Spin–phonon coupling in van der Waals antiferromagnet VOCl∗

Wen-Jun Wang(王文君) Xi-Tong Xu(许锡童) Jie Shen(沈洁)Zhe Wang(王哲) Shi-Le Zhang(张仕乐) and Zhe Qu(屈哲)

1Anhui Province Key Laboratory of Condensed Matter Physics at Extreme Conditions,High Magnetic Field Laboratory,Hefei Institutes of Physical Sciences,Chinese Academy of Sciences,Hefei 230031,China

2Science Island Branch of Graduate School,University of Science and Technology of China,Hefei 230026,China

3CAS Key Laboratory of Photovoltaic and Energy Conservation Materials,Hefei Institutes of Physical Sciences,Chinese Academy of Sciences,Hefei 230031,China

Keywords: vdW material,2D magnetism,Raman spectroscopy,spin–phonon coupling

1. Introduction

Since the discovery of single-layer graphene, twodimensional (2D) materials have attracted tremendous research focuses. Of particular interest is the 2D magnetic material,which can host strongly enhanced spin fluctuations,surface spin contributions,large magnetic moments,and less orbital moment quenching.[1–6]It was theoretically proposed that there exists no 2D long-range magnetic ordering in the isotropic Heisenberg model.[7]However,in real material systems,magnetic anisotropy enables the presence of a spin-wave excitation gap to exhibit intrinsic magnetic ordering at finite temperatures.For example,Cr2Ge2Te6exhibits ferromagnetic semiconducting state in the 2D layer form.[8]Thin flake CrI3has long-range magnetic order which can be controlled by the number of layers.[9]Two-dimensional magnets are also susceptible to external stimuli including electric field or electrostatic doping, pressure or strain, proximity effect, etc.,[10–17]which are significant to obtain desired properties by designing intentionally.

Transition-metal oxychloridesMOCl(M=Ti,V,Cr and Fe)is a new family of van der Waals(vdW)antiferromagnetic materials. It features stacking layers of Cl–M2O2–Cl sandwiches which are connected by the weak interlayer vdW interaction. According to the previous study, this family has low exfoliation energy, large spin polarization and thickness dependent magnetic order.[18]These fourMOCl compounds possess a rich variety of physical properties. Among them,TiOCl behaves like a quasi-one-dimensional magnetic system due to the orbital order from a single 3d electron in Ti3+ions.Upon cooling, it undergoes two phase transitions: an incommensurately modulated state at 90 K and a transformation towards the spin-Peierls state at 67 K.[19]Other members’magnetic structures are 2D-like.[20,21]For instance, CrOCl has a 3d3electronic configuration and a fourfold magnetic superstructure. The phase transition of CrOCl towards AFM order is observed at 13.5 K, accompanied by ana-axis monoclinic lattice distortion.[21]Interestingly,VOCl has a relatively highTN(80 K)[22]and the largest monoclinic angle (90.02°,90.22°, 90.07°, 90.09°for Ti, V, Cr, Fe, respectively) in the family,[21,23–25]which is likely due to a strong coupling between spins and phonons.

In this work, we focus on the magnetoelastic property of VOCl. High quality VOCl single crystals are synthesized via a chemical vapor transport (CVT) method. Using combined magnetization and Raman spectroscopy studies,we confirm that the phase transition point of VOCl is 79 K and the easy axis is along the direction ofaaxis. The strong coupling between the magnetic and lattice degrees of freedom is evidenced in the temperature dependence of the main Raman modes. Using Heisenberg’s spin–spin correlation function〈Si·Sj〉,the coupling constants are estimated to be as high as 3 cm−1for the 247 cm−1active mode,rendering VOCl as a potential candidate for application in magnetoelastic devices.We further identify a downward trend in 383 cm−1mode below 150 K. This temperature corresponds to the broad maximum in magnetic susceptibility,suggesting a simultaneous development of phonon-assisted short-ranged magnetic order in the 2D magnetic lattices.

2. Method

VOCl single crystals were synthesized by the CVT method.[26]Mixtures of V2O3(97%,Sigma Aldrich)and VCl3(99.9%, Sigma Aldrich) with a molar ratio of 1:2 were put into a quartz tube (length 150 mm, diameter 15 mm) which was then sealed and placed in a two-temperature-zone tube furnace. The tube was heated at a rate of 1 K/min until establishing a temperature gradient of 993–893 K. Samples were transported from the hot end to the cold end for a period of seven days,and finally cooled down to room temperature naturally.The resulting dark grey VOCl crystals were washed with alcohol several times to remove residual VCl3. Several rectangle,plate-like crystals with a typical size of 1×3 mm2can be obtained,as shown in the inset of Fig.1.Powder x-ray diffraction (XRD) measurement was performed in a Rigaku x-ray diffractometer. The reflection peak positions match well with the PDF#23-1472,as shown in Fig.1. Specific heat was measured on several single crystals stacked along thecaxis using a Quantum Design PPMS. Magnetic susceptibility was conducted with a superconductive quantum interference devices(SQUID).Temperature-dependent Raman spectroscopic measurements were performed on a freshly cleaved sample employing a 532 nm solid-state laser with 2 mW for excitation in the temperature range from 20 K to 300 K.The exposure time was set as 200 s.

Fig. 1. XRD pattern for VOCl powders at room temperature. The extra peaks(marked by asterisks)may come from the oxides of vanadium formed during growth. Inset: image of VOCl single crystals grown by the CVT method.

3. Results and discussion

VOCl is a typical MOCl, which has orthorhombic structure at room temperature (Fig. 2(b), space groupPmmn,a=3.78 °A,b=3.30 °A,c=7.91 °A).[22]Each V3+has two 3d electrons, and is located in the center of a twisted octahedra consisting of VO4Cl2. These are connected together to form a quasi-2D bilayer in theabplane. Each layer is coupled with van der Waals force in crystallographiccdirection. Magnetic measurement and powder neutron diffraction results have shown that VOCl is AFM below 80 K.[22,24]XRD results also suggest a lattice distortion towards a low temperature phaseP2/nat this temperature.[27]

Fig. 2. (a) Room-temperature crystal structure of VOCl and the distorted VO4Cl2 octahedron. (b)Magnetic structure of VOCl reflected by magnetic moments of V sublattice,showing an easy a axis AFM order.

Fig.3. Magnetic susceptibility versus temperature along the three crystallographic axes. Inset: specific heat of VOCl crystal,showing a peak at 79 K.

To study the magnetic behavior in VOCl single crystals,magnetization measurements were carried out with an applied field of 1 kOe. Figure 3 shows magnetic susceptibilityχas a function of temperature along the three crystallographic axes.The susceptibility of theaaxis sharply drops below 79 K,while those of thebandcaxes show a sudden rise. Combined with the built-in specific heat result,we conclude that in our samples,an AFM phase transition occurs at 79 K,with an easyaaxis anisotropy. This is consistent with the previous experimental results.[22,28]We also observe a broad maximum in the vicinity of 150 K in all three directions,deviating from the Curie–Weiss behavior. This is a phenomenon often found in low-dimensional materials such as CuGeO3,Sr14Cu24O41and Cu2OCl2,[29–31]reflecting strong 2D antiferromagnetic correlations in VOCl.[22,32]The rapid increase of the magnetic susceptibility below 10 K indicates the existence of paramagnetic impurities.

In order to study the connection between AFM ordering and atomic vibrations in VOCl, we now focus on measured Raman spectrum over the frequency range from 100 to 650 cm−1. Figure 4 shows the identified five Raman modes at 30 K,including three strong phonon modes(p1,p3,p4)[33]and two weak ones(p2,p5). These modes are ascribed to the stretching vibrations of V–Cl bonds.[34]The number of visible Raman modes is less than the previous report,[34]which may be ascribed to purity and defections of different crystals, the accidental degeneracy of several neighboring phonon frequencies or intensity reduction of several phonons due to smaller polarizability.[35]All these Raman peaks get smaller and wider as the temperature increases, due to enhanced phonon vibration and scattering. The peak near 630 cm−1(p5)at low temperatures is indistinguishable above 240 K due to its weak intensity.

Fig.4. (a)Raman spectrum over the frequency range 100–650 cm−1 at several typical temperatures. Five discernable peaks are labeled with p1 to p5,respectively. (b)Corresponding colormap of the Raman spectrum.

For all these five modes,no abrupt changes are observed across the Neel temperature,which is consistent with the previous suggestion that the monoclinic lattice distortion is solely driven by the magnetic interactions.[27]

The temperature dependence of the peak positions of the four major modes(p1 top4)is shown in Fig.5. Many factors can contribute to mode frequency,such as lattice anharmonicity originated from the displacement between atoms, quasiharmonicity,electron-phonon coupling,and spin–phonon coupling effect.[35]Thus,the following relation can be obtained:

ω(T)=ω0+∆ω(T)s-p+∆ω(T)qh+∆ω(T)anh+∆ω(T)el-ph,

whereω0is the phonon frequency at absolute zero temperature,ωqhrepresents the quasi-harmonic contribution,ωanhcorresponds to the contribution from phonon–phonon interaction,ωel-phandωsp-phare the electron–phonon and the spin–phonon coupling effect. As VOCl is a insulator, there is no electron–phonon coupling effect. The quasi-harmonic contribution is significant only when the distance between atoms varies,while from synchrotron-radiation powder x-ray diffraction measurements,[24]the change in unit cell volume from 15 K to 300 K is found to be only about 0.83%. Thus the part fromωqhis also ruled out. We therefore conclude only the contributions from lattice anharmonicity and spin–phonon couple effect may work on the mode frequencies in VOCl. In the paramagnetic phase,the lattice anharmonicity governs the evolution of mode frequency.We can use the Boltzmann function to describe the nature of crystals

whereω1andω0are high-temperature and low-temperature limit values of phonon frequency,T0is the center point (the point with the largest rate of change), and dTis a temperature characteristic quantity from the lowest value to the highest value. We plot all fitted curves shown in Fig.5. The profile of 199 cm−1(p1)mode frequency roughly follows the fitting curve in our measured temperature range, suggesting thatp1 is barely affected by magnetic order. The 247 cm−1(p2)and 404 cm−1(p4) modes, on the other hand, show a strong deviation from Boltzmann fitting results belowTN, indicating a large contribution from spin–phonon coupling. It is worth noticing that the deviation of 383 cm−1(p3)occurs at 150 K,well above the Neel temperature of VOCl. This temperature also corresponds to the broad maximum in the susceptibility curve in Fig.3. Note that in the 2D Heisenberg antiferromagnet model,[35]this maximum arises from spin correlations of nearest neighbors. We therefore give evidence that a shortrange magnetic order, which is strongly coupled to phonons,develops around 150 K in VOCl.

The deviation from the Boltzmann function can be used to estimate the strength of spin–phonon coupling at zero temperature viaωsp-ph=λ〈Si·Sj〉,[36]whereλis the spin–phonon coupling constant related to the magnetic exchange,and〈Si·Sj〉is spin-spin correlation function. As V3+is the only magnetic ion at 0 K,the value of〈Si·Sj〉can be defined asS2.[37]Without regard to the sign of the frequency shift,λis found to be 3 cm−1, 2 cm−1, 1.2 cm−1for thep2,p3 andp4 modes, respectively. The spin–phonon coupling constant of VOCl is larger than many 2D materials with magnetoelastic effect, such as Cr2Ge2Te6(λ=1.2 cm−1), CrSiTe3(λ=0.2 cm−1),CrCl3(λ=0.9 cm−1),[Cu(pyz)2(HF2)]PF6(λ=2 cm−1).[37–40]The large value ofλmaking VOCl a potential candidate for applications in low-dimensional magnetoelastic devices. The reason behind such a remarkable spin–phonon coupling in a short-ranged magnetic order forp3 mode deserves future studies.

Fig.5. Frequencies versus temperature for main modes at(a) 199 cm−1, (b) 247 cm−1, (c) 383 cm−1, (d) 404 cm−1, respectively. Data are fitted with the Boltzmann function illustrated by the solid red line,suggesting a spin–lattice coupling.

4. Conclusion

In conclusion,we have studied the magnetization behavior and temperature dependence of Raman spectroscopy of VOCl single crystals. The magnetic susceptibility of theaaxis sharply drops below 79 K, which implies an AFM magnetic order alongadirection. Raman spectroscopy identifies three strong phonon modes(p1,p3,p4)and two weak phonon modes (p2,p5) at 30 K. The temperature dependence of the four modes is studied in detail. BelowTN, the Raman-active modep1 at 199 cm−1is barely changed, whilep2 andp4(247 cm−1and 404 cm−1,respectively)show remarkable deviations,which is ascribed to the strong magnetoelastic coupling between spins and phonons for these two modes.Furthermore,we report a decrease of thep3(383 cm−1)mode below 150 K,which is likely due to the development of short-ranged magnetic order aboveTN. Our results reveal the existence of a strong coupling between spins and lattices, which is crucial for understanding the 2D magnetism in VOCl.