Discrete helicoidal states in chiral magnetic thin films

M. N. Wilson, E. A. Karhu, D. P. Lake, A. S. Quigley, S. Meynell, A. N. Bogdanov, H. Fritzsche, U. K. Rößler, and T. L. Monchesky

Phys. Rev. B 88, 214420 – Published 20 December 2013

Abstract

Magnetoresistance (MR), polarized neutron reflectometry (PNR), and magnetometry measurements in MnSi thin films and rigorous analytical solutions of the micromagnetic equations show that the field-induced unwinding of confined helicoids occurs via discrete steps. A comparison between the theoretical results and the PNR and magnetometry data shows that finite-size effects confine the wavelength and lead to a quantization of the number of turns in the helicoid. We demonstrate that the magnetic state of these finite helicoids can be read by electrical means.

Received 4 September 2012
Revised 2 December 2013

DOI:https://doi.org/10.1103/PhysRevB.88.214420

Authors & Affiliations

M. N. Wilson¹, E. A. Karhu¹, D. P. Lake¹, A. S. Quigley¹, S. Meynell¹, A. N. Bogdanov², H. Fritzsche³, U. K. Rößler², and T. L. Monchesky^1,*

¹Department of Physics and Atmospheric Science, Dalhousie University, Halifax, Nova Scotia, Canada B3H 3J5
²IFW Dresden, Postfach 270116, D-01171 Dresden, Germany
³Canadian Neutron Beam Centre, Chalk River Laboratories, Chalk River, Ontario, Canada K0J 1J0

^*theodore.monchesky@dal.ca

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Vol. 88, Iss. 21 — 1 December 2013

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Images

Figure 1
(a) Calculated spin configurations for a helimagnet thin film of thickness $d = 2.14 L_{D}$ with applied in-plane fields $H = 0.25 H_{D}$ (left), $0.55 H_{D}$ (middle), and $0.61 H_{D}$ (right). (b) Component of $M$ along $H$ as a function of field and depth in the film of thickness $d = 2.14 L_{D}$ . (c) The average energy density for the linear approximation given by Eq. (2) for $d = 1.83 L_{D}$ (left) and $d = 2.14 L_{D}$ (right) in applied fields $H = 0.0 H_{D}, 0.2 H_{D}, 0.4 H_{D},$ and 0.6 $H_{D}$ .
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Figure 2
Magnetoresistance measured at $T = 5$ K for film thicknesses (a) 2.14 $L_{D}$ and (b) 1.83 $L_{D}$ in a field $H ∥ MnSi [1 \bar{1} 0]$ . Open circles are the decreasing field data, and solid squares are increasing field. Marked fields $H_{h 1}$ and $H_{h 2}$ are the transition fields taken from magnetometry measurements from the increasing branch data. (c) The slope of the magnetoresistance (blue squares) compared to $η_{0}$ (black line) from Eq. (3). The red line shows $η_{0}$ with 0.9-nm rms thickness variations.
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Figure 3
(a) Magnetization (blue squares) and magnetic susceptibility (black squares) for the $1.92 L_{D}$ sample at $T = 5$ K, plotted with the PNR measurement fields indicated by the red circles and transition fields shown by dotted lines. (b) PNR cross section for $R_{-}$ (red squares) and $R_{+}$ (black circles) reflectivities for the $1.92 L_{D}$ sample measured at $T = 5$ K, $μ_{0} H = 0.7$ T. Solid lines show the calculated spin-up (red) and spin-down (black) reflectivity. (c)–(f) Measured (black circles) and calculated (red line) spin asymmetry for the $1.92 L_{D}$ sample at $T = 5$ K, $μ_{0} H = 700$ , 400, 200, and 32 mT. (g)–(j) Magnetization depth profiles used to calculate the spin asymmetries shown in (c)–(f). The blue line in (c) shows the spin asymmetry calculated for the ferromagnetic state with a depth profile shown by the blue line in (g). All error bars are $\pm 1 σ$ .
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Figure 4
(a) Critical fields extracted for increasing (solid triangles) and decreasing (open triangles) magnetic fields with $H ∥ MnSi [1 \bar{1} 0]$ at $T = 5$ K. The solid red lines are the calculated threshold fields for the removal of a turn in the helicoid. (b) The dc susceptibility measurements in an increasing magnetic field for thicknesses $L_{D} < d < 2.85 L_{D}$ , offset vertically for clarity. Red dashed lines track the observed transition fields.
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Figure 5
The field dependence of the wavelength for a bulk crystal (black) and a film with thickness $d = 2.14 L_{D}$ (red). The dashed lines indicate the critical fields $H_{h 2}$ and $H_{h 1}$ , as well as $H_{h} = π^{2} H_{D} / 16$ , where an infinite helicoid breaks into a series of isolated $360^{\circ}$ domain walls.
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