Bi2Se3 Hall Effect Magnetometer for Reliable Low Temperature UseJohn A. Woollam, Harry A. Beale, and Ian L. Spain Citation: Review of Scientific Instruments 44, 434 (1973); doi: 10.1063/1.1686151 View online: http://dx.doi.org/10.1063/1.1686151 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/44/4?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Quantum anomalous Hall effect in doped ternary chalcogenide topological insulators TlBiTe2 and TlBiSe2 Appl. Phys. Lett. 99, 142502 (2011); 10.1063/1.3645624 Vibrating Sample Magnetometer for Use at Very Low Temperatures and in High Magnetic Fields Rev. Sci. Instrum. 41, 1764 (1970); 10.1063/1.1684405 Vibrating Coil Magnetometer for Use at Very Low Temperatures Rev. Sci. Instrum. 37, 173 (1966); 10.1063/1.1720122 Magnetometer Based on the Hall Effect Rev. Sci. Instrum. 33, 537 (1962); 10.1063/1.1717911 Sampling Magnetometer Based on the Hall Effect J. Appl. Phys. 33, 1278 (1962); 10.1063/1.1728691

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434 B. RAOULT AND J. FARGES

5J. Farges, B. Raoult and G. Torchet, Eighth International Symposium on Rarefied Gas Dynamics, Stanford, California, July, 1972.

6L. O. Brockway and L. S. Bartell, Rev. Sci. Instrum. 25, 569 (1954).

'E. L. Knuth, Appl. Mech. Rev. 17, 751 (1964). 8E. W. Becker, K. Bier, and W. Henkes, Z. Phys. 146, 333

(1956). 90. F. Hagena and W. Obert, J. Chem. Phys. 56, 1793 (1972).

THE REVIEW OF SCIENTIFIC INSTRUMENTS

lOp. Audit and M. Rouault, Entropie 18, 22 (1967). 110. Bastiansen, O. Hassel, and E. Risberg, Acta Chem. Scand.

9, 232 (1955). l2B. Raoult and J. Farges, Acta Crystallogr. SA25, 70 (1969). 13B. Raoult, J. Farges, and G. Torchet (to be published). l4p. Audit, B. Raoult and J. Farges, Acta Crystallogr. SA25, 30

(1969). ISJ. Farges and B. Raoult, Third Austin Symposium on Gas

Phase Molecular Structure, Austin, Texas, March, 1970.

VOLUME 44, NUMBER 4 APRIL 1973

Bi2 Se3 Hall Effect Magnetometer for Reliable Low Temperature Use

John A. Woollam Lewis Research Center, National Aeronautics and Space Administration, Cleveland, Ohio 44135

Harry A. Beale and Ian L. Spain University of Maryland, College Park, Maryland

(Received 15 February 1972; and in final form, 4 December 1972)

Single crystals of n-type Bi2Se3 grown by the Bridgman technique are found to make excellent Hall effect magnetometers capable of repeated cycling to liquid helium temperatures. Plots of Hall resistivity, Pyx, versus magnetic field B to 11 tesla deviate from linearity by less than ±0.8% for all temperatures between 1.1 and 300 K. Furthermore, the slope of the Pyx versus B curve varies by less than 2% in the region 1.1 to 78 K.

INTRODUCTION

Accurate and convenient measurement of high magnetic fields becomes more difficult as higher field magnets and superconducting solenoids are developed.1 Nuclear mag­netic resonance is very accurate but high homogeneity of the magnetic field is needed,2 and it is often difficult to include a nuclear resonance measurement at the same time as performing other measurements.3 Copper magneto­resistors, commonly built into superconducting magnets, have nearly linear output with field at high fields, but their calibration is very temperature sensitive and a quadratic component is present in the output at low field. 4 Hall effect devices are small (dimensions typically on the order of 0.5 cm) and the outputs are quite linear in field at high temperature. Until now, most Hall effect devices had strong temperature dependent calibrations and exhibited Shubnikov-de Haas oscillations at low tem­peratures." There have been a few materials with desirable properties,6-8 but the commercially available devices change calibration after an undetermined number of thermal cyclings to liquid helium temperatures, or fail entirely.

We have found single crystals of BbSe3 grown by the Bridgman technique to be ideal magnetometers in mag­netic fields to at least 11 T and over a wide range of

temperature. In this paper, the Hall resistivity is mea­sured, and data for a representative sample presented as a function of magnetic field to 11 T. Magnetoresistivity was also measured and used with the Hall effect results to help characterize the magnetometer material. Quench­ing tests from 300 K to low temperatures demonstrate the reliability of the magnetometers for low temperature applications.

I. MATERIALS PREPARATION AND MEASUREMENT TECHNIQUE

n-type material was grown in the following manner. Samples were prepared by accurately weighing (±5 parts in 106) 99.999% pure bismuth and 99.999% pure selenium corresponding to a composition of 60.25 at. % selenium and 39.75 at.% bismuth. The mixture of shot was placed in a Vycor ampoule, evacuated to approximately 10-6

Torr and sealed. The sample was maintained at 850°C (the melting temperature is 710°C) for 12 h in a vibrating (approximately 8 Hz) furnace. Single crystals were grown using a Bridgman furnace,9 with a growth rate of 1.2 cm/h. The product was a polycrystalline boule, 7 cm long X 1.5 cm diam. Grains were large in cross section and typically the length of the boule. By chemical analysis, the composition varied from 39.97 at.% bismuth near the

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MAGNETOMETER 435

bottom of the boule to 39.82 at. % near the top. The boule was sectioned into 1.8 cm lengths using a wire saw with a diamond-impregnated wire. These shorter cylinders were etched, using a mixture of methanol and bromine, to reveal the grain boundaries and then cleaved to produce single crystals. The predominant cleavage plane was the plane perpendicular to the trigonal axis. The above pro­cedure produced n-type material as grown. n-type was also produced in a second boule, nominally 0.05% bismuth rich, and annealed for 48 h at 600°C.

Specimens were cut by sand erosion to the shape of a conventional Hall-resistivity sample as shown in Fig. 1. The Hall resistivity, Pyx, is the ratio of the electric field in the y direction to the current density in the x direction for field applied along the z direction, as shown in Fig. 1. Using hard steel masks and fine grain sand for erosion, the Hall probes are very accurately located opposite each other, thus minimizing the component of magnetoresis­tance present in the Hall leads. A magnetoresistance com­ponent present in poorly aligned probes would cause an offset voltage which would be magnetic field dependent. Due to low mobility, the field dependence would be small. If there was a problem it could be compensated by using a fraction of the magnetoresistance voltage to buck out the undesired part in the Hall voltage.

Typical sample dimensions were 0.05XO.14XO.80 cm. Bi2Sea has a trigonal unit cell and belongs to the R3m space group. If the z axis is taken as the trigonal axis and the x axis as the long axis of the sample, then the speci­mens were oriented and cut so the xz plane was one of the three equivalent reflection planes. The samples were again etched and re-examined for cracks between the layer planes using a simple light microscope. Leads were at­tached using a silver conductive epoxy, carefully covering the entire tip region. This procedure eliminated any spurious effects due to the pronounced layer structure of the crystal.

The usefulness of this material as a magnetometer comes from the linearity of Pyx (with B along the trigonal axis) versus B plots, and this property was reproducible for

Ztx

APPLIED _ MAGNETIC FIELD. B

CURRENT CURRENT LEAD LEAD

FIG. 1. Sample geometry showing voltage and current leads at­tached using conducting epoxy. Samples are precisely shaped using sand erosion and a hard steel mask.

0.9

0.8

0.7

E Cl 0.6

>< 0..>-

>­I-~ 0.5 t!i [:J a:: ..J 0.4 ..J « or I

0.3

0.2

0.1

°0~--~I~.O~--~2~.0--~3~.0~--~4~.0--~5~n~--~6~.0----7~.O~

MAGNETIC FIELD, B, TESLA

FIG. 2. Hall resistitivy Pu, vs magnetic field for several temperatures.

samples when taken from the as-grown or well-annealed boules. Another useful property is the flat surface (cleavage plane) perpendicular to the trigonal axis which could be used for easy orientation.

The current was provided by a dc constant current supply, having an output which was typically 100 rnA, calibrated to one part in 105• Magnetoresistance and Hall effect voltages were measured using a dc amplifier with linearity of one part in 105, and were plotted on a calibrated x-y recorder. A water-cooled solenoid, calibrated against the magnet current using a rotating coil magnetometer and a standard magnet, provided the magnetic field for most runs. With this magnet, field values ranged between zero and ±8 T, with the field oriented along the trigonal axis of the sample. The experimental uncertainty of ±0.8% came from uncertainty in field vs magnet current and from x-y recorder noise. Temperatures between 1.1 and 300 K were achieved by using liquid helium and liquid nitrogen with a heater-controller system employing a gallium arsenide diode temperature sensor.lO Two other magnets, generating 11 Tat 1.2 K and 15 Tat 4.2 K were also used.

II. RESULTS

Representative plots of the Hall resistivity Pyx are plotted in Fig. 2 as a function of magnetic field B for a

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436 WOOLLAM, BEALE, AND SPAIN

>-: z w 13

0.11 u: u. w 0 tJ 0.10 ...J ...J <t 0.09 :I:

I 0 40 80 120 160 200 240

TEMPERATURE. KELVIN

FIG. 3. Hall coefficient RB plotted as a function of temperature.

280

series of temperatures between 4.2 and 300 K. Over the entire temperature range Pyx is linear in B with deviations of less than the experimental uncertainty of about ±0.8% at 8 T. The sensitivity given by RB is the slope of the Hall resistivity Pyx vs field curves and is shown in Fig. 3 as a function of temperature. Easily measurable Hall effect signals (on the order of millivolts for a 0.05 cm thick sample at 8.0 T) were attained with typically 100-200 rnA. Since thermoelectrically generated spurious voltages were on the order of microvolts for samples at 4.2 K, the signal to noise (from thermoelectric sources) was roughly 500 to 1000/1 for 100 rnA sample current at a field of 8.0 T with a 0.05 cm thick sample. Samples are easily cleaved to '" 10-2 cm thickness, so thermoelectrically generated voltages become comparable to Hall-generated voltages for fields below about 20 G and very low temperatures in an optimum sample. This limits the use of BbSe3 to fields above about 0.1 T when errors of less than a few percent are desired in low temperature applications. At higher tem­peratures, thermally generated noise is not a problem.

III. THERMAL SHOCKING TESTS

One of the most serious problems with previous Hall magnetometers is the lack of reproducibility upon quench­ing into liquid helium or liquid nitrogen from room tem­perature. For this reason, we have quenched Bi2Se3 mag­netometers into liquid helium or nitrogen a total of 50 times in the following pattern:

(a) Ten direct immersions in liquid nitrogen from 300 K with Pyx measured to ±5.0 T each time the sample was in liquid. The highest and lowest values of Pyx in these tests were less than 1% apart.

(b) Ten direct immersions into liquid helium from 300 K, with Pyx measured to ±5.0 T each time the sample was in liquid. The highest and lowest values of Pyx were less than 0.2% from each other.

(c) Thirty direct immersions in liquid nitrogen with Pyx

measured at 5.0 T and at 4.2 K after each 10 immersions in liquid nitrogen. All 31 values of Pyx were within 0.3% of each other.

IV. COMPARISON WITH OTHER HALL MAGNETOMETERS

The Bi2Se3 magnetometer has comparable or better characteristics than other Hall materials. Most have a significant Shubnikov-de Haas effect, for example, whereas Bi2Se3 does not. One commercial InAs model (call it probe c) does have desirable characteristics so a com­parison is now made bet ween this and the Bi2Se3 magnetometers.

A. Sensitivity

Our Bi2Se3 samples had relatively low carrier mobility (",0.05 m2/Vsec), as measured by Hall and magneto­resistance effects. The typical sensitivity was approxi­mately 0.1 mV/T at 100 rnA or a factor of 102 smaller than the commercially manufactured InAs probes. Lower sensitivity can be partly compensated by using higher probe currents, if increased power dissipation is tolerable. Our Bi2Se3 probes had resistances on the order of -to that for InAs probes and could therefore be used with three times the current level for the same power dissipation.

B. Linearity

Our probes were linear to 8 T to within ±0.8% which was comparable to the accuracy of our measurements. This is roughly equivalent to the commercial magnetom­eter probe c which has ± 1 % at 3 T.

C. Temperature Coefficient

The Hall output changes by as much as 20% between 300 and 4.2 K (1000 ppm/K), but from 78 to 4 K this change is less than 2% ('" 250 ppm/K) for Bi2Se3. Thus, below 78 K, the temperature coefficient of the Hall output is comparable to the InAs probe c. Above 78 K the BbSe3 temperature coefficient is roughly 10 times worse.

D. Thermal Shock Resistance

This is the major defect with previous probes; they change calibration or fail completely after an indetermi­nant number of cycles to low temperatures. This can happen after one or two cycles or after 20. The BbSe3 probe has been cycled roughly 70 times with no failure, and in 50 of these tests the probe was quenched directly, and within error limits there was no change in Hall output.

E. Quantum Effects

We have studied the quantum oscillations in the Hall resistance in BbSe3 which occur between 12 and 15 T. The maximum amplitude at 15 Twas 1.8% peak to peak with a frequency 4X106 gauss. Oscillations were not ob-

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MAGNETOMETER 437

servable below 12 T at 1.5 K, and the Hall output, exclud­ing the oscillations, was still linear to 15 T. The oscillatory effects exist only at the lowest temperatures. Oscillatory effects are present in the commercial probe c above 10 T, but these data are as yet unpublished. ll Other commercial probes have very strong oscillatory effects at low tempera­tures (typically 7% at 5 Tat 4.2 K).

ACKNOWLEDGMENTS

We would like to thank Mr. Larry Rubin of the Francis Bitter National Magnet Laboratory for very helpful sug­gestions. Thanks are also due to Charles Lizanich for technical support in performing the measurements. This work was supported in part by the National Aeronautics and Space Administration and by the Center of Materials

THE REVIEW OF SCIENTIFIC INSTRUMENTS

Research, University of Maryland, administering a grant from the Advanced Research Projects Agency.

IW. D. Coles, J. C. Laurence, and G. Y. Brown, NASA TM X-52627 (1969).

2For example, see, R. J. Higgins and Y. K. Chang, Rev. Sci. Instrum. 39, 522 (1968).

3W. J. O'Sullivan and J. E. Schirber, Cryogenics 7, 118 (1967). ·W. R. Hudson, NASA TN D-3536 (1966). sr. B. Sanford, NASA TN D-2272 (1964). 6S. G. Shul'man, Instrum. Exp. Tech. 1969, No. 1,184. 7B. G. Lazarev, L. S. Lazareva, S. I. Goridov, and S. G.

Shul'man, Sov. Phys.-Dokl. 13, 696 (1969). ay. G. Yeselago, M. Y. Glushkov, Y. M. Ivanov, S. G.

Shul'man, Instrum. Exp. Tech. 1969, No.6, 1580. 9For example, see: The Art and Science of Growing Crystals.

edited by J. J. Gilman (Wiley, New York, 1963). IOJ. Arends and R. C. Wright, Cryogenics 9, 281 (1969). llL. Rubin, Francis Bitter National Magnet Laboratory (private

communication).

VOLUME 44, NUMBER 4 APRIL 1973

A Simple Method for Estimating HI in ESR Experiments-The Microwave Power Saturation of 'Y-Irradiation Induced Glycylglycine

Radicals * Edmund S. Copeland

Division of Biochemistry, Walter Reed Army Institute of Research, Washington, D.C 20012 (Received 21 April 1972; and in final form, 20 December 1972)

A technique is described whereby the shape of the first derivative electron spin resonance (ESR) spectra observed for 'Y-irradiated glycylglycine can be used in ESR experiments to estimate the microwave magnetic field H I in the 40-1000 mG range. The ratio of the minor to major derivative peak heights of the glycylglycine doublet is found to vary with HI' Slow passage progressive saturation studies are included in an attempt to explain the phenomenon. The technique provides a means of measuring HI' without knowing effective cavity Q, incident power, or the field concentrating effects of quartz inserts and is proposed as an interlaboratory ESR microwave power comparison standard.

INTRODUCTION

The results of many electron spin resonance (ESR) studies suffer from microwave power saturation. In addi­tion, because spectrometer cavities differ appreciably in loaded Q and also because cavity Q can change con­siderably when different inserts are used and different samples are examined, investigations which report incident microwave power levels do not really provide readily usable information on the effective parameter of power saturation, the microwave magnetic field strength HI. The obvious way to avoid such difficulties is to run power saturation curves on each new sample and with each cavity arrangement and to make certain that studies are done in a microwave power range where signal peak height varies linearly with the square root of microwave power. Such studies can be performed when a means of monitoring microwave power and cavity Q are available. Incident power may be measured using a power meter appropriately

coupled to the cavity arm of the bridge or HI can be evaluated in relative terms by using a dual cavity with a nonsaturating standard sample such as diphenylpicryl­hydrazyl (DPPH) in the reference cavity.!

Measurements of cavity Q require extensive microwave equipment to achieve any degree of accuracy.2 If such facilities are not available, it is difficult to achieve re­producible power saturation curves and to evaluate the microwave magnetic field strength HI.

We wish to present a study which shows that the power saturation characteristics of the radical stabilized in 'Y­

irradiated glycylglycine can be used to monitor microwave magnetic field strength without knowing incident micro­wave power, cavity Q, or the field concentrating effects of quartz Dewar inserts or sample holders. The glycylglycine radical undergoes power saturation at a few microwatts of incident power when observed at 77 K and at about 1 mW at 295 K (see below). This species is frequently saturated

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