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SCIENCE CHINA Information Sciences, Volume 62, Issue 12: 220402(2019) https://doi.org/10.1007/s11432-019-2642-6

The emerging ferroic orderings in two dimensions

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  • ReceivedJul 6, 2019
  • AcceptedSep 10, 2019
  • PublishedNov 13, 2019

Abstract

Because of the discovery of carbon atomic flatland, emerging physical phenomena are reported using the platform of two-dimensional materials and their hetero-structures. Especially, quantum orderings, such as superconductivity, ferromagnetism, and ferroelectricity in the atomically thin limit are cutting edge topics, which are of broad interest in the scope of condensed matter physics. In this study, we will recall the recent developments on two-dimensional ferroic orderings from both experimental and theoretical points of view. The booming of ferroic orderings in van der Waals two-dimensional materials are believed to hold promises for the next generation spin- or dipole-related nanoelectronics, because they can be seamlessly interfaced into heterostructures, and in principle are in line with large scale low-cost growth, flexible wearable devices, as well as semiconducting electronics thanks to the existence of band gaps in many of them.


Acknowledgment

This work was supported by National Key RD Program of China (Grant No. 2017YFA0206302), and National Natural Science Foundation of China (Grant Nos. 11504385, 51627801, 61435010, 51702219, 61975134). Han ZHANG and Yupeng ZHANG acknowledge the support from Science and Technology Innovation Commission of Shenzhen (Grant Nos. JCYJ20170818093453105, JCYJ20180305125345378). Teng YANG acknowledges supports from Major Program of Aerospace Advanced Manufacturing Technology Research Foundation NSFC and CASC, China (Grant No. U1537204). Zheng Vitto HAN acknowledges the support from Program of State Key Laboratory of Quantum Optics and Quantum Optics Devices (Grant No. KF201816).


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  • Figure 1

    (Color online) Different types of magnetic interactions in three-dimensional (3D) crystals.

  • Figure 2

    (Color online) Typical metallic magnetic vdW mateirlas. (a) The magnetic structure of layered V$_5$S$_8$. protectłinebreak (b) Atomic force microscope (AFM is short for antiferromagnetic here in our study) topography of a typical V$_5$S$_8$ flake. (c) Critical temperature $T_{\rm~C}$-thickness $t$ phase diagram. Reproduced from [53]@Copyright 2017 American Physical Society. (d) Schematic structure of layered Fe$_3$GeTe$_2$. (e) Phase diagram of FGT as number of layer and temperature. (f) $R^r_{xy}$ of a four-layer FGT flake under a gate voltage of $V_{\rm~g}$ = 2.1 V. Reproduced from [51]@Copyright 2018 Springer Nature. (g) Schematic structure of layered VSe$_2$. (h) STM images at 150 K. (i) Variations of Ms and Hc with the number of layers of VSe$_2$ film. The inset shows the $M$-$H$ loops for the mono-, bi- and multilayer samples. Reproduced from [54]@Copyright 2018 Springer Nature.

  • Figure 3

    (Color online) Crystal structure of chromium trihalides CrX$_3$. (a) The monoclinic (left panel) and rhombohedral (right panel) phase of CrX$_3$. The red arrows represent the spin direction of Cr atoms. Reproduced from [63]@Copyright 2015 the Royal Society of Chemistry. (b) The magnetic behavior of monolayer, bilayer and trilayer CrI$_3$. Reproduced from [30]@Copyright 2017 Springer Nature. (c) Schematic of magnetic states in bilayer CrI$_3$ and schematic of 2D spin-filter magnetic tunnel junction (sf-MTJ). (d) sf-TMR ratio as a function of bias based on the $\rm~I_t$-V curves in the inset. Reproduced from [70]@Copyright 2017 Science Publishing Group.

  • Figure 4

    (Color online) Controlling magnetism in 2D CrI$_3$ by electrostatic doping. (a) A schematic side view and optical micrograph of a dual-gate bilayer CrI$_3$ field-effect device. (b) MCD versus magnetic field at 4 K at representative gate voltages. (c) Doping density-magnetic field phase diagram at 4 K. Reproduced from [74]@Copyright 2018 Springer Nature.

  • Figure 5

    (Color online) Electrical control of 2D magnetism in bilayer CrI$_3$. (a) Schematic of a dual-gated bilayer CrI$_3$ device fabricated by vdW assembly. (b) RMCD signal of a bilayer CrI$_3$ device as a function of perpendicular magnetic field at zero gate voltage. (c) Intensity of the polar MOKE signal, $\theta~K$, of a non-encapsulated bilayer CrI$_3$ device as a function of both gate voltage and applied magnetic field. (d) RMCD signal of a dual-gated device when sweeping both the graphite top gate and silicon back gate. Gate-dependent MOKE signal of a bilayer CrI$_3$ device prepared in the $\uparrow~\downarrow$ state (e) and in the $\downarrow~\uparrow$ state (f). Reproduced from [61]@Copyright 2018 Springer Nature.

  • Figure 6

    (Color online) Magnon-assisted tunneling in 2D CrBr$_3$ device. (a) Optical microscope image of 2D CrBr$_3$ device. (b) Zero-field differential tunneling conductance $G$ dependence on the gate and bias voltages for the device. protect łinebreak (c) Thickness dependence of the tunneling barrier on the resistivity of the device. (d) Differential tunneling conductance $G$ as a function of $B$. (e) Calculated magnon density of states for $T$ = 10 K, $B$ = 0 T (blue line), $T$ = 10 K, $B$ = 6.25 T (black line), $T~=~T_{\rm~C}$, $B$ = 0 T (red line). (f) Calculated changes of the position of the van Hove singularities in magnon density of states (e) as a function of magnetic field for temperatures close to $T_{\rm~C}$. Reproduced from [62]@Copyright 2018 Springer Nature.

  • Figure 7

    (Color online) Electric-field control of magnetism of 2D semiconducting Cr$_2$Ge$_2$Te$_6$. (a) Schematic of a few-layered Cr$_2$Ge$_2$Te$_6$ flake encapsulated by two h-BN layers, contacted via graphene electrodes. (b) Optical image of the device. (c) Colour map of $I$-$V$ curves as a function of gate voltage at different temperatures. (d) Field effect curves of the device with different $V_{\rm~ds}$ and temperatures. Kerr angle measured at 40 K for negative (e) and positive (f) gate voltages respectively. Reproduced from [32]@Copyright 2018 Springer Nature.

  • Figure 8

    (Color online) Magnetic properties of CrOCl and CrOBr monolayers. (a) Crystal structures of transition-metal oxyhalides. (b) Specific heat CV with respective to temperature for the CrOCl and CrOBr monolayers and the inset shows the corresponding magnetization. Reproduced from [92]@Copyright 2018 American Chemical Society.

  • Figure 9

    (Color online) Layer dependence magnetic properties of NiPS$_3$. (a) Crystal structure of NiPS$_3$. (b) Optical and atomic force microscope image of the sample. (c) Temperature dependences of phonon frequency difference and susceptibility of bulk NiPS$_3$. (d) Thickness dependence of Néel temperature for few-layer NiPS$_3$. Reproduced from [96]@Copyright 2019 Springer Nature.

  • Figure 10

    (Color online) Fe-doped 2D SnS$_2$ magnetic semiconductor. (a) High-resolution scanning transmission electron microscopy (STEM) image of the Fe$_{0.021}$Sn$_{0.979}$S$_2$ flake; the red circles are Fe atoms. (b) Z-contrast mapping in the areas marked with yellow rectangles in (a). Electrical characteristics (c) and photo response (d) of the monolayer Fe$_{0.021}$Sn$_{0.979}$S$_2$ device. Magnetic hysteresis loops for SnS$_2$ (e) and Fe$_{0.021}$Sn$_{0.979}$S$_2$ (f) at 2 K using VSM, respectively. Reproduced from [105]@Copyright 2018 Springer Nature.

  • Figure 11

    (Color online) Schematic view of Zeeman effect and giant magneto band structure effect. (a) External magnetic field induced Zeeman splitting of a specific band. Calculated band splitting using toy model for a 2D system with (b) magnetization along out-of-plane $c$ axis (M//$c$), and (c) rearranged magnetization along in-plane axis (M//$a$) by applying a magnetic field $H$. Reproduced from [107]@Copyright 2018 American Chemical Society.

  • Figure 12

    (Color online) Intrinsic ferromagnetism in 2D MnSe$_x$. (a) Top and side views of MnSe$_2$ lattice. (b) Magnetic hysteresis loop of monolayer MnSe$_x$. Reproduced from [108]@Copyright 2018 American Chemical Society.

  • Figure 13

    (Color online) Data base of 2D easily exfoliatable magnetic materials. (a) The polar histogram of most common 2D structural prototypes include 1036 easily exfoliatable 2D materials. (b) Easily exfoliatable magnetic compounds. Reproduced from [109]@Copyright 2018 Springer Nature.

  • Figure 14

    (Color online) In-plane ferroelectricity in 2D SnTe. (a) Schematics of the SnTe crystal structure (upper) and the SnTe film (lower). (b) Typical STM topography image of SnTe film. The red dotted line indicates the steps of substrate. (c) The stripe domain of a 1-UC SnTe film. The arrow in each domain indicate the direction of lattice distortion. (d) Temperature dependence of the distortion angle for the 1- to 4-UC SnTe films. (e) The d$I$/d$V$ spectra acquired on the surface of a 1-UC film at 4.7 K. The arrows indicate the edges of the valence and conduction bands. The peak at 1.5 V corresponds to a van Hove singularity in the conduction band. (f) Thickness dependence of Sn vacancy density at the growth temperature of 450 K. Reproduced from [122]@Copyright 2016 Science Publishing Group.

  • Figure 15

    (Color online) Crystal structure and the ferroelectric characters of CIPS flakes. The side view (a) and top view (b) for the crystal structure of CIPS with vdW gap between the layers. Within a layer, the Cu, In and P-P form separate triangular networks. Reproduced from [127]@Copyright 1998 American Physical Society. The polarization direction is indicated in by the arrow. AFM topography (c) PFM amplitude (d) and PFM phase (e) for CIPS flakes ranging from 100 to 7 nm thick, on doped Si substrate. Scale bar in (c) is 1 $\mu$m. (f) The PFM amplitude (black) and phase (blue) hysteresis loop for a 4 nm CIPS flake. (g) The $I$-$V$ curves from the Si/CIPS (30 nm)/Au heterostructure. Inset is the schematic of the device. Reproduced from [129]@Copyright 2016 Springer Nature.

  • Figure 16

    (Color online) Crystal structure and the ferroelectric characters of $\alpha$-In$_2$Se$_3$ flakes. (a) Schematic model of IP and OOP switching coupling. (b) and (c) AFM and the corresponding IP PFM images of In$_2$Se$_3$ thin flakes. (d) Schematic model of intercorrelated OOP and IP switching. (e) OOP phase image and (f) the corresponding IP phase image of a 6 nm thick In$_2$Se$_3$ flake acquired immediately after writing two square patterns with a size of 2 and 1 mm by applying $-$7 and +6 V voltages consecutively. The scale bar is 1 mm. (g) $I$-$V$ curves and schematic structure of the planar In$_2$Se$_3$ device. The red and blue solid lines are used to guide the eyes. Reproduced from [135]@Copyright 2017 Springer Nature.

  • Figure 17

    (Color online) Nonvolatile ferroelectric memory effect in 2D $\alpha$-In$_2$Se$_3$. (a) 3D schematic model of the Fe-FET. The Fe-FET is fabricated by vertically stacking grapheme, h-BN, and In$_2$Se$_3$ thin layers in sequence. The white arrows indicate the direction of electric polarization. The zoomed area shows the crystal structure of ferroelectric In$_2$Se$_3$. (b) The hysteresis ferroelectric gating in 2D $\alpha$-In$_2$Se$_3$ based Fe-FET device. The electrical hysteresis loop can be enlarged by the range of the applied top gate voltage. (c) Equivalent capacitor model of the 2D Fe-FET and the corresponding doping level in graphene. A capacitor is used to represent the top ferroelectric gate. The light green slab stands for the insulating h-BN layer. The small color arrows represent the electric dipoles in $\alpha$-In$_2$Se$_3$. Reproduced from [139]@Copyright 2019 WILEY-VCH.

  • Figure 18

    (Color online) Out-of-plane ferroelectricity in $d$1T-MoTe$_2$. (a) PFM phase hysteretic and butterfly loops of monolayer $d$1T-MoTe$_2$. (b) PFM phase image of monolayer $d$1T-MoTe$_2$. (c) Top-view HRTEM image and intensity profile with the atomic structure of $d$1T-MoTe$_2$ placed on top, scale bar, 0.5 nm. (d) Atomic structure image of monolayer $d$1T-MoTe$_2$ and the inset shows atomic structure model (cyan and orange colors represent Mo and Te atoms, respectively), scale-bar, 2 Å (e) Side-view of charge density difference between ferroelectric $d$1T and paraelectric 1T phases (green, purple, cyan, orange, and pink colors denote negative charge, positive charge, Mo atom, Te atom, and polarization, respectively). Reproduced from [146]@Copyright 2019 WILEY-VCH.

  • Figure 19

    (Color online) Ferroelectricity in monolayer group-IV monochalcogenides. (a) The schematic side views of the two distorted degenerate polar structures (B and B$'$) and the high symmetry nonpolar phase (A). (b) The free-energy contour plot of monolayer SnSe according to the tilting angles ($\theta_1$ and $\theta_2$). The phases A, B, and B$'$ are marked. (c) Phase diagram of monolayer SnSe under strain. Reproduced from [148]@Copyright 2016 American Physical Society.

  • Figure 20

    (Color online) Schematic vision of the future applications of two-dimensional materials with ferroic orderings.

  • Table 1   2D magnets categorized according to the types of conventional 3D magnetic interactions shown in Figure
    Model system Indirect exchange
    CrI$_3$ [30,35]
    CrBr$_3$ [36,37]
    CrCl$_3$ [38-41]) Super-exchange/ CrI$_3$ [45]
    Ising Cr$_2$Si$_2$Te$_6$ [42] Double-exchange/ Cr$_2$Ge$_2$Te$_6$ [46]
    FePS$_3$ [43] Ligand
    FePSe$_3$ [44]
    Fe$_3$GeTe$_2$ [51]
    XY NiPS$_3$ [47] RKKY Experimentally missing$^{\rm~a)}$
    CoPS$_3$ [48]
    Cr$_2$Ge$_2$Te$_6$ [31]
    Heisenberg MnPS$_3$ [49] Stoner/Itinerant Fe$_3$GeTe$_2$ [51]
    MnPSe$_3$ [50]

    a

  • Table 2   The magnetic properties of known experimental 2D magnetic materials
    Materials FM/AFM Curie/Neel temperature Gap Ref.
    Fe$_3$GeTe$_2$ family Fe$_3$GeTe$_2$ FM 20 K Metallic [51]
    CrGeTe$_3$ Cr$_2$Ge$_2$Te$_6$ FM 64 K [32]
    family Cr$_2$Si$_2$Te$_6$ FM 80 K 0.4 eV/1.2 eV [111]
    FePS$_3$ AFM 123 K 1.5 eV [94]
    XPS family MnPS$_3$ AFM 78 K 2.4 eV [94]
    NiPS$_3$ AFM 130 K [96]
    Odd-layer CrI$_3$ FM 45 K Semiconducting [30]
    CrI$_3$ family Even-layer CrI$_3$ AFM 45 K Semiconducting [61]
    CrBr$_3$ FM 37 K Semiconducting [74]
    VI$_3$ FM 49 K 0.6 eV [112]
    V$_5$S$_8$ AFM 8 K Metallic [53]
    VSe$_2$ FM 300 K Metallic [54]
    Others Fe-SnS$_2$ FM 31 K 2.2 eV [105]
    Fluorinated h-BN FM Semiconducting [106]
    MnSe$_x$ FM 300 K Semiconducting [108]
    1T-CrTe$_2$ FM 310 K Metallic [110]

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