Direct probing of band-structure Berry phase in diluted magnetic semiconductors

M. Granada, D. Lucot, R. Giraud, A. Lemaître, C. Ulysse, X. Waintal, and G. Faini

Phys. Rev. B 91, 235203 – Published 11 June 2015

Abstract

We report on experimental evidence of the Berry phase accumulated by the charge-carrier wave function in single-domain nanowires made from a (Ga, Mn)(As, P) diluted ferromagnetic semiconductor layer. Its signature on the mesoscopic transport measurements is revealed as unusual patterns in the magnetoconductance that are clearly distinguished from the universal conductance fluctuations. We show that these patterns appear in a magnetic field region where the magnetization rotates coherently and are related to a change in the band-structure Berry phase as the magnetization direction changes. They should thus be considered a band-structure Berry phase fingerprint of the effective magnetic monopoles in the momentum space. We argue that this is an efficient method to vary the band structure in a controlled way and to probe it directly. Hence, (Ga, Mn)As appears to be a very interesting test bench for new concepts based on this geometrical phase.

Received 22 September 2013
Revised 20 April 2015

DOI:https://doi.org/10.1103/PhysRevB.91.235203

Authors & Affiliations

M. Granada^1,2, D. Lucot¹, R. Giraud¹, A. Lemaître¹, C. Ulysse¹, X. Waintal³, and G. Faini^1,*

¹CNRS, Laboratoire de Photonique et de Nanostructures, route de Nozay, 91460 Marcoussis, France
²CONICET, Centro Atómico Bariloche, 8400 San Carlos de Bariloche, Río Negro, Argentina
³SPSMS, UMR-E 9001, CEA-INAC/UJF-Grenoble 1,17 rue des Martyrs, 38054 Grenoble cedex 9, France

^*Author to whom correspondence should be addressed: giancarlo.faini@lpn.cnrs.fr

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Vol. 91, Iss. 23 — 15 June 2015

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Images

Figure 1
(a) Schematic view of the orientation of crystallographic axes of the sample and applied field direction angles $θ, φ$ . B denotes the applied magnetic field, M denotes magnetization, and $θ_{M}$ is the magnetization angle from the easy axis [001]. In the present work, $φ$ is fixed to $90^{\circ}$ . (b) Scanning electron microscope image of a Hall bar indicating the numbering of voltage contacts and the direction of electric current $I$ . (c)–(e) The voltage at each contact is indicated for different magnetization configurations. $V_{H}$ is the Hall voltage, $I R$ is the longitudinal voltage drop, and $V$ is an offset voltage referred to ground. (c) The magnetization is homogeneous throughout the sample. (d)–(e) There is a DW in the constriction, with the magnetization presenting opposite sign at both sides.
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Figure 2
(a) Hall voltages measured on the left (circles) and right (squares) of the constriction throughout a field sweep at $T = 4$ K. In the region between the different positive coercive fields, the Hall voltages on both sides of the constriction with opposite sign indicate that a domain wall is present in the constriction. (b) Another realization of the same experiment displaying the opposite order in the magnetization reversal on both sides of the constriction. (c)–(d) Longitudinal voltage $V_{L}^{24}$ measured simultaneously with the Hall voltages displayed on top. The presence of a domain wall can be detected in the longitudinal voltage due to a Hall effect contribution [ $I R \pm V_{H}$ in Figs. 1 and 1]. The left panels present a measurement with the magnetization configuration described in Fig. 1, while the results displayed in the right panels correspond to the case in Fig. 1.
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Figure 3
(a) Magnetoconductance measured in a four-probe configuration at different temperatures, with the magnetic field applied along the magnetization easy axis. (b) Temperature dependence of the rms amplitude $δ G$ normalized to the distance between contacts L. Red symbols are data obtained in this work for GaMnAsP, and black symbols are data presented in Ref. [15]; different symbol shapes correspond to samples of different sizes.
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Figure 4
Magnetoconductance measured at $T = 135$ mK with the magnetic field applied at different angles $θ$ from the easy axis of magnetization. The curves for $θ > 10^{\circ}$ are vertically shifted for clarity.
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Figure 5
Magnetoconductance measured at different temperatures with a fixed magnetic field direction, with $θ = 80^{\circ}$ . The curves for $T > 95$ mK are vertically shifted for clarity. The vertical gray lines are a guide to the eye, indicating the position of consecutive maxima of $G$ .
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Figure 6
Temperature dependence of (a) the pseudoperiod $B_{c}$ and (b) the amplitude $δ G$ of the fluctuations in the high-field (squares) and low-field (circles) regimes. $B_{c}$ of the low-field regime is multiplied by 10.
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