Effect of Zn doping on the magneto-caloric effect and critical constants of Mott insulator MnV₂O₄

The magnetocaloric effect (MCE) has attracted much interest because of its commercial uses in magnetic refrigeration.¹ The materials showing second order magnetic transition exhibit conventional MCE and the magnetic contribution in it is of magnetic origin.² Moreover, the materials involving first order magnetic transition show giant MCE with significant contribution from the lattice.³ Recently, in spinel ferromagnetic MnV₂O₄, which shows the orbital degeneracy, and the interplay of spin, orbital and lattice degrees of freedom, large magneto-caloric effect is reported around T_c (= 57 K).⁴ Other than the conventional spin-orbit coupling this interplay also arises due to the geometrical anisotropy in magnetic interaction (the so-called Kugel-Khomskii type coupling).⁵ Moreover, in these materials magnetic and structural these two phase transitions are separately obserevd.^6–8 This MnV₂O₄ lies in the Mott insulator regime. MnV₂O₄ exhibits a magnetic transition at T_c = 57 K (second order transition), and then a structural phase transition from a cubic to a tetragonal phase at T_s = 53 K (first order transition), with the spin structure becoming non-collinear.⁹ It was also found that the structural transition could be induced by few tesla magnetic field.^10,11 Moreover, the orbital ordering of MnV₂O₄ cannot be explained simply by anti-ferro orbital model.¹² The large magneto-caloric effect in this compound is suggested to be related to the orbital entropy change due to the change of the orbital state of V³⁺ ions with an applied field around T_c (= 57 K).⁴ Furthermore, when Zn is doped on the Mn site the value of magneto-caloric effect increases and the maximum is observed at the lower transition temperature (T_S) which has been attributed to orbital ordering.¹³ In this perspective the detail study of Zn doping on magneto-caloric effect of MnV₂O₄ will be interesting. Moreover, the critical behaviour, which has direct correlation with the MCE, of MnV₂O₄ might also be distinctive to provide interesting information about the magnetic spin ordering in this spinel Vanadate. Baek et al.¹⁴ have reported the critical exponents of this system. From the ac-susceptibility measurement they obtained very unusal values of the critical constants (β = 0.36 and γ = 0.59).¹⁴ In a recent paper Zhang et al. reported the critical constants β ∼ 0.349 (close to 3D Heisenberg model) and γ ∼ 0.909 (close to mean field model).¹⁵ Moreover, Garlea et al. determined the β value from the integrated intensity I(T) fitting.¹⁶ The I(T) can be described near the two phase transitions as I(T) ∞ (T_C,S-T)^2β. The obtained value by them was close to 3D Heisenberg and 3D Ising models. To resolve the issue we have also studied the variation of critical constants with Zn doping using modified Arrot plots.

The polycrystalline Mn_1-xZn_xV₂O₄ samples were synthesized by solid state reaction technique. The MnO, ZnO and V₂O₃ powders were mixed and pressed into pellets. The pellets were sintered in evacuated quartz tube at 950 °C for 40 hours. The samples were characterized with X-ray powder diffraction (XRD) using Rigaku MiniFlex II DEXTOP X-ray Diffractometer. The XANES measurements have been carried out at the Energy-Scanning EXAFS beamline (BL-9) in transmission mode at the INDUS-2 Synchrotron Source (2.5 GeV, 100 mA) at Raja Ramanna Centre for Advanced Technology (RRCAT), Indore, India. This beamline operates in energy range of 4 KeV to 25 KeV. The beamline optics consist of a Rh/Pt coated collimating meridional cylindrical mirror and the collimated beam reflected by the mirror is monochromatized by a Si(111) (2d = 6.2709) based double crystal monochromator. The second crystal of DCM is a sagittal cylinder used for horizontal focusing. Three ionization chambers (300 mm length each) have been used for data collection in transmission mode, one ionization chamber for measuring incident flux (I₀), second one for measuring transmitted flux (I_t) and the third ionization chamber for measuring EXAFS spectrum of a reference metal foil for energy calibration. Magnetic measurement was done using Magnetic Properties Measurement System (MPMS) SQUID (Quantum Design) magnetometer.

Fig. 1 shows the XRD patterns of Mn_1-xZn_xV₂O₄ indicating the single phase of all the samples. We have refined the diffraction data with the Reitveld refinement program (the fitted curve has also been shown in Fig. 1) and the fitted parameters are shown in Table I. The lattice parameter “a” obtained from the Reitveld refinement of the XRD data is shown as a function Zn content in the inset of Figure 1. From the figure, it is clear that with increase of Zn content the lattice parameter decreases, which is due to lower ionic size of Zn²⁺(0.74 Å) compared to Mn²⁺(0.80 Å). The linear dependence of the lattice constant on Zn concentration indicates that there is no structural change in MnV₂O₄ with Zn doping and as a matter of fact Zn is doped into the crystal lattice following the Vegard's law.¹⁷ In order to probe the oxidation state of all the transition metals i.e. Mn, Zn and V, we have performed XANES measurements at their corresponding K edges. Figure 2 shows the edge step normalized XANES spectra for Mn K-edge for the Mn_1-xZn_xV₂O₄ (x = 0, 0.05 & 0.1) samples. The XANES spectra of all the samples are plotted with three standards Mn metal foil, MnO and Mn₂O₃ with +0, +2 and +3 oxidation state respectively. A typical K edge XANES spectra exhibits structured pre-edge region and the dominant peak called white line peak followed by main rising edge.¹⁸ Here, we emphasize only the main edge part of the XANES spectra for our purpose. The pre-edge features below the main edge are due to Mn 1s transition into unoccupied O 2p-Mn 3d (or Mn 3d/4p) hybridized states, which have p components projected at the Mn site as observed in many transition-metal oxides. The main edge feature at the Mn K-edge corresponds to the high-energy Mn 4p states. Energy position of the main edge in XANES spectra of a sample may be determined either as the energy corresponding to ∼0.5 absorption or maximum energy value of a first order differentiated spectrum.¹⁸ The main edge position of Mn_1-xZn_xV₂O₄ for x = 0, 0.05 and 0.1 samples coincides with MnO, for which Mn ion has been assigned to have a valence or effective charge of +2.

Figure 3 shows the edge step normalized XANES spectra for Zn K-edge for the Mn_1-xZn_xV₂O₄ for x = 0.05 and 0.1 along with two standards namely Zn metal and ZnO with +0 and +2 oxidation state respectively. This edge position in Mn_1-xZn_xV₂O₄ for x = 0.05 & 0.1 clearly shows that Zn is present in +2 oxidation state as its edge coincide with ZnO edge.

Figure 4 shows the same edge step normalized XANES spectra for V K-edge for the Mn_1-xZn_xV₂O₄ (x = 0, 0.05 and 0.1) along with standards V metal and VOSO₄ with +0 and +4 oxidation state respectively. A visual inspection of Figure 3, the main edge energy corresponding to V K edge is close to +4 but very far from +0. Energy positions of these samples, discussed above, well matches with the earlier reports for V³⁺.¹⁹ A table for their energy positions with the corresponding references is presented in Table II, indicating +3 oxidation state of Vanadium in our studied samples. From the above discussion it is clear that no change in the valence states of Mn and V is occurring due to doping of Zn.

Fig. 5 shows the temperature dependence of magnetization of Mn_1-xZn_xV₂O₄ under zero field cooled (ZFC) condition at 100 Oe. The M-T curve of MnV₂O₄ exhibits a sharp paramagnetic-ferrimagnetic (PM-FM) phase transition. It is observed that the magnetization drops sharply for all the Zn doped MnV₂O₄ samples on cooling. This is due to the spin-pairing of V-V bonds.²⁰ Inset of Fig. 5 shows the evolution of T_C with Zn content for the Mn_1-xZn_xV₂O₄.

The M(H) curves at different temperatures (around the T_c) have been shown in Fig. 6. According to the Scaling hypothesis,²¹ a second order magnetic phase transition near the Curie point is characterized by a set of critical exponents of β, γ and δ and the magnetic ordering can be studied

which combines the relations for the spontaneous magnetization below T_c

and the inverse magnetic susceptibility above T_c

To find the correct values of β and γ, linear fits to the isotherms are made to get the intercepts giving M(T) and χ(T). These new values of β and γ are then used to make a new modified Arrott plot. New values of critical exponents thus obtained are re-introduced in the scaling of the modified Arrott plot. The process is repeated until the iteration converges, leading to an optimum fitting value.

Fig. 7 shows the final result for the Mn_1-xZn_xV₂O₄ samples. We have taken M(H) isotherms from 50 K to 70 K in every 2 K interval. The calculated values of β and γ are, respectively, 0.393 and 1.01 for x = 0 sample. For x = 0.05 the values are respectively, 0.40 and 1.02 whereas for x = 0.1 the values of β and γ are respectively, 0.42 and 1.07. Below 54 K it deviates from linearity due to the first order transition at ∼52 K.

The critical values we obtained are not from the universality class. According to the scaling theory the magnetization equation can be written as M(H,ɛ)ɛ^−β = f_±(H/ɛ^β+γ), where ɛ is the reduced temperature, f₊ for T > T_c and f₋ for T < T_c are regular functions.²² The equation states that the plot between M|ɛ|^−β vs H|ɛ^|−(β+γ) gives two universal curves: one for T > T_c and other for T < T_c. As shown in Fig. 8, the curves are divided in two parts one above T_c and one below T_c. The inset of Fig. 8 also shows log-log plot and this also falls into two classes one above T_c and one below T_c, in agreement with the scaling theory. Therefore the FM behaviour around Curie temperature get renormalized following the scaling equation of state indicating that the calculated critical exponents are reliable. Moreover, exponents often show various systematic trends or crossover phenomenon's one approaches T_c.^23,24 This occurs due to the presence of various competing couplings and/or disorder. For this reason, it is useful to introduce temperature-dependent effective exponents for ɛ ≠ 0. It can be mentioned that effective exponents are non universal properties, and they are defined as:

We have calculated the β^eff and γ^eff by using the Eq. (2) (not shown), which do not match with universality class.

It is observed from the above discussion that the critical exponents of the present investigated sample are not consistent with the universality class. The similar behaviour has been observed in perovskite Pr_0.5Sr_0.5MnO₃ (β = 0.397and γ = 1.331)²⁵ and in La_0.7Sr_0.3MnO₃ (β = 0.45 and γ = 1.2)²⁶ due to phase separation. Other than perovskite, Gd₈₀Au₂₀ also shows unusual critical exponents (β = 0.44(2) and γ = 1.29(5)) arise due to the dilution of global spin with the substitution of non-magnetic ions.²⁷ In the present case very close to the second order PM-FM transition (at ∼ 58 K) there exists a first order structural transition (∼52 K) which is associated with the collinear to non-collinear spin transition. This may cause a large spin fluctuation which may be responsible for the unusual critical exponents between the actual material and the theoretical model.

In order to further investigate we have also estimated the magneto caloric effect of all the samples. The magnetic entropy change is given by

Where M_i is the Magnetization at Temperature T_i.²⁸ The obtained |ΔS_m| has been plotted as a function of temperature in Fig. 9. In the inset of Fig. 6 the magnetic field variation of |ΔS_m| shows the H^2/3 dependency (the value of the exponent for x = 0, 0.05 and 0.1 are respectively, 0.633, 0.67 and 0.666). This is consistent with the relation between magnetic entropy and the magnetic field near the magnetic phase transition which is given by²⁹ 

where q is the number of magnetic ions, R is the gas constant, and g is the Landau factor. In Fig. 9 it is observed that as Zn content increases the magnetic entropy value decreases, which is also consistent with the Eq. (4). As with increase of Zn content the magnetic Mn ions decrease. Moreover, in Mn_1-xZn_xV₂O₄ for x = 0 and 0.1 only one peak is found and that is at T_c but for x = 0.05 two peaks are observed (one is at T_c and another is at T_oo). The observed behaviour for x = 0 and x = 0.05 is consistent with those reported.^4,13 It has been explained that the large magneto caloric effect in MnV₂O₄ is due to the change of the orbital state of V³⁺ ions with applied field around T_c which leads to the change in orbital entropy.⁴ The observed second peak in x = 0.05 is suggested to be due to the strong coupling between orbital and spin degrees of freedom.¹³ But in that case in MnV₂O₄ sample also we should get two peaks. Moreover, in the present investigation x = 0.1 sample does not show second peak. It might be the fact that in MnV₂O₄ the two transitions are very close to each other and because of that two peaks overlap into a single peak. Moreover for 10% Zn doping the chemical pressure increases which reduces the residual spins on the V-V pairs which leads to the decrease of long range magnetic ordering. As a matter of fact the coupling between orbital and spin degrees of freedom decreases. This might be the reason of diminishing the peak at low temperature when 10% Zn is doped

The XANES study indicates that no change in the valence states of Mn and V is occurring due to doping of Zn and V remains in 3+ state. The giant magneto-caloric effect value is observed in these spinel vanadates and the entropy change (MCE value) decreases with increase of Zn content. It has been shown that the obtained values of the critical exponents β, γ and δ do not belong to universal class and the values are in between the 3D Heisenberg model and mean field interaction model. The magnetization data follow the scaling equation and collapse into two branches indicating that the calculated critical exponents and critical temperatures are unambiguous and intrinsic to the system. The observed double peaks in MCE of Mn_0.95Zn_0.05V₂O₄ are due to the strong coupling between orbital and spin degrees of freedom. In this composition (x = 0.05) the orbital ordering becomes maximum which in effect increase the coupling between orbital and spin degrees of freedom at T_oo leading the second peak in magneto-caloric behavior in x = 0.05 sample. When Zn content increases (viz. x = 0.1) the chemical pressure increases which reduces the residual spins on the V-V pairs which leads to the decrease of long range magnetic ordering. As a consequence coupling between orbital and spin degrees of freedom decreases.

SC is grateful to the funding agencies DST (Grant No.: SR/S2/CMP-26/2008) and CSIR (Grant No.: 03(1142)/09/EMR-II) and BRNS, DAE (Grant No.: 2013/37P/43/BRNS) for financial support. PS is grateful to CSIR, India for providing Research Fellowship. Authors are also grateful to D. Budhikot for his help in magnetization measurement.