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Effect of magnetic ordering on the infrared spectra of holmium
ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 272–276 (2004) e1109–e1110
Effect of magnetic ordering on the infrared spectra of holmium Peter Weber*, Martin Dressel Universitat . Stuttgart, 1. Physikalisches Institut, Pfaffenwaldring 57, Stuttgart 70550, Germany
Abstract In lanthanides, such as holmium, ordering of the local magnetic moments strongly affects the scattering rate of the conduction electrons (Kondo lattice). We performed infrared measurements on single crystalline holmium in a range from 1.2 meV to 1.2 eV at temperatures between 5 and 300 K. In the ordered state a reduced scattering rate in the Drude regime reflects the decrease of phonon as well as magnetic scattering. We observe an exchange splitting of 372 meV at the Fermi level and a low-frequency feature at about 37 meV. r 2003 Elsevier B.V. All rights reserved. PACS: 71.20.Eh; 75.30.Mb; 78.20.Ci; 78.20.Ls Keywords: Lanthanides; Magnetic scattering; Exchange splitting; Infrared spectra; Optical conductivity
1. Introduction The heavy lanthanides arrange in a hexagonal closepacked crystal structure. Most of them exhibit magnetic ordering below a certain temperature. Their unique properties make the lanthanides very important in many fields of technical applications. The mechanism of magnetic interaction observed in lanthanides differs very much from that in magnetic transition metals. Their inner 4f electron shells are partially occupied, while outer shells are completely filled. The 4f levels are located close to the core and therefore are well screened from Coulomb interaction with the surrounding ions. The open 4f-shells supply non-vanishing magnetic moments, which are localized at the lattice sites. In the ordered state these moments interact indirectly, with the exchange being mediated via delocalized electrons (RKKY exchange) [1]. Pure lanthanides, with their localized magnetic moments in a sea of delocalized electrons, constitute excellent systems to test the applicability of the Kondo–lattice model [2]. Of special interest are the
subtle antiferromagnetic phases of some lanthanides, which form layered magnetic structures. We put our focus on holmium (Ho), which shows the highest paramagnetic moment per atom [3]. The transition to the ordered state takes place at fairly low temperatures, thus the contribution of phonon scattering to the resistivity is reduced. Above the Neel temperature of TN ¼ 133 K holmium is a paramagnet. Below TN the magnetic moments form layers: Within one crystal layer all moments are lined up parallel to each other, lying within the plane. Between adjacent planes the direction of the moments is rotated by a small angle, leading to a full rotation of the moments with a period of several atomic layers. When approaching the Curie temperature of TC ¼ 20 K, the magnetic moments become tilted out of the plane, leading to a total ferromagnetic moment in c-direction (perpendicular to the planes) with a circulating contribution in plane (ferro-cone-helix) [4].
2. Experimental *Corresponding author. Tel.: +0049-711-685-4974; fax: +0049-711-685-4886. E-mail address: [email protected] (P. Weber).
In general, the DC-conductivity of lanthanides reflects the temperature dependent changes in magnetic ordering as kinks in sðTÞ [5]. Much more information can be
0304-8853/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2003.12.492
ARTICLE IN PRESS e1110
P. Weber, M. Dressel / Journal of Magnetism and Magnetic Materials 272–276 (2004) e1109–e1110
extracted from the frequency-dependent conductivity sðn; TÞ: Measurements in the far-infrared spectral range reveal excitations at energies, characteristic for magnetic processes; the photon energy is also comparable to the thermal energy related to the magnetic ordering. However, to our knowledge, only very few measurements are available in this range [6]. Thus we performed optical reflection measurements on holmium single crystals at frequencies from 50 to 10000 cm1 (corresponding to photon energies between 6.2 meV and 1.2 eV) using a modified Bruker IFS 113v Fourier transform infrared spectrometer. Spectra were taken at temperatures from 5 to 300 K. Aluminium mirrors serve as reference which replace the sample by translation. By means of Kramers–Kronig analysis the conductivity was evaluated from the measured reflectivity data.
3. Results and discussion The results for 5 K (ferromagnetic phase), 70 K (antiferromagnetic phase) and 140 K (paramagnetic phase) are presented in Fig. 1. Three main features are identified: The contribution at low energies due to the motion of free electrons which is described by the Drude model. The two peaks at higher frequencies are transitions between more or less localized states. They are described as Lorentzian oscillators [7]. (i) The peak at 3300 cm1 (372 meV) can be associated with the exchange splitting of a band close to, or crossing the Fermi energy. This splitting occurs, when the localized magnetic moments start to order. They induce a magnetic field which removes the degeneracy of the outer-band exchange splitting. (ii) The exchange peak is buried in the flank of a much stronger feature which has its maximum around about 300 cm1 (37 meV) and is observed up to room temperature. Such a low-frequency maximum in the optival conductivity is rather surprising for a metal and not completely understood yet. For an interband transition the energy seems very small, even smaller, than the exchange splitting. (iii) At low frequencies the conductivity is mainly governed by the Drude contribution of free electrons leading to a low-frequency conductivity in agreement with the DC results. The width of the Drude contribution is strongly reduced when crossing from the paramagnetic to the antiferromagnetic phase. From 140 to 70 K the scattering
Fig. 1. Optical conductivity of single crystalline holmium in the ferromagnetic, the antiferromagnetic and the paramagnetic phase. The direction of polarization is in plane of the HCP lattice.
rate of the free electrons changes from 3800 to 3000 cm1. At 5 K the low-frequency behaviour becomes more complex and requires some advanced model. The project is funded by the Deutsche Forschungsgemeinschaft (DFG). References [1] J. Jensen, A.R. MacKintosh, Rare Earth Magnetism, Clarendon Press, Oxford, 1991 (Chapter 1). [2] W. Nolting, S. Rex, S. Mathi Jaya, in: M. Donath, P.A. Dowben, W. Nolting (Eds.), Magnetism and Electronic Correlations in Local-Moment Systems, World Scientific, Singapore, New Jersey, London, Hong Kong, 1998, p. 293. [3] H. Drulis, M. Drulis, in: K.-H. Hellwege (Ed.), Landolt. Bornstein: Numerical Data and Functional Relationships in Science and Technology, Vol. 19, Springer, Berlin, Heidelberg, New York, 1982. [4] W.C. Koehler, J.W. Cable, M.K. Wilkinson, E.O. Wollan, Phys. Rev. 151 (1966) 414. . [5] J. Bass, in: K.-H. Hellwege (Ed.), Landolt-Bornstein: Numerical Data and Functional Relationships in Science and Technology, Vol. 15, Springer, Berlin, Heidelberg, New York, 1982. [6] S.H. Liu, in: K.A. Gschneider, L. Eyring (Eds.), Handbook on the Physics and Chemistry of Rare Earths, Vol. 1, North-Holland, Amsterdam, New York, Oxford, 1978, p. 270. [7] M. Dressel, G. Gruner, . Electrodynamics of Solids, Cambridge University Press, Cambridge, 2002, p. 92, p. 136.
Journal of Magnetism and Magnetic Materials 272–276 (2004) e1109–e1110
Effect of magnetic ordering on the infrared spectra of holmium Peter Weber*, Martin Dressel Universitat . Stuttgart, 1. Physikalisches Institut, Pfaffenwaldring 57, Stuttgart 70550, Germany
Abstract In lanthanides, such as holmium, ordering of the local magnetic moments strongly affects the scattering rate of the conduction electrons (Kondo lattice). We performed infrared measurements on single crystalline holmium in a range from 1.2 meV to 1.2 eV at temperatures between 5 and 300 K. In the ordered state a reduced scattering rate in the Drude regime reflects the decrease of phonon as well as magnetic scattering. We observe an exchange splitting of 372 meV at the Fermi level and a low-frequency feature at about 37 meV. r 2003 Elsevier B.V. All rights reserved. PACS: 71.20.Eh; 75.30.Mb; 78.20.Ci; 78.20.Ls Keywords: Lanthanides; Magnetic scattering; Exchange splitting; Infrared spectra; Optical conductivity
1. Introduction The heavy lanthanides arrange in a hexagonal closepacked crystal structure. Most of them exhibit magnetic ordering below a certain temperature. Their unique properties make the lanthanides very important in many fields of technical applications. The mechanism of magnetic interaction observed in lanthanides differs very much from that in magnetic transition metals. Their inner 4f electron shells are partially occupied, while outer shells are completely filled. The 4f levels are located close to the core and therefore are well screened from Coulomb interaction with the surrounding ions. The open 4f-shells supply non-vanishing magnetic moments, which are localized at the lattice sites. In the ordered state these moments interact indirectly, with the exchange being mediated via delocalized electrons (RKKY exchange) [1]. Pure lanthanides, with their localized magnetic moments in a sea of delocalized electrons, constitute excellent systems to test the applicability of the Kondo–lattice model [2]. Of special interest are the
subtle antiferromagnetic phases of some lanthanides, which form layered magnetic structures. We put our focus on holmium (Ho), which shows the highest paramagnetic moment per atom [3]. The transition to the ordered state takes place at fairly low temperatures, thus the contribution of phonon scattering to the resistivity is reduced. Above the Neel temperature of TN ¼ 133 K holmium is a paramagnet. Below TN the magnetic moments form layers: Within one crystal layer all moments are lined up parallel to each other, lying within the plane. Between adjacent planes the direction of the moments is rotated by a small angle, leading to a full rotation of the moments with a period of several atomic layers. When approaching the Curie temperature of TC ¼ 20 K, the magnetic moments become tilted out of the plane, leading to a total ferromagnetic moment in c-direction (perpendicular to the planes) with a circulating contribution in plane (ferro-cone-helix) [4].
2. Experimental *Corresponding author. Tel.: +0049-711-685-4974; fax: +0049-711-685-4886. E-mail address: [email protected] (P. Weber).
In general, the DC-conductivity of lanthanides reflects the temperature dependent changes in magnetic ordering as kinks in sðTÞ [5]. Much more information can be
0304-8853/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2003.12.492
ARTICLE IN PRESS e1110
P. Weber, M. Dressel / Journal of Magnetism and Magnetic Materials 272–276 (2004) e1109–e1110
extracted from the frequency-dependent conductivity sðn; TÞ: Measurements in the far-infrared spectral range reveal excitations at energies, characteristic for magnetic processes; the photon energy is also comparable to the thermal energy related to the magnetic ordering. However, to our knowledge, only very few measurements are available in this range [6]. Thus we performed optical reflection measurements on holmium single crystals at frequencies from 50 to 10000 cm1 (corresponding to photon energies between 6.2 meV and 1.2 eV) using a modified Bruker IFS 113v Fourier transform infrared spectrometer. Spectra were taken at temperatures from 5 to 300 K. Aluminium mirrors serve as reference which replace the sample by translation. By means of Kramers–Kronig analysis the conductivity was evaluated from the measured reflectivity data.
3. Results and discussion The results for 5 K (ferromagnetic phase), 70 K (antiferromagnetic phase) and 140 K (paramagnetic phase) are presented in Fig. 1. Three main features are identified: The contribution at low energies due to the motion of free electrons which is described by the Drude model. The two peaks at higher frequencies are transitions between more or less localized states. They are described as Lorentzian oscillators [7]. (i) The peak at 3300 cm1 (372 meV) can be associated with the exchange splitting of a band close to, or crossing the Fermi energy. This splitting occurs, when the localized magnetic moments start to order. They induce a magnetic field which removes the degeneracy of the outer-band exchange splitting. (ii) The exchange peak is buried in the flank of a much stronger feature which has its maximum around about 300 cm1 (37 meV) and is observed up to room temperature. Such a low-frequency maximum in the optival conductivity is rather surprising for a metal and not completely understood yet. For an interband transition the energy seems very small, even smaller, than the exchange splitting. (iii) At low frequencies the conductivity is mainly governed by the Drude contribution of free electrons leading to a low-frequency conductivity in agreement with the DC results. The width of the Drude contribution is strongly reduced when crossing from the paramagnetic to the antiferromagnetic phase. From 140 to 70 K the scattering
Fig. 1. Optical conductivity of single crystalline holmium in the ferromagnetic, the antiferromagnetic and the paramagnetic phase. The direction of polarization is in plane of the HCP lattice.
rate of the free electrons changes from 3800 to 3000 cm1. At 5 K the low-frequency behaviour becomes more complex and requires some advanced model. The project is funded by the Deutsche Forschungsgemeinschaft (DFG). References [1] J. Jensen, A.R. MacKintosh, Rare Earth Magnetism, Clarendon Press, Oxford, 1991 (Chapter 1). [2] W. Nolting, S. Rex, S. Mathi Jaya, in: M. Donath, P.A. Dowben, W. Nolting (Eds.), Magnetism and Electronic Correlations in Local-Moment Systems, World Scientific, Singapore, New Jersey, London, Hong Kong, 1998, p. 293. [3] H. Drulis, M. Drulis, in: K.-H. Hellwege (Ed.), Landolt. Bornstein: Numerical Data and Functional Relationships in Science and Technology, Vol. 19, Springer, Berlin, Heidelberg, New York, 1982. [4] W.C. Koehler, J.W. Cable, M.K. Wilkinson, E.O. Wollan, Phys. Rev. 151 (1966) 414. . [5] J. Bass, in: K.-H. Hellwege (Ed.), Landolt-Bornstein: Numerical Data and Functional Relationships in Science and Technology, Vol. 15, Springer, Berlin, Heidelberg, New York, 1982. [6] S.H. Liu, in: K.A. Gschneider, L. Eyring (Eds.), Handbook on the Physics and Chemistry of Rare Earths, Vol. 1, North-Holland, Amsterdam, New York, Oxford, 1978, p. 270. [7] M. Dressel, G. Gruner, . Electrodynamics of Solids, Cambridge University Press, Cambridge, 2002, p. 92, p. 136.