ESR study of the spin ladder with uniform Dzyaloshinskii-Moriya interaction

V. N. Glazkov, M. Fayzullin, Yu. Krasnikova, G. Skoblin, D. Schmidiger, S. Mühlbauer, and A. Zheludev

Phys. Rev. B 92, 184403 – Published 3 November 2015

Abstract

Evolution of the ESR absorption in a strong-leg spin ladder magnet ${(C_{7} H_{10} N)}_{2} {CuBr}_{4}$ (abbreviated as DIMPY) is studied from 300 K to 400 mK. Temperature dependence of the ESR relaxation follows a staircase of crossovers between different relaxation regimes. We argue that the main mechanism of ESR line broadening in DIMPY is uniform Dzyaloshinskii-Moriya interaction $(| D | = 0.31$ K) with an effective longitudinal component along an exchange bond of Cu ions within the legs resulting from the low crystal symmetry of DIMPY and nontrivial orbital ordering. The same Dzyaloshinskii-Moriya interaction along with other weaker anisotropic spin-spin interactions results in the lifting of the triplet excitation degeneracy, revealed through the weak splitting of the ESR absorption at low temperatures.

Received 9 July 2015
Revised 28 August 2015

DOI:https://doi.org/10.1103/PhysRevB.92.184403

Authors & Affiliations

V. N. Glazkov^1,2,*, M. Fayzullin³, Yu. Krasnikova^1,2, G. Skoblin^1,2,†, D. Schmidiger⁴, S. Mühlbauer^4,‡, and A. Zheludev⁴

¹P. L. Kapitza Institute for Physical Problems RAS, Kosygin strasse 2, 119334 Moscow, Russia
²Moscow Institute of Physics and Technology, 141700 Dolgoprudny, Russia
³Institute for Physics, Kazan Federal University, 18 Kremlyovskaya strasse 18, 420008, Kazan, Russia
⁴Neutron Scattering and Magnetism, Laboratory for Solid State Physics, ETH Zürich, 8006 Zürich, Switzerland

^*glazkov@kapitza.ras.ru
^†Current address: Quantum Device Physics Laboratory, Department of Microtechnology and Nanoscience, Chalmers University of Technology, SE-412 96 Göteborg, Sweden.
^‡Current address: Heinz Maier-Leibnitz Zentrum (MLZ), Garching D-85748, Germany.

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Vol. 92, Iss. 18 — 1 November 2015

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Images

Figure 1
Crystallographic structure of DIMPY with two magnetically nonequivalent spin ladders. Only Cu and Br ions are shown along with the main exchange bonds $J_{leg}$ and $J_{rung}$ . Solid arrows (red) indicate directions of $g$ tensor main axes for inequivalent ladders. Dashed arrows (blue) indicate directions of the Dzyaloshinskii-Moriya vectors for inequivalent ladders, as found from the data fit (see text). Broad double-headed arrows links the DM vector and $g -tensor$ axis corresponding to the same ladder.
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Figure 2
Inset: Example of ESR absorption spectra at representative orientations. Symbols: experimental data, curves: best fit with Lorentzian line shape, and vertical lines correspond to corresponding $g -factor$ values. Narrow line with $g = 2.00$ (at 6.13 kOe) is a DPPH marker. Upper row: Angular dependence of the $g$ factor at 77 K. Symbols: experimental data, curves: uniaxial $g -tensor$ best fit (see text). Experimental error is about 0.1% and is within symbol size. Lower row: Angular dependence of the ESR linewidth at $f = 17.2$ GHz, $T = 77$ K (half-width at half-height). Vertical bar in left panel shows typical error bar size (double error). Curves: model description (see text), solid lines show full linewidth, dashed and dotted lines show contributions due to DM and SAE interactions, respectively. Marks “1” and “2” indicate contributions corresponding to the same ladder.
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Figure 3
ESR absorption spectra at low temperatures, $H | | (X + Y)$ . Vertical dashed lines mark resonance fields corresponding to the shown $g -factor$ values. Horizontal dashed line at the 0.45 K curve is a guide to the eye at zero-absorption level. Narrow absorption line at $g = 2.00$ is a DPPH marker.
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Figure 4
ESR absorption spectra at the temperature $T \approx 1$ K at different frequencies, $H | | (X + Y)$ . All spectra are shifted along the field axis to fit positions of the main absorption subcomponents. Left panel: Left absorption component $(g \approx 2.28)$ , weak absorption subcomponent is magnified by a factor of 5 or 10 for better presentation. Right panel: Right absorption component $(g \approx 2.05)$ . Vertical dashed lines mark positions of the absorption subcomponent at lowest frequency. Triangles on the right panel mark positions of the DPPH marker absorption $(g = 2.00)$ .
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Figure 5
Left panel: Temperature dependence of the ESR intensity below 1 K at $f = 34.6$ GHz, $H | | (X + Y)$ . Inset: Examples of ESR absorption and ESR components and subcomponents notations. Symbols: experimental data, dashed lines: fits with thermoactivation law $I \propto exp (- Δ / T)$ . Right panel: Dependence of the determined activation gaps for different spectral subcomponents. Filled symbols: intense A1 and B1 subcomponents, open symbols: weak A2 and B2 subcomponents. Lines: parameters-free model dependence calculated with the zero-field gap value $Δ_{INS}$ known from the inelastic neutron scattering experiments [9, 10]. Inset: Scheme of the energy levels of a spin-gap magnet in a magnetic field. Solid vertical arrows show transitions corresponding to the observed ESR absorption, dashed vertical arrows mark activation gaps for these transitions.
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Figure 6
Temperature dependence of the ESR linewidth. Upper panel: $H | | (X + Y)$ . Circles: low-field $(high- g)$ component, squares: high field $(low- g)$ component. All data are measured on the samples from the same batch. Lower panel: $H | | Y$ . Filled and open symbols correspond to the data measured on samples from different batches. Experimental data were collected in different experimental setups operating at different frequencies, vertical lines mark approximate temperature boundaries for different experiments, and microwave frequencies of each experiment are given. Typical error bar size is around symbol size. Curves on both panels show empirical fit equations (see text and Table 1).
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