Unconventional superparamagnetic behavior in the modified cubic spinel compound ${\mathrm{LiNi}}_{0.5}{\mathrm{Mn}}_{1.5}{\mathrm{O}}_4$

Structural, electronic, and magnetic properties of modified cubic spinel compound ${\mathrm{LiNi}}_{0.5}{\mathrm{Mn}}_{1.5}{\mathrm{O}}_4$ are studied via x-ray diffraction, resistivity, dc and ac magnetization, heat capacity, neutron diffraction, ${}^7\mathrm{Li}$ nuclear magnetic resonance, magnetocaloric effect, magnetic relaxation, and magnetic memory effect experiments. We stabilized this compound in a cubic structure with space group $P{4}_{3}32$. It exhibits semiconducting character with an electronic band gap of $\mathrm{\Delta }/k_{\mathrm{B}}\simeq 0.4$ eV. The interaction within each ${\mathrm{Mn}}^{4+}$ and ${\mathrm{Ni}}^{2+}$ sublattice and between ${\mathrm{Mn}}^{4+}$ and ${\mathrm{Ni}}^{2+}$ sublattices is found to be ferromagnetic (FM) and antiferromagnetic (AFM), respectively. This leads to the onset of a ferrimagnetic transition at $T_{\mathrm{C}}\simeq 125$ K. The reduced values of frustration parameter ($f$) and ordered moments reflect magnetic frustration due to competing FM and AFM interactions. From the ${}^7\mathrm{Li}$ nuclear magnetic resonance shift vs susceptibility plot, the average hyperfine coupling between ${}^7\mathrm{Li}$ nuclei and ${\mathrm{Ni}}^{2+}$ and ${\mathrm{Mn}}^{4+}$ spins is calculated to be $\sim 672.4$ Oe/${\mu }_{\mathrm{B}}$. A detailed critical behavior study is done in the vicinity of $T_{\mathrm{C}}$ 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 three-dimensional XY universality class. A large magnetocaloric effect is observed with a maximum value of isothermal change in entropy $\mathrm{\Delta }{S}_m\simeq -11.3$ J/Kg K and a maximum relative cooling power of $\text{RCP}\simeq 604$ J/Kg for 9 T magnetic field change. The imaginary part of the ac susceptibility depicts a strong frequency-dependent hump at $T=T_{\mathrm{f}2}$ well below the blocking temperature $T_{\mathrm{b}}\simeq 120$ K. The Arrhenius behavior of frequency dependent $T_{\mathrm{f}2}$ and the absence of zero-field-cooled memory confirm the existence of superparamagnetism in the ferrimagnetically ordered state.

Figure 1

(a) Crystal structure of LNMO in three dimensions. (b) Hyperkagome lattice made of ${\mathrm{Mn}}^{4+}$ ions. (c) Pyrochlore lattice made of ${\mathrm{Ni}}^{2+}$ and ${\mathrm{Mn}}^{4+}$ ions. (d) A section of the pyrochlore lattice showing corner-sharing tetrahedra and spin structure deduced from the neutron diffraction data at $T=5$ K.

Figure 2

Upper panel: x-ray powder diffraction pattern (open circles) of LNMO at room temperature. The red solid line is the Rietveld refinement fit with $P{4}_{3}32$ space group. The expected Bragg positions are indicated by green vertical ticks. Blue solid line at the bottom denotes the difference between observed and calculated intensities. Inset: enlarged portion of the XRD pattern to visualize small Bragg peaks. Lower panel: Rietveld refinement of the XRD pattern of LNMO at 15 K.

Figure 3

Variation of lattice constant ($a$) and unit cell volume ($V_{\mathrm{cell}}$) with temperature. The solid line represents the fit of $V_{\mathrm{cell}}\left(T\right)$ by Eq. (1).

Figure 4

The electrical resistivity $\rho \left(T\right)$ of LNMO in zero field. Inset: $\ln (\sigma$) vs $1/T$. The solid line is the fit using Eq. (3).

Figure 5

Upper panel: temperature-dependent dc magnetic susceptibility $\chi \left(T\right)$ at two different applied fields. Inset: $\chi \left(T\right)$ measured at 50 Oe in ZFC and FC conditions. Lower panel: $1/\chi$ vs $T$ in ${\mu }_{0}H=0.5$ T. Inset: magnetization isotherm at $T=2$ K.

Figure 6

Upper panel: $C_{\mathrm{p}}\left(T\right)$ measured in zero magnetic field. The dashed and solid lines represent the phonon ($C_{\mathrm{ph}}$) and magnetic ($C_{\mathrm{mag}}$) contributions, respectively. Inset: enlarged view of low-temperature portion of $C_{\mathrm{p}}\left(T\right)$ data. The solid line is the fit as described in text. Lower panel: $C_{\mathrm{mag}}/T$ and magnetic entropy ($S_{\mathrm{mag}}$) vs $T$ along the left and right $y$-axes, respectively.

Figure 7

Temperature evolution of the neutron powder diffraction pattern of LNMO shown for the low-angle regime. An enhancement in the intensity of fundamental nuclear Bragg peaks is evident below $T_{\mathrm{C}}$. These Bragg peaks at $2\theta \simeq 10.{81}^{\circ }, 13.{31}^{\circ }, 17.{17}^{\circ }$, and $18.{84}^{\circ }$ correspond to (1,1,0), (1,1,1), (2,1,0), and (2,1,1) planes, respectively.

Figure 8

Rietveld refined neutron powder diffraction patterns at $T=140$ K (upper panel) and $T=5$ K (lower panel). Open circles represent the experimental data, solid line represents the calculated curve, and difference between them is shown as a solid line at the bottom. Vertical marks correspond to the position of all allowed Bragg reflections for the nuclear (top row) and magnetic (bottom row) reflections. Inset: temperature variation of ordered magnetic moment for ${\mathrm{Ni}}^{2+}$ and ${\mathrm{Mn}}^{4+}$ ions.

Figure 9

Field-sweep ${}^7\mathrm{Li}$ NMR spectra at different temperatures for the polycrystalline LNMO sample measured at 25.58 MHz. The vertical dashed line corresponds to the ${}^7\mathrm{Li}$ resonance frequency of the nonmagnetic reference. Inset: coupling of Li nucleus with four cubic units made of ${\mathrm{Ni}}^{2+}$ and ${\mathrm{Mn}}^{4+}$ ions.

Figure 10

Upper panel: full width at half-maximum (FWHM) of ${}^7\mathrm{Li}$ NMR spectra plotted as a function temperature. Inset: FWHM vs $\chi$ measured at 1.5 T is plotted with temperature as an implicit parameter. The solid line is a linear fit. Lower panel: temperature-dependent ${}^7\mathrm{Li}$ NMR shift ($K$) vs temperature. Inset: ${}^7\mathrm{Li}$ NMR shift vs $\chi$ measured at 1.5 T is plotted with temperature as an implicit parameter. The solid line is a linear fit.

Figure 11

Spin-lattice relaxation rate $1/T_1$ vs temperature measured at 25.58 MHz. Inset: the longitudinal magnetization recovery curves at various temperatures. The solid lines are the fits, as described in the text.

Figure 12

(a) The Arrott plots ($M^2$ vs $H/M$) for LNMO at different temperatures, above and below $T_{\mathrm{C}}$. (b) The modified Arrott plots [$M^{1/\beta }$ vs ${(H/M)}^{1/\gamma }$] for LNMO at different temperatures. The solid lines are the linear fits to the data in the high-field regime ($H\ge 2.5$ T) and are extrapolated to $H/M=0$. (c) Spontaneous magnetization $M_{\mathrm{S}}$ and zero-field inverse susceptibility ${\chi }_0^{-1}$ as a function of temperature in the left and right $y$-axes, respectively, obtained from the intercepts of the modified Arrott plots in the vicinity of $T_{\mathrm{C}}$. The solid lines are the fits, as described in the text. (d) The Kouvel-Fisher plots for $M_{\mathrm{S}}$ and ${\chi }_0^{-1}$. The solid lines are the linear fits.

Figure 13

Magnetization isotherm ($M$ vs $H$) at $T\simeq T_{\mathrm{C}}$. Inset: $\log M$ vs $\log H$ plot at $T\simeq T_{\mathrm{C}}$.

Figure 14

Upper panel: the reduced magnetization $m={\mid \varepsilon \mid }^{-\beta }M(H,\varepsilon )$ vs reduced magnetic field $h={H\mid \varepsilon \mid }^{-(\beta +\gamma )}$. The renormalized curves in different temperatures, just above and below $T_{\mathrm{C}}$, are collapsing into two separate branches. Inset: the log-log plot of $m$ vs $h$ to magnify the data in the low-field region. Lower panel: $m^2$ vs $h/m$ plots where the curves just above and below $T_{\mathrm{C}}$ are collapsing into two separate branches.

Figure 15

(a) The isothermal change in magnetic entropy ($\mathrm{\Delta }{S}_{\mathrm{m}}$) as function of temperature ($T$) and field ($H$). (b) The adiabatic change in temperature ($\mathrm{\Delta }{T}_{\mathrm{ad}}$) as a function of temperature ($T$) and field ($H$). (c) Universal curve plot of normalized entropy change as a function of $\theta$ with the application of 1 to 9 T magnetic field change. (d) Absolute value of entropy change at the peak position $\mathrm{\Delta }{S}_{\mathrm{m}}^{\mathrm{peak}}$ and relative cooling power ($\text{RCP}=\mathrm{\Delta }{S}_{\mathrm{m}}^{\mathrm{peak}}\times \delta T_{\mathrm{FWHM}}$) as a function of magnetic field in the left and right $y$-axes, respectively. Solid lines are the fits as described in the text.

Figure 16

Field and temperature dependence of the exponent $n$ using Eq. (27).

Figure 17

Upper panel: real part of the ac susceptibility ${\chi }^{\prime }$ vs temperature at different frequencies. The arrow points to the change in ${\chi }^{\prime }$ with frequency. Lower panel: imaginary part of the ac susceptibility ${\chi }^{\prime \prime }$ vs temperature at different frequencies.

Figure 18

Enlarged view of ${\chi }^{\prime \prime }\left(T\right)$ at low temperatures and at different frequencies. The curves are vertically translated to get a clear view of the peak positions. The vertical arrows guide the peak positions with frequency.

Figure 19

Upper panel: $\ln \left(\tau \right)$ vs 1/$T_{\mathrm{f}2}$ plot. The solid line is the fit using Eq. (29) in the high-temperature region. Lower panel: ${\log }_{10}\left(\tau \right)$ vs ${\log }_{10}({\mathrm{T}}_{\mathrm{f}2}/{\mathrm{T}}_{\mathrm{g}}-1)$ plot. The solid line is the fit using Eq. (31). Lower inset: $T_{\mathrm{f}2}$ vs ${\log }_{10}\nu$ plot in the low-temperature region. The solid line is the fit as described in the text.

Figure 20

Time dependence of ZFC magnetization at different temperatures ($T=2,10,\mathrm{and}70$ K) in $H=200$ Oe and after a waiting time of 60 s. The solid lines are the fits using Eq. (32).

Figure 21

Memory effect measured as a function of temperature in FC (upper panel) and ZFC (lower panel) protocols in $H=100$ Oe, as described in the text. Inset of the upper panel magnifies the features at the interruption points: $T=5$, 12, and 70 K. The difference in magnetization $\mathrm{\Delta }M(=M_{\mathrm{ZFCW}}^{\mathrm{mem}}-M_{\mathrm{ZFCW}}^{\mathrm{ref}})$ vs $T$ is plotted in the inset of the lower panel.

Figure 22

Magnetic relaxation measured in negative $T$-cycle for (a) ZFC and (b) FC methods, as described in the text. Insets: magnetic relaxation at 12 K measured during $t_1$ and $t_3$ for negative $T$-cycle and in ZFC and FC methods. The solid lines are the fits using Eq. (32). Magnetic relaxation data measured in positive $T$-cycle for ZFC and FC methods are shown in (c) and (d), respectively.