1.0 T is presented in Fig. 2. At Curie temperature TC, the NMCO4 sample displays a temperature-dependent transition from FM to paramagnetic (PM) phase. The value of TC at the field 0.05 T is 129.0 K, while as at 1.0 T, we find TC1 = 137.1 K and TC2 = 98.2 K; thus it increases with an applied field. The magnetization is seen to be increasing from below the TC, hinting at the possible FM interaction.

FIG. 2.

Variation of magnetization in NdMn0.6Co0.4O3 sample with temperature in a field of 0.05 and 1.0 T.

FIG. 2.

Variation of magnetization in NdMn0.6Co0.4O3 sample with temperature in a field of 0.05 and 1.0 T.

Close modal

It is seen that the ZFC and FC curves separate at the applied field of 0.05 and 1 T. After displaying maximum (Tm), the ZFC magnetization decreases with decreasing temperature, giving rise to a cusp. Both the temperature at ZFC peak Tm and irreversibility temperature Tirr (defined from MFC = MZFC) move to the lower temperatures with a broad maximum in ZFC magnetization as the applied field is increased to 1 T, marking the setting up of FM ordering in the sample. The sharp peak in the ZFC magnetization and an enormous difference between FC and ZFC magnetization at low temperatures in the applied field of 0.05 T is an indication of AFM coupling. The increased applied field reduces the AFM contribution, which is indicated by the broad maximum in the ZFC curve.

At the applied field of 0.05 T, an AFM to FM transition is observed in the ZFC curve at the temperature of 85 K. This emergence of a feeble FM state may be attributed to the canting of the AFM coupled spins, which is caused by the antisymmetrical constituent of the superexchange (SE) interaction.16–18 The anomalies observed in the FC curve at TC1 and TC2 in the applied field of 1.0 T owe their origin to the Mn4+ and Co2+ ordering and the presence of low and high-spin Co3+ (XAS shown in the inset of Fig. 2), consequently leading to the coexistence of ordered and disordered regions because of Mn4+/Co2+ and Mn3+/Co3+ ions respectively.19 

These features of thermo-magnetic irreversibility between ZFC and FC magnetization and rising FC magnetization may be a signature of the SG state.20,21 The presence of Mn and Co in mixed valence states results in SE FM and AFM interaction.22 Besides these SE interactions, Mn3+–O–Mn4+ FM double exchange (DE) is also present. The competing SE FM, AFM, and DE FM interactions lead to frustration in magnetic couplings and, thus the formation of the SG state.

To explore the SG state in the NMCO4 sample, an ac susceptibility study was done under an ac field of 4 × 10−4 T at the 111, 311, 1011, and 1311 Hz frequencies. The variation of ac susceptibility (both χ′ and χ″) with temperature is presented in Fig. 3. It is observed that with the increase of frequency, the magnitude of peak value in χ′, corresponding to Tf, decreases and shifts towards higher temperatures: a strong indication for the SG state. The SG state is also determined by verifying whether dependence of Tirr on the external field follows the Almeida–Thouless (AT) line using the M vs T measurements in ZFC and FC mode.23 However, due to some constraints, we could not perform this measurement.

FIG. 3.

Plot of ac susceptibility vs temperature for NMCO4 sample.

FIG. 3.

Plot of ac susceptibility vs temperature for NMCO4 sample.

Close modal
The relative shift in freezing temperature (δTf) is vital in distinguishing various SG systems, which is defined as24,25
δTf=ΔTfTfΔlog10ω
(1)
where ΔTf = (Tf)v1 − (Tf)v2 and Δlog10ω = log10(2πv1) − log10(2πv2).

We obtain δTf = = 0.0089 for the NMCO4 sample, which agrees with the verified values for canonical SG (CSG) systems.24,26

These results were substantiated by fitting ac susceptibility data to the Arrhenius law24 and displayed in Fig. 4. Arrhenius law can be written as
τ=τ0expEakBTf
(2)
Here τ0 is a single spin-flip relaxation time; Ea represents activation energy, ω stands for driving frequency employed in ac susceptibility measurement, while Tf corresponds to its peak. From the plot of In(f) vs l/Tf, the estimated value of τ0 ∼ 10−122 and Ea/kB = 37407 K for the NMCO4 sample. These are incredibly unphysical values, possibly because of small changes in Tf. Thus, the existence of a superparamagnet is ruled out.
FIG. 4.

Best fit using Arrhenius law, VF law, and power law for NMCO4 sample.

FIG. 4.

Best fit using Arrhenius law, VF law, and power law for NMCO4 sample.

Close modal
The Vogel–Fulcher (VF) law, a dynamical scaling law in the context of spin glass freezing, considers the interaction between the spins. It defines the frequency-dependent Tf as24,25
τ=τ0expEakBTfT0
(3)
Where, T0 is the VF temperature, ranging between 0 K and Tf. It signifies the interaction strength among the dynamic entities. The graph illustrating ln τ vs 1/(TfT0) is depicted in Fig. 4, fitted to Eq. (3) with T0= 127.5 K for the sample under study. The value of τ0 calculated is of the order of ∼10−13 s, which is the typical value of canonical spin glass (CSG) and is comparable to the spin-flip time of atomic magnetic moments (∼10−13 s).27 The slope Ea/kB of the linear fit has a value of ∼203. As per the Tholence criterion, δTTh = (Tf − T0)/Tf,28 the value of δTTh obtained for NMCO4 is ∼0.07 which is an order lower in magnitude than the one found for cluster glass (CG).24 The obtained values agree with those acquired for a CSG system, such as CuMn.29 
The frequency dependence of Tf using the usual power law specified by the dynamic scaling theory24,30 is given as
τ=τ0TfTgTgzv
(4)
Where τ, the characteristic time, specifies the dynamical fluctuation time scale and is linked to the time of observation, tobs = 1/ω = 1/2πν, τ0 represents the relaxation time for a single spin flip, Tg is the temperature marking the SG transition and is equal to Tf when frequency ν tends to zero, z is the dynamical exponent and ν′ stands for the critical exponent of the spin correlation length ζ = (Tf/Tg − 1)ν.

The graph of ln(τ) vs ln(Tf/Tg − 1) is shown in Fig. 4 for NMCO4 with Tg = 133.5 K, determined through the best fit to the power law. The value of τ0 and z`, corresponding to the best fit, is obtained from the intercept and slope of the graph, respectively. The value achieved from the present analysis for ′ is ∼ 7 and τ0 ∼ 10−13 s. These values are distinctive of CSG (∼10−12–10−14 s).24,31,32

In our current investigation, the polycrystalline NdMn0.6Co0.4O3 sample exhibits the canonical spin glass state. This sample, synthesized via solid-state reaction method, demonstrates a single phase with a crystal structure of orthorhombic identity and Pbnm as the assigned space group. The existence of a canonical spin glass state is established by employing the ac susceptibility characterization technique and further substantiated through Arrhenius law, Vogel Fulcher law, and Power law.

We acknowledge the support Quazar Tech. New Delhi, India extended to us, to carry out the ac susceptibility measurements and to Dr. Alok Banerjee, IUC, Indore, India, for providing the facility to do the magnetization measurements.

The authors have no conflicts to disclose.

Farooq Hussain Bhat: Conceptualization (lead); Formal analysis (lead); Investigation (lead); Methodology (lead); Writing – original draft (lead). Ghazala Anjum: Data curation (equal); Software (equal); Visualization (equal).

The data supporting this study’s findings are available from the corresponding author upon reasonable request.

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