Orphan Spins in the $S=\frac{5}{2}$ Antiferromagnet ${\mathrm{CaFe}}_{2}{\mathrm{O}}_{4}$

Orphan Spins in the $S = \frac{5}{2}$ Antiferromagnet ${CaFe}_{2} O_{4}$

C. Stock, E. E. Rodriguez, N. Lee, F. Demmel, P. Fouquet, M. Laver, Ch. Niedermayer, Y. Su, K. Nemkovski, M. A. Green, J. A. Rodriguez-Rivera, J. W. Kim, L. Zhang, and S.-W. Cheong

Phys. Rev. Lett. 119, 257204 – Published 22 December 2017

Abstract

${CaFe}_{2} O_{4}$ is an anisotropic $S = \frac{5}{2}$ antiferromagnet with two competing $A$ ( $↑ ↑ ↓ ↓$ ) and $B$ ( $↑ ↓ ↑ ↓$ ) magnetic order parameters separated by static antiphase boundaries at low temperatures. Neutron diffraction and bulk susceptibility measurements, show that the spins near these boundaries are weakly correlated and a carry an uncompensated ferromagnetic moment that can be tuned with a magnetic field. Spectroscopic measurements find these spins are bound with excitation energies less than the bulk magnetic spin waves and resemble the spectra from isolated spin clusters. Localized bound orphaned spins separate the two competing magnetic order parameters in ${CaFe}_{2} O_{4}$ .

Received 12 May 2017

DOI:https://doi.org/10.1103/PhysRevLett.119.257204

Physics Subject Headings (PhySH)

Antiferromagnetism Domain walls Magnetic phase transitions Magnons Mechanical & acoustical properties Spin relaxation Spin waves

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

C. Stock¹, E. E. Rodriguez², N. Lee³, F. Demmel⁴, P. Fouquet⁵, M. Laver¹², Ch. Niedermayer⁶, Y. Su⁷, K. Nemkovski⁷, M. A. Green⁸, J. A. Rodriguez-Rivera^9,10, J. W. Kim³, L. Zhang¹¹, and S.-W. Cheong³

¹School of Physics and Astronomy and Centre for Science at Extreme Conditions, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom
²Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland 20742, USA
³Rutgers Center for Emergent Materials and Department of Physics and Astronomy, Rutgers University, 136 Frelinghuysen Road, Piscataway, New Jersey 08854, USA
⁴ISIS Facility, Rutherford Appleton Labs, Chilton, Didcot OX11 0QX, United Kingdom
⁵Institute Laue-Langevin, 6 rue Jules Horowitz, Boite Postale 156, 38042 Grenoble Cedex 9, France
⁶Laboratory for Neutron Scattering, Paul Scherrer Institut, CH-5232 Villigen, Switzerland
⁷Jülich Centre for Neuton Science JCNS, Forschungszentrum Jülich GmbH, Outstation at MLZ, Lichtenbergstraße 1, D-85747 Garching, Germany
⁸School of Physical Sciences, University of Kent, Canterbury CT2 7NH, United Kingdom
⁹NIST Center for Neutron Research, National Institute of Standards and Technology, 100 Bureau Drive, Gaithersburg, Maryland 20899, USA
¹⁰Department of Materials Science, University of Maryland, College Park, Maryland 20742, USA
¹¹Laboratory for Pohang Emergent Materials and Max Plank POSTECH Center for Complex Phase Materials, Pohang University of Science and Technology, Pohang 790-784, Korea
¹²School of Metallurgy and Materials, University of Birmingham, B15 2TT, United Kingdom

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Vol. 119, Iss. 25 — 22 December 2017

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Figure 1
(a) Illustrates the magnetic $B$ phase ( $↑ ↓ ↑ ↓$ ) of ${CaFe}_{2} O_{4}$ showing an antiphase boundary where locally (within the highlighted box) the magnetic structure is the $A$ phase ( $↑ ↑ ↓ ↓$ ). Note that this antiphase boundary carries a net ferromagnetic moment. (b) the same is illustrated for the low temperature $A$ phase where locally the magnetic structure is the $B$ phase. (c) illustrates the diffuse scattering cross section characterizing antiphase boundaries. (d–e) show results of a spin echo analysis plotting the fraction of static (on the $\sim GHz$ time scale) boundaries and the decay time. The magnetic order parameters of the $A$ and $B$ phases extracted from neutron diffraction are also plotted. The dashed line is discussed in the main text.
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Figure 2
Polarized (magnetic) diffuse scattering where $X$ is parallel to $\vec{Q}$ , $Y$ perpendicular and within the ( $H 0 L$ ) plane, and $Z$ along $b$ . Panels (a) and (c) show the magnetic scattering originating from spins aligned along the crystallographic $b$ axis at 100 and 50 K. (b) and (d) show the same but for the spins oriented perpendicular to $b$ . (e) plots the fraction of intensity originating from spins aligned along $Y$ and $Z$ . The total is shown to be in agreement of 1, required from sum rules for polarized neutron scattering.
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Figure 3
(a) Magnetization loops at 120 K and 5 K illustrating a remanent magnetization in ${CaFe}_{2} O_{4}$ . (b) plots the temperature dependence at $\vec{Q} = (- 1, 0, 1.4)$ . Zero field cooled (ZFC), zero field warmed (ZFW), and $11 T$ field cooled data were taken with the field $| |$ $b$ (vertical) axis. (c) illustrates the same cooling sequences at $\vec{Q} = (- 1, 0, 1.65)$ with the field aligned perpendicular to the $b$ axis and in the (H0L) scattering plane. (d–f) plots the diffuse scattering cross section in zero field at 75 K, 150 K, and 190 K. Further details on the experimental configuration and zero field susceptibility are given in the Supplemental Material [34].
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Figure 4
(a) displays a constant- $Q$ scan showing the presence of an in-gap mode at low temperatures fit to a harmonic oscillator line shape. (b) illustrates a constant energy slice showing that the intensity is elongated along $L$ . (c–f) displays high resolution scans taken on OSIRIS showing the gapped excitation and the response to $3 T$ and $7 T$ applied along the crystallographic $b$ axis. The solid line in (d) is a fit to underdamped harmonic oscillators with positions fixed to be the calculated dimer (solid arrow) and trimer (dashed arrows) positions. The fit in (f) is to a single damped harmonic oscillator.
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Physical Review Letters

Orphan Spins in the S=52 Antiferromagnet CaFe2O4

C. Stock, E. E. Rodriguez, N. Lee, F. Demmel, P. Fouquet, M. Laver, Ch. Niedermayer, Y. Su, K. Nemkovski, M. A. Green, J. A. Rodriguez-Rivera, J. W. Kim, L. Zhang, and S.-W. Cheong

Phys. Rev. Lett. 119, 257204 – Published 22 December 2017

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Orphan Spins in the $S = \frac{5}{2}$ Antiferromagnet ${CaFe}_{2} O_{4}$