⇦Chinese Physics Letters, 2022, Vol. 39, No. 4, Article code 047601 Magnetic Phase Transition in Two-Dimensional CrBr$_3$ Probed by a Quantum Sensor Haodong Wang (王浩东)1,2†, Peihan Lei (雷沛涵)1,2†, Xiaoyu Mao (毛晓宇)1,3†, Xi Kong (孔熙)4*, Xiangyu Ye (叶翔宇)1,2, Pengfei Wang (王鹏飞)1,2, Ya Wang (王亚)1,2, Xi Qin (秦熙)1,2, Jan Meijer5, Hualing Zeng (曾华凌)1,3*, Fazhan Shi (石发展)1,2, and Jiangfeng Du (杜江峰)1,2* Affiliations 1Hefei National Laboratory for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China 2CAS Key Laboratory of Microscale Magnetic Resonance, University of Science and Technology of China, Hefei 230026, China 3CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China 4National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China 5Felix-Bloch Institute for Solid State Physics, University Leipzig, Linné Str. 5, D-04103 Leipzig, Germany Received 2 December 2021; accepted 14 February 2022; published online 28 March 2022 †These authors contributed equally to this work.
*Corresponding authors. Email: kongxi@nju.edu.cn; hlzeng@ustc.edu.cn; djf@ustc.edu.cn Citation Text: Wang H D, Lei P H, Mao X Y et al. 2022 Chin. Phys. Lett. 39 047601    Abstract Recently, magnetism in two-dimensional (2D) van der Waals (vdW) materials has attracted wide interests. It is anticipated that these materials will stimulate discovery of new physical phenomena and novel applications. The capability to quantitatively measure the magnetism of 2D magnetic vdW materials is essential to understand these materials. Here we report on quantitative measurements of ferromagnetic-to-paramagnetic phase transition of an atomically thin (down to 11 nm) vdW magnet, namely CrBr$_3$, with a Curie point of 37.5 K. This experiment demonstrates that surface magnetism can be quantitatively investigated, which is useful for a wide variety of potential applications.
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 DOI:10.1088/0256-307X/39/4/047601 © 2022 Chinese Physics Society Article Text Magnetism of two-dimensional (2D) materials is an emergent phenomenon, which can be beneficial to numerous fields, including spintronics, quantum materials, heterostructures, and ultracompact storage.[1–6] Although the Mermin–Wagner theorem was believed to exclude the existence of 2D magnetism, anisotropic local 2D magnetism was observed in both CrI$_3$ and Cr$_2$Ge$_2$Te$_6$ in 2017.[7,8] However, a quantitative study of 2D magnetism under different external conditions is still required.[9,10] Phase transitions are observed under the application of both electrical gating[11–13] and a high stress,[14,15] whereas the stacking order may change the original magnetism.[16] Conventional methods used for probing bulk materials, such as superconducting quantum interference device magnetometry and neutron scattering, cannot easily measure the magnetism of tiny exfoliated atomic-layered films. Electrical transport measurements and magneto-optical Kerr effect imaging[17] both lack the ability to characterize the magnetization directly and quantitatively. Although the emergent spin-polarized scanning tunneling microscopy (STM) technique can measure magnetism directly on the atomic scale,[18] STM imaging can only be performed under ultrahigh vacuum conditions. The 2D vdW magnet CrBr$_3$ is more stable than CrI$_3$[17] and is believed to be an ideal platform for investigating 2D magnetic materials. The Cr$^{3+}$ ions form a hexagonal honeycomb lattice, and each ion is surrounded by six Br$^-$ ions located at the corners of an octahedron, as shown in the inset of Fig. 1. The angle of the Br–Cr–Br bonds is 95.1$^{\circ}$, indicating that the superexchange interaction between the Cr$^{3+}$ ions is ferromagnetic.[19] The magnetic phase transition temperature $T_{\rm C}$ of bulk CrBr$_3$ has been reported to be 37 K. The long-range magnetic order is suppressed by the thermal magnons above $T_{\rm C}$. In our experiment, thin layers of CrBr$_3$ were obtained via mechanical exfoliation. The Raman spectrum of these layers is shown in Fig. 1. The Raman peaks at 103 and 179 cm$^{-1}$ correspond to the optical photon scattering from the $A_{\rm g}$ Raman modes, whereas the Raman peaks at 138 and 147 cm$^{-1}$ are attributed to the scattering from the $E_{\rm g}$ Raman modes. The distinct sharp peaks are in excellent agreement with those observed in a typical Raman spectrum of the CrBr$_3$ crystal.
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Fig. 1. Raman spectrum of CrBr$_3$. The peaks correspond to the $A_{\rm g}^1$, $E_{\rm g}^1$, $E_{\rm g}^2$, and $A_{\rm g}^2$ modes. The lattice structure of the CrBr$_3$ crystal is shown in the inset (top and side views). The red spheres represent the Cr$^{3+}$ ions, whereas the blue spheres represent the Br$^-$ ions.
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Fig. 2. Quantitative imaging of magnetism in the 2D vdW material CrBr$_3$. (a) A single NV electron spin is used as a magnetic sensor to probe magnetism. The observed frequency shift is $\Delta f=\gamma_{\rm e} B_{\rm NV}$, where $B_{\rm NV}$ is the component of the sample magnetic field ${B}_{\rm sample}$ projected onto the NV main axis. (b) A few layers of CrBr$_3$ are deposited on 160-nm-thick hBN layers. The whole sample is placed on a quantum magnetic sensor, which consists of a bulk diamond with a flat surface (within 5 nm). A layer of NV electron spins is implanted in diamond at a distance of 5–7 nm from the surface. (c) AFM image of CrBr$_3$ after the experiment. (d) ODMR spectra of the NV center. The black curve represents the spectrum in a region far away from the sample center at the resonant frequency $f_0=D\pm \gamma_{\rm e} B_{\rm bias}$, where $D=2870$ MHz is the zero-field splitting along the main axis of the NV electron spin. A positive or negative sample field $B_{\rm sample}$ shifts the spectrum, i.e., $f_{\pm} =f_{0}\pm \gamma_{\rm e} B_{\rm sample}$.
Nitrogen-vacancy (NV) centers, which are atomic scale and highly magnetically sensitive quantum spin systems, have recently witnessed a considerable development in the fields of scanning magnetic imaging and magnetometry on the nanoscale.[20–24] NV centers provide a unique opportunity to measure the magnetization in a 2D plane.[25–29] The single-electron spin of the diamond NV center can be utilized to directly image the 2D magnetization distribution.[30] Furthermore, the magnetic domains and their evolution under an external magnetic field can be observed.[31] In this work, the diamond NV center was used to quantitatively measure the magnetism of a few-layer 2D material. In particular, the magnetization of few-layer CrBr$_3$ at different temperatures as well as the magnetic phase transition was directly observed. The magnetic field generated by the vdW magnets was observed through the Zeeman splitting of the NV sensor. The NV center has a magnetically sensitive ground state. The Hamiltonian reads $H=DS_z^2+{\boldsymbol B}\cdot{\boldsymbol S}$, where $D=2870$ MHz is the zero-field splitting, ${\boldsymbol B}$ is the magnetic field, ${\boldsymbol S}$ is the vector electron spin operator, and ${\boldsymbol S}=(S_x,S_y,S_z)$. Furthermore, $S_x$, $S_y$, and $S_z$ are the spin components of the NV electron spin. The experiment was performed under a static magnetic field $B_{\rm bias}$ along the main axis ${\boldsymbol e}_{\scriptscriptstyle{\rm NV}}$. The magnetic field of the sample $B_{\rm sample}$ can be measured by determining the energy shift $f_{\pm}=D\pm \gamma_{\rm e} B_{\rm bias}\pm \gamma_{\rm e} B_{\rm sample}$ corresponding to the transition frequency between $m_{\rm s}=0$ and $m_{\rm s}=\pm 1$, where the energy shift of the orthogonal field is suppressed by the large main axis energy splitting $D$. Thus, the component of the stray magnetic field $B_{\rm sample}={B}_{\rm sample}\cdot{\boldsymbol e}_{\scriptscriptstyle{\rm NV}}$ of the vdW magnet CrBr$_3$ projected along the NV main axis ${\boldsymbol e}_{\scriptscriptstyle{\rm NV}}$ could be measured directly and quantitatively. The sensing device in this experiment consisted of a thin diamond plate which was implanted with 5-keV nitrogen ions with a density of $3\times 10^{11}$ cm$^{-2}$. The diamond slab was [100]-oriented. After annealing at 800 ℃, a layer of the NV center ensemble was created within 5–7 nm from the diamond surface [Fig. 2(b)]. The sample consisted of an ultrathin layer of the vdW magnet CrBr$_3$ (with a minimum thickness of 11 nm) deposited on a thin layer of hexagonal boron nitride (hBN) [see the atomic force microscopy (AFM) image shown in Fig. 2(c) without hBN]. The bottom hBN layer was precisely measured to be 160 nm in thickness. The fabricated films were transferred onto the thin diamond plate above the NV center layer [Fig. 2(b)]. The whole system was placed in a liquid Helium-4 cryostat under an external magnetic bias field $B_{\rm bias}$ of 200 mT. The field direction was almost parallel to one of the main axes of the NV centers (i.e., the [111] axis). The measurement temperature was controlled to be in the range of 4–40 K using a feedback thermometer placed close to the sample. The optically detected magnetic resonance (ODMR) technique was used to detect the stray magnetic field $B_{\rm sample}$ of the vdW magnet CrBr$_3$. Firstly, using a confocal system, a 532-nm laser with a power of around 100 µW was focused on the NV center to excite and polarize it to the $m_{\rm s}=0$ spin state. Secondly, the NV center was subjected to a microwave pulse with frequency $f$. When the microwave frequency $f$ is resonant with the NV spin splitting $f_{\pm}=D\pm \gamma_{\rm e} B_{\rm bias}\pm \gamma_{\rm e} B_{\rm sample}$, the NV electron spin is excited to the $m_{\rm s}=-1$ or $m_{\rm s}=1$ state (where a positive sign in the above expression corresponds to a negative sign in $m_{\rm s}$, and vice versa), which exhibits a weak fluorescence. Finally, the fluorescence was collected using a confocal system, and the resonant frequency was observed. Thus, the magnetic field of the sample $B_{\rm sample}=\mp(f_{\pm}-D\mp\gamma_{\rm e}B_{\rm bias})/\gamma_{\rm e}$ could be determined by the ODMR, and the corresponding spectra are shown in Fig. 2(d).
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Fig. 3. Magnetization intensity maps of a thin layer of CrBr$_3$. (a) Sample magnetic field along the main axis $B_{\rm NV}$. The region shown corresponds to that illustrated in Fig. 2(c). (b) Surface magnetization density distribution $\sigma_{\rm s}(x,y)$ reconstructed from the magnetic field map $B_{\rm NV}$.
Figure 3(a) shows the magnetic field map of a region containing CrBr$_3$ with a minimum thickness of 11 nm [indicated by the orange box in Fig. 2(c)]. The experiment was performed in a bias field $B_{\rm bias}$ of 200 mT at 4 K. The map was obtained by conducting NV ODMR measurements at each pixel (at a rate of around 3 min/pixel). The magnetic field was determined by $B_{\rm NV}(x,y,z=z_0)$, where $z_0$ is the distance between the NV layer and the 2D CrBr$_3$ layer. The magnetic field map shows that the stray magnetic fields emerge predominantly from the edges of the thin 2D CrBr$_3$ layer. We assume that the magnetization has only a perpendicular component under $B_{\rm bias} = 200$ mT. Thus, the magnetization distribution can be reconstructed from the stray field map $B_{\rm NV}$. A reverse propagation method was used to reconstruct the surface magnetization density distribution $\sigma_{\rm s}(x,y)$ of the sample. The whole surface magnetization density distribution and the $\sigma_{\rm s}(x,y)$ distribution of the CrBr$_3$ layer are shown in Fig. 3. The thin CrBr$_3$ vdW sample was then measured at different temperatures, from 4 K to 40 K, to obtain the temperature response of the magnetization. We measured the magnetic stray field distributions at different temperatures, from which the corresponding surface magnetization density distributions of the thin material were reconstructed. The reconstructed surface magnetization density distributions at 4–35 K are shown in Figs. 4(a)–4(j). The surface magnetization density inside the material decreases as the temperature rises, and the magnetization almost vanishes at 35 K. This result indicates that the ferromagnetic-to-paramagnetic phase transition occurs at this temperature.
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Fig. 4. Magnetism at different temperatures. (a)–(j) Surface magnetization density distribution $\sigma_{\rm s}(x,y)$ of the region shown in Fig. 2(c) at different temperatures in the range of 4–35 K. The magnetism vanishes at 35 K.
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Fig. 5. Magnetic phase transition of the 2D vdW material. Magnetization density $\sigma_{\rm s}$ inside the 2D vdW material. The blue and red curves represent the experimental data and the fitting curve, respectively.
The average magnetization density $\sigma_{\rm s}$ at different temperatures is plotted in Fig. 5, and the magnetization almost vanishes at 35 K [Fig. 4(j)]. The anisotropic superexchange across the $\sim90^{\circ}\!$ Cr–Br–Cr bonds and the anisotropy of the Cr atoms with $S=3/2$ open a gap $\varDelta_0$ in the spin wave spectrum, thus contributing to the emergent stable magnetism in 2D CrBr$_3$. The XXZ Heisenberg exchange model Hamiltonian adopted from Refs. [17,32] is $H=-(\sum D(S_i^z)^2+J/2\sum_{i,j}{\boldsymbol S}_i\cdot{\boldsymbol S}_j+\lambda/2\sum_{i,j}S_i^z\cdot S_j^z)$, where $D$ is the single-ion anisotropy, $J$ is the exchange coupling, and $\lambda$ is the anisotropic exchange. The Cr–Br–Cr bond angle and the positive exchange coupling ($J>0$) indicate the existence of a ferromagnetic phase at low temperature, which is consistent with the magnetization distribution shown in Figs. 4(a)–4(j). The 2D CrBr$_3$ magnetization ($\mu_{\scriptscriptstyle{\rm B}}$ per Cr atom) can be described as $M(T)=S-k_{\scriptscriptstyle{\rm B}}Te^{-\varDelta_0/k_{\scriptscriptstyle{\rm B}}T}/2\pi JS$,[17,32] where $S=3/2$, and $k_{\scriptscriptstyle{\rm B}}$ is the Boltzmann constant. Through fitting, the transition temperature of the CrBr$_3$ vdW material was found to be 37.5 K (Fig. 5), which is in agreement with the previous work.[33] In summary, we have used an ensemble of NV centers to quantitatively investigate 2D magnetic materials. Nondestructive measurements on the nanoscale can be realized using our setup. Through these experiments, we observed the occurrence of a magnetic phase transition in an atomically thin vdW magnet (CrBr$_3$) with a thickness down to 11 nm. The surface magnetization distributions at different temperatures were also determined quantitatively. Our method is nondestructive, is compatible with other measuring techniques, and can be used in the study of antiferromagnetic materials[25,34,35] as well as magnons and related surface magnetism in 2D magnets. On can see the Supplementary Material for sample preparation, equipment setup, and a description of the magnetization density distribution reconstruction of the 2D material. The data that support the findings of this study are available from the corresponding authors upon reasonable request. Acknowledgments. This work was supported by the National Natural Science Foundation of China (Grant Nos. 81788101, T2125011, and 11874338), the National Key R&D Program of China (Grant No. 2018YFA0306600), Chinese Academy of Sciences (Grants Nos. XDC07000000, GJJSTD20200001, QYZDY-SSW-SLH004, and ZDZBGCH2021002), Anhui Initiative in Quantum Information Technologies (Grant No. AHY050000), and Fundamental Research Funds for the Central Universities. 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