## 1 Introduction  
A rapidly expanding application of THz radiation in science and technology has been marked, in particular, with construction of many new types of detectors which were not considered in the old era of \"far-infared physics\". Development of a THz time-domain spectroscopy technique with THz emitters and detectors activated with fs laser pulses has confered a special status to THz spectroscopy. On the other hand, detectors working in a continuous wave mode are also required. A typical example is a bolometer coupled to a Fourier spectrometer. Let us notice that in this case, as well in the case of a detector used in a time-domain spectroscopy arrangement, one deals with a device with a broad-band response and a spectral dependence of the measured signal is obtained due to off-detector instrumentation: a Fourier spectrometer itself or measurements in the time domain, respectively. An important problem which has been attacted for decades from different directions is to construct a resonant and tuneable THz detector, possibly working at room temperature. Such a detector could work as a spectrometer, giving a spectrum of measured signal without necessity of application of additional intrenmentation. Great expectations were awaken with two seminal papers of [PERSON] and [PERSON] [1, 2] who proposed that plasma oscillations in a gated two-dimensional electron gas (2 DEG)in the channel of a field-effect transistor could lead to emission [1] or detection [2] of THz radiation. An important prediction of these papers was tuneability of the frequency of plasmonic resonances with the gate voltage or drain current. An experimental proof of feasibility of detection of THz radiation with Silicon nanotransistors at room temperature [3] triggered two paths of research. One of them was a rapid development of Silicon-based detectors (see, e.g., [4]) while the other was to look for other semiconductor structures with a 2 DEG which included, in particular, GaAs/GaAlAs heterostructures [5; 6] and graphene [7]. Although tuneability of the resonant response was shown in these detectors by adjustment of the substrate thickness [6] or gate voltage [7], there is still need to look for other solutions. The present study aims to characterize a resonant response of THz detectors based on CdTe/CdMgTe quantum wells with magnetic field (\(B\)) as the tuning parameter. Magnetic-field-tuneable detectors are cryogenic detectors and require a strong magnetic field of a few T which can be thought of, at first sight, as a disadvantage. However, modern cryogen-free technologies allow to generate low temperatures and magnetic fields up to a few T so this is not a real obstacle (if one accepts the cost of equipment). On the other hand, such detectors show a number of advantages. First, their working temperature suppresses the thermal noise which limits performance of room-temperature detectors. This seems to be crucial when such detectors are used to characterize new THz sources which can be rather weak at the first stages of development [8; 9]. Second, depending on the material chosen, one can get quite a broad tuneablity of a few THz of the resonant response sweeping the magnetic field by a few T.  
The principle of operation of these detectors, i.e., resonant detectors tuneable with magnetic field, is based either on intra shallow impurity transitions [10] or a cyclotron resonance (CR) transition [11]. Practically, at the moment, there are only two materials which are used for fabrication of resonant detectors tuneable with \(B\): GaAs which can be used both as a detector working on intra impurity and CR transitions, and InSb which can be used as a detector working only on CR transitions because of a negligible energy of ionization of impurities in this material. These detectors are mainly used as photocurrent detectors and then their applicability is limited by two factors.