With this subsystem, one can make conventional Raman measurements under low temperature (4 K), magnetic field (9 T), and high pressure (20 GPa). The vertical backscattering configuration is adopted to fit the magnet and cryostat.

Light source. Single-frequency solid state lasers are employed for the subsystem. The wavelengths sparsely cover the visible range from red to blue. This enables to check the photoluminescence effect and do some resonance Raman studies. In some particular cases, Raman signal strongly depends on the wavelength of incident light and the optional wavelengths will be very helpful in such cases. The incident laser beam passes through a pair of Bragg gratings which can filter out the unwanted lines generated in the optical cavity and guarantee a clean laser line with a narrow linewidth.

Spectrometer. Single-grating monochromator (Jobin Yvon HR800) is used in the subsystem. The spectral resolution is ∼ 1.2 cm⁻¹ at 633 nm. Compared to the double-or triple-grating one, it provides a good balance between efficiency and performance. The application of the suite of volume Bragg grating can push the measurable lowest wavenumbers down to 5–10 cm⁻¹. The spectrometer is equipped with a liquid-nitrogen-cooled and back-illuminated CCD.

Magnet and cryostat. Sample environments or extreme conditions are provided by a close-cycled magnet and cryostat system which integrates low temperatures down to 4 K and magnetic fields up to 9 T. The system takes an anti-vibration design to avoid the vibration generated by the refrigerator. A customized optical insert is used to couple the incident light/the scattered light in/out of the cryostat. The customized objective lens is made of non-magnetic and low-thermal-expansion materials since it is placed inside the cryostat and the magnet. The application of high pressure together with low temperatures and high magnetic fields is a real challenge. Both the magnet bore diameter and the working distance of the objective lens strongly limit the size of the diamond anvil cell. It means that for the magnet and cryostat, we need to customize a pressure cell as small as possible.

Precise positioning and rotating stages. For a microscopic Raman measurement, an XYZ-stage with a resolution of ∼ μm is very helpful to select an optimal focus spot and compensate the drift of the focus spot when varying temperatures. A precise sample positioning mechanism, which is also made of non-magnetic and low-thermal-expansion materials for the same reason as mentioned above, is applied in the cryostat and magnet. The sample positioner is an XYZ-stage driven by piezoelectric actuators (attoCube). Symmetry analysis is one of the unique and powerful functions of Raman scattering. For this purpose, a piezo-driven rotator mounted on the positioner will allow us to conveniently make rotation measurements under extreme conditions. It would be particularly useful for studying structural phase transitions or symmetry breaking.

Time-resolved Raman scattering is an emerging and rapidly developing branch of Raman scattering. It presents us an alternative degree of freedom beyond temperature and magnetic field to look into Raman process. It can tell us the important information on the non-equilibrium dynamics of electrons or other excitations involved in Raman process. We can expect that the time-resolved technique under low temperatures and high magnetic fields will open a fascinating and unique window for exploring novel quantum phases.

There are different scenarios to realize time-resolved Raman scattering. A direct way is to excite the sample with a fast laser and collect Raman spectra with a high-speed gated detector synchronized with the excitation pulse. However, it is limited by available high-speed detectors and their sensitivity. Here we employ the standard pump-probe technique (Fig. 2). A key question for this technique is to get rid of the Raman signal excited by the pump. Surely one can separately produce the probe pulse, by using a CW laser with a mechanical high-speed chopper or a Q-switch laser. However, this will reach the time-scale ceiling in the ultrafast region (∼nanosecond).

Fig. 2.

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	Fig. 2. (color online) Schematic diagram of time-resolved Raman scattering. Pump–probe technique is used here. Probe pulse is generated within an optical parameter oscillation (OPO) box and modulated by optical delay setup to realize the time delay from pump pulse. The idler light emitted out of OPO can be taken as a backup for pump sources.

In our case, the original intense pulse coming out of the ultrafast laser (∼ 100 fs) is spilt into two beams by a 90/10 beam splitter. One beam is taken as the pump and the other as the probe after frequency-doubled in an OPO box. The large difference in frequency between the pump and probe allow us to clearly distinguish the Raman signal excited by the pump from the one by the probe. The orthogonal polarization configuration for the pump and the probe can further reduce the influence from the pump. The idler light emitted out of the OPO can be taken as a backup of pump sources, which effectively extends the frequency range of pump light. The optical delay setup consists of two motorized stages and two mirrors mounted on them. The programmable stages allow to be driven in a micrometer scale and hence can realize a precise time delay between the pump and probe (better than 50 fs).

Besides the ultrafast laser, the subsystem is also equipped with a broadband white light source developed very recently. It is particularly helpful for resonance studies. Therefore, we use the triple-grating spectrometer here (T64000), whose subtractive mode ideally matches the white light source.

Extreme conditions applied to this subsystem are quite similar to the ones for the CW Raman subsystem. Both systems have the similar optical inserts which is composed of many non-magnetic and low-thermal-expansion components like objective lens, precise XYZ stages and rotator. The maximum magnetic field here is 14 T rather than 9 T. It should be pointed out that high pressure up to 20 GPa is designed just to be applied to CW measurements using white light source. At present it is not clear if high pressure cell can work well with time-resolved measurements, since the Raman signal may be extremely weak in this case.

Now we can have a summary for the Raman facility. The extreme conditions applied to the facility include low temperature (4 K), high magnetic field (14 T), high pressure (20 GPa), and high time resolution (< 50 fs). In principles, one can combine one or more of these conditions to realize multi-dimensional Raman measurements and reveal novel condensed matter phases and excitations. According to the incident light source, the available Raman measurement modes can be divided into conventional CW Raman/photoluminescence mode, resonance mode and time-resolved mode. We put all these modes in the following table.

Table 1.

Table 1.

Table 1. Available measurement modes of SECUF Raman facility. . Measurement modes Extreme conditions simultaneously available Temperature/K Magnetic fields/T Pressure/GPa Time resolution/ps Conventional Raman/photoluminescence 4 9/14 20(LT)/100(RT) – Resonance Raman/photoluminescence 4 9/14 20(LT)/100(RT) – Time-resolved Raman/photoluminescence 4 9/14 – < 50

Table 1. Available measurement modes of SECUF Raman facility. .

Under compression most solids eventually undergo one or more structural phase transformations. The scope extends from drastic changes in volume, symmetry, and electronic properties to subtle shifts of lattice parameters. Raman scattering can catch the symmetry of a high-pressure phase through the assignment of new features and/or excitations. Thus, it has been widely applied to probe structural properties of solids under high pressures and to identify pressure-induced phase transitions.^[3–6] A good example is to resolve pressure-induced successive structural changes in bromine (iodine).^[7] Bromine shows a structural phase transformation from the molecular phase I to the intermediate phase V near 80 GPa (20 GPa for Iodine), and then to the monatomic phase II around 118 GPa (31 GPa for Iodine), as illustrated in Fig. 3(a).

Fig. 3.

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Fig. 3. (color online) (a) Crystal structures of three different phases. The open circles correspond to the parent structure without modulation (phase II). In phase I, there are two Raman active stretching ( , ) and librational ( , ) modes, while in phase V, only the amplitude (AMP) mode is Raman active. Raman spectra obtained for solid iodine up to 30 GPa (b) and for solid bromine up to 108 GPa (c), respectively. Open and closed circles correspond to X bands in phase I and new bands in phase V, respectively. Reprinted with permission from Ref. [7], copyright 2005 by the American Physical Society.

Figures 3(b) and 3(c) show Raman spectra obtained for iodine and bromine up to 30 and 108 GPa, respectively. In the low-pressure region (< 20 GPa for iodine and < 80 GPa for bromine), the spectra have five distinct bands, originating from two librational modes ( , ), two stretching modes ( , ), and an unassigned X band. With increasing pressure Raman spectra drastically change and a new band grows up at 23 GPa for iodine (80 GPa for bromine). This new band originates neither from monatomic phase II nor from molecular phase I, because phase II has no Raman active band, and phase I has not shown any band in this low-frequency region. On the other hand, for the incommensurate intermediate phase V, there are two types of characteristic vibrational modes,^[8] i.e., the amplitude mode (AMP, Fig. 3(a)) and the phase mode, and only the AMP mode is Raman active. Thus the new mode can be assigned to the AMP mode of phase V. This indicates a structural phase transformation from the molecular phase I to the intermediate phase V near 80 GPa for bromine (near 20 GPa for iodine).

The pressure dependence of the observed bands for iodine and bromine are shown in Figs. 4(a) and 4(b), respectively. The AMP modes show a softening behavior with increasing pressure and decreases to zero frequency at a critical pressure P_c. To estimate P_c, one can take a phenomenological function to fit the pressure dependence of the AMP mode frequencies. The fitting gives a P_c of 31 GPa for iodine (118 GPa for bromine). The zero frequency of AMP modes suggests another structural phase transformation from the intermediate phase V to the monatomic phase II near 118 GPa for bromine (near 31 GPa for iodine).

Fig. 4.

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	Fig. 4. Pressure dependence of vibrational frequencies of (a) solid iodine and (b) solid bromine, respectively. The dashed curves are the fitting results with a phenomenological function of . A critical pressure Pc at ω = 0 was obtained (31 and 118 GPa for iodine and bromine, respectively). Reprinted with permission from Ref. [7], copyright 2005 by the American Physical Society.

A more detailed discussion about the pressure-induced phase transformations in Bromine and Iodine is beyond the scope of this review, but the above results clearly demonstrate that Raman scattering is powerful to probe structural properties of solids under high pressures and to identify pressure-induced phase transitions.

In addition to the structural phase transition, pressure can also drastically alter the properties of the electronic subsystem and induce an electronic transition. This can be observed by electronic Raman scattering via light scattering from electronic fluctuations at Fermi surface. A nice demonstration is seen in Bi_1.98Sr_2.06Y_0.68Cu₂O_8+δ,^[9] a slightly doped (δ ∼ 0.03) and insulating parent compound of cuprates. Raman scattering studies reveal a pressure-tuned electronic phase transition at ∼ 21 GPa.

Figure 5(a) shows Raman spectra of Bi_1.98Sr_2.06Y_0.68 Cu₂O_8+δ at several pressures. The peaks at ∼ 340, ∼ 490, and ∼ 620 cm⁻¹ come from the out-of-phase vibrations of in-plane oxygen (B_1g “bond-buckling” mode), the oxygen vibration in the Bi–O block layer, and the vibration of apical oxygen.^[10] The oxygen vibration in the block layers remains nearly constant with pressure, while B_1g and the apical oxygen modes shift by over ∼ 100 cm⁻¹.

Fig. 5.

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Fig. 5. (color online) (a) Raman spectra obtained at ∼ 20 K under pressure. (b) Slope of linear electronic background from 200–300 cm−1 at ∼ 20 K. Spectra under pressure were normalized to the intensity at 850 cm−1. (c) Pressure dependence of electron–phonon coupling parameter λ obtained by fitting the B1g phonon using the theory of Ref. [12]. (d) Raman spectra of two-magnon peak at ∼ 20 K under pressure. The inset is the ratio of the integrated spectral weight below 1000 cm−1 to that above 1000 cm−1 for each pressure. Reprinted with permission from Ref. [9], copyright 2008 by the American Physical Society.

In general, Raman cross section is related to optical conductivity in the following way: χ″ (Ω) ∝ Ωσ′(Ω), and thus a change in optical conductivity causes a change of low-frequency linear background of Raman cross section. Figure 5(b) shows a linear fit of electronic background, which exhibits a sharp step at ∼ 21 GPa. Consistent with this change in the electronic background, electron–phonon coupling parameter λ (Fig. 5(c)) also shows a rapid increase at ∼ 21 GPa. Furthermore, the ratio of integrated spectral weight of two-magnon peak (inset of Fig. 5(d)) has a similar behavior at ∼ 21 GPa. The results indicate that an electronic phase transition in Bi_1.98Sr_2.06Y_0.68Cu₂O_8+δ occurs at ∼ 21 GPa.

On the other hand, two-magnon peak positions deviate from the power behavior (1/d_Cu−o)^α at ∼ 21 GPa (Fig. 6(a)), which has been observed in many other Mott–Hubbard insulators, such as K₂NiF₄.^[11] The derivative of two-magnon peak positions has a minimum at ∼ 21 GPa (inset of Fig. 6(a)), which is consistent with the maximum of the Grüneisen parameter at ∼ 21 GPa (inset of Figs. 6(b) and 6(c)). These anomalous behaviors further support the electronic phase transition in Bi_1.98Sr_2.06Y_0.68Cu₂O_8+δ at ∼ 21 GPa.

Fig. 6.

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Fig. 6. (color online) Two-magnon peak positions (a), B1g phonon frequencies (b), and apical phonon frequencies (c), at low (20 K) and high (300 K) temperatures versus the c-axis lattice density and pressure. The inset of panel (a) shows the derivative of fitting curve (dotted curve). Insets of panels (b) and (c) show the same derivative for phonons. Solid lines in panels (b) and (c) are guides to the eye, following the slope under low pressures. Reprinted with permission from Ref. [9], copyright 2008 by the American Physical Society.

The above example clearly demonstrates that electronic Raman scattering under high pressure is a sensitive probe for pressure-induced electronic phase transition.

In Bi_1.98Sr_2.06Y_0.68Cu₂O_8+δ, electronic phase transition is evidenced by electronic Raman signals. In fact, electronic information can also be obtained through its coupling to the lattice, i.e., phonons, particularly for the systems involving a strong electron–lattice coupling. Numerous studies have been conducted in this aspect.^[13–16] A good example is 1T-TiSe₂, which is a semimetal or small-gap semiconductor in the normal state and eventually develops into a commensurate CDW (inset of Fig. 7(a)) below a second-order phase transition near T_CDW ∼ 200 K.^[13]

Fig. 7.

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Fig. 7. (color online) (a) Temperature-dependent Raman spectra of TiSe2. The inset shows the displacement pattern associated with the CDW distortion, for Ti atoms (solid circles), Se atoms above Ti layer (open circles), and Se atoms below Ti layer (shaded circles). Pressure dependence of Raman spectra at T = 3.5 K for Eg CDW mode (b), A1g CDW and Eg optical phonon modes (c), and A1g optical phonon mode (d). The inset of panel (d) shows the pressure dependence of A1g (red circles) and A1g-CDW (blue squares) phonon linewidths (FWHM). Pressure dependence of peak energies (circles) and normalized intensities, I(P)/I(P = 0) (squares) at T = 3.5 K for A1g (e), Eg (f), A1g-CDW (g), and Eg-CDW (h) modes. The hatched lines denote rough boundaries between crystalline CDW, soft CDW, and disordered CDW regimes. Reprinted with permission from Ref. [13], copyright 2003 by the American Physical Society.

Figure 7(a) shows that the transition to CDW state in 1T-TiSe₂ results in several new modes, like E_g mode at ∼ 75 cm⁻¹ and A_1g mode at ∼ 115 cm⁻¹. The two modes soften dramatically as the temperature increases toward CDW transition temperature, indicating that the two modes are CDW-related “amplitude” modes, denoted as E_g-CDW and A_1g-CDW, respectively. A_1g-CDW mode reflects the fluctuations of CDW amplitude that preserves the symmetry of CDW ground state, while E_g-CDW mode involves out-of-phase fluctuations of CDW amplitude away from the ground-state symmetry. By tracking the pressure dependence of the mode energies, lifetimes, and intensities of the two phonons, one can get insight into the CDW state.

Figures 7(b)–7(d) show pressure-dependent Raman spectra of TiSe₂ at 3.5 K. The intensities of E_g-CDW and A_1g-CDW disappear above a critical pressure P* ∼ 25 kbar. The intensities of the modes serve as an order parameter of the CDW state, since CDW mode reflects fluctuations of the CDW state. The absence of the modes above P* suggests that the CDW phase in 1T-TiSe₂ collapses above 25 kbar. A detailed pressure study of the energies and intensities of the two modes reveals more regimes about the CDW state.

(i) Crystalline CDW regime. From P = 0 to 5 kbar, the intensity of A_1g-CDW slightly decreases, but its energy increases linearly with increasing pressure. This is similar to that of 203 cm⁻¹ and 134 cm⁻¹ modes (Figs. 7(e) and 7(f)), indicating that the CDW state remains commensurate with the lattice in this regime.

(ii) Soft CDW regime. From P = 5 to 25 kbar, A_1g-CDW mode exhibits a softening with a rapid decrease in intensity and linewidth (inset of Fig. 7(d)). The behaviors are substantially different from that of 203 cm⁻¹ and 134 cm⁻¹ phonon modes (Figs. 7(e) and 7(f)), suggesting that the charge density wave becomes incommensurate in this pressure regime.

(iii) Disordered CDW regime. Above 25 kbar, both E_g-CDW and A_1g-CDW modes are completely suppressed, which means that the CDW state has melted into a metallic or semi-metallic phase.

A detailed discussion on the pressure-induced phases of 1T-TiSe₂ is beyond the scope of this review. Anyway, the results shown here demonstrate that the Raman scattering high pressure is a powerful tool to study electronic phase transition through electron–phonon coupling.

The application of magnetic field to Raman scattering allows us to study a lot of magnetic systems, particularly spin-lattice coupling systems. Magnetic-field-dependent Raman scattering has been widely used to study structural phase transitions.^[17–23] Here a nice example is Mn₃O₄.^[17] Raman scattering under magnetic fields offers field-dependent structural phase diagrams, and many microscopic details of field-dependent phase changes.

Mn₃O₄ has a spinel structure, , which consists of two basic structural blocks, tetrahedra and octahedra (Fig. 8(a)). Below T_c = 43 K, Mn spins are ferrimagnetically ordered with Mn³⁺ spins antiparallel to [110] direction of tetrahedrally coordinated Mn²⁺ spins.^[24] Below T₂ = 33 K, Mn₃O₄ has a commensurate spin structure, in which the net Mn spins are oriented along the [110] direction and the magnetic unit cell is doubled.^[25] Figure 8(b) shows temperature dependence of ∼ 295 cm⁻¹ T_2g mode which is a triply degenerate mode associated with Mn–O bond-stretching vibrations of the ions at tetrahedral sites. From these spectra, one can find that T_2g mode splits into two modes near 290 cm⁻¹ and 300 cm⁻¹. The splitting is consistent with a tetragonal-to-monoclinic distortion below T₂ = 33 K, which removes the degeneracy of T_2g mode. The distortion expands Mn²⁺–O²⁻ bond length along the easy-axis [110] direction and decreases the energy for Mn–O vibrations in the [110] direction while it simultaneously contracts Mn²⁺–O²⁻ bond length along the easy-axis [1-10] direction and increases the energy for Mn–O vibrations along the direction. The high Raman intensity of the ∼ 300 cm⁻¹ mode suggests that the contracted Mn²⁺–O²⁻ bonds are oriented in the direction of incident light polarization [1-10]. It can be expected that if the ∼ 290 cm⁻¹ mode has a higher intensity, the expanded Mn²⁺–O²⁻ bond will be oriented along the [1-10] direction.

Fig. 8.

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Fig. 8. (color online) (a) Crystal structure of Mn3O4 in the low-field monoclinic phase (top), intermediate undistorted tetragonal phase (middle), and high-field monoclinic phases (bottom). (b) Temperature dependence of T2g Mn–O stretch mode, showing a mode splitting due to the removal of mode degeneracy from tetragonal II to monoclinic I transition. The inset shows an expanded view from 10 to 300 K. (c) Magnetic field dependence of T2g mode at T = 7 K, showing the field-induced phase changes for H ∥ [1-10]. Reprinted with permission from Ref. [17], copyright 2010 by the American Physical Society.

Figure 8 shows the field-dependent Raman spectra of Mn₃O₄ at T = 7 K and H ∥ [1-10]. The ∼ 300 cm⁻¹ mode has a higher intensity below H = 1 T, while between 1 T and 4 T, the ∼ 295 cm⁻¹ T_2g mode appears with a high intensity. Above H = 4 T, the ∼ 290 cm⁻¹ mode has a higher intensity. The results indicate that with increasing magnetic fields along [1-10] direction, Mn₃O₄ undergoes a structural phase transformation from the monoclinic (structure I) to tetragonal phase (structure I) at ∼ 1 T, and then to the monoclinic phase (structure III) at ∼ 4 T. The major difference between structure I and structure III is that the structure I has an expanded Mn²⁺–O²⁻ bond length along the [110] direction, while in structure III the expanded Mn²⁺–O²⁻ bond length is along the [1-10] direction (Fig. 8(a)). Such a difference reflects structural response to the competition between the internal field and applied transverse field, which tend to align the Mn moments along the [110] and [1-10] directions, respectively.

Electronic Raman scattering in metals results from electron–hole or multi-quasi-particle excitations around Fermi surface and may offer us charge and spin dynamics in different regions of Brillouin zone. For strongly correlated systems, incoherent quasiparticle scattering can usually lead to finite Raman intensity over a broad frequency range.^[26,27] For the superconducting cuprates a flat continuum extending to at least 2 eV has been observed. On the other hand, the opening of a superconducting gap, Δ(k), will result in the so-called 2Δ/pair-breaking peak^[28] in electronic Raman response due to the renormalization of the electronic continuum in the superconducting state. Thus, (i) the position of the 2Δ peak is proportional to a weighted average of the superconducting gap value; (ii) the peak intensity is proportional to the density of the superconducting condensate. When applying magnetic fields, Raman scattering can show us the field dependence of the 2Δ peak and get insight into the microscopic mechanism of superconductivity.^[29–31] Here we will see a nice demonstration in overdoped Tl₂Ba₂Cu₂O_6+Δ.^[29]

Figure 9(a) shows field-dependent Raman spectra of Tl₂Ba₂Cu₂O_6+Δ at T = 5 K. The pair-breaking peak is substantially suppressed by magnetic fields, and gives a nonlinear field dependence (Fig. 9(b)). Blumberg et al.^[29] attributed this behavior to a renormalization of density of states of quasiparticles near vortex cores. Through the field-dependent 2Δ-peak intensity at different temperature, one can obtain the effective critical field and its temperature dependence (inset of Fig. 9(b)). The temperature dependence is similar to that in the conventional superconductors, but in contrast to the anomalous temperature dependence of extracted from magnetoresistance measurements.^[32,33]

Fig. 9.

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Fig. 9. (a) Magnetic field dependence of electronic Raman scattering response in the superconducting state of overdoped Tl2Ba2Cu2O6+Δ. Magnetic field clearly suppresses pair-breaking peak. (b) Field and temperature dependence of pair-breaking peak intensity. Inset: temperature dependence of upper critical field, , obtained from Raman spectra. Reprinted with permission from Ref. [29], copyright 1997 by the American Physical Society.

Generally, external magnetic fields have two main effects that can be detected by Raman scattering. One is single spin effect, Zeeman splitting^[34–36] and the other one is energy band effect, the formation of Landau levels.^[37–39] Magnetic fields can continuously tune excitation energies and thus offer us an opportunity to manipulate multiple interactions. In the following we take Raman studies of Co[N(CN)₂]₂ under magnetic fields^[34] as a good example.

Figure 10(a) displays magneto-Raman spectra of Co[N(CN)₂]₂ in the low-frequency range. The peaks near 147 and 158 cm⁻¹ observed at zero field, originate from the wagging motions of Co-N_axC₍₂₎ and Co-N_eq(2). A new feature appears at ∼ 142 cm⁻¹ at 15 T, and it grows with increasing magnetic fields by transferring intensities from the 147 and 158 cm⁻¹ phonon modes. Its peak has a strong field dependence (Fig. 10(b)), pointing to either an electronic or magnetic origin. However, the position seems insensitive to Curie temperature (∼ 9 K) (Fig. 10(c)). This excludes the scenarios involving magnons. The authors^[34] assigned the feature as the Co²⁺ crystal-field excitation from the ground state Γ₆ level to the higher lying doublets of⁴T_1g term. The term moves with field as Zeeman effect comes into play (inset of Fig. 10(b)). Thus the following physical picture was proposed.

Fig. 10.

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Fig. 10. (color online) (a) Magneto-Raman spectra of Co[N(CN)2]2 at T = 5.5 K under magnetic fields up to 34 T. The strong field-dependent feature, assigned as a Co2+ electronic excitation, is marked with an asterisk. (b) Raman shift versus applied fields, showing the hybridized electronic and phonon excitations in Co[N(CN)2]2. The red curves are fitting results using the theory of Ref. [36]. The inset shows a schematic energy level diagram for Co2+ electronic states. The red (solid) arrow shows a plausible candidate for the 114 ± 5 cm−1 excitation in Raman spectra. (c) Temperature dependence of magneto-Raman spectra at 18.6 ± 0.1 T. Black (dashed) lines are peak fits tracking the behavior of Co2+ electronic excitations, which displays no sensitivity to Curie temperature ∼ 9 K. Reprinted with permission from Ref. [34], copyright 2013 by the American Physical Society.

At 0 T, the intensity of the crystal-field excitation is too low to be observed, and there are only two phonons located at 147 and 158 cm⁻¹. The excitation energy continuously increases with increasing magnetic fields due to Zeeman splitting. When the excitation energy is close to 147 cm⁻¹ phonon frequency, it will strongly interacts with the phonon mode and becomes observable by transferring intensity from the phonon mode. With further increasing magnetic fields, the electronic excitation moves close to and interacts with the second phonon mode, and repeats a similar behavior as the first one. In this process, the energies of the three modes can be well described by the crystal-field-phonon coupling theory (Fig. 10(b)).^[36] At larger field, the energy of the electronic excitation is even bigger than that of the second phonon and becomes unobservable.

In addition to the structural and electronic phase transition, Raman scattering is also an excellent technique for studying magnetic excitations,^[40–44] including one- and two-magnon excitations. As a combined application of low temperatures, magnetic fields, and pressure to light scattering studies of magnons, here we consider Ca₃Ru₂O₇,^[45,46] a bilayered, Ruddlesden-Popper-phase compound that exhibits a magnetic transition from a paramagnetic to an A-type antiferromagnetic state below T_N = 56 K, and a structural transition below T₀ ∼ 48 K.

As shown in Fig. 11(a), below T_N = 56 K, a sharp peak appears near 56 cm⁻¹ in Raman spectra of Ca₃Ru₂O₇. The mode can be assigned as magnon scattering for the following reasons: (i) the magnon mode energy increases with decreasing temperature below T_N (Fig. 11(b)), reflecting the increase in 〈S_z〉 of Ru⁴⁺ spin with decreasing temperature; (ii) the magnon mode linewidth increases dramatically with increasing temperature below T_N, as observed in numerous different antiferromagnets;^[48,49] (iii) the peak is observed only in the crossed scattering geometry ( ), consistent with theoretical expectations that magnon scattering involves off-diagonal terms in Raman tensors; (iv) the peak shows a clear Zeeman splitting when applied magnetic field H ∥ ab plane (Fig. 12(b)).

Fig. 11.

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Fig. 11. (color online) (a) Temperature dependence of magnon scattering in Ca3Ru2O7 (TN = 56 K). (b) Normalized frequency, ωo(T)/ωo(0) (squares), and linewidth, Γ (circles), as a function of normalized temperature, T/TN. (c) Pressure dependence of magnon mode in Ca3Ru2O7 at T = 3.5 K. (d) Magnon mode frequency (ωo) and linewidth (Γ) versus pressure, and evidence for a pressure-induced phase change above 46 kbar where no magnon scattering is observed. Reprinted with permission from Refs. [45] and [46], copyright 2006 by the American Physical Society.

Fig. 12.

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Fig. 12. (color online) Magnon scattering spectra of Ca3Ru2O7 at T = 11.5 K under applied magnetic fields parallel to the c-axis (a) and the a-axis (b). (c) Magnon energies versus magnetic fields for H ∥ c-axis (red diamonds) and H ∥ a-axis (blue circles). (d) Magnon energy in Ca3Ru2O7 as a function of magnetic-field orientations at T = 11.5 K. Reprinted with permission from Refs. [45] and [46], copyright 2006 by the American Physical Society.

Figure 11(c) shows the evolution of the magnon with pressure at 3.5 K and the pressure dependence of its frequency and linewidth is summarized in Fig. 11(d). Below P = 46 kbar, magnon frequency decreases with increasing pressure. This behavior is remarkably different from that observed in many Mott systems, in which magnon energy increases with increasing pressure.^[50–52] The difference reflects a slight decrease in the zero-field magnon energy. The magnon mode disappears above P = 46 kbar, suggesting the collapse of the antiferromagnetic state in Ca₃Ru₂O₇.

More interestingly, Raman spectra of the magnon mode has an anisotropic magnetic field dependence, as shown in Fig. 12. The magnon mode energy is field-independent for H ∥ c axis. However, for H ∥ ab plane, the magnon mode shows a splitting and the splitting energy changes with magnetic field direction in ab plane (Figs. 12(c) and 12(d)). The splitting reaches its maximum for H ∥ [110], suggesting that Ru spins are oriented at [110] direction (inset of Fig. 12(c)). The magnon modes collapse into a single mode at H_c = 5.9 T, suggesting a metamagnetic transition from A-type antiferromagnetic to ferromagnetic alignment.

The interplay between different excitations in condensed matter, like phonons, magnons, electron–hole excitations, etc., plays a crucial role in determining their physical properties. Optically induced excitations typically leads to the creation of excited electron–hole pairs, which relax to a thermal equilibrium state in a fast time scale. For a modest level of optically induced excitations, the process of electron–hole excitation and subsequent relaxation can be considered as a near-equilibrium phenomenon and the structural and electronic properties of materials do not change much. However, optically induced phase transitions may occur if the density of optically induced excitations is high enough. Here we will discuss an example, A7 semimetal antimony,^[53] which undergoes a structural phase transition when the pump excitation density exceeds 5 mJ/cm².

Most elemental metals crystallize into a cubic or hexagonal closed structure. Crystalline Sb may be described as a distorted simple cubic structure (Fig. 13(a)). The unusual structure stems from strong electron–phonon coupling in antimony. In one dimension, this type of distortion is the well-known Peierls distortion. As shown in Fig. 13(a), the distortion will open a gap at Fermi level and reduce the energy of electronic subsystem. The energy cost due to the structural distortion is compensated by the electronic energy gain and results in a net energy gain. Therefore, it is expected that a sufficiently high occupation of conduction band, realized by photo-excitation, will lead to a recovery of the undistorted cubic structure. The idea can be well examined by time-resolved Raman experiment, where the pump light is used to stimulate valence-band electrons and the structural information is detected through the probe light.

Fig. 13.

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Fig. 13. (color online) (a) Structure of A7 semimetals and photo-induced reversed Peierls transition. Photo-excitation reduces the population of valence bands, hence reducing the electronic energy gain of Peierls distortion, and driving the system toward the undistorted phase. (b) A1g phonon frequency in Sb measured at 15 ps after photo-excitation. The agreement between the model and the data indicates that electronic heat diffusion plays a minor role in the relaxation processes. (c) The symmetry reduction due to the photo-induced phase transition leads to the emergence of an additional phonon mode on the low-energy side of Ag mode for excitation densities larger than 5 mJ/cm2. Reprinted with permission from Ref. [53], copyright 2009 by the American Physical Society.

The difference between A7 and “cubic” structures is that (111) plane of A7 structure has an alternating displacement along the [111] direction. This corresponds to Raman active A_1g phonon mode (Fig. 13(a)), whose frequency is linearly proportional to the applied optical pump excitation density (Fig. 13(b)). The behavior is consistent with the calculated temperature dependence of this phonon frequency.^[54] More interestingly, a second mode is observed under the excitation density of pump laser exceeding 5 mJ/cm² (L2, Fig. 13(c)). The new mode reflects an optically induced structural phase transition. Surprisingly, the induced phase is not the expected simple cubic structure since there is no optical phonon in this structure, but rather a phase with symmetry lower than A7 structure. The observations suggest that the photo-induced phase might be understood in terms of an additional E_g distortion.

One of the most intriguing open problems in condensed matter is the origin of high-temperature superconductivity. So far, the superconducting phase has been widely studied at thermal equilibrium through numerous techniques. However, few experiments have been performed to investigate their non-equilibrium properties. The development of Ti:Sapphire pulsed laser makes it possible. It was proposed that time-resolved Raman spectroscopy can be employed to probe the non-equilibrium properties of high-temperature superconductors (HTSCs).^[55–57] The non-equilibrium properties in the superconducting phase has been first reported by Saichu et al.^[55] They studied the superconducting order parameter in slightly over-doped Bi₂Sr₂CaCu₂O_8+δ(Bi-2212, T_c = 82 K) and found two different coupling mechanisms that contribute equally to the pair-breaking peak.

Figure 14(a) displays Bose-factor-corrected steady state spectra between 100 and 600 cm⁻¹ in the normal and superconducting state of Bi-2212. In the normal state one can see a flat background, while in the superconducting state a pair-breaking peak develops at ∼ 420 cm⁻¹ ≃ 52 meV, which is the so-called 2Δ peak. Figure 14(b) displays three differential Raman spectra (i.e., I^1.65(ω) - I⁰(ω)) at 10 K as a function of delay time between pump and probe pulses. The contour plot of differential spectra are shown in Fig. 14(c). The high-energy wing of pair-breaking peak (above the dashed line in Fig. 14(c)) shows a fast decrease (2 ps), while the low-energy spectral weight (100–200 cm⁻¹) increases at roughly 3 ps, reflecting a spectral weight transfer from the pair-breaking peak to the sub-gap region upon photo-excitation. However, a closer observation leads one to conclude that the relaxation of the non-equilibrium state occurs in a nontrivial way and can be divided into two stages.

Fig. 14.

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Fig. 14. (color online) (a) Steady-state Raman spectra of Bi2Sr2CaCu2O8+δ in B1g geometry (in Porto notation z(xy)z, where z is perpendicular to the CuO planes) at 10 and 300 K. A gap opens below 250 cm−1 (blue area) and a pair-breaking peak appears around 420 cm−1 (red area). (b), (c) Temporal evolution of time-resolved differential Raman spectra at 10 K in B1g geometry. Three differential spectra at three delay times are shown in panel (b), while a contour plot consisting of 12 differential Raman spectra is presented in panel (c). The dashed line separates pair-breaking peak into two energy regions that have distinct characteristic behaviors. The change in intensity is colored. There is a transfer of spectral weight from high to low energies after 1 ps. Reprinted with permission from Ref. [55], copyright 2009 by the American Physical Society.

(i) The high-energy part of pair-breaking peak (∼ 420–600 cm⁻¹, above the dashed line in Fig. 14(c)), shows a fast (2 ps) decrease followed by a slow relaxation (7.4 ps). Saichu et al. suggested that this decay may be related to hole–phonon coupling via in-plane breathing mode.

(ii) At the same time, the low-energy part of pair-breaking peak (∼ 220–420 cm⁻¹ in Fig. 14(c)) starts to decay at 5 ps after photo-excitation, followed by a fast relaxation (1.4 ps). The authors argued that this behavior might be understood by a second coupling mechanism arising from hole–spin coupling.

The work by Saichu et al.^[55] have demonstrated that time-resolved Raman spectroscopy is an effective tool to probe the non-equilibrium electronic properties of HTSCs and shed light on the origin of superconductivity.