Chiral properties of hematite $\ensuremath{\alpha}$-Fe${}_{2}$O${}_{3}$ inferred from resonant Bragg diffraction using circularly polarized x rays

Chiral properties of hematite $α$ -Fe $_{2}$ O $_{3}$ inferred from resonant Bragg diffraction using circularly polarized x rays

A. Rodríguez-Fernández, J. A. Blanco, S. W. Lovesey, V. Scagnoli, U. Staub, H. C. Walker, D. K. Shukla, and J. Strempfer

Phys. Rev. B 88, 094437 – Published 26 September 2013

Abstract

Chiral properties of the two phases—collinear motif (below Morin transition temperature, $T_{M} \approx 250$ K) and canted motif (above $T_{M}$ )—of magnetically ordered hematite ( $α$ -Fe $_{2}$ O $_{3}$ ) have been identified in single-crystal resonant x-ray Bragg diffraction using circular polarized incident x rays tuned near the iron $K$ edge. Magnetoelectric multipoles, including an anapole, fully characterize the high-temperature canted phase, whereas the low-temperature collinear phase supports both parity-odd and parity-even multipoles that are time odd. Orbital angular momentum accompanies the collinear motif, whereas it is conspicuously absent with the canted motif. Intensities have been successfully confronted with analytic expressions derived from an atomic model fully compliant with chemical and magnetic structures. Values of Fe atomic multipoles previously derived from independent experimental data are shown to be completely trustworthy.

Received 20 June 2013

DOI:https://doi.org/10.1103/PhysRevB.88.094437

Authors & Affiliations

A. Rodríguez-Fernández¹, J. A. Blanco¹, S. W. Lovesey², V. Scagnoli³, U. Staub³, H. C. Walker⁴, D. K. Shukla^4,*, and J. Strempfer⁴

¹Departamento de Física, Universidad de Oviedo, E-33007 Oviedo, Spain
²ISIS Facility and Diamond Light Source Ltd, Oxfordshire OX11 0QX, United Kingdom
³Paul Scherrer Institut, 5232 Villigen, Switzerland
⁴Deutsches Elektronen-Synchrotron, 22607 Hamburg, Germany

^*Present address: UGC DAE Consortium for Scientific Research, Khandwa Road, Indore 01, India.

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Vol. 88, Iss. 9 — 1 September 2013

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Figure 1
Crystal and magnetic structure of hematite. The small orange dots represent ferric ions while the large blue dots present the oxygen atoms’ positions. The vertical line at left denotes the magnetic motif along the $c$ axis below the Morin temperature (phase I). The vertical line at right denotes the motif above the Morin temperature, where iron moments are contained in the $a$ - $b$ plane (phase II).Reuse & Permissions
Figure 2
Cartesian coordinates $(x, y, z)$ and x-ray polarization and wave vectors. The plane of scattering spanned by primary ( $q$ ) and secondary ( $q^{'}$ ) wave vectors coincides with the $x - y$ plane. Polarization labeled $σ$ and $σ^{'}$ is normal to the plane and parallel to the $z$ axis, while polarization labeled $π$ and $π^{'}$ lies in the plane of scattering. The beam is deflected through an angle of $2 θ$ .Reuse & Permissions
Figure 3
X-ray energy dependence below $T_{M}$ $T = 150$ K for both reflections ${(003)}_{H}$ and ${(009)}_{H}$ in the vicinity of the iron $K$ edge. The open blue circles (triangles) show the linear polarized $π^{'} σ$ ( $σ^{'} σ$ ) data for the ${(003)}_{H}$ reflection, while the red circles (triangles) define the data from the $π^{'} σ$ ( $σ^{'} σ$ ) polarized channel for the ${(009)}_{H}$ reflection. The solid lines present the fitting to a model of a single oscillator.Reuse & Permissions
Figure 4
Azimuthal-angle scans for phase II (canted motif) at 300 K. Difference between circular left ( $C_{L}$ ) and circular right ( $C_{R}$ ) polarization for the ${(003)}_{H}$ reflection (top) and the ${(009)}_{H}$ reflection (bottom). The red circles represent the experimental data while the blue line shows expression (5) for pure $E 1 - E 2$ resonance evaluated with multipoles taken from Ref. 5 and reproduced in Table .Reuse & Permissions
Figure 5
Azimuthal-angle scan for phase I (collinear motif) at 150 K. Difference between circular left ( $C_{L}$ ) and circular right ( $C_{R}$ ) polarization for ${(003)}_{H}$ reflection. The red circles represent the experimental data while the blue line shows expressions (3) and (4) for a mixture of $E 1 - E 2$ and $E 2 - E 2$ resonances evaluated with multipoles taken from Ref. 5 and reproduced in Table . In Eq. (4) the parity-even and time-odd octupole ${〈 T_{3}^{3} 〉}^{''}$ is given a nominal value of $1 (\pm 0.1) \times 10^{- 4}$ .Reuse & Permissions
Figure 6
Azimuthal-angle scan for phase I (collinear motif) at 150 K. Difference between circular left ( $C_{L}$ ) and circular right ( $C_{R}$ ) polarization for the ${(009)}_{H}$ reflection. As in Fig. 5, the red circles represent the experimental data while the blue line shows a mixture of $E 1 - E 2$ and $E 2 - E 2$ resonances. Data are compared to pure $E 1 - E 2$ [Eq. (3)] (dashed line) and pure $E 2 - E 2$ [Eq. (4)] (dotted line) resonances, with multipoles taken from Ref. 5 and reproduced in Table . In Eq. (4) the octupole ${〈 T_{3}^{3} 〉}^{''}$ is given a nominal value of 0.0001.Reuse & Permissions

Physical Review B

covering condensed matter and materials physics

Chiral properties of hematite $α$ -Fe $_{2}$ O $_{3}$ inferred from resonant Bragg diffraction using circularly polarized x rays

A. Rodríguez-Fernández, J. A. Blanco, S. W. Lovesey, V. Scagnoli, U. Staub, H. C. Walker, D. K. Shukla, and J. Strempfer

Phys. Rev. B 88, 094437 – Published 26 September 2013

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Physical Review B

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Chiral properties of hematite α-Fe2O3 inferred from resonant Bragg diffraction using circularly polarized x rays

A. Rodríguez-Fernández, J. A. Blanco, S. W. Lovesey, V. Scagnoli, U. Staub, H. C. Walker, D. K. Shukla, and J. Strempfer

Phys. Rev. B 88, 094437 – Published 26 September 2013

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Chiral properties of hematite $α$ -Fe $_{2}$ O $_{3}$ inferred from resonant Bragg diffraction using circularly polarized x rays