We study experimentally and theoretically the temperature dependence of transverse magnetic routing of light emission from hybrid plasmonic-semiconductor quantum well structures where the exciton emission from the quantum well is routed into surface plasmon polaritons propagating along a nearby semiconductor-metal interface. In II-VI and III-V direct band semiconductors the magnitude of routing is governed by the circular polarization of exciton optical transitions, that is induced by a magnetic field. For structures comprising a (Cd,Mn)Te/(Cd,Mg)Te diluted magnetic semiconductor quantum well we observe a strong directionality of the emission up to 15% at low temperature of 20 K and magnetic field of 485 mT due to giant Zeeman splitting of holes mediated via the strong exchange interaction with Mn$^{2+}$ ions. For increasing temperatures towards room-temperature the magnetic susceptibility decreases and the directionality strongly decreases to 4% at T = 45 K. We also propose an alternative design based on a non-magnetic (In,Ga)As/(In,Al)As quantum well structure, suitable for higher temperatures. According to our calculations, such structure can demonstrate emission directionality up to 5% for temperatures below 200 K and moderate magnetic fields of 1 T.
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