Direct evidence for anisotropic three-dimensional magnetic excitations in a hole-doped antiferromagnet

Rajesh Dutta, Avishek Maity, Anna Marsicano, J. Ross Stewart, Matthias Opel, and Werner Paulus

Phys. Rev. B 102, 165130 – Published 15 October 2020

Abstract

We report a neutron-scattering study on $\Pr_{2 - x} {Sr}_{x} {NiO}_{4}$ ( $x \approx 0.5$ ) with magnetic incommensurability $ε = 0.461$ at 10 K, showing direct evidence for out-of-plane magnetic excitations caused by a non-negligible interlayer spin coupling ( $J_{⊥}$ ). The magnetic spectrum is fully represented by linear spin wave theory considering an unconventional body-centered-like stacking of discommensurated spin stripes. A large easy-plane-type single-ion anisotropy ( $\approx 1.5$ meV) has been found to be responsible for a finite-energy ( $\approx 13$ meV) Goldstone mode at the magnetic zone center. Our results validate the presence of a sizable out-of-plane interaction resulting in an anisotropic three-dimensional nature of spin dynamics in $\Pr_{2 - x} {Sr}_{x} {NiO}_{4}$ near the half-doped region.

Received 6 July 2020
Accepted 28 September 2020

DOI:https://doi.org/10.1103/PhysRevB.102.165130

Physics Subject Headings (PhySH)

Charge order Magnetic order Magnons Spin dynamics Spin waves Stripes

Inelastic neutron scattering

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Rajesh Dutta ^1,2,*, Avishek Maity ^3,4,†, Anna Marsicano ⁵, J. Ross Stewart⁶, Matthias Opel ⁷, and Werner Paulus ⁵

¹Institut für Kristallographie, RWTH Aachen Universität, 52066 Aachen, Germany
²Jülich Centre for Neutron Science at Heinz Maier-Leibnitz Zentrum, 85747 Garching, Germany
³Institut für Physikalische Chemie, Georg-August-Universität Göttingen, 37077 Göttingen, Germany
⁴Heinz Maier-Leibnitz Zentrum, Technische Universität München, 85747 Garching, Germany
⁵Institut Charles Gerhardt Montpellier, Université de Montpellier, 34095 Montpellier, France
⁶ISIS Neutron and Muon Source, Rutherford Appleton Laboratory, Didcot OX11 0QX, United Kingdom
⁷Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, 85748 Garching, Germany

^*Corresponding author: rajesh.dutta@frm2.tum.de
^†Corresponding author: avishek.maity@frm2.tum.de

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Vol. 102, Iss. 16 — 15 October 2020

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Images

Figure 1
Spin stripe discommensuration in $\Pr_{1.5} {Sr}_{0.5} {NiO}_{4}$ . (a) DCSS unit cell corresponding to the magnetic incommensurability $ε = 0.461$ for one twin domain. The average chemical unit cell ( $F 4 / m m m$ ) is indicated in black dashes. Green and red shading represents 1/3-stripe and CB unit, respectively. For the other orthogonal twin domain the model is exactly the same but rotated by $90^{\circ}$ around the $c$ axis. Magnetic exchange interactions are indicated by the solid lines in different colors. (b), (c) 2D cuts of ( $H K 2$ ) and ( $H K 3$ ) planes, obtained using the horace software [14] from wide crystal-rotation-scan ( $80^{\circ}$ around the vertical $c$ axis) data at MAPS with incident neutron energy $E_{i} = 60$ meV, representing four elastic spin order peaks modulated from ( $0, - 1, L = integer$ ) AFM zone centers. Yellow and red boxes indicate respectively the strong and weak intensity variation along $L$ . (d), (e) 2D slices of ( $0 K L$ ) and ( $H - 1 L$ ) planes showing the intensity variation of the spin order peaks along $L$ . (f)–(i) Elastic scans through the AFM zone centers in different $L$ planes from data measured at PUMA confirming the magnetic incommensurability $ε = 0.461$ and the intensity variation in different $L$ . Horizontal bars represent the instrumental resolution and vertical lines are error bars.
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Figure 2
In-plane magnetic excitations in discommensurated $\Pr_{1.5} {Sr}_{0.5} {NiO}_{4}$ at 10 K. (a) Constant- $E$ scans performed at PUMA using final neutron energy of $E_{f} = 14.68$ meV. All the scans are measured along $K$ through the (0, 1.461, 7) magnetic zone center. (b) Constant- $E$ scan profiles integrated within an energy range of $Δ E = \pm 2$ meV for a $K$ range of $Δ K = \pm 0.1$ reciprocal lattice units (r.l.u.) and obtained from narrow crystal-rotation-scan ( $\pm 3^{\circ}$ around the vertical $a$ axis, keeping the $c$ axis almost parallel to the neutron beam) data measured at MAPS with incident neutron energy $E_{i} = 60$ meV. All the scans are background subtracted and fitted with multiple Gaussian profiles. (c) Intensity convoluted in-plane spin wave spectra with overplotted magnetic wave vectors and full widths at half maximum (FWHMs) as horizontal bars. The strong crystal-electric-field excitation observed in the measurement is indicated in blue green shading in the energy range 6–13 meV. No constant- $E$ scans were performed on PUMA in this energy range. In (a) and (b) vertical lines represent error bars.
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Figure 3
Out-of-plane magnetic excitations in discommensurated $\Pr_{1.5} {Sr}_{0.5} {NiO}_{4}$ at 10 K. Data in this figure are measured at MAPS (wide crystal rotation scan) using incident neutron energies $E_{i} = 60$ meV, and at PUMA using a final neutron energy of $E_{f} = 14.68$ meV. (a)–(d) Constant- $E$ scan profiles along $L$ at two orthogonal spin satellite positions ( $0, 1.461, L$ ) and ( $1, 0.461, L$ ). All the scans are background subtracted and fitted with multiple Gaussian profiles to extract the magnetic wave vectors. Vertical lines represent the error bars. (e) Calculated out-of-plane excitations with overplotted magnetic wave vectors and FWHMs as horizontal bars. Please note that the spin wave modes are the same for both satellites as indicated by the two different $x$ axes. The bottom axis corresponds to those data measured along ( $1, 0.461, L$ ) where modes from $L = even$ peaks are strong. The top axis represents the data along ( $0, 1.461, L$ ), where modes from $L = odd$ peaks are strong. (f), (g) Two constant- $E$ slices of ( $1 K L$ ) plane from MAPS (top) presented with their corresponding simulations (bottom). White sinusoidal-like dashed lines are visual guides for the inelastic intensity distribution. (h), (i) Low- and high- $T$ maps of the out-of-plane excitations measured at PUMA for the rectangular section of the $L$ dispersion indicated by red dashes in (e). Lines in black dashes are visual guides for the magnon modes of $L$ dispersion.
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