Investigation of spinel oxide, NiCr2O4, began in 1950’s. It has very complicated crystal and magnetic structures. Here we will review some of the earlier works based on this compound in order to know its different physical properties.
1.10.1 Crystal and Magnetic Structure
Lotgering in 1956 reported that NiCr2O4 is a normal spinel compound with Jahn- Teller active Ni2+ (3d8) ions in the tetrahedral site and Cr3+ (3d3) ions in the octahedral site. It undergoes a structural transition from cubic to tetragonal phase at 310 K and it is followed by the PM to FIM transition (TC) at 80 K [121]. Low saturation magnetization (Ms) of about 0.3 µB/f.u. for NiCr2O4 raises the question about its magnetic structure: is it a collinear FIM or a non-collinear FIM with triangular (canted) arrangement described by Yafet-Kittel theory?
Large increase in net magnetization at high applied magnetic field provides the evidence for a non-collinear FIM arrangement, since such behavior is not expected for the Néel model of FIM. Jacobs [122] confirmed the non-collinear FIM structure in NiFe2-tCrtO4 series with t >
1, i.e. in the chromite rich samples, but it was not confirmed by neutron diffraction study.
Several authors have confirmed the JTD induced structural transition at around 310 K and the FIM transition in the range of 65 – 79 K by X-ray diffraction study and neutron diffraction study [17, 123-126]. Crottaz et al. [17] have studied the crystal structure of NiCr2O4 both above and below the structural transition temperature. At 353 K, NiCr2O4 is cubic (Fd3m space group) with lattice parameter, a = 8.3155 Å while at 298 K it is tetragonal (I41/amd space group) with a = b =5.8369 Å and c = 8.4301 Å. The respective atomic positions of Ni, Cr and O in tetragonal structure are reported to be 4b (0, 1/4, 3/8), 8c (0, 0, 0) and 16h (0, 0.506, 0.2387). In the year of 2002, Klemme et al. [18] discovered a new peak at 29 K in their heat capacity data [Fig. 1.15(a)]. This additional low temperature transition is later confirmed by Tomiyasu and Kagomiya (TS = 31 K) [54] from magnetization measurements and it is explained in terms of ordering of the AFM transverse components. In order to explain the low Ms of NiCr2O4 (0.3 µB / f. u.), they also worked out its magnetic structure below TS from neutron diffraction measurement. According to them, the A sublattice is classified into A1-A2 pairs and B sublattice is classified into B1-B3 and B2-B4 pairs with each having longitudinal and transverse components such that the total longitudinal component of moment is 0.3 µB / f. u. The FIM and the AFM components are depicted in Fig.
1.15(b) & (c). Thus the total magnetization per formula unit can be written as M = | ↑ µA1-A2 +
↑ µB1-B3 − ↓ µB2-B4 |, where ↑ µA1-A2, ↑ µB1-B3 and ↓ µB2-B4 are the longitudinal components of the magnetic moments of A1-A2, B1-B3 and B2-B4 sublattices, respectively along the field
direction. Ishibashi and Yasumi [127] performed the high resolution X-ray diffraction measurements using synchrotron radiation on NiCr2O4 and found that the FIM transition at TC = 74 K is associated with structural transition into orthorhombic phase from tetragonal at ambient pressure. This highlights the presence of important magneto-elastic behavior. The spin induced structural changes in NiCr2O4 was studied by Suchomel et al. [19] by recording the high resolution synchrotron X-ray powder diffraction as a function of temperature. They found that the structural transition from tetragonal to orthorhombic phase with Fddd space group occurs concurrently with the onset of FIM ordering and also found the evidence of further subtle structural changes at the AFM transition temperature (30 K).
Figure 1.15: (a) Heat capacity of NiCr2O4 [18]. Schematic diagram of (b) longitudinal FIM and (c) transverse AFM components of group of A (Ni2+) and B (Cr3+) sublattices [54].
1.10.2 Other Salient Properties
After the discovery of crystal and magnetic structure of NiCr2O4, several authors have tried to explore its other exciting properties like magnetodielectric, magnetoelectric, magnetoelastic, EB, etc. Spinel chromites are generally known to have strong correlation between spin, charge and lattice degree of freedom. Mufti et al. [23] have studied the magnetodielectric coupling in the pollcrystalline samples of NiCr2O4 and observed a clear anomaly in the dielectric constant in the vicinity of TS. The dielectric response in an applied magnetic field was found to scale with the square of the magnetization and thus they predicted that the magnetodielectric coupling originates from P2M2 term in the free energy.
In the context of this magnetodielectric coupling, magnetocapacitance is also discussed in
this sample by Sparks et al. [128]. The magnetoelastic measurements are also shown to exhibit anomalies at different magnetic transitions of NiCr2O4 [21].
The coexistence of ferroelectric and magnetic properties in a single phase material is a subject of great interest from fundamental as well as application point of view. Frustrated magnets like CoCr2O4, RMnO3 and RMn2O5 (R = Tb, Dy and Ho), exhibit multiferroic property with large magnetoelectric coupling, i.e. here the electric polarization (P) has magnetic origin and can be reversibly switchable by applying magnetic field [13, 129, 130].
In spinel oxides like CoCr2O4 [13], conical spiral magnetic ordering below TS = 26 K is responsible for the inversion symmetry breaking and hence the magnetically induced polarization. This process can be explained by combining spin current model and the inverse DM interaction [13, 131],
( )
ij i j
p = ae × S × S
(1.24)
where Si and Sj
are the canted spin vector,
e
ijdenotes the vector connecting the two sites, and a is a proportionality constant. NiCr2O4 do not exhibit any spiral magnetic structure. But an evidence of electrical polarization below TC has been observed by Maignan et al. in NiCr2O4 [22]. They have attributed the existence of the polar state in NiCr2O4 due to its complex magnetic structure with different A – O – B, A – O – A, B – O – B magnetic interactions.
Interaction through such different exchange pathways probably is responsible for local symmetry breaking and leads to electrical polarization in the system.
Existence of EB phenomenon in multiferroic materials enhances their multifunctionality and thus their potential for suitable applications in spintronics. Signature of EB (shifting of hysteresis loop) was observed in bulk NiCr2O4 sample which was explained due to the presence of some Cr2O3 impurity [132, 133]. But the detailed study by varying the temperature and field are not available. Later EB study has been carried out in NiCr2O4 nanoparticles where it was attributed to the coupling between surface spin and ferrimagnetically ordered spin [100]. EB was also observed in NiCr2O4 /NiO [134] and NiCr2O4/Cr2O3 [98] composites and was explained in terms of the exchange coupling between FIM NiCr2O4 and AFM NiO and Cr2O3.
Although lots of reports are available on different properties of parent NiCr2O4, very few studies have been carried out on the effect of substitutions at Ni or Cr site. Structural analysis were carried out in M1-xNixCr2O4 (M = Cu and Fe) [135], Ni1-xCuxCr2O4 [136] and Ni(Fe1-xCrx)2O4 [137] in order to understand the cooperative JTD. FIM behavior with increasing TC was reported in Ni1-xCuxCr2O4 [138] and NiCr2-xFexO4 [139]. The Neel temperature for NiCr1.7Fe0.3O4 was reported to be 250 K and the Mössbauer spectra detected the distribution of Fe3+ ions in the two sites of Cr3+ [139, 140]. Strong orthorhombic distortions into Fddd space group was observed in Ni1-xCuxCr2O4 due to competing Jahn- Teller activities between the Cu2+ and Ni2+ ions [141]. Multiferroic properties were studied recently in Co1-xNixCr2O4 (x = 0.2, 0.4, 0.6) [142] and Ni1-xZnxCr2O4 (x = 0.05) solid solutions [143]. The remarkable multiferroic nature of Ni0.95Zn0.05Cr2O4 might originate from the DM interaction [143]. Recently, EB behavior was also evidenced in Mn doped NiCr2O4 sample (NiCr1.90Mn0.10O4) [144].