We have conducted a terahertz spectroscopic study of antiferromagnetic resonances in bulk orthoferrite YFe1−xMnxO30x0.4. Both the quasi-ferromagnetic resonance mode and the quasi-antiferromagnetic resonance mode in the weak ferromagnetic Γ4 phase disappear near the spin reorientation temperature, TSR, for the onset of the collinear antiferromagnetic Γ1 phase (x  0.1). Below TSR, an antiferromagnetic resonance mode emerges and exhibits a large blueshift with decreasing temperature. However, below 50 K, this mode softens considerably, and this tendency becomes stronger with Mn doping. We provide a deeper understanding of such behaviors of the antiferromagnetic resonance modes in terms of the influence of the Mn3+ ions on the magnetocrystalline anisotropy. Our results show that terahertz time-domain spectroscopy is a useful, complementary tool in tracking magnetic transitions and probing the interaction between disparate magnetic subsystems in antiferromagnetic materials with multiple ionic species.

Rare-earth orthoferrites RFeO3, where R is a rare-earth, with the orthorhombic perovskite structure (space group Pbnm) have been investigated extensively as a representative multiferroic system.1–3 In particular, YFeO3 with nonmagnetic Y3+ has been studied as a reference phase, in which the magnetic activity is solely due to Fe3+ ions.4 YFeO3 undergoes a magnetic transition from the high-temperature paramagnetic phase into the low-temperature antiferromagnetic Γ4 phase at the Néel temperature of TN = 650 K.5 In this antiferromagnetic phase, the Fe3+ spins align essentially along the a axis, but the residual Dzyaloshinskii–Moriya (DM) interaction induces canting of the Fe3+ spins, which leads to weak ferromagnetism (WFM) along the c axis.2,6 This Γ4(Ga, Ab, Fc) phase is believed to prevail at all temperatures below TN, and YFeO3 goes through a spin-reorientation transition (SRT) only in the presence of an external magnetic field along the a axis.7 Such features of YFeO3 have been studied by various techniques including magnetometry,8 neutron scattering,9 Raman spectroscopy,10 and terahertz spectroscopy.11–13 

Extensions to the cases, where R is a magnetic rare-earth, have been explored, especially in the interest of looking for an interplay of competing magnetic orders of Fe3+ ions and R ions, which led to the discovery of R-dependent spin-reorientation phenomena.5,14,15 Interestingly, doping transition metal ions into the Fe3+ sites has been attempted as well as a means to disrupt the prevailing antiferromagnetic order supported by the Fe3+ ions and thereby to induce a spin-reoriented phase.16,17 In fact, it has been reported that Mn substitution of Fe leads to the Morin-type SRT from Γ4(Ga, Ab, Fc) to the collinear antiferromagnetic phase Γ1(Gb, Aa, Cc).18,19 Apart from a few studies of this kind, not much is known about the effect of Mn substitution and its physical ramifications. Therefore, further in-depth study of the YFe1−xMnxO3 system can add an exciting facet to the ongoing study of magnetism in the RFeO3 materials family.

Here, we present our terahertz spectroscopic study of YFe1−xMnxO3 (x = 0–0.4), focusing on the antiferromagnetic resonance modes and their temperature and Mn doping dependence. Our terahertz time-domain spectroscopy (THz-TDS) measurement can locate the phase boundary separating the Γ4 and Γ1 phases by tracking the antiferromagnetic resonance modes over wide ranges of temperature and Mn doping. From such data, we can access the changes in the magnetic dynamics across the phase transition and hence gain much insight into the role of Mn doping that alters the underlying antiferromagnetic order and drives the transition. In this way, the terahertz technique provides a useful means to study the antiferromagnetic resonances, complementing Raman spectroscopy and neutron scattering techniques. While the latter two techniques can yield equivalent data with similar energy resolution and bulk sensitivity, studies on Mn doped YFeO3 employing those tools are yet to be carried out.

Polycrystalline YFe1−xMnxO3 (x = 0–0.4) compounds were synthesized by a conventional solid state reaction method. A stoichiometric mixture of Y2O3 (99.98% Alfa Aesar), Fe2O3 (99.998% Alfa Aesar), and MnO2 (99.997% Alfa Aesar) powders was ground by using a pestle in a corundum mortar, followed by pelletizing and calcining at 1100 °C for 5 h. The calcined pellet was reground and sintered at 1200 °C for 12 h. The compound was again finely reground and then sintered at 1300 °C for 30 h and cooled to room temperature at a rate of 100 °C/h. The crystallographic structure of the YFe1−xMnxO3 samples was confirmed by using an x-ray diffractometer (Ultima IV, Rigaku) with Cu-Kα radiation. The temperature and magnetic field dependences of DC magnetization were examined by a vibrating sample magnetometer for temperatures of 2–300 K and magnetic fields of −9 to 9 T by using a physical properties measurement system (PPMS, Quantum Design, Inc.).

Our terahertz transmission measurements were conducted on a Teraview TPS3000 (Teraview Ltd., UK) in the frequency range of 0.1–3 THz with the sample temperature controlled over the range of 4–300 K by a helium-free optical cryostat (Cryostation, Montana Instruments, Ltd., USA). All measurements were carried out in dry nitrogen or in vacuum to remove the water-vapor absorption. For transmission measurements, the samples were attached to a holder with a 3 mm hole by using silver paste. Our THz-TDS technique yielded raw data in the form of time-dependent waveforms of electric fields, and these were converted into complex-valued functions of frequency through the fast Fourier transform (FFT). The absorption coefficient α was then extracted from the absolute-squared transmission coefficient t2 via the usual formula α=1/dlnt2, where d is the thickness of the sample.

The phase diagram of YFe1−xMnxO3 (x = 0–0.45) is shown in Fig. 1(a). The values of the Néel temperature (TN) and the spin reorientation temperature (TSR) for x = 0–0.45 were obtained from Ref. 18, where the spin reorientation under consideration here was reported earlier according to their neutron diffraction work. Below TN and above TSR, the Fe3+ spins exhibit WFM due to the weak ferromagnetic moment formed by the Fe3+ spins slightly tilted along the c axis. As seen in Fig. 1(b), this magnetic structure is denoted as the Γ4(Ga, Ab, Fc) phase. For 0.1 ≤ x ≤ 0.4, we observe a spin reorientation transition from the Γ4 phase to the Γ1(Gb, Aa, Cc) phase [Fig. 1(c)]. This transition is known to be the Morin type according to Stanislavchuk et al.20 Specifically, the anisotropy energy of Mn3+ ions was invoked by Mandal et al. in Ref. 18 to explain the reorientation of Fe spins. The subsequent loss of WFM was explained by Gorodetsky et al. in terms of the change of the easy axis from perpendicular to parallel orientation with respect to the DM vector.21 Here, the net moment of two nearly parallel Fe3+ spins [S1 and S3 in Fig. 1(c)] is antiparallel to that of the other two such spins [S2 and S4 in Fig. 1(c)]. This collinear antiferromagnetic Γ1 phase occurs at higher TSR as the doping x increases. Above x = 0.5, the Γ1 phase loses its homogeneity, beginning to mix with a hexagonal phase.22 The substantial difference in the magnetic structures of the Γ4 and Γ1 phases manifests itself in the antiferromagnetic resonance spectra as revealed by terahertz spectroscopy.

FIG. 1.

Phase diagram and magnetic structure of Mn doped YFeO3. (a) Néel and spin reorientation temperatures as a function of Mn doping x are shown by the blue and red lines, respectively. The blue and red solid circles were obtained from Ref. 18. The solid lines represent guides to the eye. Insets show four sublattice spin structures of Fe3+ spins. (b) The spins are antiferromagnetically ordered along the a axis and slightly canted along the b axis, generating WFM (Γ4 phase). (c) The spins are antiferromagnetically oriented along the c axis (Γ1 phase). WFM is absent in this phase.

FIG. 1.

Phase diagram and magnetic structure of Mn doped YFeO3. (a) Néel and spin reorientation temperatures as a function of Mn doping x are shown by the blue and red lines, respectively. The blue and red solid circles were obtained from Ref. 18. The solid lines represent guides to the eye. Insets show four sublattice spin structures of Fe3+ spins. (b) The spins are antiferromagnetically ordered along the a axis and slightly canted along the b axis, generating WFM (Γ4 phase). (c) The spins are antiferromagnetically oriented along the c axis (Γ1 phase). WFM is absent in this phase.

Close modal

Figure 2 shows representative absorption spectra observed in our YFe1−xMnxO3 samples in the Γ4 and Γ1 phases at 4 K. In the Γ4 phase at 4 K of Fig. 2(a), three peaks were detected in agreement with a previous report.13 The main excitations of our interest are the quasi-ferromagnetic resonance (qFMR) mode at 11 cm−1 and the quasi-antiferromagnetic resonance (qAFMR) mode at 19.5 cm−1, which are detected commonly in most WFM ferrites.10 The two modes can be interpreted, respectively, as a precession and a vibration of the WFM moment.23 In principle, these two modes are subject to optical selection rules, but our polycrystalline samples conveniently display both modes for easy tracking of their frequencies and temperature dependence. The sharp peak at 9 cm−1 is known as an impurity mode.24 On the other hand, only one broad peak was detected in the Γ1 phase. This particular antiferromagnetic resonance (AFMR) mode has never been reported in doped rare-earth orthoferrites in the Γ1 phase. In the absence of WFM, this mode is the only antiferromagnetic resonance mode in an easy-plane antiferromagnet (in the absence of an external field).25 

FIG. 2.

Antiferromagnetic resonance modes of Mn doped YFeO3. (a) Absorption spectrum observed in pristine YFeO3 at 4 K in the Γ4 phase. Two resonance modes corresponding to the qFMR and qAFMR modes were found at 11 and 19.5 cm−1. The impurity peak is marked with a star (see the text). (b) Absorption spectrum observed in YFe0.8Mn0.2O3 at 4 K in the Γ1 phase. Only a single AFMR mode was observed at 15 cm−1.

FIG. 2.

Antiferromagnetic resonance modes of Mn doped YFeO3. (a) Absorption spectrum observed in pristine YFeO3 at 4 K in the Γ4 phase. Two resonance modes corresponding to the qFMR and qAFMR modes were found at 11 and 19.5 cm−1. The impurity peak is marked with a star (see the text). (b) Absorption spectrum observed in YFe0.8Mn0.2O3 at 4 K in the Γ1 phase. Only a single AFMR mode was observed at 15 cm−1.

Close modal

We now discuss the temperature and doping dependence of the antiferromagnetic resonance modes observed in our series of YFe1−xMnxO3 samples. Figure 3 presents a series of contour plots of the absorption coefficients as functions of temperature (4–295 K) and Mn doping (x = 0–0.4). Within the Γ4 phase, we observe both qFMR and qAFMR modes. These modes are located at 10 and 17.5 cm−1 in pristine YFeO3 at 295 K and show a clear change with Mn doping x. Both the qFMR and the qAFMR modes show a marked change across the spin reorientation transition. In fact, both modes redshift substantially as Mn doping increases. The redshift is stronger in the qAFMR mode, and it even disappears well above TSR as x increases. Already at x = 0.15, the mode moves out of the temperature range of our measurement [Fig. 3(e)]. Interestingly, while the qAFMR mode moves out of the picture, it appears to coalesce with the qFMR mode, especially near its minimum temperature of detection.

FIG. 3.

Temperature and Mn doping dependences of the antiferromagnetic resonance modes of YFe1−xMnxO3 (x = 0–0.4) in the terahertz region. (a)–(h) Contour plots of the absorption coefficients as functions of temperature (4–295 K) and Mn doping (x = 0–0.4). The open circles and open triangles represent the qFMR and qAFMR modes, respectively, in the Γ4 phase. The open stars represent the AFMR mode in the Γ1 phase. The black dashed lines mark the temperature TSR for the onset of the spin reorientation transition from the Γ4 phase to the Γ1 phase. (i) Phase diagram of YFe1−xMnxO3 (x = 0–0.45). The dotted line represents the maximum temperature (295 K) of our terahertz absorption measurement, and the blue arrow the measurement temperature range for each sample with a given Mn doping x. The rest of the symbols and curves have the same meaning as in Fig. 1(a).

FIG. 3.

Temperature and Mn doping dependences of the antiferromagnetic resonance modes of YFe1−xMnxO3 (x = 0–0.4) in the terahertz region. (a)–(h) Contour plots of the absorption coefficients as functions of temperature (4–295 K) and Mn doping (x = 0–0.4). The open circles and open triangles represent the qFMR and qAFMR modes, respectively, in the Γ4 phase. The open stars represent the AFMR mode in the Γ1 phase. The black dashed lines mark the temperature TSR for the onset of the spin reorientation transition from the Γ4 phase to the Γ1 phase. (i) Phase diagram of YFe1−xMnxO3 (x = 0–0.45). The dotted line represents the maximum temperature (295 K) of our terahertz absorption measurement, and the blue arrow the measurement temperature range for each sample with a given Mn doping x. The rest of the symbols and curves have the same meaning as in Fig. 1(a).

Close modal

We can attempt to understand the role of Mn doping in this context via the well-established theory of antiferromagnetic resonance dynamics of the Γ4 phase. According to Shapiro et al.26 and Yamaguchi et al.,15 the qFMR and qAFMR mode energies are, respectively, given by

ωqFMR2=4E/2S2AaaAcccos 2θ4K4cos 4θ,
(1)
ωqAFMR2=4E/2S212Aaa+Acc+12AaaAcccos2θ4K4cos 4θ,
(2)

where Aaa and Acc are the second-order anisotropy energy, K4 is the fourth-order anisotropy energy, E is an exchange constant, S is the magnetic moment of the sublattice, and θ is the angle between the c axis and the direction of WFM. Noting θ=0 in the Γ4 phase and neglecting the fourth-order term, we arrive at

ωqFMR2=4E/2S2AaaAcc,
(3)
ωqAFMR2=4E/2S2Aaa.
(4)

From this, we immediately notice that Mn doping reduces the in-plane anisotropy constant Aaa, thereby reducing ωqAFMR. Since ωqFMR redshifts with x also but in a slower pace, the out-of-plane Acc should also decrease with x but more slowly than Aaa. This clearly demonstrates that Mn doping mainly reduces the in-plane anisotropy of the Fe3+ antiferromagnetic order. In addition, the merging of the qFMR and the qAFMR found at relatively low temperatures indicates that Acc itself also goes to zero with Mn3+ doping. All these are consistent with the Morin-type SRT where the spins rotate out of the a axis toward the b axis.

In contrast to the Γ4 phase, we observe only a single resonance mode, the AFMR mode below TSR [Figs. 3(d)–3(h)]. Interestingly, the AFMR appears to be inherited from the qFMR of the Γ1 phase at the inception point of x = 0.1. As x increases, the two modes decouple, especially at lower temperatures. As x increases beyond 0.3, the AFMR mode was not observed close to TSR, which is natural as higher TSR brings in more paramagnetic thermal fluctuations, which act to disrupt the existing AFM order. Individual AFMR curves show strong temperature dependence as x increases progressively for x ≥ 0.15. The mode frequency more significantly blueshifts compared to the situation in the Γ4 phase, but for x ≥ 0.15, redshifts below about 50 K. This back-bending effect should clearly be a consequence of Mn doping as this effect becomes stronger as x increases.

This behavior in the Γ1 phase can also be interpreted quantitatively. After the spin reorientation, the c axis anisotropy nearly goes to zero with the disappearance of WFM, and the a axis anisotropy Aaa converts to Abb because of the rotation of the easy axis from the a axis to the b axis. Then, Eq. (2) for the qAFMR mode reduces to a new expression for the AFMR mode given by

ωAFMR2=4E/2S2Abb4K4.
(5)

A significant change in the Γ1 phase is the survival of the fourth-order anisotropy. We propose to retain this fourth-order anisotropy constant, K4, which originates from the next-nearest neighbor (NNN) exchange field.27–30 As Mn doping increases, the mean distance between Mn3+ ions becomes short enough to activate the NNN exchange interaction among Mn3+ ions. So, the anisotropy constant K4, growing with doping and cooling, reduces the frequency of the AFMR mode as observed in our experiment. In a similar manner, Millev et al.29 report a case where the contribution of NNN to K4 plays a critical role, dominating that of the nearest neighbor (NN).

In conclusion, we have studied a series of YFe1−xMnxO30x0.4 samples by using our THz-TDS system for temperatures from 295 down to 4 K. A comprehensive set of temperature- and doping-dependent absorption spectra identified the phase boundary between the Γ4(WFM) and Γ1(collinear AFM) phases. The behavior of the qFMR and qAFMR modes shows that Mn doping reduces the single ion anisotropy along the a and c axes in the Γ4 phase. As doping progresses, the easy axis rotates from the a axis to the b axis with the SRT from the Γ4 phase into the Γ1 phase. In the Γ1 phase, a new AFMR mode appears, which sequentially blueshifts with doping but back-bends with cooling. This abnormal back-bending was ascribed to the fourth order anisotropy caused by the NNN exchange field of doped Mn. Our study clearly reveals a unique role of Mn3+ ions played in generating spin reorientation and transforming the antiferromagnetic order supported by Fe3+ ions. All of these interesting features were understood via the observation of antiferromagnetic resonance modes through the terahertz spectroscopy technique, which will certainly contribute to the exploration and understanding of a variety of antiferromagnetic systems actively studied today at the frontier of condensed matter research.

This research was supported by the National Research Foundation (NRF) of Korea grants funded by the Korea government (MIST) (Nos. NRF-2021R1A2C3004989, NRF-2017R1A5A1014862, and NRF-2019R1A2C2002601) and by the Institute for Basic Science (No. IBS-R011-D1).

H.L. and T.S.J. contributed equally to this work.

The data that support the findings of this study are available from the corresponding authors upon reasonable request.

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