Large Magnetocaloric Effect in the Kagome Ferromagnet ${\mathrm{Li}}_9{\mathrm{Cr}}_3({\mathrm{P}}_2{\mathrm{O}}_7{)}_3({\mathrm{PO}}_4{)}_2$

Single-crystal growth, magnetic properties, and magnetocaloric effect of the $S=3/2$ kagome ferromagnet ${\mathrm{Li}}_9{\mathrm{Cr}}_3({\mathrm{P}}_2{\mathrm{O}}_7{)}_3({\mathrm{PO}}_4{)}_2$ (trigonal, space group: $P\overline{3}c1$) are reported. Magnetization data suggest dominant ferromagnetic intraplane coupling with a weak anisotropy and the onset of ferromagnetic ordering at $T_C\simeq 2.6$ K. Microscopic analysis reveals a very small ratio of interlayer to intralayer ferromagnetic couplings ($J_{\perp }/J\simeq 0.02$). Electron spin-resonance data suggest the presence of short-range correlations above $T_C$ and confirms the quasi-two-dimensional character of the spin system. A large magnetocaloric effect characterized by isothermal entropy change of $-\mathrm{\Delta }{S}_m\simeq 31\mathrm{J}{\mathrm{kg}}^{-1}{\mathrm{K}}^{-1}$ and adiabatic temperature change of $-\mathrm{\Delta }{T}_{\mathrm{ad}}\simeq 9\mathrm{K}$ upon a field sweep of 7 T is observed around $T_C$. This leads to a large relative cooling power of $\mathrm{RCP}\simeq 284\mathrm{J}{\mathrm{kg}}^{-1}$. The large magnetocaloric effect, together with negligible hysteresis render ${\mathrm{Li}}_9{\mathrm{Cr}}_3({\mathrm{P}}_2{\mathrm{O}}_7{)}_3({\mathrm{PO}}_4{)}_2$ a promising material for magnetic refrigeration at low temperatures. The magnetocrystalline anisotropy constant $K\simeq -7.42\times {10}^4\mathrm{erg}{\mathrm{cm}}^{-3}$ implies that the compound is an easy-plane-type ferromagnet with the hard axis normal to the $a$$b$ plane, consistent with the magnetization data.

Figure 1

(a) Corner-sharing equilateral triangles of ${\mathrm{Cr}}^{3+}$ form a kagome lattice. The intraplane ($J$) and interplanar ($J_{\perp }$) couplings are shown. The kagome lattice layers are well separated from each other with interlayer distance of 6.9034 Å. (b) Interactions between the magnetic ${\mathrm{Cr}}^{3+}$ ions via ${\mathrm{PO}}_4$ tetrahedra are shown.

Figure 2

Powder XRD data measured at (a) $T=300$ K and (b) $T=15$ K. The black solid line represents the Le Bail fit of the data. Bragg positions are indicated by vertical bars and the solid green line at the bottom denotes the difference between experimental and calculated intensities. The inset of (b) shows a representative single crystal.

Figure 3

Variation of lattice parameters ($a$, $c$, and $V_{\mathrm{cell}}$) with temperature. The solid line denotes the fit of $V_{\mathrm{cell}}(T)$ by Eq. (2).

Figure 4

(a) $\chi (T)$ measured in the field of $H=0.5$ T applied perpendicular ($H\perp c$) and parallel ($H\parallel c$) to the $c$ axis. (b) Magnetization at $T=1.8$ K as a function of applied field for both $H\perp c$ and $H\parallel c$ after correcting for the demagnetization effect. (c) Inverse susceptibility ($1/\chi$) as a function of temperature for $H\perp c$ and solid line is the CW fit. (d) $\chi T$ versus $T$ in different fields for $H\perp c$ in low temperatures.

Figure 5

(a) Heat capacity ($C_p$) of LCPP measured in zero applied field. The solid line represents the simulated phonon contribution [$C_{\mathrm{ph}}(T)$] and the dotted line represents the magnetic contribution [$C_{\mathrm{mag}}(T)$]. Inset: low-temperature $C_p$ measured in various applied fields. (b) $C_{\mathrm{mag}}/T$ and $S_{\mathrm{mag}}/R\ln 4$ in left and right $y$ axes, respectively, are plotted as a function of temperature. Inset: $C_{\mathrm{mag}}(T)$ versus $T$. Solid line is the power-law ($C_{\mathrm{mag}}=a{T}^{\alpha }$) fit in the low-$T$ regime.

Figure 6

(a) Isothermal magnetization ($M$ versus $H$) curves for $H\perp c$ and (b) their corresponding Arrott plots [$M^2$ versus $(H/M)$] for LCPP at different temperatures around $T_C$.

Figure 7

(a) Isothermal entropy change ($\mathrm{\Delta }{S}_m$) versus $T$ plotted upon sweeping the field to 0 T starting from different fields from 1 to 7 T, calculated using $M$ versus $H$ data of single crystals for $H\perp c$ and employing Eq. (8). (b) $\mathrm{\Delta }{S}_m$ versus $T$ plot for 5 and 7 T, calculated using $C_p(T)$ of polycrystalline sample in Eq. (9).

Figure 8

(a) $\mathrm{\Delta }{T}_{\mathrm{ad}}$ versus $T$ plotted for different field changes of $\mathrm{\Delta }H=1$ T to 7 T calculated using Eq. (10). (b) $\mathrm{\Delta }{T}_{\mathrm{ad}}$ versus $T$ plotted for $\mathrm{\Delta }H=5$ T and 7 T calculated using Eq. (11).

Figure 9

(a) Relative cooling power ($\mathrm{RCP}=\mathrm{\Delta }{S}_m^{\mathrm{peak}}\times \delta T_{\mathrm{FWHM}}$) as a function of magnetic field and the inset shows the value of entropy change at the peak position $\mathrm{\Delta }{S}_m^{\mathrm{peak}}$. Solid lines are the fits as described in the text. (b) The exponent $n$ plotted as a function of temperature, which is obtained from fitting power law to $\mathrm{\Delta }{S}_m$ versus H isotherms. Inset shows the $\mathrm{\Delta }{S}_m$ isotherms for temperatures near and well above $T_C$.

Figure 10

Left vertical scale: frequency as a function of resonant field measured for both orientations at $T=1.8$ K. The hollow red and solid black squares represent the measured resonance fields for orientations $H\parallel c$ and $H\perp c$, respectively. Right vertical scale: selected HF ESR spectra.

Figure 11

Temperature dependence of the HF ESR spectra at an excitation frequency of 141.310 GHz for (a) $H\perp c$ and (b) $H\parallel c$. Line shape distortions at $T<20$ K in the $H\perp c$ field geometry are instrumental artifacts arising due to the strong magnetization of the sample.

Figure 12

Temperature dependence of (a) the resonance field $H_{\mathrm{res}}$ and (b) the resonance shift $\delta H=H_{\mathrm{res}}(T)-H_{\mathrm{res}}(300\mathrm{K})$ (left $y$ axis) and the magnetization $M$ in an applied field of $H=0.5$ T (right $y$ axis), for both $H\parallel c$ and $H\perp c$.

Figure 13

(a) PBE density of states for LCPP with the Fermi level placed at zero energy. (b) Nearest-neighbor Cr–Cr hopping amplitudes within the kagome plane.

Figure 14

Magnetic susceptibility of LCPP measured in the applied field of 0.01 T upon field cooling and its fit using the model of ferromagnetic kagome planes (dashed line) and coupled ferromagnetic kagome planes ($J_{\perp }/J=0.01$, solid line). The inset shows calculated heat capacity for the coupled kagome planes, with $T_C\simeq 2.8$ K.