Splitting of antiferromagnetic resonance modes in the quasi-two-dimensional collinear antiferromagnet $\mathrm{Cu}(\mathrm{en})({\mathrm{H}}_{2}\mathrm{O}){}_{2}{\mathrm{SO}}_{4}$

Splitting of antiferromagnetic resonance modes in the quasi-two-dimensional collinear antiferromagnet $Cu (en) (H_{2} O)_{2} {SO}_{4}$

V. N. Glazkov, Yu. V. Krasnikova, I. K. Rodygina, J. Chovan, R. Tarasenko, and A. Orendáčová

Phys. Rev. B 101, 014414 – Published 10 January 2020

Abstract

A low-temperature magnetic resonance study of the quasi-two-dimensional antiferromagnet $Cu (en) {(H_{2} O)}_{2} {SO}_{4}$ (en = $C_{2} H_{8} N_{2}$ ) was performed down to 0.45 K. This compound orders antiferromagnetically at 0.9 K. The analysis of the resonance data within the hydrodynamic approach allowed us to identify anisotropy axes and to estimate the anisotropy parameters for the antiferromagnetic phase. Dipolar spin-spin coupling turns out to be the main contribution to the anisotropy of the antiferromagnetic phase. The splitting of the resonance modes and its nonmonotonous dependence on the applied frequency were observed below 0.6 K in all three field orientations. Several models are discussed to explain the origin of the nontrivial splitting, and the existence of inequivalent magnetic subsystems in $Cu (en) {(H_{2} O)}_{2} {SO}_{4}$ is chosen as the most probable source.

Received 26 July 2019
Revised 27 November 2019

DOI:https://doi.org/10.1103/PhysRevB.101.014414

Physics Subject Headings (PhySH)

Antiferromagnetism Spin dynamics

2-dimensional systems Antiferromagnets

Electron spin resonance

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

V. N. Glazkov^1,2,*, Yu. V. Krasnikova^1,2, I. K. Rodygina^1,3, J. Chovan^4,5, R. Tarasenko⁶, and A. Orendáčová ⁶

¹P.L. Kapitza Institute for Physical Problems, RAS, Kosygina 2, Moscow 119334, Russia
²International Laboratory for Condensed Matter Physics, National Research University “Higher School of Economics,” Myasnitskaya strasse 20, 101000 Moscow, Russia
³Faculty of Physics, National Research University “Higher School of Economics,” Myasnitskaya strasse 20, 101000 Moscow, Russia
⁴IT4Innovations National Supercomputing Center, VSB-Technical University of Ostrava, 17, listopadu 2172/15, CZ 708 33 Ostrava, Czech Republic
⁵International Clinical Research Center, St. Anne's University Hospital, Pekarska 53, 656 91 Brno, Czech Republic
⁶Institute of Physics, P. J. Šafárik University, Park Angelinum 9, 040 00 Košice, Slovakia

^*glazkov@kapitza.ras.ru

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Vol. 101, Iss. 1 — 1 January 2020

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Figure 1
(a) Fragment of the $Cu (en) {(H_{2} O)}_{2} {SO}_{4}$ crystal structure projected on the $(b c)$ plane. Only copper ions are shown; thicker lines correspond to the strongest in-plane couplings. Layers shown by different shades of color are formed by atoms with a fractional $x$ coordinate of 0, 0.5, and 1.0. Relevant in-plane and interplane couplings are shown according to Ref. [11]. Ions within the adjacent $(a b)$ planes coupled by the DM interaction are marked as A, B1, and B2 ( $α$ , $β 1$ , and $β 2$ ). Schemes of (b) antiferromagnetic and (c) ferromagnetic stacking of the antiferromagnetically ordered $(b c)$ planes; blue and red arrows show ordered magnetic moment orientation, and green arrows show elementary translation $T = (a + b) / 2$ linking the neighboring planes.
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Figure 2
Temperature evolution of the resonance absorption in $Cu (en) {(H_{2} O)}_{2} {SO}_{4}$ at low temperatures. $f = 11.6$ GHz, $H | | b$ .
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Figure 3
Left: Temperature dependencies of the resonance field for three principal field directions, $f = 14.3$ GHz. Horizontal dashed lines mark the paramagnetic resonance field for the $g$ factor values for corresponding field directions. Right: Temperature dependencies of the apparent gap for three principal field directions. Symbols show the experimental data; solid lines show phenomenological fits of the temperature behavior of the gap below the transition point as described in the text. The vertical bar shows the error estimate.
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Figure 4
Frequency-field diagrams of resonance absorption at the base temperature $T = 0.45$ K. The top row shows low-frequency and low-field parts of $f (H)$ ; the bottom row shows higher-frequency or higher-field $f (H)$ for principal field directions. Symbols show experimental data, solid lines show low-field theory as described in the text, and the dashed line shows the high-field fit as described in the text. Numbers at data points x1, x2, and x3 show the number of split components observed below 0.6 K at a particular frequency.
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Figure 5
Dependence of the dipolar coupling energy per spin (in terms of effective field) on the order parameter orientation for ferromagnetic (blue circles) and antiferromagnetic (red squares) stacking of adjacent $(b c)$ planes. Symbols show computed values, and curves show the fit of the computed values by $A + B cos [2 (φ + δ)]$ ; the shift $δ$ is set to zero for the $(b a)$ -plane rotation and is used as a fit parameter for the $(a c)$ -plane rotation.
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Figure 6
Frequency dependence of the observed splitting of the AFMR resonance absorption line at the base temperature of 0.45 K (symbols). Solid curves show the model of two decoupled antiferromagnets with slightly different anisotropy parameters and the change in the anisotropy parameters above the spin-flop transition as described in the text. This model includes the $2^{\circ}$ tilt of the magnetic field at the nominal $H | | b$ orientation. The dotted curve in the middle panel represents the same model assuming zero tilt at $H | | b$ . The dashed curve corresponds to the model without a change in the anisotropy parameters above the spin-flop transition.
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Physical Review B

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Splitting of antiferromagnetic resonance modes in the quasi-two-dimensional collinear antiferromagnet $Cu (en) (H_{2} O)_{2} {SO}_{4}$

V. N. Glazkov, Yu. V. Krasnikova, I. K. Rodygina, J. Chovan, R. Tarasenko, and A. Orendáčová

Phys. Rev. B 101, 014414 – Published 10 January 2020

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Splitting of antiferromagnetic resonance modes in the quasi-two-dimensional collinear antiferromagnet Cu(en)(H2O)2SO4

V. N. Glazkov, Yu. V. Krasnikova, I. K. Rodygina, J. Chovan, R. Tarasenko, and A. Orendáčová

Phys. Rev. B 101, 014414 – Published 10 January 2020

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Splitting of antiferromagnetic resonance modes in the quasi-two-dimensional collinear antiferromagnet $Cu (en) (H_{2} O)_{2} {SO}_{4}$