Journal of Physics: Condensed Matter
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Micro-Raman and infrared studies of multiferroic TbMn2O5 To cite this article: S Mansouri et al 2016 J. Phys.: Condens. Matter 28 055901
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- Study of crystal-field excitations and infrared active phonons in the multiferroic hexagonal DyMnO3 S Jandl, S Mansouri, J Vermette et al. - Electromagnons in multiferroic RMn2O5 compounds and their microscopic origin A B Sushkov, M Mostovoy, R Valdés Aguilar et al. - Collective phase-like mode and the role of lattice distortions at TNsim TC in RMn2O5 (R = Pr, Sm, Gd, Tb, Bi) Néstor E Massa, Ali F García-Flores, Domingos De Sousa Meneses et al.
Recent citations - Raman and crystal field studies of Tb-O bonds in TbMn2O5 S. Mansouri et al
This content was downloaded from IP address 155.69.24.171 on 13/10/2017 at 19:22
Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 28 (2016) 055901 (6pp)
doi:10.1088/0953-8984/28/5/055901
Micro-Raman and infrared studies of multiferroic TbMn2O5 S Mansouri1, S Jandl1, B Roberge1, M Balli1, D Z Dimitrov2, M Orlita3, C Faugeras3 1
Université de Sherbrooke, Département de Physique, 2500 Boulevard Université, Sherbrooke, Canada J1K 2R1 2 Institute of Optical Materials and Technologies, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria 3 Grenoble High Magnetic Field Laboratory, 25, Avenue des Martyrs, Boîte Postale 166 F-38042 Grenoble, France E-mail: [email protected] Received 6 November 2015, revised 22 December 2015 Accepted for publication 4 January 2016 Published 20 January 2016 Abstract
We have studied the Raman and infrared spectral response of TbMn2O5 under an applied magnetic field parallel to the easy magnetic a-axis at 4.2 K. Strong spin-lattice coupling in TbMn2O5 is evidenced by a frequency shift of Raman and infrared phonons as a function of magnetic field compared to the phonon response of BiMn2O5 that remains unaffected. The magnetic field behavior of the highest frequency phonons retraces the polarization switching in TbMn2O5 and shows an important frequency softening below 3 T that is modulated by the J3 and J4 exchange parameters. The role of the Tb3+ spin alignment with H is interpreted in terms of a local lattice striction and the contribution of the charge transfer mechanism to the magnetoelectric process is evaluated. Keywords: multiferroics, Raman spectroscopy, infrared spectroscopy, magnetization curve (Some figures may appear in colour only in the online journal)
1. Introduction
connected to a symmetric Mn–Mn interaction and a Tb3+ spin alignment with the applied magnetic field. Nevertheless, there is a little progress in our understanding of the important microscopic parameters controlling this effect [4, 9–11]. RMn2O5 (R = rare earth, Bi and Y) compounds structure is orthorhombic [12, 13] where edge-shared Mn4+O6 octahedra are connected along the c-axis and pairs of Mn3+O5 pyramids are linked to two Mn4+O6 chains. RMn2O5 are multiferroic systems that exhibit a rather complex magnetic structure [4, 14]. Mn3+ and Mn4+ are coupled antiferromagnetically via the exchange parameters J4 along the a-axis and J3 along the b-axis [15]. Also, the Mn3+ ions, in two connected pyramids, couple antiferromagnetically through J5. As a function of temperature, a magnetic transition to an antiferromagnetic order with an incommensurate propagation vector is observed above 40 K. Around 38 K, they exhibit a commensurate magn etic order with a ferroelectric state. The spontaneous polarization arises along the b-axis, Pb ~ 45 nC cm−2 at 5 K [4]. Close to 25 K, a transition to a weakly ferroelectric state with an incommensurate magnetic-order occurs. This last transition is
Similarly to the perovskite ferroelectrics where the unconventional polarizability of the oxygen plays an essential role in strong spin-phonon interactions [1, 2], the discovery of a colossal magnetoelectric effect in the perovskite manganites has renewed an increasing interest for these materials [3–5]. Under an applied magnetic field, their electric polarizations can be reoriented, like in TbMnO3 [3], reversed like in TbMn2O5 [4], or modulated like in the hexagonal HoMnO3 compound [5, 6]. A number of models providing fundamental and plausible explanations have been suggested [7–11]. For orthorhombic TbMnO3, the magnetoelectric effect is attributed to the ability of the magnetic field to switch the direction of the bc-plane spiral of Mn3+ spins [7]. For hexagonal HoMnO3 system, the magnetoelectric effect is associated to a mechanism of charge transfer between Ho3+ and apical oxygen ions triggered when the Mn spins rotate in the ab-plane, and the symmetry group of the spin frustration changes from P63cm to P63c′m′ [8]. For orthorhombic TbMn2O5, the magnetoelectric effect is often 0953-8984/16/055901+6$33.00
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© 2016 IOP Publishing Ltd Printed in the UK
S Mansouri et al
J. Phys.: Condens. Matter 28 (2016) 055901
followed by a rare-earth magnetic order at lower temperatures [4, 14]. The polarisation of TbMn2O5 increases below 15 K up to ~40 nC cm−2 at 5 K, it coincides with the increase of the Tb3+ magnetic moment observed by neutron scattering [15] suggesting a coupling between Pb and Tb3+ spins. The positive polarization of TbMn2O5 is completely reversed when a magnetic field of 2 T is applied along the easy magnetization a-axis at T = 3 K. To explain this interesting phenomenon, Oh et al [11] have reported comparative studies of magnetoelectric susceptibility, magnetization (M), and magnetostriction (u) in TbMn2O5. Their results show a strong coupling between the macroscopic physical quantities, M, P and u. In particular, they show that the change of M due to the Tb3+ spin alignment with H determines the evolution of both P and u. However, their results do not inform on the microscopic mechanism controlling the magnetoelectric properties of TbMn2O5 and how the Tb3+ spin alignment with H affects the P variation. The authors suggest that this issue can be linked to either a local strain field of Tb3+ magnetostriction or direct exchange coupling between Mn3+/4+ and Tb3+ spins. Garcia-Flores et al [16] have studied RMn2O5 (R = Bi, Eu and Dy) compounds Raman active phonons. They have observed anomalous phonon shifts below T* ~ 1.5 × TN and TC attributed to a spin-phonon coupling mechanism. The lattice dynamical properties and the spin-phonon coupling in TbMn2O5 and DyMn2O5 were studied using the densityfunctional theory [17–19] indicating that the spin configuration dramatically influences the phonon frequencies. Aguilar et al [20] have studied the infrared active phonons of TbMn2O5 as a function of temperature. They have reported that the high frequency b polarized phonon around 703 cm−1, only Raman-active in the paraelectric phase, becomes IR active at the ferroelectric transition with a strength proportional to the square of the ferroelectric order parameter. Litvinchuk [21] have calculated within the shell model the Raman-active phonon frequencies of RMn2O5 (R = Ho and Dy). They have predicted that the frequencies of Raman-active modes, which involve Mn3+–O–Mn4+ bond vibrations, could be sensitive to the magnetic order as they modulate the Mn–Mn exchange interactions. In this paper, we present Raman and infrared studies of TbMn2O5 as a function of magnetic field at 4.2 K. These measurements are preceded by isothermal magnetization curves of TbMn2O5 along the a, b and c-axes at 4 K. Also, the magnetic field dependences of TbMn2O5 and BiMn2O5 infrared phonons are compared. The main objective of this paper is to investigate, under applied magnetic field, the spinlattice interaction in TbMn2O5 in order to learn more about the Tb3+ role and the microscopic mechanisms including the charge transfer that control the low temperature magnetoelectric polarization reversal.
Figure 1. Isothermal magnetization curves of TbMn2O5 at 4 K for H // to a, b and c-axes.
backscattering configuration using a He–Ne laser (632.8 nm) and a Labram-800 Raman spectrometer equipped with a microscope with a X-50 objective (focus diameter around ~3 microns), an appropriate notch filter and a nitrogen-cooled CCD detector. The samples were mounted on the cold finger of a micro-Helium Janis cryostat. The laser power was kept at ~0.8 mW (with an attenuator filter D1) to avoid local heating. Raman spectra under magnetic field used an Argon laser (514.5 nm) at liquid helium temperature. Optical fibers, both with a core diameter of 200 μm, were used for excitation and for collection. The resulting laser spot on the sample had a diameter of 600 μm with a typical power around 4 mW. The infrared spectra were obtained with a Bruker Instrument model 113 Fourier Transform Spectrometer, equipped with a mercury light source, and a composite Si bolometer used to collect the reflected phonon spectra. The samples were placed in the bore of a superconducting magnet and in a helium bath cryostat at 4.2 K, with the magnetic field up to 10 T and parallel to the a-axis. Magnetization as a function of magnetic field was measured using a superconducting quantum interferometer device magnetometer from Quantum Design (SQUID). 3. Results and discussion Isothermal magnetization curves of TbMn2O5 (for H // a, b and c) at 4 K shown in figure 1 confirm that the a-axis is the easy magnetic axis along which the magnetic field will be applied in our measurements. At T = 4 K, the terbium sublattice saturates at H ~ 3 T with an average moment of 8.4 μB close to the paramagnetic moment 9.72 μB [4, 11, 23]. Figure 2(a) shows polarized Raman spectra of TbMn2O5 and BiMn2O5 (inset) at T = 5 K. Typical Raman spectra associated with the orthorhombic RMn2O5 manganites are observed and the symmetry analysis of TbMn2O5 is in
2. Experimental TbMn2O5 and BiMn2O5 were grown by the high temper ature solution growth method using PbO–PbF2–B2O3 flux as described in [22]. The Raman spectra were recorded at temperatures between 300 and 5 K and were obtained in the 2
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J. Phys.: Condens. Matter 28 (2016) 055901
Figure 3. (a) Magnetic field dependence of TbMn2O5 Raman spectra for zero and 10 T (E ┴ a). The inset shows the magnetic field dependence of the relative Raman intensity I704/I625. (b) Evolution of the peak position of 704 cm−1 Raman line as a function of magnetic field. Magnetic dependence of the induced electric polarization as measured by Oh et al [11] (Black line).
Figure 2. (a) Polarized Raman spectra of TbMn2O5 at 5 K. The inset shows the Raman spectra of BiMn2O5 at 5 K measured with E // bc-plane. (b) Temperature dependence of the highest frequency phonons of TbMn2O5 (blue) and BiMn2O5 (red) below 25 K.
agreement with previous studies [16, 22]. The most sensitive phonon to the Tb3+ spin antiferromagnetic alignment at low temperatures is the 704 cm−1 highest frequency phonon as compared to its correspondent phonon at 662 cm−1 in BiMn2O5 (figure 2(b)). Such phonon is most affected by various transitions implying the J3 and J4 exchange parameters, since it involves the motion of the O3 oxygen that connects Mn3+ and Mn4+ along the a-axis [18, 21] and the O4 oxygen along the b-axis [21]. In particular, its frequency softening of ~1.8 cm−1 (figure 3(a)), when a magnetic field is applied at low temperatures and the electric polarization is reversed, confirm the role of the exchange parameters as discussed by Lee and Jang [9]. Also, this frequency softening is consistent with the magnetic field dependence of the longitudinal a [11, 24] and b-axis [25] magnetostriction at ~3 K that shows a significant increase with H up to 2 T and underlines the role of the exchange striction modulated by the rare-earth magn etic order as observed in DyMn2O5 [26]. Similar behavior is also observed for the relative intensity I704/I625 (inset of figure 3(b)) indicating a renormalization of oxygen hybridization and superexchange interaction under applied magn etic field.
In order to determine which microscopic parameters and atoms play a major role in the low-temperature magnetoelectric process, we have studied the infrared magneto-reflectances of TbMn2O5 and BiMn2O5 under an applied magnetic field parallel to the easy magnetic axis. Figure 4(a) presents the reflectance spectra of TbMn2O5 at 4.2 K (E // bc-plane) and B = 0 T, 10 T. The optical transverse (TO) and longitudinal (LO) phonon frequencies correspond to the peak positions in the imaginary parts of the dielectric functions Im(ε) and in the loss functions Im(−1/ε) respectively. The dielectric function is obtained through Kramers–Kronig analysis. The evolutions of the peak position of the TO and LO modes as a function of magnetic field are shown in figures 4(b) and (c). At low frequencies, the phonons most affected by the magn etic field are at 89 and 105 cm−1. Their corresponding atomic displacements are given in [27]. They involve the motion of Tb3+ centers and manganese oxide polyhedra. Both their TO and LO mode frequencies harden as a function of magnetic field. At high frequencies, the phonons at 641 and 704 cm−1 are most sensitive to the magnetic field. Their TO and LO modes soften significantly as a function of magnetic field. The 704 cm−1 infrared active mode is the Raman mode described earlier. It becomes infrared active because of the inversion 3
S Mansouri et al
J. Phys.: Condens. Matter 28 (2016) 055901
Figure 4. (a) shows the far-infrared reflectance (top panel), imaginary part of the dielectric function Im(ε) (middle panel), and loss function Im(−1/ε) (bottom panel) for TbMn2O5 at 4.2 K (E ┴ a). Frequency evolutions of TO and LO modes as a function of the magnetic field are shown in (b) and (c).
Figure 5. (a) Far-infrared reflectance spectra of BiMn2O5 (top panel), imaginary part of the dielectric function Im(ε) (middle panel), and loss function Im(−1/ε) (bottom panel) at zero and 10 T. (b) and (c) show the evolution of TO and LO modes as a function of magnetic field.
center loss at low temperatures [20]. Such magnitude of mode energy shift is indicative of a renormalization of the Mn–Mn and Tb–Mn interactions under the applied magnetic field. For the sake of comparison and in order to determine the Tb3+ magnetic moment role we have also studied the infrared magnetoreflectance of BiMn2O5 under an applied magnetic field parallel to the a-axis (figure 5(a)). The magn etic field dependence of the frequencies of their TO and LO modes are shown in figures 5(b) and (c). The correspondent phonons to 89, 105, 641 and 704 cm−1 in TbMn2O5 are 83, 94, 605 and 662 cm−1 in BiMn2O5. They actually show no
significant magnetic field dependence. Under applied magn etic field the Tb3+ sublattice adopts a canted antiferromagn etic structure with a large component of magnetic moment parallel to the a-axis [4, 11]. This implies a prominent role for the Tb3+ spin alignment in the spin-lattice interaction and the coupling between the Mn and Tb3+ sublattices that results in the electric polarization reversal. Actually, despite the similar Mn magnetic orders in the (Tb,Bi)Mn2O5 compounds, a magnetic field of 18 T is needed to reverse the spontaneous polarization in BiMn2O5 [10] while only 2 T is sufficient in TbMn2O5 [4]. 4
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J. Phys.: Condens. Matter 28 (2016) 055901
1 P(B ) − P(B = 0) = − ∑ δ Z*Ok(B )τ (4) νc k
ΔP varies by ~ − 12 nC cm−2 when a magnetic field of 3 T is applied. Compared with the experimental measurements of Hur et al [4], the calculated ΔP is about 15% of the absolute value of the polarization magnitude change ΔP ~ −80 nC cm−2. This suggests non-negligible contribution of the charge transfer mechanism to the magnetoelectric effect of TbMn2O5. Also, the Tb3+ spin alignment with H introduces a charge transfer which is however not dominant in readjusting the electric polarization as compared to hexagonal HoMnO3 compound [8] and polymeric multiferroics [31]. Actually, the magnetoelectric phenomenon introduced exclusively by a magnetic modulation of charge transfer is only observed in multiferroics with weak magnetoelectric coupling [32]. This is not the case of the RMn2O5 family where a strong magnetoelectric coupling exists ~10 times the one in the hexagonal RMnO3 compounds [33]. Raman and infrared results indicate that the magnetoelectric phenomenon in TbMn2O5 is mainly modulated by a magnetostriction effect induced by the Tb3+ spin alignment with H. We speculate that the magnetism of Tb3+ ions amplifies the effect of the magnetic field on the Mn spins configuration via a magnetostrictive effect induced by a symmetric exchange striction of the Tb3+–Mn3+–Tb3+ blocks that modulate the J3 and J4 exchange parameters. This is in agreement with a recent pyroelectric study concluding that the polarization of DyMn2O5 at low temperature is mainly controlled by a symmetric exchange striction in Dy3+–Mn3+–Dy3+ blocks with the ↓↓↑ and ↑↑ ↓ spin alignments, which is very sensitive to temperature and magnetic field [26]. This indicates that a proper control or a realistic simulation of the magnetoelectric coupling in TbMn2O5 should consider the major role of the rare-earth magnetization along the easy magnetic axis.
Figure 6. Magnetic field dependence of the induced electric polarization as predicted by our infrared magnetoreflectance measurements at 4.2 K in TbMn2O5.
Lee and Jang [9] have proposed recently a modulated spin structure responsible for the magnetic field induced polarization switching in TbMn2O5. They particularly predicted that the sign of the excess valence-electron density undergoes a concomitant switching with the polarization. In order to evaluate the charge transfer in the reversed polarization transition under applied magnetic field we have calculated the magnetic field dependence of the Born effective charges from the frequency evolutions of the TO and LO modes. Within this formalism, Vermette et al [8] have reproduced the macroscopic electric polarization of HoMnO3, at low temperature, with no adjustable parameters. The sum of the Born effective charge Z*k is connected to the frequencies of the TO and LO modes as follows [28]: N 4π n Z*k 2 2 π = 4 (1) ∑ ∑ (ω2LOj − ω2TOj) νc k = 1 mk j=1
4. Conclusion
Where vc represents the unit cell volume, mk the atom k mass and j the phonon mode. With the electrical neutrality of TbMn2O5 per formula unit (∑k Z*k = 0) and considering an average valence state of Mn ions (Z*Mn) [29, 30], we obtain:
. The variation * of the effective charges of oxygen (δ Z O), induced by a magn etic field, is determined according to the following equation:
In summary, we have studied the Raman and infrared spectral response of TbMn2O5 and BiMn2O5 under an applied magn etic field parallel to the easy magnetic a-axis at 4.2 K. We have found that Mn–O and Tb phonons are sensitive to the applied magnetic field which is amplified by the Tb3+ spins alignment. Also, the high-frequency O3 and O4 vibrational modes are significantly shifted specially below 3 T due to the modulation of the J3 and J4 exchange parameters. Finally, the TO and LO phonon frequency shifts indicate that the magnetostrictive effect dominates the Born effective charge transfer in the studied magnetoelectric process.
4π 2 N * δ Z = (3) ∑ (ω LOjδω LOj − ω TOjδω TOj ) O µ Z*O j = 1
Acknowledgment
with Z*O equal to −2.13e [29, 30]. Using the variation of the effective charges and the τ distance between the negative −Q and positive Q centers of charge in the TbMn2O5 unit cell, we calculate the polarization variation ΔP = (ΔQ/νc) τ as a function of the applied magnetic field (figure 6)
S M, S J, B R and M B acknowledge support from the National Science and Engineering Research Council of Canada and the Fonds Québécois de la Recherche sur la Nature et les Technologies. D Z D acknowledges the INERA REGPOT-2012-2013-1 project support.
2⎤ 2 ⎡ * 2 (Z*O) ⎥ (Z Tb) (Z*Mn) Z*k 2 ν ⎢ 4 2 5 = + + = c µ Z*O2 (2) ∑ m ⎢ ⎥ m m m 4 π k Mn O ⎦ k=1 ⎣ Tb n
In the last equation,
νc µ 4π
=
(
9 mTb
+
49 2mMn
+
20 mO
)
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J. Phys.: Condens. Matter 28 (2016) 055901
[16] Garcia-Flores A F, Granado E, Martinho H, Urbano R R, Rettori C, Golovenchits E I, Sanina V A, Oseroff S B, Park S and Cheong S-W 2006 Phys. Rev. B 73 104411 [17] Shen T, Cao K, Guo G-C and He L 2008 Phys. Rev. B 78 134413 [18] Wang C, Guo G-C and He L 2008 Phys. Rev. B 77 134113 [19] Cao K, Guo G-C, Vanderbilt D and He L 2009 Phys. Rev. Lett. 103 257201 [20] Aguilar R V, Sushkov A B, Park S, Cheong S-W and Drew H D 2006 Phys. Rev. B 74 184404 [21] Litvinchuk A P 2009 J. Magn. Magn. Mater. 321 2373–2377 [22] Mihailova B, Gospodinov M M, Güttler B, Yen F, Litvinchuk A P and Iliev M N 2005 Phys. Rev. B 71 172301 [23] Johnson R D, Mazzoli C, Bland S R, Du C-H and Hatton P D 2011 Phys. Rev. B 83 054438 [24] dela Cruz C R, Lorenz B, Sun Y Y, Chu C W, Park S and Cheong S-W 2006 Phys. Rev. B 74 180402 [25] Radulov I, Lovchinov V, Dimitrov D and Apostolov A 2009 J. Phys.: Conf. Ser. 153 012064 [26] Zhao Z Y, Liu M F, Li X, Lin L, Yan Z B, Dong S and Liu J-M 2014 Sci. Rep. 4 3984 [27] Cao J, Vergara L I, Musfeldt J L, Litvinchuk A P, Wang Y J, Park S and Cheong S-W 2008 Phys. Rev. B 78 064307 [28] Tochi K, Ohgaku T and Takeuchi N 1989 J. Mat. Sci. Lett. 8 1331 [29] Giovannetti G and van den Brink J 2008 Phys. Rev. Lett. 100 227603 [30] Neng L, Kailun Y, Guoying G, Sun Z and Li L 2011 Phys. Chem. Chem. Phys. 13 9418–24 [31] Qin W, Jasion D, Chen X, Wuttig M and Ren S 2014 ACS Nano 8 3671 [32] Khomskii D 2009 Physics 2 20 [33] Cheong S-W and Mostovoy M 2007 Nat. Mater. 6 13
References [1] Bilz H, Benedek G and Bussmann-Holder A 1987 Phys. Rev. B 35 4840 [2] Bussmann-Holder A 2012 J. Phys.: Condens. Matter 24 273202 [3] Kimura T, Goto T, Shintani H, Ishizaka K, Arima T and Tokura Y 2003 Nature 426 55 [4] Hur N, Park S, Sharma P, Ahn J, Guha S and Cheong S-W 2004 Nature 429 392 [5] Hur N, Jeong I K, Hundley M F, Kim S B and Cheong S-W 2009 Phys. Rev. B 79 134120 [6] Lottermoser T, Lonkai T, Amann U, Hohlwein D, Ihringer Jand Fiebig M 2004 Nature 430 541 [7] Yamasaki Y, Sagayama H, Abe N, Arima T, Sasai K, Matsuura M, Hirota K, Okuyama D, Noda Y and Tokura Y 2008 Phys. Rev. Lett. 101 097204 [8] Vermette J, Jandl S, Orlita M and Gospodinov M M 2012 Phys. Rev. B 85 134445 [9] Lee J-H and Jang H M 2015 Phys. Rev. B 91 014403 [10] Kim J W et al 2009 Proc. Natl Acad. Sci. USA 106 15573 [11] Oh Y S, Jeon B G, Haam S Y, Park S, Correa V F, Lacerda A H, Cheong S W, Jeon G S and Kim K H 2011 Phys. Rev. B 83 060405 [12] Alonso J A, Casais M T, Martinez-Lope M J, Martinez J L and Fernandez-Diaz M T 1997 J. Phys.: Condens. Matter 9 8515 [13] Kimura H, Kobayashi S, Fukuda Y, Osawa T, Kamada Y, Noda Y, Kagomiya I and Kohn K 2007 J. Phys. Soc. Japan 76 074706 [14] Blake G R, Chapon L C, Radaelli P G, Park S, Hur N, Cheong S-W and Rodriguez-Carvajal J 2005 Phys. Rev. B 71 214402 [15] Chapon L C, Blake G R, Gutmann M J, Park S, Hur N, Radaelli P G and Cheong S-W 2004 Phys. Rev. Lett. 93 177402
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Micro-Raman and infrared studies of multiferroic TbMn2O5 To cite this article: S Mansouri et al 2016 J. Phys.: Condens. Matter 28 055901
View the article online for updates and enhancements.
- Study of crystal-field excitations and infrared active phonons in the multiferroic hexagonal DyMnO3 S Jandl, S Mansouri, J Vermette et al. - Electromagnons in multiferroic RMn2O5 compounds and their microscopic origin A B Sushkov, M Mostovoy, R Valdés Aguilar et al. - Collective phase-like mode and the role of lattice distortions at TNsim TC in RMn2O5 (R = Pr, Sm, Gd, Tb, Bi) Néstor E Massa, Ali F García-Flores, Domingos De Sousa Meneses et al.
Recent citations - Raman and crystal field studies of Tb-O bonds in TbMn2O5 S. Mansouri et al
This content was downloaded from IP address 155.69.24.171 on 13/10/2017 at 19:22
Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 28 (2016) 055901 (6pp)
doi:10.1088/0953-8984/28/5/055901
Micro-Raman and infrared studies of multiferroic TbMn2O5 S Mansouri1, S Jandl1, B Roberge1, M Balli1, D Z Dimitrov2, M Orlita3, C Faugeras3 1
Université de Sherbrooke, Département de Physique, 2500 Boulevard Université, Sherbrooke, Canada J1K 2R1 2 Institute of Optical Materials and Technologies, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria 3 Grenoble High Magnetic Field Laboratory, 25, Avenue des Martyrs, Boîte Postale 166 F-38042 Grenoble, France E-mail: [email protected] Received 6 November 2015, revised 22 December 2015 Accepted for publication 4 January 2016 Published 20 January 2016 Abstract
We have studied the Raman and infrared spectral response of TbMn2O5 under an applied magnetic field parallel to the easy magnetic a-axis at 4.2 K. Strong spin-lattice coupling in TbMn2O5 is evidenced by a frequency shift of Raman and infrared phonons as a function of magnetic field compared to the phonon response of BiMn2O5 that remains unaffected. The magnetic field behavior of the highest frequency phonons retraces the polarization switching in TbMn2O5 and shows an important frequency softening below 3 T that is modulated by the J3 and J4 exchange parameters. The role of the Tb3+ spin alignment with H is interpreted in terms of a local lattice striction and the contribution of the charge transfer mechanism to the magnetoelectric process is evaluated. Keywords: multiferroics, Raman spectroscopy, infrared spectroscopy, magnetization curve (Some figures may appear in colour only in the online journal)
1. Introduction
connected to a symmetric Mn–Mn interaction and a Tb3+ spin alignment with the applied magnetic field. Nevertheless, there is a little progress in our understanding of the important microscopic parameters controlling this effect [4, 9–11]. RMn2O5 (R = rare earth, Bi and Y) compounds structure is orthorhombic [12, 13] where edge-shared Mn4+O6 octahedra are connected along the c-axis and pairs of Mn3+O5 pyramids are linked to two Mn4+O6 chains. RMn2O5 are multiferroic systems that exhibit a rather complex magnetic structure [4, 14]. Mn3+ and Mn4+ are coupled antiferromagnetically via the exchange parameters J4 along the a-axis and J3 along the b-axis [15]. Also, the Mn3+ ions, in two connected pyramids, couple antiferromagnetically through J5. As a function of temperature, a magnetic transition to an antiferromagnetic order with an incommensurate propagation vector is observed above 40 K. Around 38 K, they exhibit a commensurate magn etic order with a ferroelectric state. The spontaneous polarization arises along the b-axis, Pb ~ 45 nC cm−2 at 5 K [4]. Close to 25 K, a transition to a weakly ferroelectric state with an incommensurate magnetic-order occurs. This last transition is
Similarly to the perovskite ferroelectrics where the unconventional polarizability of the oxygen plays an essential role in strong spin-phonon interactions [1, 2], the discovery of a colossal magnetoelectric effect in the perovskite manganites has renewed an increasing interest for these materials [3–5]. Under an applied magnetic field, their electric polarizations can be reoriented, like in TbMnO3 [3], reversed like in TbMn2O5 [4], or modulated like in the hexagonal HoMnO3 compound [5, 6]. A number of models providing fundamental and plausible explanations have been suggested [7–11]. For orthorhombic TbMnO3, the magnetoelectric effect is attributed to the ability of the magnetic field to switch the direction of the bc-plane spiral of Mn3+ spins [7]. For hexagonal HoMnO3 system, the magnetoelectric effect is associated to a mechanism of charge transfer between Ho3+ and apical oxygen ions triggered when the Mn spins rotate in the ab-plane, and the symmetry group of the spin frustration changes from P63cm to P63c′m′ [8]. For orthorhombic TbMn2O5, the magnetoelectric effect is often 0953-8984/16/055901+6$33.00
1
© 2016 IOP Publishing Ltd Printed in the UK
S Mansouri et al
J. Phys.: Condens. Matter 28 (2016) 055901
followed by a rare-earth magnetic order at lower temperatures [4, 14]. The polarisation of TbMn2O5 increases below 15 K up to ~40 nC cm−2 at 5 K, it coincides with the increase of the Tb3+ magnetic moment observed by neutron scattering [15] suggesting a coupling between Pb and Tb3+ spins. The positive polarization of TbMn2O5 is completely reversed when a magnetic field of 2 T is applied along the easy magnetization a-axis at T = 3 K. To explain this interesting phenomenon, Oh et al [11] have reported comparative studies of magnetoelectric susceptibility, magnetization (M), and magnetostriction (u) in TbMn2O5. Their results show a strong coupling between the macroscopic physical quantities, M, P and u. In particular, they show that the change of M due to the Tb3+ spin alignment with H determines the evolution of both P and u. However, their results do not inform on the microscopic mechanism controlling the magnetoelectric properties of TbMn2O5 and how the Tb3+ spin alignment with H affects the P variation. The authors suggest that this issue can be linked to either a local strain field of Tb3+ magnetostriction or direct exchange coupling between Mn3+/4+ and Tb3+ spins. Garcia-Flores et al [16] have studied RMn2O5 (R = Bi, Eu and Dy) compounds Raman active phonons. They have observed anomalous phonon shifts below T* ~ 1.5 × TN and TC attributed to a spin-phonon coupling mechanism. The lattice dynamical properties and the spin-phonon coupling in TbMn2O5 and DyMn2O5 were studied using the densityfunctional theory [17–19] indicating that the spin configuration dramatically influences the phonon frequencies. Aguilar et al [20] have studied the infrared active phonons of TbMn2O5 as a function of temperature. They have reported that the high frequency b polarized phonon around 703 cm−1, only Raman-active in the paraelectric phase, becomes IR active at the ferroelectric transition with a strength proportional to the square of the ferroelectric order parameter. Litvinchuk [21] have calculated within the shell model the Raman-active phonon frequencies of RMn2O5 (R = Ho and Dy). They have predicted that the frequencies of Raman-active modes, which involve Mn3+–O–Mn4+ bond vibrations, could be sensitive to the magnetic order as they modulate the Mn–Mn exchange interactions. In this paper, we present Raman and infrared studies of TbMn2O5 as a function of magnetic field at 4.2 K. These measurements are preceded by isothermal magnetization curves of TbMn2O5 along the a, b and c-axes at 4 K. Also, the magnetic field dependences of TbMn2O5 and BiMn2O5 infrared phonons are compared. The main objective of this paper is to investigate, under applied magnetic field, the spinlattice interaction in TbMn2O5 in order to learn more about the Tb3+ role and the microscopic mechanisms including the charge transfer that control the low temperature magnetoelectric polarization reversal.
Figure 1. Isothermal magnetization curves of TbMn2O5 at 4 K for H // to a, b and c-axes.
backscattering configuration using a He–Ne laser (632.8 nm) and a Labram-800 Raman spectrometer equipped with a microscope with a X-50 objective (focus diameter around ~3 microns), an appropriate notch filter and a nitrogen-cooled CCD detector. The samples were mounted on the cold finger of a micro-Helium Janis cryostat. The laser power was kept at ~0.8 mW (with an attenuator filter D1) to avoid local heating. Raman spectra under magnetic field used an Argon laser (514.5 nm) at liquid helium temperature. Optical fibers, both with a core diameter of 200 μm, were used for excitation and for collection. The resulting laser spot on the sample had a diameter of 600 μm with a typical power around 4 mW. The infrared spectra were obtained with a Bruker Instrument model 113 Fourier Transform Spectrometer, equipped with a mercury light source, and a composite Si bolometer used to collect the reflected phonon spectra. The samples were placed in the bore of a superconducting magnet and in a helium bath cryostat at 4.2 K, with the magnetic field up to 10 T and parallel to the a-axis. Magnetization as a function of magnetic field was measured using a superconducting quantum interferometer device magnetometer from Quantum Design (SQUID). 3. Results and discussion Isothermal magnetization curves of TbMn2O5 (for H // a, b and c) at 4 K shown in figure 1 confirm that the a-axis is the easy magnetic axis along which the magnetic field will be applied in our measurements. At T = 4 K, the terbium sublattice saturates at H ~ 3 T with an average moment of 8.4 μB close to the paramagnetic moment 9.72 μB [4, 11, 23]. Figure 2(a) shows polarized Raman spectra of TbMn2O5 and BiMn2O5 (inset) at T = 5 K. Typical Raman spectra associated with the orthorhombic RMn2O5 manganites are observed and the symmetry analysis of TbMn2O5 is in
2. Experimental TbMn2O5 and BiMn2O5 were grown by the high temper ature solution growth method using PbO–PbF2–B2O3 flux as described in [22]. The Raman spectra were recorded at temperatures between 300 and 5 K and were obtained in the 2
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J. Phys.: Condens. Matter 28 (2016) 055901
Figure 3. (a) Magnetic field dependence of TbMn2O5 Raman spectra for zero and 10 T (E ┴ a). The inset shows the magnetic field dependence of the relative Raman intensity I704/I625. (b) Evolution of the peak position of 704 cm−1 Raman line as a function of magnetic field. Magnetic dependence of the induced electric polarization as measured by Oh et al [11] (Black line).
Figure 2. (a) Polarized Raman spectra of TbMn2O5 at 5 K. The inset shows the Raman spectra of BiMn2O5 at 5 K measured with E // bc-plane. (b) Temperature dependence of the highest frequency phonons of TbMn2O5 (blue) and BiMn2O5 (red) below 25 K.
agreement with previous studies [16, 22]. The most sensitive phonon to the Tb3+ spin antiferromagnetic alignment at low temperatures is the 704 cm−1 highest frequency phonon as compared to its correspondent phonon at 662 cm−1 in BiMn2O5 (figure 2(b)). Such phonon is most affected by various transitions implying the J3 and J4 exchange parameters, since it involves the motion of the O3 oxygen that connects Mn3+ and Mn4+ along the a-axis [18, 21] and the O4 oxygen along the b-axis [21]. In particular, its frequency softening of ~1.8 cm−1 (figure 3(a)), when a magnetic field is applied at low temperatures and the electric polarization is reversed, confirm the role of the exchange parameters as discussed by Lee and Jang [9]. Also, this frequency softening is consistent with the magnetic field dependence of the longitudinal a [11, 24] and b-axis [25] magnetostriction at ~3 K that shows a significant increase with H up to 2 T and underlines the role of the exchange striction modulated by the rare-earth magn etic order as observed in DyMn2O5 [26]. Similar behavior is also observed for the relative intensity I704/I625 (inset of figure 3(b)) indicating a renormalization of oxygen hybridization and superexchange interaction under applied magn etic field.
In order to determine which microscopic parameters and atoms play a major role in the low-temperature magnetoelectric process, we have studied the infrared magneto-reflectances of TbMn2O5 and BiMn2O5 under an applied magnetic field parallel to the easy magnetic axis. Figure 4(a) presents the reflectance spectra of TbMn2O5 at 4.2 K (E // bc-plane) and B = 0 T, 10 T. The optical transverse (TO) and longitudinal (LO) phonon frequencies correspond to the peak positions in the imaginary parts of the dielectric functions Im(ε) and in the loss functions Im(−1/ε) respectively. The dielectric function is obtained through Kramers–Kronig analysis. The evolutions of the peak position of the TO and LO modes as a function of magnetic field are shown in figures 4(b) and (c). At low frequencies, the phonons most affected by the magn etic field are at 89 and 105 cm−1. Their corresponding atomic displacements are given in [27]. They involve the motion of Tb3+ centers and manganese oxide polyhedra. Both their TO and LO mode frequencies harden as a function of magnetic field. At high frequencies, the phonons at 641 and 704 cm−1 are most sensitive to the magnetic field. Their TO and LO modes soften significantly as a function of magnetic field. The 704 cm−1 infrared active mode is the Raman mode described earlier. It becomes infrared active because of the inversion 3
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J. Phys.: Condens. Matter 28 (2016) 055901
Figure 4. (a) shows the far-infrared reflectance (top panel), imaginary part of the dielectric function Im(ε) (middle panel), and loss function Im(−1/ε) (bottom panel) for TbMn2O5 at 4.2 K (E ┴ a). Frequency evolutions of TO and LO modes as a function of the magnetic field are shown in (b) and (c).
Figure 5. (a) Far-infrared reflectance spectra of BiMn2O5 (top panel), imaginary part of the dielectric function Im(ε) (middle panel), and loss function Im(−1/ε) (bottom panel) at zero and 10 T. (b) and (c) show the evolution of TO and LO modes as a function of magnetic field.
center loss at low temperatures [20]. Such magnitude of mode energy shift is indicative of a renormalization of the Mn–Mn and Tb–Mn interactions under the applied magnetic field. For the sake of comparison and in order to determine the Tb3+ magnetic moment role we have also studied the infrared magnetoreflectance of BiMn2O5 under an applied magnetic field parallel to the a-axis (figure 5(a)). The magn etic field dependence of the frequencies of their TO and LO modes are shown in figures 5(b) and (c). The correspondent phonons to 89, 105, 641 and 704 cm−1 in TbMn2O5 are 83, 94, 605 and 662 cm−1 in BiMn2O5. They actually show no
significant magnetic field dependence. Under applied magn etic field the Tb3+ sublattice adopts a canted antiferromagn etic structure with a large component of magnetic moment parallel to the a-axis [4, 11]. This implies a prominent role for the Tb3+ spin alignment in the spin-lattice interaction and the coupling between the Mn and Tb3+ sublattices that results in the electric polarization reversal. Actually, despite the similar Mn magnetic orders in the (Tb,Bi)Mn2O5 compounds, a magnetic field of 18 T is needed to reverse the spontaneous polarization in BiMn2O5 [10] while only 2 T is sufficient in TbMn2O5 [4]. 4
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J. Phys.: Condens. Matter 28 (2016) 055901
1 P(B ) − P(B = 0) = − ∑ δ Z*Ok(B )τ (4) νc k
ΔP varies by ~ − 12 nC cm−2 when a magnetic field of 3 T is applied. Compared with the experimental measurements of Hur et al [4], the calculated ΔP is about 15% of the absolute value of the polarization magnitude change ΔP ~ −80 nC cm−2. This suggests non-negligible contribution of the charge transfer mechanism to the magnetoelectric effect of TbMn2O5. Also, the Tb3+ spin alignment with H introduces a charge transfer which is however not dominant in readjusting the electric polarization as compared to hexagonal HoMnO3 compound [8] and polymeric multiferroics [31]. Actually, the magnetoelectric phenomenon introduced exclusively by a magnetic modulation of charge transfer is only observed in multiferroics with weak magnetoelectric coupling [32]. This is not the case of the RMn2O5 family where a strong magnetoelectric coupling exists ~10 times the one in the hexagonal RMnO3 compounds [33]. Raman and infrared results indicate that the magnetoelectric phenomenon in TbMn2O5 is mainly modulated by a magnetostriction effect induced by the Tb3+ spin alignment with H. We speculate that the magnetism of Tb3+ ions amplifies the effect of the magnetic field on the Mn spins configuration via a magnetostrictive effect induced by a symmetric exchange striction of the Tb3+–Mn3+–Tb3+ blocks that modulate the J3 and J4 exchange parameters. This is in agreement with a recent pyroelectric study concluding that the polarization of DyMn2O5 at low temperature is mainly controlled by a symmetric exchange striction in Dy3+–Mn3+–Dy3+ blocks with the ↓↓↑ and ↑↑ ↓ spin alignments, which is very sensitive to temperature and magnetic field [26]. This indicates that a proper control or a realistic simulation of the magnetoelectric coupling in TbMn2O5 should consider the major role of the rare-earth magnetization along the easy magnetic axis.
Figure 6. Magnetic field dependence of the induced electric polarization as predicted by our infrared magnetoreflectance measurements at 4.2 K in TbMn2O5.
Lee and Jang [9] have proposed recently a modulated spin structure responsible for the magnetic field induced polarization switching in TbMn2O5. They particularly predicted that the sign of the excess valence-electron density undergoes a concomitant switching with the polarization. In order to evaluate the charge transfer in the reversed polarization transition under applied magnetic field we have calculated the magnetic field dependence of the Born effective charges from the frequency evolutions of the TO and LO modes. Within this formalism, Vermette et al [8] have reproduced the macroscopic electric polarization of HoMnO3, at low temperature, with no adjustable parameters. The sum of the Born effective charge Z*k is connected to the frequencies of the TO and LO modes as follows [28]: N 4π n Z*k 2 2 π = 4 (1) ∑ ∑ (ω2LOj − ω2TOj) νc k = 1 mk j=1
4. Conclusion
Where vc represents the unit cell volume, mk the atom k mass and j the phonon mode. With the electrical neutrality of TbMn2O5 per formula unit (∑k Z*k = 0) and considering an average valence state of Mn ions (Z*Mn) [29, 30], we obtain:
. The variation * of the effective charges of oxygen (δ Z O), induced by a magn etic field, is determined according to the following equation:
In summary, we have studied the Raman and infrared spectral response of TbMn2O5 and BiMn2O5 under an applied magn etic field parallel to the easy magnetic a-axis at 4.2 K. We have found that Mn–O and Tb phonons are sensitive to the applied magnetic field which is amplified by the Tb3+ spins alignment. Also, the high-frequency O3 and O4 vibrational modes are significantly shifted specially below 3 T due to the modulation of the J3 and J4 exchange parameters. Finally, the TO and LO phonon frequency shifts indicate that the magnetostrictive effect dominates the Born effective charge transfer in the studied magnetoelectric process.
4π 2 N * δ Z = (3) ∑ (ω LOjδω LOj − ω TOjδω TOj ) O µ Z*O j = 1
Acknowledgment
with Z*O equal to −2.13e [29, 30]. Using the variation of the effective charges and the τ distance between the negative −Q and positive Q centers of charge in the TbMn2O5 unit cell, we calculate the polarization variation ΔP = (ΔQ/νc) τ as a function of the applied magnetic field (figure 6)
S M, S J, B R and M B acknowledge support from the National Science and Engineering Research Council of Canada and the Fonds Québécois de la Recherche sur la Nature et les Technologies. D Z D acknowledges the INERA REGPOT-2012-2013-1 project support.
2⎤ 2 ⎡ * 2 (Z*O) ⎥ (Z Tb) (Z*Mn) Z*k 2 ν ⎢ 4 2 5 = + + = c µ Z*O2 (2) ∑ m ⎢ ⎥ m m m 4 π k Mn O ⎦ k=1 ⎣ Tb n
In the last equation,
νc µ 4π
=
(
9 mTb
+
49 2mMn
+
20 mO
)
5
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