Magnetic-Field-Induced Quantum Phase Transitions in a van der Waals Magnet

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Magnetic-Field-Induced Quantum Phase Transitions in a van der Waals Magnet

Siwen Li, Zhipeng Ye, Xiangpeng Luo, Gaihua Ye, Hyun Ho Kim, Bowen Yang, Shangjie Tian, Chenghe Li, Hechang Lei, Adam W. Tsen, Kai Sun, Rui He, and Liuyan Zhao

Phys. Rev. X 10, 011075 – Published 31 March 2020

See synopsis: Solving a Magnetic Puzzle

Abstract

Exploring new parameter regimes to realize and control novel phases of matter has been a main theme in modern condensed matter physics research. The recent discovery of two-dimensional (2D) magnetism in nearly freestanding monolayer atomic crystals has already led to observations of a number of novel magnetic phenomena absent in bulk counterparts. Such intricate interplays between magnetism and crystalline structures provide ample opportunities for exploring quantum phase transitions in this new 2D parameter regime. Here, using magnetic field- and temperature-dependent circularly polarized Raman spectroscopy of phonons and magnons, we map out the phase diagram of chromium triiodide ( ${CrI}_{3}$ ) that has been known to be a layered antiferromagnet (AFM) in its 2D films and a ferromagnet (FM) in its three-dimensional (3D) bulk. However, we reveal a novel mixed state of layered AFM and FM in 3D ${CrI}_{3}$ bulk crystals where the layered AFM survives in the surface layers, and the FM appears in deeper bulk layers. We then show that the surface-layered AFM transits into the FM at a critical magnetic field of 2 T, similar to what was found in the few-layer case. Interestingly, concurrent with this magnetic phase transition, we discover a first-order structural phase transition that alters the crystallographic point group from $C_{3 i}$ (rhombohedral) to $C_{2 h}$ (monoclinic). Our result not only unveils the complex single-magnon behavior in 3D ${CrI}_{3}$ , but it also settles the puzzle of how ${CrI}_{3}$ transits from a bulk FM to a thin-layered AFM semiconductor, despite recent efforts in understanding the origin of layered AFM in ${CrI}_{3}$ thin layers, and reveals the intimate relationship between the layered AFM-to-FM and the crystalline rhombohedral-to-monoclinic phase transitions. These findings further open opportunities for future 2D magnet-based magnetomechanical devices.

Received 17 January 2020
Revised 24 February 2020
Accepted 27 February 2020

DOI:https://doi.org/10.1103/PhysRevX.10.011075

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Magnetic order Phase transitions by order Quantum phase transitions Spin dynamics

Condensed Matter, Materials & Applied Physics

synopsis

Solving a Magnetic Puzzle

Published 31 March 2020

Spectroscopic measurements explain why a van der Waals ferromagnet displays different magnetic behavior in its layered and bulk forms.

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Authors & Affiliations

Siwen Li¹, Zhipeng Ye², Xiangpeng Luo¹, Gaihua Ye², Hyun Ho Kim³, Bowen Yang³, Shangjie Tian⁴, Chenghe Li⁴, Hechang Lei⁴, Adam W. Tsen³, Kai Sun¹, Rui He ^2,*, and Liuyan Zhao ^1,†

¹Department of Physics, University of Michigan, 450 Church Street, Ann Arbor, Michigan 48109, USA
²Department of Electrical and Computer Engineering, Texas Tech University, 910 Boston Avenue, Lubbock, Texas 79409, USA
³Institute for Quantum Computing, Department of Chemistry, and Department of Physics and Astronomy, University of Waterloo, Waterloo, 200 University Avenue W, Ontario N2L 3G1, Canada
⁴Department of Physics and Beijing Key Laboratory of Opto-electronic Functional Materials & Micro-nano Devices, Remin University of China, Beijing 100872, China

^*Corresponding author. rui.he@ttu.edu
^†Corresponding author. lyzhao@umich.edu

Popular Summary

The recent discovery of 2D magnetism in freestanding monolayer atomic crystals has led to observations of a number of novel magnetic phenomena absent in 3D counterparts. Such intricate interplays between magnetism and crystalline structures provide ample opportunities for exploring quantum phase transitions in two dimensions. To further those goals, we map out the phase diagram of chromium triiodide ( ${CrI}_{3}$ ), an extraordinary material known to be a layer antiferromagnet in 2D films and a ferromagnet in its 3D form. We find a novel mixed state of layer antiferromagnetism and ferromagnetism along with several intriguing phase transitions, all of which shed light on the unusual properties of this material.

Our team used polarized Raman spectroscopy to probe the collective excitations of both spin precessions (magnons) and lattice vibrations (phonons) in a sample of ${CrI}_{3}$ . By tracking the evolution of magnons and phonons as functions of temperature and magnetic field, we map out the phase diagram.

Among several findings, we find a novel mixed state where the layered antiferromagnetism survives in the surface layers and the ferromagnetism appears in deeper layers. We also find that the surface layer creeps into the interior at a critical magnetic field of 2 T. This magnetic phase transition coincides with a structural phase transition that alters the material’s crystalline architecture.

Our results address the crossover from 3D ferromagnetism to 2D layered antiferromagnetism and show the intimate relationship between the spin and lattice degrees of freedom in ${CrI}_{3}$ . Using ${CrI}_{3}$ as an example, we believe that our work represents a major milestone in the rapidly developing field of correlated physics in 2D atomic crystals.

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Issue

Vol. 10, Iss. 1 — January - March 2020

Subject Areas

Condensed Matter Physics

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Images

Figure 1
Identifying the magnetism-related Raman modes in 3D ${CrI}_{3}$ . (a) Raman spectra taken at 10 K and 0 T in the LL and LR channels. LL(R) stands for the polarization channel in which the incident and scattered light is left and left (right) circularly polarized, respectively. Solid dots are raw data points and solid lines are Lorentzian fits. The multiplication factors to the spectra intensities are labeled in the corresponding panels. The Raman modes are labeled as $M_{0, 1, 2}$ for the magnetism-related ones (shaded in orange), $P (A_{g})$ and $P (E_{g})$ for the phonon modes of the $A_{g}$ and $E_{g}$ symmetries of the $C_{3 i}$ point group, respectively, and $N$ for the noise line from the incident light (shaded in gray stripes). Inset shows the legends for the polarization channels. (b) A color map of magnetic field-dependent Raman spectra taken over a magnetic field range of 0–7 T at 10 K in the LL channel. The gray stripe-patterned shade is to block the noise line. (c) Raman spectra taken at 10 K and 7 T in the LL and LR channels. (d) Temperature dependence of the $M_{0}$ frequency (including data for the LL anti-Stokes, LR anti-Stokes, and Stokes shifts) and $M_{1, 2}$ intensities at zero magnetic field ( $B = 0 T$ ) showing a clear onset at $T_{c}$ of 45 K. Error bars are defined as one standard error of the fitting parameters in the Lorentzian fit to the Raman modes.
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Figure 2
Establishing the mixed SAFM and BFM phase in 3D ${CrI}_{3}$ . (a) Experimental data (left) and spin-wave calculations (right) for the magnetic field dependence of $M_{0}$ -type mode frequencies. $M_{0 a}$ , $M_{0 b}$ , and $M_{0 c}$ label the three spin-wave branches below the critical magnetic field $B_{c}$ of 2 T. Error bars correspond to one standard error of the fitted central frequencies for the $M_{0}$ -type Raman modes and are mostly smaller than the data point symbols. (b) Schematic illustration of the mixed state of the surface-layered AFM (SAFM for the state with alternating spin moments in the adjacent layers) and the deep bulk FM (BFM for the state with all the spin moments along one direction) below $B_{c}$ and the pure FM state above $B_{c}$ .
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Figure 3
Revealing the rhombohedral-to-monoclinic structural phase transition at $B_{c}$ in 3D ${CrI}_{3}$ . Magnetic field dependence of (a) a representative $A_{g}$ phonon (at approximately $129 {cm}^{- 1}$ ) intensity leakage into the LR channel, (b) an example of an $E_{g}$ phonon (at approximately $109 {cm}^{- 1}$ ) intensity showing up in the LL channel, which corresponds to the $E_{g}$ phonon of the $C_{3 i}$ structure [i.e., $E_{g} (C_{3 i})$ ] transforming into the $A_{g}$ phonon of the $C_{2 h}$ structure [i.e., $A_{g} (C_{2 h})$ ], (c) an example of the $E_{g}$ phonon (at approximately $240 {cm}^{- 1}$ ) intensity experiencing a clear discontinuity in the LR channel but remaining absent in the LL channel corresponding to an $E_{g} (C_{3 i})$ phonon transforming into a $B_{g} (C_{2 h})$ mode, and (d) $M_{2}$ -mode intensity. Inset shows an enlargement between 1.5 and 2.5 T with both increasing ( $+ B$ ) and decreasing ( $- B$ ) magnetic fields. Error bars correspond to one standard error of the fitted peak intensities. (e) Schematic illustration of the shearing of ${CrI}_{3}$ layers across the magnetic phase transition $B_{c}$ . The light blue ellipses represent the directors between layers formed because of this lattice deformation.
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Figure 4
Constructing the temperature vs external magnetic field phase diagram for 3D ${CrI}_{3}$ . (a) Temperature dependence of the $M_{0 c}$ frequency for the FM spin-wave branch at multiple magnetic fields of 1.5 T (below $B_{c}$ ), 3.5, 5, and 7 T (above $B_{c}$ ). The dashed line is a fit to the data taken at 1.5 T, while the solid lines are guide to the eyes. The striped pattern highlights the crossover between the paramagnetism (PM) and ferromagnetism (FM). (b) Magnetic field dependence of the $M_{2}$ intensity at multiple temperatures of 11, 25, 35, 40 K (below $T_{c}$ ), and 70 K (above $T_{c}$ ). Error bars correspond to one standard error of the fitted parameters. (c) A temperature vs external magnetic phase diagram constructed based on both the findings from the current work (blue open and brown filled circles) and the literature (blue open and filled diamonds, Ref. [13]). The brown solid line represents a true phase boundary between the mixed magnetic phase with a rhombohedral structure and the FM phase with a monoclinic structure. The gray dashed line is for a potential phase boundary between the rhombohedral and monoclinic PM phases. The blue stripped pattern indicates the crossover between the PM and FM phases.
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