Unconventional superparamagnetic behavior in the modified cubic spinel compound LiNi${0.5}$Mn${1.5}$O$_{4}$

Structural, electronic, and magnetic properties of modified cubic spinel compound LiNi$_{0.5}$Mn$_{1.5}$O$_{4}$ are studied via x-ray diffraction, resistivity, DC and AC magnetization, heat capacity, neutron diffraction, $^7$Li nuclear magnetic resonance, magnetocaloric effect, magnetic relaxation, and magnetic memory effect experiments. We stabilized this compound in a cubic structure with space group $P4_{3}32$. It exhibits semiconducting character with an electronic band gap of $\Delta/k_{\rm B} \simeq 0.4$~eV. The interaction within each Mn$^{4+}$ and Ni$^{2+}$ sub-lattice and between Mn$^{4+}$ and Ni$^{2+}$ sublattices is found to be ferromagnetic (FM) and antiferromagnetic (AFM), respectively. This leads to the onset of a ferrimagnetic transition at $T_{\rm C} \simeq 125$~K. The reduced values of frustration parameter ($f$) and ordered moments reflect magnetic frustration due to competing FM and AFM interactions. From the $^7$Li NMR shift vs susceptibility plot, the average hyperfine coupling between $^7$Li nuclei and Ni$^{2+}$ and Mn$^{4+}$ spins is calculated to be $\sim 672.4$~Oe/$\mu_{\rm B}$. A detailed critical behaviour study is done in the vicinity of $T_{\rm C}$ using modified-Arrott plot, Kouvel-Fisher plot, and universal scaling of magnetization isotherms. The magnetic phase transition is found to be second order in nature and the estimated critical exponents correspond to the 3D XY universality class. A large magneto-caloric effect is observed with a maximum value of isothermal change in entropy $\Delta S_m \simeq - 11.3$~J/Kg-K and a maximum relative cooling power of $RCP \simeq 604$~J/Kg for 9~T magnetic field change. The imaginary part of the AC susceptibility depicts a strong frequency dependent hump at $T=T_{\rm f2}$ well below the blocking temperature $T_{\rm b}\simeq120$~K. The Arrhenius behaviour of frequency dependent $T_{\rm f2}$ and the absence of ZFC memory confirm the existence of superparamagnetism in the ferrimagnetically ordered state.