Spin-phonon coupling in van der Waals antiferromagnet VOCl^*

Since the discovery of single-layer graphene, two-dimensional (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, Cr₂Ge₂Te₆ exhibits ferromagnetic semiconducting state in the 2D layer form.^[8] Thin flake CrI₃ has 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 oxychlorides MOCl (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 four MOCl 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 3d³ electronic configuration and a fourfold magnetic superstructure. The phase transition of CrOCl towards AFM order is observed at 13.5 K, accompanied by an a-axis monoclinic lattice distortion.^[21] Interestingly, VOCl has a relatively high T_N (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 of a axis. 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 〈 S_i ⋅ S_j 〉, the coupling constants are estimated to be as high as 3 cm⁻¹ for the 247 cm⁻¹ active mode, rendering VOCl as a potential candidate for application in magnetoelastic devices. We further identify a downward trend in 383 cm⁻¹ mode 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.

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 mm² can 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 the c axis 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.

Zoom In Zoom Out Reset image size

VOCl is a typical MOCl, which has orthorhombic structure at room temperature (Fig. 2(b), space group Pmmn, a = 3.78 Å, b = 3.30 Å, c = 7.91 Å).^[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 the ab plane. Each layer is coupled with van der Waals force in crystallographic c direction. 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 phase P2/n at this temperature.^[27]

Zoom In Zoom Out Reset image size

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 susceptibility χ as a function of temperature along the three crystallographic axes. The susceptibility of the a axis sharply drops below 79 K, while those of the b and c axes 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 easy a axis 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, Sr₁₄Cu₂₄O₄₁ and 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.

Zoom In Zoom Out Reset image size

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.

Zoom In Zoom Out Reset image size

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 to p4) is shown in Fig. 5. Many factors can contribute to mode frequency, such as lattice anharmonicity originated from the displacement between atoms, quasi-harmonicity, electron-phonon coupling, and spin–phonon coupling effect.^[35] Thus, the following relation can be obtained:

$$\begin{eqnarray}&&\omega (T)={\omega }_{0}+\Delta \omega {(T)}_{{\rm{s}}0{\rm{p}}}+\Delta \omega {(T)}_{{\rm{qh}}}+\Delta \omega {(T)}_{{\rm{anh}}}+\Delta \omega {(T)}_{{\rm{el}}0{\rm{ph}}},\end{eqnarray}$$

where ω₀ is the phonon frequency at absolute zero temperature, ω_qh represents the quasi-harmonic contribution, ω_anh corresponds to the contribution from phonon–phonon interaction, ω_el-ph and ω_sp-ph are 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 from ω_qh is 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

$$\begin{eqnarray}&&\omega (T)=\displaystyle \frac{{\omega }_{0}-{\omega }_{1}}{1+\exp \left(\displaystyle \frac{T-{T}_{0}}{{\rm{d}}T}\right)}+{\omega }_{1},\end{eqnarray}$$

where ω₁ and ω₀ are high-temperature and low-temperature limit values of phonon frequency, T₀ is the center point (the point with the largest rate of change), and d T is 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 that p1 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 below T_N, 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 short-range magnetic order, which is strongly coupled to phonons, develops around 150 K in VOCl.

Zoom In Zoom Out Reset image size

The deviation from the Boltzmann function can be used to estimate the strength of spin–phonon coupling at zero temperature via ω_sp-ph = λ〈 S_i ⋅ S_j 〉,^[36] where λ is the spin–phonon coupling constant related to the magnetic exchange, and 〈S_i ⋅ S_j 〉 is spin-spin correlation function. As V³⁺ is the only magnetic ion at 0 K, the value of 〈 S_i ⋅ S_j 〈 can be defined as S².^[37] Without regard to the sign of the frequency shift, λ is found to be 3 cm⁻¹, 2 cm⁻¹, 1.2 cm⁻¹ for the p2, p3 and p4 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 of λ making 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 for p3 mode deserves future studies.

In conclusion, we have studied the magnetization behavior and temperature dependence of Raman spectroscopy of VOCl single crystals. The magnetic susceptibility of the a axis sharply drops below 79 K, which implies an AFM magnetic order along a direction. 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. Below T_N, the Raman-active mode p1 at 199 cm⁻¹ is barely changed, while p2 and p4 (247 cm⁻¹ and 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 the p3 (383 cm⁻¹) mode below 150 K, which is likely due to the development of short-ranged magnetic order above T_N. Our results reveal the existence of a strong coupling between spins and lattices, which is crucial for understanding the 2D magnetism in VOCl.