Magnetic Order and Spin Dynamics in Ferroelectric ${\mathrm{H}\mathrm{o}\mathrm{M}\mathrm{n}\mathrm{O}}_{3}$

Magnetic Order and Spin Dynamics in Ferroelectric ${H o M n O}_{3}$

O. P. Vajk, M. Kenzelmann, J. W. Lynn, S. B. Kim, and S.-W. Cheong

Phys. Rev. Lett. 94, 087601 – Published 4 March 2005

Abstract

Hexagonal ${H o M n O}_{3}$ is a frustrated antiferromagnet ( $T_{N} = 72 K$ ) ferroelectric ( $T_{C} = 875 K$ ) in which these two order parameters are coupled. Our neutron measurements of the spin-wave dispersion for the $S = 2$ ${M n}^{3 +}$ on the layered triangular lattice are well described by a two-dimensional nearest-neighbor Heisenberg exchange $J = 2.44 m e V$ , and an anisotropy $D$ that is 0.28 meV above the spin-reorientation transition at 40 K and 0.38 meV below. For $H ∥ c$ the magnetic structures and phase diagram have been determined, and reveal additional transitions below 8 K where the ferroelectrically displaced ${H o}^{3 +}$ ions are ordered magnetically.

Received 26 October 2004

DOI:https://doi.org/10.1103/PhysRevLett.94.087601

Authors & Affiliations

O. P. Vajk¹, M. Kenzelmann^1,2, J. W. Lynn¹, S. B. Kim³, and S.-W. Cheong³

¹NIST Center for Neutron Research, Gaithersburg, Maryland 20899, USA
²Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218, USA
³Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854, USA

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Vol. 94, Iss. 8 — 4 March 2005

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Figure 1
Neutron diffraction measurements of the $(1, 0, 0)$ and $(1, 0, 1)$ magnetic Bragg reflection integrated intensity. Two spin-reorientation transitions (indicated by dashed lines) lead to changes in the intensities of both peaks. The ${M n}^{3 +}$ spin configurations for these phases are shown in the schematics to the right, where open circles indicate the position of Mn ions at $z = 0$ , filled circles indicate Mn ions at $z = c / 2$ , and arrows indicate the direction of the local magnetic moment. ${H o}^{3 +}$ moments (not shown) order in the low-temperature phase.Reuse & Permissions
Figure 2
Spin-wave dispersion at 20 K. (a) Measurements of the spin waves at $Q = (1.3, 0, 0)$ . Data were taken on BT2 with horizontal collimations of 60′-40′-40′-80′ and a fixed final energy of 14.7 meV. The line shows a fit to the data using two modes convoluted with the resolution function. Peak positions from both constant-energy and constant- $Q$ scans are plotted for two in-plane directions in reciprocal space in (b) and (c), along with the three modes of the dispersion curve (solid lines) given by Eq. (4) [ $J = 2.44 (7) m e V$ and $D = 0.38 (7) m e V$ ]. Dashed lines indicate two (dispersionless) crystal field levels of Ho at 1.5(1) and 3.1(1) meV. Inset: $L$ dependence of the spin-wave spectrum, showing no discernible dispersion.Reuse & Permissions
Figure 3
(a) Inelastic neutron measurements at $Q = (2, 0, 0)$ at 20 and 50 K. Data were taken on BT9 with horizontal collimations of 40′-40′-40′-40′ and fixed incident energy of 13.7 meV. Lines show fits to the data. The increase in intensity at lower energies is primarily due to a crystal field excitation at 3.1 meV. (b) Comparison of 20 and 50 K dispersion data near the zone center. Data have been reduced to the first Brillouin zone. Dotted lines show spin-wave dispersion curves for 20 K data, as in Fig. 2. Solid lines show fits of Eq. (4) to 50 K data [ $J = 2.44 m e V$ is fixed and $D = 0.28 (3) m e V$ ].Reuse & Permissions
Figure 4
(a) $(1, 0, 0)$ magnetic Bragg peak intensity versus magnetic field for different temperatures (offset by 15 000 counts for clarity). (b) $(2, 1, 0)$ magnetic Bragg peak intensity versus magnetic field for different temperatures. Circles are data taken with increasing field, while triangles are data taken with decreasing field. Dashed lines show 0.4 K transitions, with two intermediate phases $a$ and $c$ and hysteretic overlap in region $b$ .Reuse & Permissions
Figure 5
Temperature and magnetic field phase diagram for ${H o M n O}_{3}$ obtained from diffraction measurements of the $(1, 0, 0)$ and $(2, 1, 0)$ Bragg reflections. Lines are guides to the eye. Regions $a$ and $c$ are intermediate phases, with hysteretic overlap in region $b$ , as in Fig. 4. Region $d$ is an intermediate region where peak intensities change continuously. The dashed line is the approximate location of the low-temperature ${H o}^{3 +}$ ordering transition, and the dotted line is the approximate transition observed by SHG and magnetic susceptibility measurements [13, 16]. These transitions were not observable from the $(1, 0, 0)$ and $(2, 1, 0)$ diffraction data.Reuse & Permissions

Physical Review Letters

Magnetic Order and Spin Dynamics in Ferroelectric HoMnO3

O. P. Vajk, M. Kenzelmann, J. W. Lynn, S. B. Kim, and S.-W. Cheong

Phys. Rev. Lett. 94, 087601 – Published 4 March 2005

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Magnetic Order and Spin Dynamics in Ferroelectric ${H o M n O}_{3}$