Manipulation and control of spin wave and spin flip are crucial for future developments of magnonic and spintronic devices. We present that the spin wave in hexagonal LuMnO3 single crystal can be selectively excited with laser polarization perpendicular to the c-axis of hexagonal LuMnO3 and photon energy ∼1.8 eV. The selective excitation of spin wave also suggests that the spin flip can be selectively controlled in hexagonal manganites. In addition, a microscopic model of the spin wave generation correlated with the four-spin-flip in hexagonal manganites is suggested to account for the line-shape of the observed spin wave.

Today's electronic devices operate on electron charge. Based on electron spin, a new generation of smaller, faster, and more efficient spintronic devices could be developed.1–5 Recently, the idea of magnonic devices, in which spin waves (magnons) are carrying information, has received increasing attention in the magnetics community.6–8 When developing spintronic and magnonic devices, it is crucial to control spin flip and spin wave. Therefore, understanding the mechanisms of spin wave and spin flip in magnetic materials and thus searching for convenient method to control spin wave and spin flip would be of great importance for future developments of magnonic and spintronic devices.

Hexagonal manganites RMnO3 (R = rare earth) belong to the class of multiferroic oxides, which possess coexisting magnetic and ferroelectric phases, with cross-correlation effects between magnetic and electric degrees of freedom.9–12 As such, they could potentially be used in applications of electric-controlled magnonic and spintronic devices. In this study, we present interesting selective excitation of spin wave in hexagonal LuMnO3 single crystal and suggest the mechanism of selective control of spin flip. Also, the physical origin of spin wave correlated with spin flip in hexagonal manganites is discussed.

Hexagonal LuMnO3 single crystal was grown using the traveling floating zone method. The characterizations of magnetization, resistivity, and X-ray powder diffraction have shown super crystalline quality of the single crystal sample. Polarized Raman scattering spectra were obtained in backscattering configuration with a Jobin-Yvon LabRam spectrometer. The single crystal sample was mounted in a helium closed cycle cryostat, and the sample temperature was cooled up to 20 K.

Figure 1 shows the Raman scattering spectra of hexagonal LuMnO3 single crystal obtained at 20 K under three different polarization configuration conditions. The narrow peaks ∼695 cm−1 and 650 cm−1 can be assigned to A1 and E1 phonon mode, respectively. The broad band ∼815 cm−1 would be originated from spin wave (magnon) scattering.13–15 An interesting feature of Fig. 1 is that the spin wave at ∼815 cm−1 shows unique polarization selection rule: the spin wave can be excited under z(yx)z¯ configuration, but not detectable under x(yz)x¯ and y(zx)y¯ configurations; i.e., the spin wave can be selectively excited with laser polarization parallel to the a-b plane of hexagonal manganites.

FIG. 1.

Raman spectra of hexagonal LuMnO3 single crystal at 20 K obtained in the z(yx)z¯, y(zx)y¯, and x(yz)x¯ configurations using 633 nm laser excitation.

FIG. 1.

Raman spectra of hexagonal LuMnO3 single crystal at 20 K obtained in the z(yx)z¯, y(zx)y¯, and x(yz)x¯ configurations using 633 nm laser excitation.

Close modal

The Néel temperature of hexagonal LuMnO3 single crystal is ∼90 K.16,17 Below Néel temperature, the spins of the Mn moments are aligned antiferromagnetically in the basal a-b plane of hexagonal manganites.17–19 In the z(yx)z¯ configuration, under which the spin wave can be selectively excited, the magnetic field of laser excitation is also in the a-b plane. Therefore, Fig. 1 may suggest that to excite spin wave scattering, magnetic field of laser excitation should be parallel to the plane of spin alignment.

In addition to the unique polarization selection rule, the spin wave of hexagonal manganites also exhibits unique resonance effect. Figure 2 shows the Raman scattering spectra of hexagonal LuMnO3 single crystal obtained at 20 K under z(yx)z¯ configuration with excitations of 633 nm red laser and 514 nm green laser. As can be seen in Fig. 2, the spin wave can be excited with 633 nm red laser, but not detectable with 514 nm green laser. This is consistent with our previous resonance study of spin wave in hexagonal HoMnO3 thin film, which showed that the spin wave can be excited with 647 and 671 nm red lasers, but not detectable with 532 nm green laser.13 There are two main optical transitions in hexagonal manganites: a sharp peak at ∼1.8 eV with linewidth ∼0.2 eV and a broad band centered at ∼5 eV with linewidth ∼2 eV.16,20 The unique resonance effect of spin wave would be correlated with the narrow optical transition ∼1.8 eV in hexagonal manganites.

FIG. 2.

Raman spectra of hexagonal LuMnO3 single crystal at 20 K obtained in the z(yx)z¯ configuration using 633 nm and 514 nm laser excitations.

FIG. 2.

Raman spectra of hexagonal LuMnO3 single crystal at 20 K obtained in the z(yx)z¯ configuration using 633 nm and 514 nm laser excitations.

Close modal

The studies of electronic structure of hexagonal manganites showed that the optical transition ∼1.8 eV is correlated with the on-site Mnd-d transitions: d(x2y2),(xy)d(3z2r2) (transitions between Mnd orbitals hybridized with oxygen orbitals, since pure d-d transitions are not allowed).16,20 It was reported that the on-site Mnd-d optical transitions are only allowed with Ec polarization of light; while in the case of Ec polarization of incident light, the optical matrix elements for the on-site Mnd-d transitions are zero.16 Therefore, the unique polarization selection rule of the spin wave observed in hexagonal LuMnO3 would also have a connection with the on-site Mnd-d transitions.

Among the three polarization configurations in Fig. 1, the x(yz)x¯ configuration has laser polarization of Ey and thus Hz, so that the spin wave could not be excited in this configuration. This further supports that the direction of the magnetic field of laser excitation should be parallel to the plane of spin alignment in order to excite spin wave scattering. Therefore, to excite spin wave in hexagonal manganites, not only the electric field of laser excitation should be perpendicular to the c axis, but the magnetic field of laser excitation should also be parallel to the plane of spin alignment. Under z(yx)z¯ configuration, Ec and Hab-plane; thus, spin wave can be excited. Under y(zx)y¯ configurations, Hab-plane but Ec; thus, spin wave cannot be excited. Under x(yz)x¯ configuration, Ec but Hz; thus, spin wave cannot be excited.

Figures 1 and 2 indicated that the excitation of spin wave in hexagonal manganites can be selectively controlled with on-site Mnd-d transition. This selective excitation of spin wave in hexagonal manganites would be very helpful for their future applications in magnonic devices. In addition, spin wave is originated by excitation of spin flip. The selective excitation of spin wave in hexagonal manganites would suggest that spin flip in hexagonal manganites could also be selectively controlled, which is crucial for developing spintronic devices. Furthermore, it would be important to understand what kind of spin flip is correlated with the observed spin wave, i.e., the physical origin of spin wave. In the following paragraphs, we will suggest the mechanism of spin flip and discuss the physical origin of spin wave in hexagonal manganites.

To understand the spin flip in hexagonal manganites, the knowledge of Mnd-d transition below Néel temperature would be helpful. The temperature dependent study of Mnd-d transition had shown that the transition has a blueshift of ∼0.1 eV with cooling in the antiferromagnetic state.16,20 Furthermore, Souchkov et al.16 suggested that this ∼0.1 eV magnetic-originated blueshift of the Mnd-d transition can be attributed to the differences in exchange interaction in the excited and ground states of a given Mn ion. The spin wave scattering in hexagonal manganite is observed ∼815 cm−1, i.e., hasan energy of ∼0.1 eV. This is in good agreement with the blueshift of the Mnd-d transition. The Heisenberg Hamiltonian model (to be discussed in the later part of this paper) indicated that the spin wave scattering at ∼815 cm−1 would be correlated with 4-spin-flip. Therefore, the ∼0.1 eV blue shift of Mnd-d transition in the antiferromagnetic state would be correlated with 4-spin-flip.

The above results and discussions suggest that the processes of spin flip, spin relaxing, and spin wave scattering in hexagonal manganites can be schematically represented, as shown in Fig. 3. In this figure, it is assumed that the 4-spin-flip occurs in one Mn3+ ion with all four electrons flipping spin. The positive direction is defined as the spin direction of the Mn3+ ion before spin flip, i.e., before spin flip ms = 2, and after spin flip ms = − 2. The energy difference of d(3z2r2) states with ms = 2 and ms = −2 drawn in Fig. 3 is only for indicating the energy of the spin-flipped Mn3+ ion interacting with its neighboring Mn3+ ions. It is not the energy difference of different magnetic states of a single Mn3+ ion.

FIG. 3.

Schematic energy diagram of a possible process of spin flip, spin relaxing, and spin wave scattering in hexagonal manganites.

FIG. 3.

Schematic energy diagram of a possible process of spin flip, spin relaxing, and spin wave scattering in hexagonal manganites.

Close modal

A microscopic picture of the model in Fig. 3 would be as following. In the ground state d(x2y2),(xy) of Mn3+ ion, four electrons occupy four lowest orbitals giving ms = 2. The state of d(x2y2),(xy) with ms = −2 is difficult to achieve, i.e., spin flip without d(x2y2),(xy)d(3z2r2) transition is difficult in the ground state d(x2y2),(xy). The spin flip is accompanied with resonant excitation of d(x2y2),(xy)d(3z2r2) transition, i.e., d(3z2r2) with ms = – 2 can be much more easily achieved. During the spin relaxing, the spin flipped Mn3+ ion interacts with the neighboring Mn3+ ions, which changes only the direction of neighboring spin vectors, and thus forming spin wave propagating in hexagonal manganites. The experimentally observed spin wave scattering in Figs. 1 and 2 would be originated from scattering of excited electronic states of d(3z2r2). In addition, Fig. 3 suggests that when resonantly pumped to excited states, spin wave scattering can be observed with non-resonance probe source. To verify the proposed model in Fig. 3, extensive experimental and theoretical studies would be needed.

In addition to the interesting selective excitation property of spin wave in hexagonal manganites, Figs. 1 and 2 also showed an abnormal observation. Due to the superb crystalline quality, the phonon mode of hexagonal LuMnO3 single crystal did show narrower linewidth than that of hexagonal HoMnO3 thin film. However, the spin wave of hexagonal LuMnO3 single crystal showed significantly broader linewidth than that of hexagonal HoMnO3 thin film. In addition, the spin wave of hexagonal LuMnO3 single crystal is much more asymmetric than that of hexagonal HoMnO3 thin film; shoulder peaks on both higher and lower energy sides were observed. A recent 2-Dimensional Correlation Spectroscopy study showed that the broad spin-wave band centered at ∼815 cm−1 of hexagonal LuMnO3 single crystal would be contributed by five individual peaks at 741, 783, 812, 839, and 872 cm−1.21 These indicate that the experimentally observed broad spin wave band in hexagonal manganites has complex multiple origins.

A simple method of understanding spin wave is to consider the spin exchange interaction Heisenberg Hamiltonian. Below Néel temperature, the spins of the Mn3+ ions forming triangular networks in the a-b plane in hexagonal manganite:9,17,22 each Mn3+ ion has two nearest neighbors and four next nearest neighbors. Thus, in the a-b plane, there are two exchange interactions J1 (nearest neighbor: intratrimer Mn-Mn interaction) and J2 (next nearest neighbor: intertrimer Mn-Mn interaction), and H=J1i,j(SiSj)+J2i,k(SiSk), where Si is the spin on site i, the summation on j is over the nearest-neighbor Mn3+ ion pairs and the summation on k is over the next-nearest-neighbor Mn3+ ion pairs. Neutron scattering experiments had estimated that J1 ≈ –4.1 meV and J2 ≈ –1.5 meV of hexagonal LuMnO3 single crystal.17 For spin wave scattering with four electrons flipping spin in one Mn3+ ion, the Heisenberg Hamiltonian model indicates that the energy of this 4-spin-flip spin wave scattering would be −16J1–32J2, i.e., ∼900 cm−1. This is in good agreement with the energy of the broad spin wave scattering in Figs. 1 and 2. Therefore, the broad spin wave band of 700–900 cm−1 would be mainly originated from 4-spin-flip process.

For multiple spin flip in the spin-network of magnetic ion with spin state ≥1, different types of multiple spin flip states are possible.23 In hexagonal manganites, the Mn3+ ions (spin state of S = 2) form triangular networks. Then, there would be five possible states of 4-spin-flip: i.e., (1) the 4-spin-flip occurs in one Mn3+ ion with all four electrons flipping spin, and this is the case proposed in Fig. 3; (2) the 4-spin-flip occurs in two neighboring Mn3+ ions with three electrons flipping spin in one Mn-ion and another one electron flipping spin in the neighboring Mn-ion; (3) the 4-spin-flip occurs in two neighboring Mn3+ ions with two electrons flipping spin in both Mn-ions; (4) the 4-spin-flip occurs in three neighboring Mn3+ ions with two electrons flipping spin in one Mn-ion and one electron flipping spin in both the neighboring Mn-ions; and (5) the 4-spin-flip occurs in four neighboring Mn3+ ions with one electron flipping spin in all the four Mn-ions. In single crystal, due to the super crystalline quality, all the above five possible states of 4-spin-flip could be observed. These five modes would have similar energy, but different scattering cross section. Thus, the observed 4-spin-flip spin wave scattering of hexagonal LuMnO3 single crystal would be a broad asymmetric band constituted by five individual peaks. This is in good agreement with the spin wave spectrum and 2-Dimentional Correlation Spectroscopy results. The 2-Dimentional Correlation Spectroscopy study showed five individual peaks at 741, 783, 812, 839, and 872 cm−1,21 and the observed broad spin wave band also indicated those five individual peaks, as indicated by solid lines in Fig. 4.

FIG. 4.

The broad spin wave band of hexagonal LuMnO3 single crystal is constituted by five individual peaks at 741, 783, 812, 839, and 872 cm−1. These peaks are not fitted; they are presented only for indicating the possible origins of the broad spin wave band.

FIG. 4.

The broad spin wave band of hexagonal LuMnO3 single crystal is constituted by five individual peaks at 741, 783, 812, 839, and 872 cm−1. These peaks are not fitted; they are presented only for indicating the possible origins of the broad spin wave band.

Close modal

The Heisenberg Hamiltonian model suggests that the frequency of the five possible states of 4-spin-flip spin wave decreases systematically from (1) to (5). The Raman experiments indicate that mode (3) has the highest scattering intensity. This suggests that the 4-spin-flip process of two neighboring Mn3+ ions with two spin flip in both ions would have the highest probability. In thin films, this mode would have the major contribution to the spin wave scattering. Thus, the observed spin wave in thin film has much narrower linewidth and is much more symmetric than the spin wave in single crystal. A systematic comparison study of pressure-dependent Raman, magnetic-field dependent Raman, and resonance-effect-dependent Raman of spin wave scattering between single crystal and thin film would be very helpful for further understanding the physical origins of spin wave in hexagonal manganites.

In conclusion, we presented that the excitation of spin wave in hexagonal manganites can be selectively controlled with on-site Mnd-d transition. This property of spin wave in hexagonal manganites would be very helpful for their future applications in magnonic devices. The selective excitation of spin wave also indicated that the spin flip in hexagonal manganites could be selectively controlled, and the processes of spin flip, spin relaxing, and spin wave scattering in hexagonal manganites were proposed. In addition, we suggested a microscopic model to describe the physical origin of spin wave correlated with spin flip in hexagonal manganites.

X. B. Chen acknowledges the support by the National Natural Science Foundation of China (Grant No. 11574241). I. S. Yang acknowledges the support by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2015001948). X. Wang and S. W. Cheong are supported by the DOE under Grant No. DE-FG02-07ER46382.

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