Magnetic criticality and magnetocaloric response in MnBi$_2$Te$_4$ and MnBi$_4$Te$_7$

Abstract

MnBi$_2$Te$_4$ and MnBi$_4$Te$_7$ are antiferromagnetic topological insulators belonging to the MnBi$_{2n}$Te$_{3n+1}$ series, where structural layering provides a natural route to tune magnetic interaction in van der Waals magnets. Despite extensive interest in their topological properties, how the insertion of Bi$_2$Te$_3$ quintuple layers modifies magnetic critical fluctuations near the antiferromagnetic transition remains unresolved. Here, we combine scanning tunneling microscopy (STM), critical scaling analysis, and magnetocaloric measurements to directly correlate real-space structures with magnetic criticality. STM reveals atomically flat septuple-layer terraces in MnBi$_2$Te$_4$ whereas MnBi$_4$Te$_7$ displays coexisting septuple and quintuple layer terminations reflecting its alternating stacking sequence. MnBi$_2$Te$_4$ exhibits robust three-dimensional Ising-like critical behavior together with a distinct low-temperature first-order transition. In contrast, MnBi$_4$Te$_7$ displays crossover-dominated criticality arising from weakened interlayer exchange and competing magnetic phases. Correspondingly, the magnetocaloric response differs significantly between the two compounds. MnBi$_2$Te$_4$ shows dual-type magnetocaloric behavior with a sharp field-induced sign reversal of the isothermal magnetic entropy change ($-ΔS_M$). It exhibits both inverse ($-ΔS_M < 0$) and conventional ($-ΔS_M > 0$) magnetocaloric effects. In contrast, MnBi$_4$Te$_7$ shows only conventional magnetocaloric response with a broad positive entropy peak. These results establish structural layering as a key parameter governing magnetic critical fluctuations and magnetocaloric behavior in MnBi$_{2n}$Te$_{3n+1}$ topological magnets.

Figures (7)

• Figure 1: (a) Crystal structure of MnBi$_2$Te$_4$ composed of septuple layers (SL) stacked along the $c$-axis. (b) Crystal structure of MnBi$_4$Te$_7$, where MnBi$_2$Te$_4$ septuple layers alternate with Bi$_2$Te$_3$ quintuple layers (QL). (c) Large-scale (400 nm $\times$ 400 nm) constant current STM topography(U = 0.5 V, I = 60 pA) obtained on freshly cleaved (0001) surface of MnBi$_2$Te$_4$, displaying atomically flat terraces separated by sharp step edges. The height profile along the indicated direction yields a step height $\sim$1.41 nm consistent with a single septuple-layer thickness as shown in (d). (e) Atomically-resolved STM image (20 nm $\times$ 20 nm) of the SL-terminated surface of MnBi$_2$Te$_4$, clearly depicting the hexagonal lattice of Te-terminated surface (U = 150 mV, I = 300 pA). (f) Large-scale STM topography (50 nm $\times$ 50 nm) taken (U = 900 mV, I = 140 pA) of the Te-terminated (0001) surface of MnBi$_4$Te$_7$, exhibiting terraces with two discrete step heights corresponding to distinct surface terminations. (g) Line profile across the step in (f), revealing step heights of $\sim$1.38 nm and $\sim$1.02 nm, consistent with septuple- and quintuple-layer thicknesses, respectively. (h) High-resolution STM image (10 nm $\times$ 10 nm) acquired on the SL-terminated terrace (U = 500 mV, I = 460 pA) of MnBi$_4$Te$_7$. (i) Atomic-resolution STM image (10 nm $\times$ 10 nm) acquired (U = 400 mV, I = 150 pA) on the QL-terminated terrace, both depicting the hexagonal Te- terminated surface lattice.
• Figure 2: (a) M–T curves of MnBi$_2$Te$_4$ single crystals under different magnetic field with $H \parallel c$. The anomaly at $\sim$24.1 K marks the AFM transition. Inset: zoomed M-T curves for lower fields. (b, c) Isothermal magnetization of MnBi$_2$Te$_4$, for $H \parallel c$ and $H \parallel ab$, respectively. We observe a metamagnetic transition (spin--flip) around 2-4 $T$ in $H \parallel c$, evolving into a gradual response toward $T_N$ in $H \parallel c$ configuration. (d) M–T curves of MnBi$_4$Te$_7$ single crystals under ZFC and FC with $H \parallel c$. The transition at $\sim$12.9 K indicates layered AFM ordering. (e, f) Isothermal magnetization of MnBi$_4$Te$_7$, for $H \parallel c$ and $H \parallel ab$, respectively. We observe a weak anomaly at lower temperatures and magnetic fields compared with MnBi$_2$Te$_4$.
• Figure 3: Normalized slope of the Arrott plots as a function of temperature in MnBi$_2$Te$_4$. (b) Temperature dependence of the spontaneous magnetization $M_{S}$ (left axis) and the inverse initial susceptibility $\chi_{0}^{-1}$ (right axis) fitted with the power-law relations in Eqs. (3) and (5). The solid lines represent the best fits. (c) Modified Arrott plots $(M^{1/\beta}$ vs. $(H/M)^{1/\gamma})$ yields $\beta$=0.319 and $\gamma$=1.221. (d) Kouvel--Fisher plots of $M_{S}(dM_{S}/dT)^{-1}$ (left axis) and $\chi_{0}^{-1}(d\chi_{0}^{-1}/dT)^{-1}$ (right axis) as a function of temperature.
• Figure 4: (a) Scaling plots of the renormalized magnetization $M|\varepsilon|^{-\beta}$ versus renormalized field $H|\varepsilon|^{-(\beta+\gamma)}$ for MnBi$_2$Te$_4$, confirms the validity of the critical exponents $\beta = 0.319$ and $\gamma = 1.221$. The inset shows the same data on a log--log scale, confirming consistency with the scaling hypothesis. (b) Enlarged view of the low-temperature region of the log–log Renormalized Arrott Plots, where arrows indicate characteristic phase-boundary points. (c) Magnetic phase diagram of MnBi$_2$Te$_4$ obtained by combining the results from the renormalized Arrott plot (RAP) analysis with field-dependent magnetization measurements.
• Figure 5: (a) Normalized slope of the Arrott plots as a function of temperature in MnBi$_4$Te$_7$. (b) Modified Arrott plots (MAPs) constructed using the critical exponents obtained from the modified iteration method.