new cavity design for broad-band quasi-optical hf-epr spectroscopy

New Cavity Design for Broad-Band Quasi-OpticalHF-EPR Spectroscopy

Petr Neugebauer • Anne-Laure Barra

Received: 15 May 2009 / Revised: 28 June 2009 / Published online: 16 November 2009

� Springer 2009

Abstract The design and performance of two new devices adapted for high-

frequency electron paramagnetic resonance (HF-EPR) in a broad frequency range

are described. Both systems, a Fabry–Perot resonator and a rotating sample holder,

rely on similar construction schemes and on the use of submicrometer piezoelectric

positioners. A study of a single crystal of graphite allows illustrating the operation

of these two new systems associated with our quasi-optical HF-EPR spectrometer.

1 Introduction

High-frequency/high-field electron paramagnetic resonance (HF-EPR) has seen a

continuous growth during the last decades and this trend is still developing. From

the beginning of HF-EPR and even nowadays, very different spectrometers have

been built and used, ranging from the simple single-pass transmission systems [1–3]

to the highly optimized single-frequency spectrometers [4, 5] using resonant cavities

and waveguide techniques. Several reviews illustrating the advances of HF-EPR

spectroscopy have now been published [6–9]. Single-pass transmission spectrom-

eters allow very broad frequency operation but have low sensitivity; they are thus

well suited for the study of concentrated spin systems like low-dimensional

magnetic complexes. Conversely, optimized single-frequency HF-EPR spectrom-

eters are particularly useful for the study of diluted spin systems and/or species

available in very small quantities as it is often the case with biological paramagnetic

species. However, most of the HF-EPR spectrometers are now using quasi-optical

(QO) techniques [4–15], especially when dealing with frequencies higher than

200 GHz. The predominance of QO systems has followed the work of the group of

P. Neugebauer � A.-L. Barra (&)

Grenoble High Magnetic Field Laboratory, LNCMI-CNRS,

B.P. 166, 38042 Grenoble Cedex 9, France

e-mail: [email protected]

123

Appl Magn Reson (2010) 37:833–843

DOI 10.1007/s00723-009-0092-5

Applied

Magnetic Resonance

Riedi and Smith [13] in St. Andrews, with the association of QO components

(mirrors, polarizers, Faraday rotators, etc.) outside the cryostat to corrugated

waveguides in the confined space of the cryostat. Similarly, besides the standard

single-pass transmission system used in our laboratory for more than two decades,

we implemented a few years ago a new setup, relying on quasi-optical techniques

but still working within a simple transmission scheme [15]. This intermediate

approach was developed with the goal of maintaining as much as possible the

multifrequency property of the basic single-pass spectrometer, while overcoming its

main imperfections, namely low sensitivity and phase mixing problems.

To extend and improve the spectrometer operation with the QO configuration, we

recently developed two new devices. Both systems imply similar designs and

depend primarily upon piezoelectric submicropositioners, able to operate at low

temperature and in the presence of an external magnetic field, and being small

enough for the space available in the cryostat. The first system is a one-axis rotating

holder for single-crystal measurements allowing an almost complete rotation

(*340�), while the other one is a semiconfocal Fabry–Perot resonator. In both

cases, the use of the piezoelectric steppers leads to a net gain in precision with

respect to the previous purely mechanical constructions. These two devices can be

associated to multifrequency operation. However, the Fabry–Perot resonator has

also been designed as a part of a new pulsed high-field EPR spectrometer, which

will operate at a unique frequency close to 283 GHz. In this frame, the QO bridge is

modified for heterodyne operation and the bolometric detection is replaced by a

mixer. This allowed showing that the increase in resolution on the position of the

movable mirror of the Fabry–Perot resonator leads to an important improvement of

the finesse of the resonator.

Here we wish to illustrate the performances of these new devices, mostly

focusing on continuous-wave HF-EPR spectroscopy.

2 Experimental Setup

Most of the measurements presented here have been performed with the QO bridge

(Thomas Keating, UK) in homodyne configuration. Only the determination of the

finesse of the Fabry–Perot resonator was done with the heterodyne configuration. A

sketch of the QO setup for both configurations is presented in Fig. 1. For the

homodyne measurements (Fig. 1a), the exciting frequencies used range from 190 to

285 GHz and are supplied by two Gunn oscillators (basic frequencies of 95 and

115 GHz) and their multipliers (Radiometer Physics, Germany). For heterodyne

operation (Fig. 1b), the exciting frequency is 283.2 GHz supplied by a Gunn

oscillator with a basic frequency of 141.6 GHz, equipped with a doubler

(Radiometer Physics, Germany), while the reference frequency is 285 GHz

(95 GHz Gunn oscillator with frequency tripler). Inside the cryostat, a corrugated

waveguide with an inner diameter of 18 mm is used, propagating a main HE11

mode. At the end of the corrugated waveguide, a corrugated taper with an output

diameter of 6 mm is used for the interconversion of the HE11 mode to a Gaussian

beam with a waist of 1.9 mm. There, either the rotating system associated to a

834 P. Neugebauer, A.-L. Barra

123

smooth 6 mm diameter guide with simple transmission configuration, or the Fabry–

Perot open-type resonator are connected.

The measurements are performed in a 12 T superconducting magnet (Cryogen-

ics, UK) equipped with a bipolar power supply (Oxford Instruments, UK). A

variable-temperature insert (Oxford Instruments, UK) allows covering a tempera-

ture range from 1.5 to 300 K, with the sample being directly in the helium flux. The

detection is performed either with a hot electron InSb bolometer (QMC Instruments,

Detector Source DetectorLocal Osc.

WirePolarizer

Quartz Osc.

(b)

(a)

Source

Faraday Rotator

BeamSplitter

EllipticalMirror

Corrugated Waveguide

Superconducting Magnet

FP Cavity

Sample Position

Fig. 1 Simplified scheme of the EPR spectrometer with the QO bridge. The linearly polarized excitingbeam (black arrow) is led through the QO bridge toward the corrugated guide and taper, placed on top ofthe Fabry–Perot (EP) cavity inside the modulation coil, by a series of refocusing elliptical mirrors andpolarizers (dotted lines). The spectrometer operates in induction mode; thus the EPR signal (white arrow)is selected by the polarizer on top of the cryostat and sent to the detector. The backward reflectedmicrowave (gray arrow) is filtered out by the Faraday rotator. a Homodyne configuration with bolometerdetection and a beam splitter producing the reference signal (dashed arrow) for homodyne operation.b Heterodyne configuration with a mixer used for the detection. The reference frequency is produced byan additional source (local oscillator), both sources (exciting and reference) being looked to the samequartz oscillator

Broad-Band Quasi-Optical HF-EPR Spectroscopy 835

123

UK) for most of the measurements, or with a tuned, electronically biased GaAs

Schottky diode acting as a mixer (Radiometer Physics, Germany) for the heterodyne

operation. In this last case, the 283.2 GHz frequency of the signal is mixed with the

local oscillator signal at 285 GHz and thus is downconverted to an intermediate

frequency of 1.8 GHz, which is amplified (Miteq, USA), filtered (Microtronics, USA)

and detected with a coaxial tunnel diode detector (Advancd Control Components,

USA).

The two new devices have been designed to be connected at the end of the

corrugated taper. They both consist of a plastic structure made of Torlon (polyamide

imide), a thermoplastic material with high strength and stiffness, housing a

submicropositioner (Attocube, Germany). For the Fabry–Perot cavity, the submicro-

positioner is a linear one with an intrinsic minimum step of about 0.1 lm and

a maximum range of 2.5 mm, whereas for the rotating single-crystal holder, it is a

horizontal-axis rotating one with an intrinsic minimum angle variation of 0.01� and a

total encoded range of 340� (actually, the piezoelement can rotate over 360� but the

resistive encoding used for the position determination reduces the angle range to 340�).

2.1 Fabry–Perot Resonator

The Fabry–Perot resonator has a semiconfocal configuration, with a flat partially

reflective mirror, placed at the beam waist of the Gaussian beam, on the one side

and a spherical mirror on the otherside. A scheme of the Fabry–Perot resonator

design is shown in Fig. 2. The partially reflective mirror, used to couple microwaves

into the resonator, is obtained by a square mesh of inductive type prepared in-house

by ultraviolet lithography of gold on silica cover glass. Thus meshes are easy to

handle and keep their characteristics down to low temperatures. A typical mesh has

75 lines/inch, which corresponds to a grid spacing g of 0.34 mm. With a typical

Fig. 2 Scheme of the Fabry–Perot cavity with the housingsupporting the partiallyreflective mirror (dashed line).The piezoelectric positioner isshown in dashed area. Themodulation coil is representedby the crossed area


123

width (2a) of the lines of about 200 lm, the g/(2a) ratio amounts to about 1.7. This

ratio describing the grid pattern affects strongly the resonant behavior of the

inductive mesh, which, in turn, drives the frequency dependence of its reflectivity

[16]. For g/(2a) = 1.7, the reflectivity is essentially constant for a reduced

wavelength g/k ranging from 0 to about 0.5. As our frequency range of interest

corresponds to g/k varying between 0.2 and 0.32, the mesh presents essentially

constant reflectivity. Commercial concave glass mirrors coated by gold (Thorlabs)

are used for the spherical mirror, with a radius curvature of 24 or 50 mm.

The concave bottom mirror is glued on a plunger placed on the piezoelectric

submicropositioner, which controls the distance between the two mirrors. On

mounting, the position of the mesh can be adjusted over more than 1 mm with

respect to the corrugated waveguide, allowing taking into account different waist

positions. The mirrors distance can be varied over 2.5 mm, allowing coming across

several modes of the Fabry–Perot resonator (5 modes at 283 GHz, for instance). At

283 GHz, the mirror is placed at a distance of about 2 mm from the mesh, which

corresponds to a fourth mode of operation (TEM004).

The performance of a Fabry–Perot resonator is better described by its finesse Fthan by its quality factor Q, the finesse being defined by F = Q/n, where n is the

order of the mode. Theoretically, the finesse Fth depends only on the reflection

coefficients of the mirrors, but any imperfection in the system will reduce the real

value. Experimentally, it is defined as the ratio of the distance D between successive

resonance modes with the resonance full line width at half-maximum dFWHM:

Fexp = D/dFWHM. The heterodyne operation of the spectrometer allows measuring

precisely the finesse (Figs. 3, 4 inset). At 283.2 GHz, Fexp varies from 140 to 200,

depending on the mode considered for the resonator loaded with a grain of graphite,

whereas it reaches 400 for a thin polystyrene film with a,c-bisdiphenylene-

0 150 300 450 600 750 900

A

B

6 57 4

Sig

nal

inte

nsi

ty (

dB

m)

Position (a.u.)

8

Fig. 3 Resonance fringes of the Fabry–Perot resonator loaded with a single crystal of graphite at283.2 GHz as a function of the mirrors distance. The modes numbers are indicated on the graph. For eachnumber n, besides the main TE00n mode, higher-order resonances are observed. The finesse Fexp isobtained from the ratio A/B. Fexp varies from 140 to 200 depending on n


123

b-phenylallyl (BDPA) deposited on the mirror (Fig. 4 inset). This is a good result as

the theoretical value, calculated using the formula Fth = (pffiffiffi

Rp

)/(1 - R) [17], with

R being the gold power reflection coefficient [18], is found to be Fth * 1800.

A modulation coil is wound outside the housing for continuous-wave operation.

It has a maximum field amplitude of about 10 G at frequencies below 1 kHz. The

measurements presented here have been performed with the sample placed on the

bottom mirror.

2.2 Rotating Sample Holder

The new rotating holder has been designed for operation in transmission, without

the Fabry–Perot resonator. The approach developed for the construction of the

Fabry–Perot resonator was adapted for building a rotating holder for orientation

study (Fig. 5). The system relies on a rotating piezoelectric positioner with a

resistive encoder allowing an absolute measurement of the angle. Due to the lack of

space in the cryostat, it has not been possible to use directly the piezoelectric

element to rotate the sample holder. Thus, a gear mechanism had to be introduced,

with one gear driven by the rotating piezoelectric device. The driven gear bears the

10.10 10.11 10.12 10.13

Sig

nal

inte

nsi

ty (

a.u

.)

Magnetic Field (T)

800 900 1000 1100 1200 1300Position (a u )

Sig

nal

inte

nsi

ty

45

B

A

Fig. 4 EPR spectrum of a thin film of BDPA, containing *2 9 1014 spins, recorded with the Fabry–Perot resonator at 283.2 GHz and 10 K, with a modulation amplitude of 0.9 G. The spectrometer wasoperated in heterodyne configuration. The S/N is higher than 5 9 105. Inset resonance fringes for thismeasurement (Fexp = 400)


123

Teflon holder for the sample. The mechanical gear is responsible for the main

uncertainty on the rotation position, which is, however, less than 1�. A direct use of

the rotating piezoelectric positioned should allow decreasing this uncertainty by one

order of magnitude. A flat mirror is placed below the sample for the reflection of the

far infrared excitation. A smooth guide with an inner diameter of 6 mm is used to

propagate the exciting millimeter wave from the corrugated taper to the top of the

gear mechanism, a few millimeters apart from the sample. Similarly to the previous

device, a modulation coil is wound directly onto the Torlon housing of the rotating

sample holder. It has a maximum field amplitude of 25 G (with respect to only 10 G

for the Fabry–Perot system), resulting from the smaller dimensions of the rotating

holder assembly which allowed having more turns for the coil.

3 Results

The sensitivity of the resonator, associated to the heterodyne QO configuration of

the spectrometer, was tested by measuring several samples. Here we report the

results obtained on BDPA dissolved in toluene together with polystyrene. The

solution was deposited on the bottom mirror and the solvent was let to evaporate to

obtain the film. The number of spins was estimated to be about 2 9 1014. The

spectrum obtained at 10 K at 283.2 GHz is shown in Fig. 4. It gave a signal-to-noise

ratio S/N * 5 9 105, to be associated to the loaded finesse Fexp = 400 (Fig. 4

inset). Taking into account the resonance line width of 6 G and a time constant of

0.3 ms, the absolute sensitivity at 10 K is found to be 2 9 107 spins/(G.s), which

corresponds to a room-temperature absolute sensitivity of 3 9 108 spins/(G.s).

Similar results were obtained for the other test samples. This sensitivity compares

Fig. 5 Scheme of the rotatingholder showing the gears and thepiezoelectric rotator (dashedarea). The sample (black point)is placed on a teflon support.The modulation coil isrepresented by the crossed area


123

very well, even if measured at a unique frequency in heterodyne configuration up to

now, to previously reported results on high-field multifrequency Fabry–Perot

resonator [19].

So far, the best illustration of the performances of both devices, the Fabry–Perot

resonator, on the one hand, and the rotating sample holder, on the other hand, has

been obtained with a study performed on a natural graphite single-crystal sample.

The interest into this well-known bulk material has been recently renewed due to

fabrication of graphene, a single layer of graphite, i.e., a two-dimensional (2-D)

lattice of carbon atoms with honeycomb symmetry, and the subsequent discovery of

Dirac fermions in it. Indeed, it remains an open question whether graphite is a 2-D

material with very loosely coupled layers or whether it is a 3-D material, in which

the sheets are coupled by overlapping wavefunctions [20]. The coupling between

the layers drastically changes the physical properties of the system: at the K point,

carriers in graphite are massive electrons, whereas the presence of Dirac-like charge

carriers with a zero rest mass was evidenced in graphene.

Using the Fabry–Perot resonator together with the heterodyne configuration of

the spectrometer, a cyclotron resonance study of a single crystal of natural graphite

with the magnetic field applied perpendicular to the carbon layers was performed at

283.2 GHz and 7.5 K. Cyclotron resonance allows probing the transitions between

the Landau levels induced in graphite by the application of a static magnetic field.

Precise cyclotron resonance measurements on massive electrons in the vicinity of

the K point of the graphite Brillouin zone (an electron pocket located along the

vertical edge of the hexagonal Brillouin zone) were obtained (Fig. 6), revealing the

presence of numerous cyclotron-resonance harmonics in the spectra [21]. This is a

direct consequence of the non-zero trigonal warping in bulk graphite. In order to

illustrate the performance of the Fabry–Perot resonator with respect to the simple

0.015 0.020 0.025 0.030 0.035 0.040 0.045 0.050

Inte

nsi

ty (

a. u

.)

Magnetic Field (T)

Fig. 6 Single-crystal cyclotron resonance of graphite at 283.2 GHz and 7.5 K for the magnetic fieldapplied perpendicular to the carbon sheets. Upper spectrum recorded with the QO transmission setup(modulation amplitude, 28 G); lower spectrum recorded with the Fabry–Perot cavity (modulationamplitude, 6.8 G)


123

transmission QO setup, two spectra are presented in Fig. 6, both of them measured

within the heterodyne configuration of the spectrometer, allowing direct comparison of

the results. The upper spectrum was obtained with the simple transmission, whereas the

lower one was recorded with the Fabry–Perot. In order to obtain signals with

comparable intensity, it was necessary to use a modulation amplitude four times larger

for the simple transmission measurement than for the Farby-Perot one, resulting in

overmodulated signals in the first case as shown by the increased line width. More

interestingly, weaker cyclotron-resonance harmonics could be observed at low field

with the Fabry–Perot resonator. It allows approaching closer to the K point, a

particularly relevant issue for the understanding of graphite properties.

This initial single-crystal Landau level spectroscopy study was then completed

with an orientation dependence study, in which the field direction with respect to the

crystal was varied from perpendicular to parallel to the carbon layers. Very different

cyclotron resonance patterns are expected along with this rotation because of the

strongly anisotropic character of bulk graphite. Figure 7 demonstrates the spectra

recorded with the new rotating sample holder at 190 GHz and 5 K with the

magnetic field varying from 0� (perpendicular to the carbon layers) to almost 90�,

showing indeed significant variations of the cyclotron-resonance harmonics. The

90� spectrum is not shown because the cyclotron resonances almost disappeared due

to broadening and because higher and higher, thus weaker and weaker, harmonics

are observed at low field, when going from 0� to 90�. The use of the new rotating

sample holder allowed measuring with angular steps as small as 1.7�, as shown in

Fig. 8, in the regions where the cyclotron resonance is very sensitive to the change

of the field direction, thus resulting in a very detailed description of the behavior of

the Landau levels in the system.

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45

0.0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7

70.5°

Magnetic Field (T)

Inte

nsi

ty (

a.u

.)

0.0°

84.0°

37.0°

59.0°

Magnetic Field (T)

Fig. 7 Single-crystal cyclotron resonance of graphite at 190 GHz and 5 K measured with the rotatingsample holder, for the magnetic field varying from perpendicular to the carbon sheets (0�) to parallel tothe sheets (90�), illustrating the high anisotropy of the system. The orientation of the field is indicatedalong each spectrum. The 84� spectrum is presented in the inset, as the signal appears at higher fields(with amplification of the signal intensity)


123

4 Discussion and Conclusion

A Fabry–Perot resonator and a rotating sample holder have been designed and built,

with the aim of improving and extending the operation of our multifrequency QO

EPR spectrometer. Both systems involve the same conception with a plastic housing

made of Torlon, supporting a modulation coil and allowing an easy loading of the

sample. This housing is then connected to the bottom of the corrugated taper. Both

devices also rely on submicrometer piezoelectric positioners, able to work at low

temperature and under high magnetic field.

A study performed on a single crystal of natural graphite involving the use of

both devices has been presented to illustrate their performances. The sensitivity of

the Fabry–Perot resonator was determined by the measurement of a reference

BDPA sample. These studies first establish the interest of the submicrometer

piezoelectric positioners to greatly improve the capabilities of both devices with

respect to systems involving mechanical arrangements. Indeed, the figures reported

for the finesse of the Fabry–Perot resonator with the heterodyne configuration of the

QO EPR spectrometer are really high. This increase in sensitivity definitely appears

in the measurements performed on the graphite sample, where it has been possible

to evidence that the surface layers behave differently than the bulk ones and

represent high-quality graphene sheets [21]. Similarly, the high precision obtained

on the angle for the rotating sample holder also allowed obtaining a very precise

description of the warping of the Fermi surface.

The performances of both devices for these first samples are very promising for

broader applications, and especially the Fabry–Perot resonator is a key element for

the development of a pulsed spectrometer operating at 283 GHz.

Acknowledgments We gratefully thank Dr. M. Orlita (Laboratoire National des Champs Magnetiques

Intenses, Grenoble) for enlightening discussions about graphite and grapheme, and J. Florentin for

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45Magnetic Field (T)

39.1°

40.8°

42.5°

Fig. 8 Zoom of single-crystal cyclotron resonance of graphite at 190 GHz and 5 K in the 40� region, forthe magnetic field varied with small steps (1.7�) due to the pronounced orientation effect


123

technical assistance. The financial support of the European Union through European Research Training

Network ‘‘Quantum Effects in Molecular Nanomagnets’’ (EC-RTN QuEMolNa, nr. FP6-CT-2003-

504880) and Network of Excellence ‘‘Molecular Approach to Nanomagnets and Multifunctional

Materials’’ (NE MagMaNet, nr. FP6-NMP3-CT-2005-515767) is also acknowledged.

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new cavity design for broad-band quasi-optical hf-epr spectroscopy

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