⇦Chinese Physics Letters, 2020, Vol. 37, No. 7, Article code 076202 Possible Tricritical Behavior and Anomalous Lattice Softening in van der Waals Itinerant Ferromagnet Fe$_{3}$GeTe$_{2}$ under High Pressure Jie-Min Xu (许劼敏)1,2, Shu-Yang Wang (王舒阳)1,2, Wen-Jun Wang (王文君)1,2, Yong-Hui Zhou (周永惠)1,2, Xu-Liang Chen (陈绪亮)1, Zhao-Rong Yang (杨昭荣)1, and Zhe Qu (屈哲)1* Affiliations 1Anhui Key Laboratory of Condensed Matter Physics at Extreme Conditions, High Magnetic Field Laboratory, Hefei Institutes of Physical Science, Chinese Academy of Sciences, Hefei 230031, China 2Science Island Branch of Graduate School, University of Science and Technology of China, Hefei 230026, China Received 10 March 2020; accepted 2 May 2020; published online 21 June 2020 Supported by the National Key Research and Development Program of China (Grant Nos. 2018YFA0305704 and 2016YFA0401804), the National Natural Science Foundation of China (Grant Nos. 11774352, U1832214, U19A2093, 11804344, U1632275, 11874362, 11704387, and U1932152), the Users with Excellence Project of Hefei Center CAS (Grant No. 2018HSC-UE012), the Major Program of Development Foundation of Hefei Center for Physical Science and Technology (Grant No. 2018ZYFX002), the Youth Innovation Promotion Association CAS (Grant No. 2020443).
*Corresponding author. Email: zhequ@hmfl.ac.cn Citation Text: Xu J M, Wang S Y, Wang W J, Zhou Y H and Chen X L et al. 2020 Chin. Phys. Lett. 37 076202    Abstract We present a high-pressure study of van der Waals ferromagnetic metal Fe$_{3}$GeTe$_{2}$ through electrical transport and Raman scattering measurements in diamond anvil cells at pressures up to 22.4 GPa. Upon compression, the ferromagnetic transition temperature $T_{\rm c}$ manifested by a kink in resistance curve decreases monotonically and becomes undiscernable around $P_{\rm c} = 10$ GPa, indicative of suppression of the itinerant ferromagnetism. Meanwhile, by fitting the low temperature resistance to the Fermi liquid behavior of $R =R_{0} + AT^{2}$, we found that $R_{0}$ shows a cusp-like anomaly and the coefficient $A$ diverges around $P_{\rm c}$. These transport anomalies imply a tricritical point as commonly observed in itinerant ferromagnets under pressure. Unexpectedly, the Raman-active $E_{2g}$ and $A_{1g}$ modes soften remarkably after an initial weak hardening and the peak widths of both modes broaden evidently on approaching $P_{\rm c}$, followed by complete disappearance of both modes above this critical pressure. A possible underlying mechanism for such anomalous lattice softening near $P_{\rm c}$ is discussed. DOI:10.1088/0256-307X/37/7/076202 PACS:62.50.-p, 63.20.-e, 78.30.-j, 72.90.+y © 2020 Chinese Physics Society Article Text Quasi-two-dimensional (quasi-2D) layered magnetic van der Waals (vdW) materials have attracted much attention due to their great tunability in physical properties, enabling flexibility in fabrications of heterostructures and spin devices with exceptional functionalities. This is well exemplified by the recent observation of 2D long-range ferromagnetism in magnetic semiconductors Cr$_{2}$Ge$_{2}$Te$_{6}$ and CrI$_{3}$.[1–4] In particular, quasi-2D vdW material Fe$_{3}$GeTe$_{2}$ (FGT) has received special interest owing to its rare metallic itinerant ferromagnetism.[5–9] FGT crystallizes in the hexagonal symmetry (space group: $P6_{3}/mmc$) with the Fe$_{3}$Ge layer sandwiched by two layers of Te atoms linked by weak vdW interactions. Fe atoms form a triangular sub-lattice which is normal to the $c$ axis. The ferromagnetic Curie temperature $T_{\rm c}$ of bulk FGT is sample dependency due to Fe vacancy, ranging from about 150 to 220 K.[10] In addition, strong magnetic anisotropy exists in both bulk and nanoflake manifestations of FGT. However, the coercivity of the former is much smaller than that of the latter.[11] By thinning down to monolayer, the itinerant ferromagnetism of FGT remains and the $T_{\rm c}$ can even ramp up to room temperature upon modulating the carrier by the electric field.[12] High pressure technology, as a new dimension in sciences, can effectively tune the structures, properties of materials and, thus, provide exciting opportunities to explore new physics, novel phenomena and exotic states of matter.[13–17] A previous study reported the effect of high pressure on the anomalous Hall effect in FGT through Hall transport measurements and synchrotron x-ray diffraction (XRD).[18] The anomalous Hall conductivity was found to be tuned nonmonotonically with pressure; theoretical calculations revealed that it can be closely related to changes of the electronic structures. In addition, no structural phase transitions were observed from XRD and the $T_{\rm c}$ decreases monotonically as inferred from transports. To date, there are still no high-pressure studies on the dynamic properties of FGT, which can offer local structural symmetry information and may be helpful for understanding the transport properties. In this letter, we investigate the transport and dynamic properties under pressure of FGT by electrical transport and Raman scattering measurements in diamond anvil cells. Our transport data shows that the itinerant ferromagnetism of FGT disappears at a critical pressure point $P_{\rm c} \sim 10$ GPa. The anomalies in the fitting parameters of the low-temperature resistance to the Fermi liquid model, suggesting a pressure-induced tricritical phenomena as commonly observed in itinerant ferromagnets. Concomitantly, the Raman scattering measurements reveal an anomalous lattice softening near a quantum critical point. FGT single crystals were grown by a chemical vapor transport method using a two-temperature-zone tube furnace. High-purity powder elements Fe, Ge and Te were mixed with stoichiometric molar ratio of $3\!:\!1\!:\!2$ (Fe:Ge:Te). Iodine (3 mg/cm$^{3}$) was used as a transport agent. The mixtures were ground and put into a dry quartz glass ampoule. Then, the ampoule was sealed and placed in the tube furnace with the cold and hot ends staying at 700℃ and 750℃, respectively, for one week. Finally, the furnace was cooled down to 450℃ at a rate of 1℃/min, followed by natural cooling to room temperature. The crystal structure and the composition of the single crystal samples were confirmed by single-crystal x-ray diffraction measurement (Cu $K_\alpha$ radiation, $\lambda = 1.54184$ Å) and energy dispersive x-ray spectrometry. A standard four-probe method was used to perform the temperature dependent electrical transport measurements with the current applied along the in-plane direction in a BeCu alloy diamond anvil cell with a culet of 300 µm in diameter. An FGT single crystal was loaded into the cell with NaCl powder as the pressure transmitting medium. High-pressure Raman scattering experiments were performed on a freshly cleaved sample at room temperature employing a 532 nm solid-state laser for excitation.
cpl-37-7-076202-fig1.png
Fig. 1. (a) Energy dispersive spectrum of single crystal Fe$_{3}$GeTe$_{2}$. The inset shows a photo of the measured single crystal. (b) Standard Rietveld refinements of the powder x-ray diffraction pattern under ambient conditions using the RIETICA program. The I(obs) (open circles) and I(calc) (red solid line) represent the observed and calculated data, respectively. The marker points (blue vertical bars) indicate the Bragg peak positions. The Obs-Calc (green solid line) at the bottom denotes the residual intensities of observed data and calculated data.
The energy dispersive spectroscopy is shown in Fig. 1(a) and the element molar ratio of Fe:Ge:Te is $2.83\!:\!1\!:\!2$. This suggests some Fe deficiency, which is a common case.[10] Figure 1(b) displays the powder x-ray diffraction pattern under ambient conditions and its standard Rietveld refinements. The observed peaks can be well indexed by the space group $P6_{3}/mmc$ and the extracted lattice parameters are $a = b = 4.01$ Å, $c = 16.33$ Å, in accordance with the previous reports.[5,18] A small peak marked by an asterisk is due to the transport agent I$_{2}$. The temperature ($T$) dependence of resistance ($R$) of FGT at various pressures is shown in Fig. 2(b). Starting at ambient pressure, the $R$–$T$ curve shows a metallic behavior. It exhibits a kink anomaly at $T_{\rm c} \sim 206$ K, which is determined as the maximum of $dR/dT$ (indicated by arrows in Figs. 2(b) and 2(c)). This is consistent with the previous reports and the kink signals the Curie temperature $T_{\rm c}$ corresponding to a paramagnetic-to-ferromagnetic transition upon cooling.[5,12] With the application of external pressure, $T_{\rm c}$ gradually decreases to $\sim $70 K at 9.5 GPa, and is hardly discernable above $P_{\rm c} \sim 10$ GPa. This indicates a suppression of the itinerant ferromagnetism of FGT. The pressure evolution of $T_{\rm c}$ can also be clearly drawn from the first-order temperature derivative of resistance, as shown in Fig. 2(c), which is in good agreement with a previous work.[18]
cpl-37-7-076202-fig2.png
Fig. 2. (a) Schematic setup of diamond anvil cell (DAC) transport experiment. (b) Temperature dependence of resistance ($R$) in the pressure range of 0–22.31 GPa. A kink anomaly can be observed, which corresponds to the PM-FM transition and is determined by the maximum in the corresponding first-order temperature derivative of resistance curve (c).
Raman spectroscopy has been proven to be a powerful and effective means to probe the local structural symmetry of 2D vdW materials.[19] The room-temperature Raman scattering spectrum of FGT at 0.6 GPa in the frequency range 80–180 cm$^{-1}$ is displayed in Fig. 3(a). Three Raman-active vibrational modes can be observed, similar to the ambient-pressure case.[7,10] Accordingly, the two remarkable modes, locating at 123.1 cm$^{-1}$ and 141.1 cm$^{-1}$ drawn by fitting using the Lorentzian lineshapes, can be assigned to the $E^2_{2g}$ and $A^1_{1g}$ modes, respectively. The relative small peak at $\sim 105$ cm$^{-1}$ should be the $E^1_{2g}$ mode.[10] The atomic displacement vectors of the two evident modes are schematically shown in Fig. 3(b). It can be seen that the $E^2_{2g}$ mode involves in-plane vibrations of the Fe, Ge and Te ions and the $A^1_{1g}$ mode is related to out-of-plane vibrations of the Fe and Te ions. The Raman scattering spectra of FGT under higher pressures up to 22.44 GPa are presented in Fig. 3(c). With increasing pressure, both the $E^2_{2g}$ and $A^1_{1g}$ modes first blue shift and then red shift, showing softmode behaviors. In addition, the mode intensity weakens with pressure and all modes completely disappear above $P_{\rm c}$.
cpl-37-7-076202-fig3.png
Fig. 3. (a) A fitting of the Raman spectrum at 0.6 GPa by using three Lorentzian functions. (b) Schematics of the two Raman vibrational modes. (c) Raman scattering spectra of FGT single crystal under various pressures at room temperature.
We plot the variation of transition temperature $T_{\rm c}$ induced by pressure in Fig. 4(a). In addition, in Fig. 4(b) we show the pressure dependences of parameters $R_{0}$ and $A$, which are drawn by fittings of the resistance in the low temperature range 5–30 K to the Fermi-liquid model of $R(T)=R_{0} + A T^{2}$.[20,21] A typical fitting at 0.44 GPa is presented in the inset of Fig. 4(b). To gain a comprehensive understanding of our results, in Figs. 4(c) and 4(d) we also draw the quantitative Raman mode shifts and the full width at half maximum (FWHM) of the modes as a function of pressure. Clearly, concomitant anomalies can be observed around $P_{\rm c} \sim$ 10 GPa. From Fig. 4(a), we know that $P_{\rm c}$ indicates the vanishing of the ferromagnetism. At the meantime, the coefficient $A$ of Fermi liquid, which is related to the effective mass of the carriers ($m^{\ast}$) via $A \propto (m^{\ast} /m_{0})^{2}$ with $m_{0}$ being the naked electron mass, shows a divergent behavior and the parameter $R_{0}$ exhibits a cusp-like anomaly. These transport characteristics resemble the signals usually observed in the literature,[21,22] which was related to a quantum critical point. In fact, tremendous previous studies show that a pressure-induced tricritical point is a universal phenomenon in itinerant ferromagnets.[23–25] On the other hand, our Raman data shows that softmodes appear and the FWHMs of both modes broaden gradually with pressure, which may indicate a dynamical instability of the lattice and would lead to a structural change.[23,24,26] However, according to a previous high-pressure XRD investigation, no evident structural transitions were observed up to 25.9 GPa.[18] In addition, reported work has proved that there is no temperature-induced structural phase transition in FGT[10] and the trend of the structure obtained by high-pressure Raman spectroscopy at room temperature roughly matches with ambient pressure at low temperature. Therefore, we investigate the magnetic properties at low temperature based on the high-pressure Raman data at room temperature.
cpl-37-7-076202-fig4.png
Fig. 4. (a) Variation of the transition temperature $T_{\rm c}$ from ambient to 9.50 GPa. PM and FM stand for the paramagnetic and ferromagnetic phases, respectively. (b) Pressure dependences of parameters $R_{0}$ and $A$ drawn from the power law fitting of the resistance in the low temperature range 5–30 K. The inset shows a typical fitting at 0.44 GPa. (c) Frequency versus pressure for various Raman modes. (d) FWHM of the $E^2_{2g}$ and $A^1_{1g}$ Raman-active modes versus pressure.
FGT is a typical itinerant ferromagnet, in which some $3d$ electrons in Fe contribute to local magnetic moments and the others conduct as carriers.[5,27] Under ambient pressure, FGT stays in the FM state at low temperature due to the ferromagnetic exchange interaction $J$ between Fe moments. Thermal fluctuations exaggerate with increasing temperature and eventually overcome the ferromagnetic exchange interaction $J$ above $T_{\rm c}$, resulting in the destroy of the ferromagnetic order. Thus, FGT enters the PM state. As shown in Fig. 2(b), the low-temperature resistance gradually reduces with the application of pressure. Since the carrier mobility ($\mu$) usually keeps almost constant, the carrier concentration should increase according to the relation $\rho = 1/ne\mu$. This means that the $3d$ electrons conducting as carries should increase, which in turn leads to the diminish of the electrons contributing to the local moments. Hence, the moment of Fe will reduce, which is supported by the previous theoretical calculation.[18] As a result, the ferromagnetic exchange interaction $J$ will weaken. The thermal fluctuations required to completely destroy the ferromagnetism decrease. Therefore, $T_{\rm c}$ first drops upon increasing pressure. With further increasing pressure, $T_{\rm c}$ becomes unrecognizable above $P_{\rm c}=10$ GPa rather than keep decreasing. Since the thermal fluctuations are weak at low temperatures, this suggests that non-thermal fluctuations take effect in this pressure-induced FM-PM transition. The observations that an anomalous lattice softening behavior happens and the width of the Raman mode broadens [Figs. 4(c) and 4(d)] indicate that the spin fluctuations are enhanced due to spin-phonon coupling and strong spin-orbit effect.[28] As discussed above, the pressure dependence of the Fermi coefficient $A$ shows divergence near $P_{\rm c}$, which indicates the occurrence of the tricritical QCP.[21–25] When the tricritical point $P_{\rm c}=10$ GPa is approached, the spin fluctuations are strongly enhanced so that it could completely suppress the ferromagnetic exchange interaction $J$. Therefore, the FM state is destroyed and FGT enters the PM state. This picture may be applicable to the present case since both the Raman-active modes involve vibrations of the heavy Te atoms relating to spin-orbit effect. Further theoretical and experimental studies are needed to uncover the detailed underlying mechanism. In conclusion, we have systematically studied the high-pressure electrical transport and lattice dynamic properties of FGT. It is found that the ferromagnetism is gradually suppressed with increasing pressure and indistinguishable above $P_{\rm c} \sim 10$ GPa. Consistent anomalies are also observed from parameters $R_{0}$ and $A$ through detailed analysis of the low temperature resistance. Our Raman scattering measurements reveal an anomalous lattice softening near $P_{\rm c}$, which may be due to the spin-orbit interaction and enhanced by quantum fluctuations. These are related to a pressure-induced tricritical behavior. 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