High-frequency EPR at frequencies above 100 GHz

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Morgan Bell
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1 High-frequency EPR at frequencies above GHz Introduction High frequency EPR actually seems to have started off seriously already more than 3 years ago in Moskou under Y. Lebedev. Perhaps not too surprising as also the first EPR was recorded in Kazan. While the western world was still working on the first 35 GHz spectrometers, Yacov Lebedev pioneered at frequencies around 45 GHz. This didn t get a lot of attention in the west as most of the work was published in Russian, until in the eighties more people became aware and saw the possibilities of these techniques. Here one should especially mention J. Schmidt in Leiden and K. Mobius in Berlin, both of whom built sensitive, pulsed 95 GHz spectrometers, and which are still producing excellent results. This of course also caught the attention of Bruker, who now started a project of building a commercial spectrometer at 95 GHz. And with great success. Their spectrometer with its many possibilities and high sensitivity has made high-field magnetic resonance accessible to everyone, and has become an invaluable tool in the research in many disciplines. Now the 95 GHz is getting accessible to an ever growing community, more and more interest is focused towards the utilization of even higher frequencies. Currently home-build pulsed spectrometers exist at frequencies of 4 GHz in several places, based principally on the same techniques as at 95 GHz, and often with a signal-to-noise of the same order as at 95 GHz, which is 7-8 spins/g Hz. The highest-frequency pulsed spectrometer currently is in Frankfurt built by Thomas Prisner and his group operating at 8 GHz with a sensitivity of 9 spins/g Hz and a π/ pulse length of 6 ns. What will be focussed on here is to look at some technical and experimental aspects of high-frequency EPR that are less conventional and which focus primarily at the very-high-frequency applications.

2 Motivation The motivation for going to higher frequencies depends really on the spin system that one is interested in but they can be categorized as follows: Resolution Perhaps the most evident. While most interactions in the spin-hamiltonian are field-independent (fine-structure, hyperfine structure) the electron Zeeman term in the Hamiltonian is proportional to the field. (Biology). Sensitivity The sensitivity in terms of absolute number of spins that can be measured increases greatly with the frequency. (biology/chemistry). High-spin systems Some spin systems with S > ½ have such high zero-field splittings that transitions cannot be observed at ordinary frequencies. (chemistry/physics) High-field phases Coupled spin systems sometimes have different phases at high fields. (solid-state physics) The time factor The inherent timescale of an EPR experiment is inversely proportional to the frequency, while the experimental timescale could also be inversely proportional to the frequency. After discussing several technical aspects of high-frequency EPR, the sensitivity and time factor will be discussed in somewhat greater detail.

3 Techniques We will look at three facets here, and again focus on the very high frequencies:. Generation of (sub)millimeter waves. Transport of (sub)millimeter waves 3. Detection of (sub)millimeter waves (sub)millimeter wave sources We ll consider four types of sources, the Gunn diode, the molecular gas laser, the BWO, and the Gyrotron.. Gunn diodes and multipliers. Gunn-diodes are semi-conductor devices made from GaAs or InP. Their operation depends on a region of negative resistance (di/dv <) in their current voltage characteristics. This results in a bunched charge transport over the element, which will give rise to oscillations and radiation of microwaves, which are maintained by a resonant cavity coupled to the element. The maximum operating frequency is of the order of 4 GHz and output powers range from about 5 mw at GHz to 6 mw at 4 GHz. As a source for higher frequencies these sources have to be frequency multiplied, which in general is achieved with Schottky diodes. The power, however, goes down pretty quickly with the multiplication. In practice the multiplication loss (in db) is of the order 5log(N) with N the harmonic to be generated. So for the second harmonic one might achieve 7.5 db (6%), while for the 5 th harmonic 7.5 db (.8%) would be typical. These devices are usually mounted in single mode waveguide, and generate the output in a well-defined mode. The noise characteristics are quite reasonable, and they can be relatively easily locked to a low-frequency source. Power requirements: V. Price range: $7,-. Molecular gas lasers Molecular gas lasers have been used as a source for millimeter-waves also for EPR. The gas laser itself consists of a laser-cavity with a length of the order of.5 m filled with medium-pressure (around.- mbar) molecular gas. Metallic mirrors on each end form the cavity, while a metallic or dielectric tube both contains the gas and serves as an oversized waveguide. This gas is usually excited by a tunable single-mode CO laser with a power of the order of 5 W, and a wavelength around µm. While the gas is excited in some vibronic transition, the actual laser action then takes place between rotational levels of the molecular gas. Though in principal many different frequencies can be obtained this way, by changing the gas and the excitation wavelength,

4 they are always discrete frequencies and cannot easily be changed or locked to an external frequency source. The efficiency of the laser increases with frequency and quite decent power levels can be obtained from to GHz. The stability of the laser is one of the main concerns, and relatively long warm-up times are necessary. A good temperature stability of the room is great, and don t walk around too much. The /f noise is quite bad, but at frequencies above khz-khz, the noise get as good or better than that of a Gunn-diode. In general coupling out of the laser is achieved with a hole in one of the mirrors, and the mode is not always well-defined. Price range $,.-- Gunn Laser BWO Gyrotron Power (mw) Frequency Figure Typical power levels of different sources 3. Backward-wave oscillators (carcinotrons) The backward wave oscillators are related to traveling wave tubes. The principle of operation (like klystrons) is the bunching of electrons that are generated in an electron gun. The method of bunching in principle is nonresonant and the BWO s often can be tuned over a little less than an octave. Their availability is limited to the FSU, though some western companies will serve as middle man. They provide higher power than Gunn diodes, but tend to be a little noisier. They exist from Q-band frequencies to up to GHz, and the price is linear with the frequency. One disadvantage is the lifetime, which usually is specified to be of the order of hours. 4. Gyrotrons Gyrotrons also depend on bunching of electrons, but now the mechanism to do that is the cyclotron resonance. This gives it a very high efficiency and very high power levels of a couple of Watts can be achieved. This also means that a gyrotron requires magnetic fields of the same order of magnitude than the EPR field. This makes the device bulky and expensive. They are relatively noisy, but can be injection-locked.

5 Radiation transport waveguides and what not Single mode waveguide An efficient transport of the (sub)millimeter wave radiation to and from the sample is quite important at high frequencies. Superconducting magnets and the necessity to keep crucial equipment out of too high stray fields lead to a total pathway source-sampledetector easily of the order of 6 m or more. At lower frequencies rectangular single-mode waveguide is used and its beauty is precisely its single-mode character. You don t have to worry about exciting higher-order modes, you can make simple bends and twist and nice directional couplers and other passive components in a relatively simple way. However at high frequencies they are to be avoided wherever possible, and the simple reason is the attenuation. For the resistive losses in a waveguide we have α a λ with a the dimension of the waveguide. For a single-mode waveguide we thus find that the losses are proportional to ω 3/. For X-band and the TE rectangular mode the losses are of the order of.7 db per meter. For W-band (WR-) we thus get 6 db/m. For 3 GHz, db/m. That while the power is not too large to start with. Unacceptable. Oversized waveguide In oversized waveguide the losses are much smaller. There is no reason why X-Band waveguide does not transport GHz radiation. The attenuation will still increase with frequency but proportional to only ω /. The only danger is that many higher order modes fit in the waveguide and all elements not just straight waveguide and susceptible of exciting higher modes must be avoided. Tapers from single-mode to oversized with small tapering angles (~.5 degr) are needed and for bends and turns one still needs single-mode waveguide. For some applications, people are less worried about conservation of a well defined mode, in which case even gas-pipes will do as waveguides. Corrugated waveguides A recent introduction into EPR is the use of corrugated waveguides (Graham Smith). These have been used longer in plasma physics and astrophysics, but never quite made it to the EPR field. They are a special form of oversized waveguide, and consist in general of circular metallic waveguide that have corrugations of the order of λ/4 wide and deep. They actually behave much like dielectric waveguides, and the principal mode is the EH. The losses can be extremely small, down

6 to about. db/m. It is important to align the system well, and to couple into the waveguides correctly. That can be done either from a corrugated horn or from free space, as the EH mode couples well to a free space TEM -like mode. Free space transport In free space the attenuation is very small, and in vacuum zero. The question gets how to keep the beam together, how to avoid it diverging away. In combination with elements that act on the beam like directional couplers and wire-grid polarizers, this is now the realm of what is generally referred to as quasi-optics. Thus we make a side-step towards gaussian beam-mode optics.

7 ω beam waist Distance along beam Gaussian Beam Mode Optics Radiation moves in a paraxial beam, who s cross-sectional size is not sufficiently large to be able to treat it as a plane parallel beam The radiation can be treated as a scalar field distribution, with the wave equation Ñ \k \ and k = Sf/c For a beam moving in z-direction: Define u(x,y,z) with \ u(x,y,z) e -j(kz-5ft) Define : beam size/radius: Z beam curvature: R The waist is defined as the position of flat wavefront. Now we can use optical elements like lenses and mirrors to keep the beam together. However, optics are now frequency dependent: ω Amplitude ) ( ω r e r u = + = πω λ ω ω z + = z z R λ πω + + = f f o f o f i λ πω R s R i f + =

8 5 4 3 i/f s/f So using this kind of quasi-optics and quasi-optical elements one can construct a largeband high-frequency microwave bridge with very low losses. Various passive elements of a typical microwave bridge like attenuators, circulators, directional couplers have a quasioptical solution with small insertion loss. An example of a super-heterodyne quasi-optical microwave bridge will be shown.

9 (Sub)millimeter wave detectors: Current detection systems are either bolometric or heterodyne with Schottky diodes. Recently the bolometric detectors are being used as homodyne mixers. The main advantage of the bolometric detection is its large frequency range, while the main disadvantage is the small bandwidth, making it unsuitable for any pulsed applications. Faster bolometers exist, usually based on superconducting materials, but their sensitivity is still too small. Schottky diodes can in principle operate up to 8 GHz with for EPR very reasonable noise levels. However, homodyne detection is not a real option with this type of detector, and the spectrometer needs to be of the heterodyne or superheterodyne type. Bolometers Ge/Ga, Si bolometers : sensitive but 3 Hz bandwidth only NEP : - W/Hz / InSb hot-electron bolometers : 5-5 GHz, MHz bandwidth NEP : - W/Hz / Can be used as a homodyne mixer. Schottky diodes Other detectors Suitable for heterodyne detection (only) Noise temperature ~5 K ( -9 W/Hz) ¾ GHz bandwidth Needs to be optimized for frequency. SIS mixers for very low powers ~5 K Noise temperature (to 6 GHz)

10 Sensitivity Just some remarks with respect to sensitivity at high frequencies. Whereas the absolute sensitivity dramatically increases with frequency, of the order of / 4 ω for constant B in a cavity (Eaton&Eaton), the same is not true for the concentration sensitivity as also the sample decreases in size if coupling to a cavity. In some cases the use of a cavity at high fields does not have much advantages with respect to a cavity-less system. X-band (. nm/g) W-band x 7 (cyl) 4 x 8 (FP) x 8 x -33 GHz transmission 3 8 x 3 4 GHz CW superheterodyne 5 x 5 x 4 GHz FP cavity 5 x 8. 5 x 3

11 Time As the measurement time is inversely proportional to the frequency, in general we are able to perform faster measurements. This means that we are more sensitive to faster spin dynamics in CW experiments. This was already demonstrated by Y. Lebedev in the early seventies, and greatly exploited by J. Freed and others. Related to the faster measurement time this is the fact that we can also measure faster, we have shorter dead-times in a pulsed experiment, and can in principle measure faster in transient EPR. On the other hand not so much is known about the changes in relaxation rates by going to high fields. The general consensus is that T rates get longer. However, concerning T not much experimental data exist although the higher phonon density at higher frequency would suggest that T decreases with field in the case of direct relaxation processes. ENDOR and ESE at higher frequencies ESE and ENDOR at 95 and 4 GHz have shown some very beautiful results, but what is its future at even higher frequencies. Some exotic approaches and some typical highfield results will be discussed.

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