Critical behavior of CrTe1-xSbx ferromagnet

The modified Arrott plots and Kouvel${\text -}$Fisher analysis are used to investigate the critical behavior of $CrTe_{1-x}Sb_{x}$ ferromagnetic material near its transition temperature $T_{c}$. The Ferro${\text -}$Paramagnetic transition is found to be a second${\text -}$order phase transition. For $x=0.2$, the critical exponents closely follow the Mean Field Model with the estimated values of the exponents: $\beta$ =0.60 $\pm$ 0.03, $\gamma$ =1.00 $\pm$ 0.03 and $\delta$ =2.67 $\pm$ 0.03. We also found with increasing Sb${\text -}$concentrations, the critical exponents significantly deviate from the mean field values and gradually shift towards the 3${\text -}$Dimensional behavior. The deviation may indicate changes in the spin configuration with increasing Sb concentrations.


INTRODUCTION
Reduced dimensional magnetic materials are coming out as promising materials for new potential applications and the emerging field of spintronics. The interplay of electrical and magnetic properties of these materials seems to be important for these new applications. Their electrical and magnetic properties can be tuned using the charge and spin degree of freedom [1]. However, the lack of long-range ferromagnetic order in many 2D materials hinders such possibility [1,2].
Recently, Cr-based ternary chalcogenides, CrMX3, where M is a non-transition metal (Sb, Ge) and X is chalcogenides: S, Se or Te, have renewed the interest in their magnetic state and critical behavior as well as practical applications. These materials are exfoliatable magnetic layers with van der Waals forces weakly binding the ferromagnetic layers. For example, CrTe is a ferromagnetic conductor with Tc~350K [3], while CrSb is antiferromagnetic with TN ~700K [4].
According to the de Gennes theory and the double exchange interaction, substituting Sb on the Te site affects the magnetic state of the solid solution CrTe1-xSbx and continually reduces the ferromagnetic transition [5].
In this work, we investigate the effect of Sb substitution on the ferromagnetic state of CrTe1-xSbx and the critical behavior near FM-PM phase transition. We used an iterative procedure of the modified Arrott plot along with the Kouvel-Fisher to evaluate the critical exponents and compare the results for x=0.2 and x=0.5 samples [6,7].

EXPERIMENTAL DETAILS
Stoichiometric ratios of high purity (4N) Cr, Te, and Sb were used to prepare CrTe1-xSbx samples using a conventional solid-state reaction method. The elements are mixed, ground, pressed and sealed in a quartz tube under partial pressure of high purity Argon. The samples are annealed at 800 o C for 10 hours. The process is repeated twice, and the samples are annealed at 1000 o C for 24 hours. Magnetization measurements were performed using a 9-Tesla PAR-Lakeshore (Model 4500/150A) vibrating sample magnetometer (VSM).

RESULTS AND ANALYSIS
The magnetization isotherms for the CrTe0.8Sb0.2 sample are presented as modified Arrott plots M 1/ vs. (H/M) 1/ graphs as shown in Fig. 1 (a, b, c and d) [6]. Different theoretical models along with their critical exponents are used to construct the modified Arrott-Noakes plots: Landau mean-3 field model (=0.5, =1), 3D Heisenberg model (=0.365, =1.386), 3D Ising model (=0.325, =1.24) and the Tricritical mean-field model ( = 0.25,  = 1.0). At low fields, the changes in the initial magnetization is mainly due to the rotation of the domain-magnetization. At high fields (>3Tesla -see Fig. 1), the isotherms are nearly straight lines in most models. The lines are nearly parallel except for the Tricritical mean field model Fig.1d suggesting that it may not correctly represent the isotherms. Moreover, the positive slopes seen in the modified Arrott plots Fig. 1(a) indicate a second-order phase transition according to the criterion set by Banerjee [8].
To identify the best model that represents the data, the relative slopes (RS) of the magnetization isotherms at high fields are plotted in Fig. 2a. The slopes are normalized to the slope at Tc=296K  The spontaneous magnetization ( ) and the inverse initial susceptibility 0 −1 ( ) are obtained from the intercepts of linear fit of the magnetization isotherms with the y and x-axis respectively (Fig. 1a). The values of ( ) and 0 −1 ( ) are used to construct the Kouvel-Fisher plots (Fig.   2b), which in turn is used to evaluate the critical exponents β and γ. Linear fits of the data in Fig.   2b are used to estimate the initial values of the critical exponents β = 0.52±0.03 and γ = 0.83±0.03.
An iteration method along with KF analysis can be used to obtain a better estimate to the critical exponents [7]. The initial values of the critical exponents are used to re-construct the modified  The third critical exponent δ has been evaluated using Widom's identity which yield δ=2.67±0.06 which is lower than the value (δ=3.22±0.03) obtained from the critical isotherm at Tc [10]. Similar behavior has been found in CrSbSe3 and CrxTe3 single crystals [9,11]. We conclude from these findings that the Mean Field Model closely represents the critical exponents of CrTe0.8Sb0.2.
We carried out the iteration analysis of the modified Arrott plots and Kouvel-Fisher plots to evaluate the critical exponents for CrTe0.5Sb0.5. The relative slope and the Kouvel Fisher plot are shown in Fig. 3 (a and b) respectively. Clearly, the RS values shows that the Mean Field model best represents the magnetization isotherms. Near Tc, the RS values obtained from the Mean Field model and the 3D Heisenberg model are very close to each other (Fig. 3a).

Conclusion:
The modified Arrott plots and Kouvel-Fisher critical exponents' analyses revealed that upon increasing the Sb in CrTe1-xSbx, the critical exponents' values for samples deviate significantly from mean field values and gradually shifts towards 3D models. This may suggest that the interlayer coupling is affected by Sb-substitutions and may not be neglected. Moreover, the magnetic state is developing to a more complex ferromagnetic state.