Energy-Resolved Ultrafast Spectroscopic Investigation on the Spin-Coupled Electronic States in Multiferroic Hexagonal HoMnO3.

A complete temperature-dependent scheme of the Mn3+ on-site d-d transitions in multiferroic hexagonal HoMnO3 (h-HoMnO3) thin films was unveiled by energy-resolved ultrafast spectroscopy. The results unambiguously revealed that the ultrafast responses of the e1g and e2g states differed significantly in the hexagonal HoMnO3. We demonstrated that the short-range antiferromagnetic and ferroelectric orderings are more relevant to the e2g state, whereas the long-range antiferromagnetic ordering is intimately coupled to both the e2g and e1g states. Moreover, the primary thermalization times of the e2g and e1g states were 0.34 ± 0.08 ps and 0.38 ± 0.08 ps, respectively.

1. Introduction

The emergent physical properties resulting from the coupled ferroic orders in multiferroic manganites and their potential applications have attracted considerable research interest [1,2]. In rare-earth manganites, hexagonal RMnO3 structures with small R3+ ions (In, Sc, Y, and the lanthanum atoms from Dy to Lu) exhibit coexisting coupled ferroelectric (FE) and antiferromagnetic (AFM) orders [3,4]. In hexagonal HoMnO3 (h-HoMnO3), ferroelectricity occurs below the Curie temperature TC (870 K) because structural distortion takes place during the transition from the P63/mmc to the P63cm symmetry, as well as the polarization associated with the bonds of Ho and planar oxygen [5]. In P63cm hexagonal manganites, each ion is surrounded by five ions, forming triangular planar sub-lattices in the basal plane (ab-plane). The magnetic order of is mainly dominated by antiferromagnetic planar superexchange interactions [6,7]. The AFM spin ordering on the high-spin Mn3+ ions occur at the Néel temperature TN (76 K). The symmetry of the short-range AFM order of the hexagonal HoMnO3 has been derived by second harmonic generation (SHG). Below TN, the symmetry of the AFM phase is P63cm and experiences a sudden rotation by an angle of 90° to P63cm at around 40 K [8].

Hexagonal HoMnO3 structures comprise layers of bipyramid MnO5 separated by layers of Ho3+ ions along the c-axis. The Mn3+ ions are located near the center of the MnO5 bipyramids, forming triangular planar sublattices along the ab-plane. Because of the crystal field of the bipyramid structure, the 3d-orbit state of the Mn3+ ions split into lower-lying doublet states e1g (/) and e2g (/) and an upper-lying singlet state a1g () [9], as shown in the inset of Figure 1. Therefore, the four d electrons of Mn3+ in the ground state occupy e1g and e2g and leave a1g vacant. Previous studies have determined the band structure of the Mn3+ d orbits in RMnO3 (R = Gd, Tb, Dy, Ho, Er, and Lu) by using optical absorption spectroscopy [9,10,11,12,13]. The absorption spectrum exhibits two peaks around 1.7 and 2.2 eV corresponding to the transitions from e2g to a1g and e1g to a1g, respectively, in the on-site Mn3+. In addition, the short-range AFM ordering leads to a blue shift in the absorption peaks as the temperature decreases, which further induces a marked change near TN. The indirect exchange interactions, including double-exchange [14], superexchange [15], and super-superexchange [6], play a key role in explaining the spin-ordering in manganite [16]. Specifically, the magnetic exchange interaction between the Mn3+ ions induce the anomalous shift of Mn d levels, indicating a strong correlation between the electronic structure and spin ordering [10,12]. Moreover, in addition to hexagonal manganites exhibiting large atomic displacements at TN [17,18], the optical phonon frequency also shows an unexpected shift because of the magnetic ordering [19,20,21]. The large atomic displacements combined with phonon anomalies further demonstrate the coupling between the magnetic order and electric dipole moments through the lattice. Accordingly, multiferroic manganites exhibit an intimate coupling between the charge, lattice, and spin degrees of freedom.

Figure 1

Stationary absorption spectrum of a hexagonal HoMnO3 thin film and the laser spectrum used in this study. The inset shows the electronic levels of the five-fold coordinated Mn3+ ion in the MnO5 trigonal bipyramidal field of the five surrounding O2− ligands.

Time-resolved optical pump-probe spectroscopy is effective for demonstrating and quantifying the interaction strength among quasiparticles and various degrees of freedom [22,23,24,25,26]. This technique has been extensively employed to identify the underlying physical mechanisms of hexagonal manganites [27,28,29,30,31]. However, most previous studies on transient spectroscopy have focused only on the dynamics of the e2g state, and the other unobservable Mn3+ d orbits remain unclear. In the present study, we adopted an advanced ultrafast spectroscopy technique that involved using a broadband and ultrashort pulse laser to comprehensively examine the complete temperature-dependent scheme of the Mn3+ on-site d-d transitions in rare-earth multiferroic hexagonal manganite HoMnO3.

2. Materials and Methods

The samples used in this study were hexagonal c-axis HoMnO3 thin films with a thickness of 180 nm. The films were deposited on double-sided polished yttria-stabilized zirconia (111) substrates through pulsed-laser (KrF excimer laser) deposition [28]. The thin films were employed to measure both the stationary and transient spectra in a transmissivity configuration to obtain high-quality data. Figure 1 shows the stationary absorption spectrum of the hexagonal HoMnO3 thin film measured at room temperature. The absorption spectrum clearly shows the Mn3+ d-d transition around 1.7 eV (e2g to a1g, Edd2) and 2.2 eV (e1g to a1g, Edd1). The transition peak centered at about 1.7 eV is consistent with previous optical absorption spectra in hexagonal-phase RMnO3 (R = Gd, Tb, Dy, Ho, Er, and Lu) [9,10,11,12,13]. The other hidden d-d transition around 2.2 eV, which is embedded in the substantially more intense absorption peak, was verified using second-harmonic generation [8,13,32]. To simultaneously reveal the strongly AFM- and temperature-dependent Mn3+ d-d transitions (i.e., Edd1 and Edd2), a light source with a broad spectrum in the visible range is required [33]. The time-resolved spectroscopic measurements in this study were based on 10 fs visible pulses generated by a noncollinear optical parametric amplifier (NOPA) [34,35]. A generative amplifier (800 nm, 5 kHz, 1.8 W, Legend-USP-HE; Coherent, Santa Clara, CA, USA) seeded with a Ti:sapphire laser oscillator (Micra 10; Coherent) was used as the pump source of the NOPA. Figure 1 shows that the laser spectrum (1.7–2.3 eV) covered the targeted whole Mn3+ d-d transition bands. For the pump-probe measurements, a beam splitter splits the visible pulses into pump and probe beams with the same spectrum. The fluences of pump and probe were 0.85 and 0.07 mJ/cm2, respectively, and focused on the samples. The normalized transient transmittance changes ΔT/T (ΔT: the transmittance changes induced by the pump pulses; T: the transmittance of the probe pulses) spectra were captured using a wavelength-resolved multichannel lock-in amplifier as a function of delay time between pump and probe pulses [36].

3. Results and Discussion

Figure 2a,b display the two-dimensional (2D) plots of the relative transient transmittance change (ΔT/T) spectra as functions of the probe photon energy and delay time at temperatures above (T = 100 K) and below (T = 35 K) TN. In the 2D plots, the black lines represent the borders of the positive and negative components of the ΔT/T(υ, t) signals. The temperature dependence of the positive ΔT/T signal in the range of approximately 1.7–2.3 eV was attributed to photobleaching resulting from the depletion of the initial state and the population of the excited state, indicating the d-d transitions of Edd1 and Edd2. As a result, the energy dependence of the positive ΔT/T signals (in Figure 2c) is similar to that of the stationary absorption spectrum shown in Figure 1. By contrast, the induced absorption to the higher excited states resulted in a negative ΔT/T signal in the blocked-photon energy range, which did not correspond to the on-site Mn3+ d-d transition bands. Therefore, the zero-amplitude position distinctly indicated the boundary of the d-d transitions Edd1 and Edd2 as the solid black lines in Figure 2a,b. The transition band edges Edd1 and Edd2 were extracted to further investigate the transient dynamics of the Mn3+ d bands at various temperatures, as shown in Figure 3, and both transition bands Edd1 and Edd2 clearly exhibited blue shift when the temperature decreased. Furthermore, in addition to the monotonic blue shift, the transient curves revealed the significant characteristics within the short period at temperatures below TN.

Figure 2

(a,b) Two-dimensional plots of the transient difference transmittance ΔT/T at temperatures below (35 K) and above (100 K) TN. (c) Time-resolved ΔT/T spectra at different delay time between the pump and probe pulses at 35 K (blue) and 100 K (red). The horizontal gray lines show where ΔT/T = 0. The solid and hollow dots represent the boundary of d-d transitions, and the solid and hollow dots respectively indicate the time-resolved Edd2 (e2g → a1g) and Edd1 (e1g → a1g) transitions. The dashed lines are guides for eyes to represent the time evolution of these transitions.

Figure 3

Time evolution of Mn3+ on-site d-d transition of (a) Edd1 (e1g → a1g) and (b) Edd2 (e2g → a1g) at different temperatures.

The time-resolved traces of Edd1(t) and Edd2(t) at each photon energy level can be phenomenologically expressed as where E is the amplitude of the exponential function, and τ represents the relaxation time for the corresponding component. Figure 4 shows the fitting results (for the detailed fitting results, please see Table S1 in Supplementary Materials). The constant term Econst in Figure 4c,f indicates the transition energy level after thermal equilibrium was reached. In consistence with the temperature-dependent stationary absorption spectra in previous studies [10,12], the transition energies shifted and exhibited an anomaly at TN. In Edd2 (see Figure 4d,e), both the amplitudes (E1 and E2) and time constants (τ1 = 0.38 ± 0.08 ps and 0.95 ± 0.50 ps; τ2 = 2.40 ± 0.40 ps and 5.90 ± 0.70 ps; below and above TN, respectively) exhibited noticeable changes across TN. On the other hand, the time-dependent Edd1 (see Figure 4a,b) differed markedly at temperatures above and below TN. The fast component (0.34 ± 0.08 fs) was observed only at temperatures below TN, whereas the slow component (2.00 ± 0.60 ps) was preserved at all of the measured temperatures.

Figure 4

Fitting results of the Edd1 (e1g → a1g) and Edd2 (e2g → a1g) spectra in Figure 3 obtained by using Equation (1). (a,d) Amplitudes E1 and E2, (b,e) relaxation times and of Edd1 and Edd2 spectra at various temperatures. (c,f) The constant term of Equation (1) for the energy relaxations in Edd1 and Edd2 spectra. The black dashed lines indicate TN.

The assignment of the relaxation components in multiferroic materials has been a challenging subject for decades because of the complicated correlations among the electron, lattice, charge polarization, and AFM spin ordering. A previous study [37] attributed a relaxation time of approximately 0.4 ps to phonon thermalization. On the same time scale, Satoh et al. [38] assigned a relaxation time of approximately 0.9 ps to the demagnetization of AFM compounds. Additionally, previous studies have attributed the few-ps component to electron-lattice relaxation [39,40] or spin-lattice relaxation [28]. In this paper, we propose a model based on our results as well as those from previous studies. The few-ps component occurred in both Edd1 and Edd2 at all of the measured temperatures. Thus, the few-ps component could be attributed to the relaxation of the excited carriers in a1g, which is the final state of both Edd1 and Edd2 transitions from the initial states and , respectively. The excited electrons relaxed to the bottom of a1g and banded through the electron–phonon coupling with a few-ps relaxation time, and the transition band exhibited a blue shift induced by the disappearance of the renormalization of the bandgap [41]. This has also been observed in other manganites [27,42]. The significant changes in the amplitudes and relaxation time across TN indicate an intimate correlation among the electron, lattice, and spin, which corresponds to the sudden shift in the positions of relevant atoms [17,18] and the anomaly in the Raman spectra [19,20] at the spin-ordering temperature.

In contrast, the sub-ps component cannot be assigned to population relaxation in the common final state because it exists only in Edd2 at high temperatures, as shown in Figure 4b,e. Therefore, the sub-ps component in Edd1 and Edd2 are ascribed to the relaxation in e1g and e2g, respectively. The e2g state comprises the and orbits, which lie on the basal plane. These orbits are strongly hybridized with the planar oxygen of the bipyramid structure, indicating a close correlation with the charge-ordering characteristic of the geometric ferroelectricity. Below the FE transition temperature (TC = 870 K in HoMnO3), the FE moment is along the c-axis between the rare-earth ion (Ho3+ in this case) and the planar oxygen on the distorted trigonal bipyramid MnO5 [5]. Accordingly, the sub-ps lifetime is considered to correlate with the destruction of the FE state. Besides, the superexchange in the planar Mn-O-Mn chain combined with the magnetoelastic coupling [17,18] modifies the e2g state and induces a significant difference in both the amplitude and lifetime (including and in Figure 4d,e) of the pump-probe spectra across TN, particularly for the sub-ps component exhibiting the magnetoelectric coupling. Moreover, this sub-ps (0.38 ± 0.08 ps and 0.95 ± 0.50 ps below and above TN, respectively) component, which is associated with spin ordering, can be observed at temperatures far above TN, indicating that the e2g state essentially couples with the short-range AFM spin ordering, which cannot be reliably obtained from standard magnetization measurements. This is in consistence with the previous results of stationary absorption spectra [9,10,11,12] and our time-resolve spectroscopies [29,31], which have demonstrated that the e2g state is highly sensitive to short- and long-range AFM spin ordering.

However, the sub-ps component can be observed only in the presence of long-range spin ordering in the e1g state (Figure 4b). The e1g state comprises and , which are not as sensitive to the planar oxygen as the e2g state. The time-dependent Edd1 shows significant larger fluctuations at temperatures above TN in Figure 3a. According to a previous study [43] on PL, the electronic transfer from a1g to e1g was strongly blocked by spin fluctuations at temperatures above TN, indicating that the Edd1 is dominated by long-range AFM spin ordering. Therefore, the spin-e1g orbit interaction was attributed as the main contributor to the sub-ps component in the e1g state [44]. Furthermore, the temperature dependence of the Raman-active phonons, inducing anharmonicity in the A1 phonon mode (which is the oxygen vibrate along the c-axis) below TN, indicates that the spin-orbit interaction is strongly influenced by the anisotropic superexchange between the Mn3+ and Ho3+ ions and the super-superexchange of Mn-O-O-Mn along the c-axis [19,45,46]. This component (0.34 ± 0.08 ps) can be ascribed to the thermalization of the spin subsystem in the e1g state.

4. Conclusions

In summary, we have demonstrated that the Mn3+ d orbit electronic states are strongly affected by the electric–magnetic coupling in multiferroic h-HoMnO3 thin films. The 2D energy- and time-resolved spectroscopy measurements carried out at various temperatures have unambiguously disclosed the characteristics of Mn3+ d orbits. Short-range AFM spin ordering and FE ordering are related to the e2g state. By contrast, long-range AFM spin ordering is strongly coupled to both the e2g and e1g states. The slow electron–phonon relaxation time in the a1g state is 2.70 ± 1.50 ps. Moreover, the depolarization time in the e2g state above TN is 0.95 ± 0.50 ps, and an anomaly is observed at the AFM spin-ordering temperature, further shortening of the fast relaxation time to 0.38 ± 0.08 ps. In addition, the fast spin-thermalization time caused by the spin-orbit (dyz and dzx orbits) interaction in the e1g state is 0.34 ± 0.08 ps. Therefore, this study has demonstrated that magnetic ordering in HoMnO3 intimately coupled with the electronic structure of both the e1g and e2g states, respectively, can be investigated using the proposed energy-resolved ultrafast spectroscopy technique.