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Orbital ordering in YTiO3 observed by NMR
Journal of Magnetism and Magnetic Materials 226}230 (2001) 874}875
Orbital ordering in YTiO observed by NMR Masayuki Itoh *, Michitoshi Tsuchiya
Department of Physics, Faculty of Science, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522, Japan Graduate School of Science and Technology, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522, Japan
Abstract The Ti NMR spectrum in ferromagnetic YTiO has been numerically calculated on the basis of an orbital ordering model theoretically proposed. Agreement between calculated and experimental NMR spectra supports the orbital ordering model. 2001 Elsevier Science B.V. All rights reserved. Keywords: Ferromagnetism; Hyper"ne "elds; Magnetic oxides; NMR
A perovskite oxide with the GdFeO -type distortion, YTiO , is a ferromagnet with the Curie temperature T &30 K [1]. Recently, the e!ect of the freedom of ! degenerate 3d orbitals on magnetic properties of RTiO (R: rare earth) has theoretically attracted much attention. In particular, the origin of the ferromagnetic order in YTiO was argued to come from an orbital ordering of the Ti 3d wave function. Mizokawa et al. proposed a model of the orbital ordering on the basis of the Hartree}Fock calculation [2}4]. That is, the four Ti (1)}Ti (4) sites have orbitals expressed by
"c d #c d , "c d #c d , "c d ! WX VW XV VW WX c d and "c d !c d (c #c "1, c &0.8), VW XV VW respectively. This type of orbital ordering with c "1/(2 was also pointed out by Sawada et al. from the band calculations in the generalized gradient approximation (GGA) and local density approximation (LDA)#U [5, 6]. Previously, we observed the Ti NMR spectrum in zero external "eld at 4.2 K in the ferromagnetic state of YTiO as presented in Fig. 1(a) [7]. This NMR spectrum is expected to provide information on such an orbital ordering. In this study, we numerically calculate the NMR spectrum in YTiO on the basis of the orbital ordering model and compare it with the experimental result.
* Corresponding author. Tel.:#81-43-290-2766; fax:#8143-290-2874. E-mail address: [email protected] (M. Itoh).
In a magnetically ordered state an NMR spectrum, which can be generally observed in zero external "eld owing to the internal "eld, is governed by the hyper"ne interaction. The magnetic hyper"ne interaction H of
a 3d transition metal ion with an (¸, S) term can be expressed as [8] H "2 r\ [!S ) I#L ) I
#¸(¸#1)!3/2(L ) I)(L ) S) !3/2(L ) S)(L ) I)]
(1)
with "(2l#1!4S)/S(2l!1)(2l#3)(2L!1),
(2)
where is the nuclear gyromagnetic ratio ( "2;2.400;10 and "2;2.405;10 Hz/ Oe), r\ is the expectation value of r\ for the 3d
orbital, S is the total spin, L is the total orbital momentum, l is the orbital momentum and I is the nuclear spin (I" and I"). For Ti>, ¸"2, S" and l"2. In Eq. (1), the "rst term is the Fermi contact interaction due to core polarization with a parameter , the second is the orbital one and the third is the dipole one. The electric hyper"ne interaction H is expressed as [8] H"SeQr\ 3(L ) I)#3/2(L ) I) !¸(¸#1)I(I#1)/I(2I!1),
0304-8853/01/$ - see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 0 0 ) 0 0 6 3 4 - X
(3)
M. Itoh, M. Tsuchiya / Journal of Magnetism and Magnetic Materials 226}230 (2001) 874}875
875
Fig. 1. (a) Observed (solid circles, Ref. [7]) and calculated (the solid curve) Ti NMR spectra in ferromagnetic YTiO . The calculated one is the summation of Ti spectra in (b).
where Q is the nuclear quadrupole moment (Q"#0.29 and Q"#0.24 b) and r\ is intro duced to take into account the di!erence of r\ between H and H. In addition to H the electric
quadrupole interaction has a contribution coming from outer ions expressed as [8] H"(1! )eQ < 3/2(I I #I I ) ?@ ?@ ? @ @ ? ! I/6I(2I!1), (4) ?@ where is the Sternheimer antishielding factor and < ( , "x, y and z) is a component of the electric?@ "eld-gradient tensor generated by surrounding ions. By solving the secular equation for the nuclear Hamiltonian H"H #H#H, we can obtain energy eigen values and eigenstates. From these energy levels we can evaluate the NMR frequency and intensity. In YTiO , we calculate the Ti NMR spectrum with r\ , r\ , , and c as parameters, using
the orbitals } at the four Ti sites mentioned above. Also, we evaluate < based on the point-charge model. Consequently, the parameter c was found to in#uence the NMR spectrum as shown in Fig. 2. This "gure shows NMR spectra calculated for various values of c in the case of S//c-axis, "0.83, r\ "0.5r\ ,
&$ r\ "0.6r\ and "!4 where r\ is &$ &$ the Hartree}Fock value of 2.552 a.u. [8]. Each line is assumed to be a Gaussian with a full-width at halfmaximum of 2.0 MHz and the natural abundance of Ti is taken into account for the NMR intensity. With increasing c the NMR spectrum moves towards low frequency side. After studying the parameters, we obtained the best-"tting parameter values of c "0.8,
Fig. 2. Ti NMR spectra calculated for c "(a) 1.0, (b) 0.8, (c) 1/(2 and (d) 0 on the basis of the theoretical model of the orbital ordering in ferromagnetic YTiO
"0.83, r\ "0.5r\ , r\ "0.6r\
&$ &$ "!4 and S//c-axis. Fig. 1(a) shows the "nal cal culated spectrum which is compared with the experimental spectrum. In this "gure, we can see a considerably good agreement between both spectra, although there is a discrepancy around 35 MHz. The "tted values of r\ and r\ are reasonably reduced from
r\ , which may come from a covalent e!ect. The &$ obtained c value is consistent with the theoretical one of 0.8 or 1/(2. Thus, we can conclude that the NMR result supports the theoretical model of the orbital ordering. In summary, we have performed a numerical calculation of the Ti NMR spectrum in YTiO . It was con cluded that the model of the orbital ordering proposed by the Hartree}Fock and the band calculations is plausible.
References [1] [2] [3] [4] [5] [6] [7] [8]
J.E. Greedan, J. Less-Common Met. 111 (1985) 335. T. Mizokawa, A. Fujimori, Phys. Rev. B 51 (1995) 12 880. T. Mizokawa, A. Fujimori, Phys. Rev. B 54 (1996) 5368. T. Mizokawa, D.I. Khomskii, G.A. Sawatzky, Phys. Rev. B 60 (1999) 7309. H. Sawada, N. Hamada, K. Terakura, Physica B 237}238 (1997) 46. H. Sawada, K. Terakura, Phys. Rev. B 58 (1998) 6831. M. Itoh, H. Tanaka, K. Motoya, Physica B 237}238 (1997) 19. A. Abragam, B. Bleaney, Electron Paramagnetic Resonance of Transition Ions, Clarendon Press, Oxford, 1970.
Orbital ordering in YTiO observed by NMR Masayuki Itoh *, Michitoshi Tsuchiya
Department of Physics, Faculty of Science, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522, Japan Graduate School of Science and Technology, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522, Japan
Abstract The Ti NMR spectrum in ferromagnetic YTiO has been numerically calculated on the basis of an orbital ordering model theoretically proposed. Agreement between calculated and experimental NMR spectra supports the orbital ordering model. 2001 Elsevier Science B.V. All rights reserved. Keywords: Ferromagnetism; Hyper"ne "elds; Magnetic oxides; NMR
A perovskite oxide with the GdFeO -type distortion, YTiO , is a ferromagnet with the Curie temperature T &30 K [1]. Recently, the e!ect of the freedom of ! degenerate 3d orbitals on magnetic properties of RTiO (R: rare earth) has theoretically attracted much attention. In particular, the origin of the ferromagnetic order in YTiO was argued to come from an orbital ordering of the Ti 3d wave function. Mizokawa et al. proposed a model of the orbital ordering on the basis of the Hartree}Fock calculation [2}4]. That is, the four Ti (1)}Ti (4) sites have orbitals expressed by
"c d #c d , "c d #c d , "c d ! WX VW XV VW WX c d and "c d !c d (c #c "1, c &0.8), VW XV VW respectively. This type of orbital ordering with c "1/(2 was also pointed out by Sawada et al. from the band calculations in the generalized gradient approximation (GGA) and local density approximation (LDA)#U [5, 6]. Previously, we observed the Ti NMR spectrum in zero external "eld at 4.2 K in the ferromagnetic state of YTiO as presented in Fig. 1(a) [7]. This NMR spectrum is expected to provide information on such an orbital ordering. In this study, we numerically calculate the NMR spectrum in YTiO on the basis of the orbital ordering model and compare it with the experimental result.
* Corresponding author. Tel.:#81-43-290-2766; fax:#8143-290-2874. E-mail address: [email protected] (M. Itoh).
In a magnetically ordered state an NMR spectrum, which can be generally observed in zero external "eld owing to the internal "eld, is governed by the hyper"ne interaction. The magnetic hyper"ne interaction H of
a 3d transition metal ion with an (¸, S) term can be expressed as [8] H "2 r\ [!S ) I#L ) I
#¸(¸#1)!3/2(L ) I)(L ) S) !3/2(L ) S)(L ) I)]
(1)
with "(2l#1!4S)/S(2l!1)(2l#3)(2L!1),
(2)
where is the nuclear gyromagnetic ratio ( "2;2.400;10 and "2;2.405;10 Hz/ Oe), r\ is the expectation value of r\ for the 3d
orbital, S is the total spin, L is the total orbital momentum, l is the orbital momentum and I is the nuclear spin (I" and I"). For Ti>, ¸"2, S" and l"2. In Eq. (1), the "rst term is the Fermi contact interaction due to core polarization with a parameter , the second is the orbital one and the third is the dipole one. The electric hyper"ne interaction H is expressed as [8] H"SeQr\ 3(L ) I)#3/2(L ) I) !¸(¸#1)I(I#1)/I(2I!1),
0304-8853/01/$ - see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 0 0 ) 0 0 6 3 4 - X
(3)
M. Itoh, M. Tsuchiya / Journal of Magnetism and Magnetic Materials 226}230 (2001) 874}875
875
Fig. 1. (a) Observed (solid circles, Ref. [7]) and calculated (the solid curve) Ti NMR spectra in ferromagnetic YTiO . The calculated one is the summation of Ti spectra in (b).
where Q is the nuclear quadrupole moment (Q"#0.29 and Q"#0.24 b) and r\ is intro duced to take into account the di!erence of r\ between H and H. In addition to H the electric
quadrupole interaction has a contribution coming from outer ions expressed as [8] H"(1! )eQ < 3/2(I I #I I ) ?@ ?@ ? @ @ ? ! I/6I(2I!1), (4) ?@ where is the Sternheimer antishielding factor and < ( , "x, y and z) is a component of the electric?@ "eld-gradient tensor generated by surrounding ions. By solving the secular equation for the nuclear Hamiltonian H"H #H#H, we can obtain energy eigen values and eigenstates. From these energy levels we can evaluate the NMR frequency and intensity. In YTiO , we calculate the Ti NMR spectrum with r\ , r\ , , and c as parameters, using
the orbitals } at the four Ti sites mentioned above. Also, we evaluate < based on the point-charge model. Consequently, the parameter c was found to in#uence the NMR spectrum as shown in Fig. 2. This "gure shows NMR spectra calculated for various values of c in the case of S//c-axis, "0.83, r\ "0.5r\ ,
&$ r\ "0.6r\ and "!4 where r\ is &$ &$ the Hartree}Fock value of 2.552 a.u. [8]. Each line is assumed to be a Gaussian with a full-width at halfmaximum of 2.0 MHz and the natural abundance of Ti is taken into account for the NMR intensity. With increasing c the NMR spectrum moves towards low frequency side. After studying the parameters, we obtained the best-"tting parameter values of c "0.8,
Fig. 2. Ti NMR spectra calculated for c "(a) 1.0, (b) 0.8, (c) 1/(2 and (d) 0 on the basis of the theoretical model of the orbital ordering in ferromagnetic YTiO
"0.83, r\ "0.5r\ , r\ "0.6r\
&$ &$ "!4 and S//c-axis. Fig. 1(a) shows the "nal cal culated spectrum which is compared with the experimental spectrum. In this "gure, we can see a considerably good agreement between both spectra, although there is a discrepancy around 35 MHz. The "tted values of r\ and r\ are reasonably reduced from
r\ , which may come from a covalent e!ect. The &$ obtained c value is consistent with the theoretical one of 0.8 or 1/(2. Thus, we can conclude that the NMR result supports the theoretical model of the orbital ordering. In summary, we have performed a numerical calculation of the Ti NMR spectrum in YTiO . It was con cluded that the model of the orbital ordering proposed by the Hartree}Fock and the band calculations is plausible.
References [1] [2] [3] [4] [5] [6] [7] [8]
J.E. Greedan, J. Less-Common Met. 111 (1985) 335. T. Mizokawa, A. Fujimori, Phys. Rev. B 51 (1995) 12 880. T. Mizokawa, A. Fujimori, Phys. Rev. B 54 (1996) 5368. T. Mizokawa, D.I. Khomskii, G.A. Sawatzky, Phys. Rev. B 60 (1999) 7309. H. Sawada, N. Hamada, K. Terakura, Physica B 237}238 (1997) 46. H. Sawada, K. Terakura, Phys. Rev. B 58 (1998) 6831. M. Itoh, H. Tanaka, K. Motoya, Physica B 237}238 (1997) 19. A. Abragam, B. Bleaney, Electron Paramagnetic Resonance of Transition Ions, Clarendon Press, Oxford, 1970.