Collan, Heikki K.

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Department of Technical PhysicsHelsinki University of TechnologyOtaniemi, FinlandSOME HEAT CAPACITY AND THERMOMETRICINVESTIGATIONS AT ULTRALOWTEMPERATURESH. K. COLLANTHESIS FOR THE DEGREE OF DOCTOR OF TECHNOLOGY TO BEPRESENTED WITH DUE PERMISSION  FOR PUBLIC EXAMINATIONIN THE AUDITORIUM S4 OF THE HELSINKI UNIVERSITY OFTECHNOLOGY, ON THE 1ST OF OCTOBER, 1971, AT 12 NOON.HELSINKI 1971Vammala  1971, Vammalan Kirjapaino OyACKNOWLEDGEMENTSThe research on which this thesis is basedwas carried out at the Low TemperatureLaboratory of the Department of TechnicalPhysics  during the period from 1967 to1971. The major part of the work wassupervized   by   Prof. Olli  V. Lounasmaa,to whom I am deeply grateful for hiscontinuous interest and encouragement.Especially  I  want to thank him fornumerous fruitful discussions and helpfulsuggestions  which facilitated the comple-tion of this thesis. This  research would not have beenpossible without sophisticated machineryfor attaining and maintaining low temper-atures. The author’s contribution was notmainly  in  the construction of  this  machin-ery.  Rather, this was the  achievement  ofhis co-workers P. M. Berglund, G. J.Ehnholm, R. G. Gylling, T. Heikkilä, M.Krusius and G. R. Pickett . The contribu-tion of M. I. Aalto in designing and con-structing  the electronics of the pulsedNMR thermometer, employed in the latterpart  of  this  work,  was  invaluable.   Tothe persons mentioned I should like toexpress  my  sincere  thanks, as well as toall  other  laboratory personnel for theirhelp throughout the experiments.The author obtained a first introduction tonuclear orientation  work  during  his visitto Clarendon Laboratory in Spring 1967.Otaniemi, August 1971    Heikki CollanSUMMARYThis  thesis  consists of  the following pa-pers:1. H. K. Collan,  M. Krusius, and G. R.Pickett,  ”Suppression of  the nuclearheat  capacity in  bismuth metal by veryslow spin-lattice relaxation and a newvalue for the electronic specific heat”,Phys. Rev. Letters 23, 11 (1969)2. H. K. Collan, T. Heikkilä, M. Krusius,and  G. R. Pickett, ”On the measure-ment   of   small   heat   capacities   atlow temperatures”, Cryogenics 10, 389(1970)3. H. K. Collan, M. Krusius, and G. R.Pickett,  ”Specific  Heat of Antimonyand Bismuth between 0.03 and 0.8 K”,Phys. Rev. B1, 2888 (1970)4. H. K.  Collan,   P. E. Gregers-Hansen,M. Krusius, and G. R. Pickett, ”Quad-rupole Interactions in the Semimetals,As, Sb, and Bi”,  Proc. 12th Interna-tional  Conference  on Low Tempera-ture Physics, E. Kanda, ed. (KeigakuPublishing Co, Tokyo 1971), p. 5375. P. M. Berglund, H. K. Collan, G. J.Ehnholm, R. G. Gylling, and O. V. Lou-nasmaa, ”The Design and Use of Nu-clear Orientation Thermometers Em-ploying 54Mn and 60Co Nuclei in Fer-romagnetic  Hosts”, Report TKK-F-A155 (1971), to be published in Journalof  Low Temperature Physics6. M. I. Aalto, P. M. Berglund, H. K.Collan, G. J. Ehnholm,  R. G. Gylling,M. Krusius, and G. R. Pickett, ”Con-struction and Use of a Pulsed CopperNuclear Magnetic Resonance Thermo-meter”, Report TKK-F-A156 (1971), tobe published in Cryogenics                           ______________The interactions between the nuclearmagnetic moment and the magnetic hy-perfine (hf)  field  acting on the nucleus,and between the nuclear electric quadru-pole moment and the electric field  gra-dient  at   the  site of  the  nucleus  lead  tohf energy levels. The splittings betweenthese  levels  are  in general measurablewith high accuracy, for example  by nu-clear magnetic resonance (NMR) and bynuclear quadrupole resonance (NQR).The nuclear heat capacity is caused bychanges  in  the  populations  of the hflevels  with  temperature  and measuresonly a weighted average  of the hf inter-action energy, but not the splittings them-selves. With no further knowledge it doesnot give detailed information about thehyperfine interaction, especially becauseheat capacity work essentially relies onmeasurement of the absolute temperatureand  small temperature increments. Sincethe form of the hf Hamiltonian is oftenknown from other considerations, mea-suring the nuclear heat capacity, never-theless,  provides  an important independ-ent possibility for checking the resultsobtained by resonance techniques.The first paper reports results of a mea-surement of the specific heat of bismuthmetal.  In  bismuth  the  hf  energy  is  dueto the coupling between the nuclear quad-rupole moment and the electric field gra-dient resulting from the noncubic sym-metry  of  the  lattice.  Prior to this worktwo contradictory determinations of thequadrupole  coupling constant e2qQ ex-isted, one done by NMR and the other by anuclear heat capacity measurement. Ourwork was aimed at resolving this dis-crepancy. Paradoxically, we could assign novalue at all to the coupling constant,because  it  was  found that the nuclearspin-lattice relaxation was too slow forestablishing thermal equilibrium betweenthe nuclear system and the lattice. Thisresult provided strong evidence that theearlier heat capacity determination waserroneous. Assuming that the Korringarelation is valid, a lower limit of the Kor-ringa constant was estimated to be 100 sK.Because of the decoupling of the hf ther-mal reservoir from the lattice, we couldseparate the electronic heat capacity moreaccurately  than  earlier.  The new valuewas significantly smaller than earlier  de-terminations.The main experimental difficulty in thework of the first paper was due to theunexpectedly small heat capacity. Thecommon nearly  adiabatic  principle  ofheat capacity determination was aban-doned,  and  a  more  accurate methodtaking into account the energy exchangebetween the sample and the surroundingswas employed. The author’s independentcontribution was to work out the method,and to carry out a full analysis of the ex-perimental data. He also took part in allother aspects of the work.The measurement of small heat capaci-ties  in non-adiabatic conditions is dealtwith in more detail in the second paper. Thethree co-authors gave only minorcontributions.The third paper reports results of a spe-cific heat determination of the semimetalantimony. The results of the bismuthmeasurement of the first paper are alsofurther discussed. The higher conductionelectron  density   of   antimony   gives  riseto  a  larger  electronic  heat   capacity  anda  faster  relaxation between the nuclearspin  system and the lattice than in bis-muth.  Now  the  hf  energy contributesfully to the total heat capacity, and anaccurate calorimetric determination ofe2qQ is possible. A nearly adiabatic tech-nique of measurement was possible be-cause  the  total heat capacity was large.The results were in accordance with anearlier NQR measurement and, in the hightemperature  range of the present work,with several other heat capacity determi-nations.  The  author participated in all sidesof the experimental work of thismeasurement.In the first paper it was suggested thatthe  nuclear  heat  capacity  of bismuthcould  be made visible by doping a bis-muth  sample  with  tellurium. Results ofthe heat capacity measurement of dopedbismuth are reported in the fourth paperconfirming this prediction and the earlierNMR determination of e2qQ. The magni-tude of e2qQ was found to depend morestrongly  on  alloying than anticipated.Apart from the suggestion of the dopedbismuth measurement the author’s con-tribution to the new results of the fourthpaper was nominal.In the heat capacity work the temper-ature scale was based on a downwardsextrapolation of the 3He vapour pressurescale with the aid of the susceptibility ofcerous magnesium nitrate (CMN). At thelow temperature end of the measurementsthe  temperature determination accuracywas thus limited by the non-ideal para-magnetic behaviour of interacting mag-netic moments. In order to determine ac-curately  even lower temperatures, a sys-tem  with  smaller  internal  interactionsthan   a   paramagnetic  salt  is  preferable.A good  choice  is a nuclear spin systemwhere the ordering temperature arising fromdipole-dipole interactions between spins isseveral orders of magnitude lower than withelectronic spins.The fifth paper deals with absolutetemperature measurement by employingdilute     radioactive    impurity   nuclei   im-bedded  into  a  ferromagnetic  metal lattice.The  hf  Hamiltonian  governing the polari-zation  of  these  nuclei  is  well known. Thedegree  of polarization can be determinedby observing  the anisotropic -radiationemitted by the nuclei.  The magnitude ofthe hf  splitting  has been determined ear-lier for a number of combinations of im-purity  nuclei  and  host  metals, and is ofthe order of 10 mK for the cases con-sidered. Therefore, by nuclear orientation(NO) techniques the standard temperaturescale can be established at around 10 mK.This is important as recently the lowestexperimental thermal equilibrium condi-tions have been pushed down  to  0.5 mKby nuclear  spin  refrigeration.  The advan-tages of  NO thermometry do not, how-ever, seem to have been generally ap-preciated, partly because of the instru-mental corrections needed in practicalwork. In this paper we show that thesecorrections  do  not  present insurmoun-table difficulties. The low temperatures,down  to 2 mK, necessary for this workwere obtained by employing the nuclearrefrigerating  cryostat  of  this  laboratory. NO   thermometry    was    used  simultane-ously   with a pulsed copper NMR thermo-meter;  it   was   concluded  that  at  about10 mK the absolute temperature can bedetermined  with 2% accuracy, removingthe necessity of long extrapolations whencalibrating  thermometers for work below10 mK.  The  author took care of the de-sign  of  the  NO system and of the ana-lysis of the relevant data.Ultralow temperature thermometry isfurther investigated in the sixth paper.CMN  thermometry and NMR thermo-metry on one hand, and NMR and NOthermometry on the other are comparedwith each other. A pulsed copper NMRthermometer was found to be an easy tomanage and accurate  thermometer belowabout 0.5 K.  The  author  participated inthe   experimental  work of  the latter  partof  these  experiments  and in the analysisof the results. These results give, a pos-teriori, additional evidence that the tem-perature scale used in the heat capacitywork of this thesis has indeed been wellfounded.

Some heat capacity and thermometric investigations at ultralow temperatures

Aaltodoc

Department of Technical Physics
Helsinki University of Technology
Otaniemi, Finland
SOME HEAT CAPACITY AND THERMOMETRIC
INVESTIGATIONS AT ULTRALOW
TEMPERATURES
H. K. COLLAN
THESIS FOR THE DEGREE OF DOCTOR OF TECHNOLOGY TO BE
PRESENTED WITH DUE PERMISSION  FOR PUBLIC EXAMINATION
IN THE AUDITORIUM S4 OF THE HELSINKI UNIVERSITY OF
TECHNOLOGY, ON THE 1ST OF OCTOBER, 1971, AT 12 NOON.
HELSINKI 1971
Vammala  1971, Vammalan Kirjapaino Oy
ACKNOWLEDGEMENTS
The research on which this thesis is based
was carried out at the Low Temperature
Laboratory of the Department of Technical
Physics  during the period from 1967 to
1971. The major part of the work was
supervized   by   Prof. Olli  V. Lounasmaa,
to whom I am deeply grateful for his
continuous interest and encouragement.
Especially  I  want to thank him for
numerous fruitful discussions and helpful
suggestions  which facilitated the comple-
tion of this thesis.
 This  research would not have been
possible without sophisticated machinery
for attaining and maintaining low temper-
atures. The author’s contribution was not
mainly  in  the construction of  this  machin-
ery.  Rather, this was the  achievement  of
his co-workers P. M. Berglund, G. J.
Ehnholm, R. G. Gylling, T. Heikkilä, M.
Krusius and G. R. Pickett . The contribu-
tion of M. I. Aalto in designing and con-
structing  the electronics of the pulsed
NMR thermometer, employed in the latter
part  of  this  work,  was  invaluable.   To
the persons mentioned I should like to
express  my  sincere  thanks, as well as to
all  other  laboratory personnel for their
help throughout the experiments.
The author obtained a first introduction to
nuclear orientation  work  during  his visit
to Clarendon Laboratory in Spring 1967.
Otaniemi, August 1971
    Heikki Collan
SUMMARY
This  thesis  consists of  the following pa-
pers:
1. H. K. Collan,  M. Krusius, and G. R.
Pickett,  ”Suppression of  the nuclear
heat  capacity in  bismuth metal by very
slow spin-lattice relaxation and a new
value for the electronic specific heat”,
Phys. Rev. Letters 23, 11 (1969)
2. H. K. Collan, T. Heikkilä, M. Krusius,
and  G. R. Pickett, ”On the measure-
ment   of   small   heat   capacities   at
low temperatures”, Cryogenics 10, 389
(1970)
3. H. K. Collan, M. Krusius, and G. R.
Pickett,  ”Specific  Heat of Antimony
and Bismuth between 0.03 and 0.8 K”,
Phys. Rev. B1, 2888 (1970)
4. H. K.  Collan,   P. E. Gregers-Hansen,
M. Krusius, and G. R. Pickett, ”Quad-
rupole Interactions in the Semimetals,
As, Sb, and Bi”,  Proc. 12th Interna-
tional  Conference  on Low Tempera-
ture Physics, E. Kanda, ed. (Keigaku
Publishing Co, Tokyo 1971), p. 537
5. P. M. Berglund, H. K. Collan, G. J.
Ehnholm, R. G. Gylling, and O. V. Lou-
nasmaa, ”The Design and Use of Nu-
clear Orientation Thermometers Em-
ploying 54Mn and 60Co Nuclei in Fer-
romagnetic  Hosts”, Report TKK-F-
A155 (1971), to be published in Journal
of  Low Temperature Physics
6. M. I. Aalto, P. M. Berglund, H. K.
Collan, G. J. Ehnholm,  R. G. Gylling,
M. Krusius, and G. R. Pickett, ”Con-
struction and Use of a Pulsed Copper
Nuclear Magnetic Resonance Thermo-
meter”, Report TKK-F-A156 (1971), to
be published in Cryogenics
                           ______________
The interactions between the nuclear
magnetic moment and the magnetic hy-
perfine (hf)  field  acting on the nucleus,
and between the nuclear electric quadru-
pole moment and the electric field  gra-
dient  at   the  site of  the  nucleus  lead  to
hf energy levels. The splittings between
these  levels  are  in general measurable
with high accuracy, for example  by nu-
clear magnetic resonance (NMR) and by
nuclear quadrupole resonance (NQR).
The nuclear heat capacity is caused by
changes  in  the  populations  of the hf
levels  with  temperature  and measures
only a weighted average  of the hf inter-
action energy, but not the splittings them-
selves. With no further knowledge it does
not give detailed information about the
hyperfine interaction, especially because
heat capacity work essentially relies on
measurement of the absolute temperature
and  small temperature increments. Since
the form of the hf Hamiltonian is often
known from other considerations, mea-
suring the nuclear heat capacity, never-
theless,  provides  an important independ-
ent possibility for checking the results
obtained by resonance techniques.
The first paper reports results of a mea-
surement of the specific heat of bismuth
metal.  In  bismuth  the  hf  energy  is  due
to the coupling between the nuclear quad-
rupole moment and the electric field gra-
dient resulting from the noncubic sym-
metry  of  the  lattice.  Prior to this work
two contradictory determinations of the
quadrupole  coupling constant e2qQ ex-
isted, one done by NMR and the other by a
nuclear heat capacity measurement. Our
work was aimed at resolving this dis-
crepancy. Paradoxically, we could assign no
value at all to the coupling constant,
because  it  was  found that the nuclear
spin-lattice relaxation was too slow for
establishing thermal equilibrium between
the nuclear system and the lattice. This
result provided strong evidence that the
earlier heat capacity determination was
erroneous. Assuming that the Korringa
relation is valid, a lower limit of the Kor-
ringa constant was estimated to be 100 sK.
Because of the decoupling of the hf ther-
mal reservoir from the lattice, we could
separate the electronic heat capacity more
accurately  than  earlier.  The new value
was significantly smaller than earlier  de-
terminations.
The main experimental difficulty in the
work of the first paper was due to the
unexpectedly small heat capacity. The
common nearly  adiabatic  principle  of
heat capacity determination was aban-
doned,  and  a  more  accurate method
taking into account the energy exchange
between the sample and the surroundings
was employed. The author’s independent
contribution was to work out the method,
and to carry out a full analysis of the ex-
perimental data. He also took part in all
other aspects of the work.
The measurement of small heat capaci-
ties  in non-adiabatic conditions is dealt
with in more detail in the second paper. The
three co-authors gave only minor
contributions.
The third paper reports results of a spe-
cific heat determination of the semimetal
antimony. The results of the bismuth
measurement of the first paper are also
further discussed. The higher conduction
electron  density   of   antimony   gives  rise
to  a  larger  electronic  heat   capacity  and
a  faster  relaxation between the nuclear
spin  system and the lattice than in bis-
muth.  Now  the  hf  energy contributes
fully to the total heat capacity, and an
accurate calorimetric determination of
e2qQ is possible. A nearly adiabatic tech-
nique of measurement was possible be-
cause  the  total heat capacity was large.
The results were in accordance with an
earlier NQR measurement and, in the high
temperature  range of the present work,
with several other heat capacity determi-
nations.  The  author participated in all sides
of the experimental work of this
measurement.
In the first paper it was suggested that
the  nuclear  heat  capacity  of bismuth
could  be made visible by doping a bis-
muth  sample  with  tellurium. Results of
the heat capacity measurement of doped
bismuth are reported in the fourth paper
confirming this prediction and the earlier
NMR determination of e2qQ. The magni-
tude of e2qQ was found to depend more
strongly  on  alloying than anticipated.
Apart from the suggestion of the doped
bismuth measurement the author’s con-
tribution to the new results of the fourth
paper was nominal.
In the heat capacity work the temper-
ature scale was based on a downwards
extrapolation of the 3He vapour pressure
scale with the aid of the susceptibility of
cerous magnesium nitrate (CMN). At the
low temperature end of the measurements
the  temperature determination accuracy
was thus limited by the non-ideal para-
magnetic behaviour of interacting mag-
netic moments. In order to determine ac-
curately  even lower temperatures, a sys-
tem  with  smaller  internal  interactions
than   a   paramagnetic  salt  is  preferable.
A good  choice  is a nuclear spin system
where the ordering temperature arising from
dipole-dipole interactions between spins is
several orders of magnitude lower than with
electronic spins.
The fifth paper deals with absolute
temperature measurement by employing
dilute     radioactive    impurity   nuclei   im-
bedded  into  a  ferromagnetic  metal lattice.
The  hf  Hamiltonian  governing the polari-
zation  of  these  nuclei  is  well known. The
degree  of polarization can be determined
by observing  the anisotropic -radiation
emitted by the nuclei.  The magnitude of
the hf  splitting  has been determined ear-
lier for a number of combinations of im-
purity  nuclei  and  host  metals, and is of
the order of 10 mK for the cases con-
sidered. Therefore, by nuclear orientation
(NO) techniques the standard temperature
scale can be established at around 10 mK.
This is important as recently the lowest
experimental thermal equilibrium condi-
tions have been pushed down  to  0.5 mK
by nuclear  spin  refrigeration.  The advan-
tages of  NO thermometry do not, how-
ever, seem to have been generally ap-
preciated, partly because of the instru-
mental corrections needed in practical
work. In this paper we show that these
corrections  do  not  present insurmoun-
table difficulties. The low temperatures,
down  to 2 mK, necessary for this work
were obtained by employing the nuclear
refrigerating  cryostat  of  this  laboratory.
 NO   thermometry    was    used  simultane-
ously   with a pulsed copper NMR thermo-
meter;  it   was   concluded  that  at  about
10 mK the absolute temperature can be
determined  with 2% accuracy, removing
the necessity of long extrapolations when
calibrating  thermometers for work below
10 mK.  The  author took care of the de-
sign  of  the  NO system and of the ana-
lysis of the relevant data.
Ultralow temperature thermometry is
further investigated in the sixth paper.
CMN  thermometry and NMR thermo-
metry on one hand, and NMR and NO
thermometry on the other are compared
with each other. A pulsed copper NMR
thermometer was found to be an easy to
manage and accurate  thermometer below
about 0.5 K.  The  author  participated in
the   experimental  work of  the latter  part
of  these  experiments  and in the analysis
of the results. These results give, a pos-
teriori, additional evidence that the tem-
perature scale used in the heat capacity
work of this thesis has indeed been well
founded.


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Some heat capacity and thermometric investigations at ultralow temperatures

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