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Point-contact spectroscopy of magnons in metals
GA 1
Physica 107B (1981) 369-370 North-Holland Publishing Company
POINT . CONTACT SPECTROSCOPY OF MAGNONS IN METALS A.I.Akimenko, A.B.Verkin, N.M.Ponomarenko and l.K.Yanson Physico-Technical Institute of Low Temperatures, UkrSSR Academy of Sciences, Kharkov, USSH The nonlinear current-voltage characteristics of point-contacts of Gd, and Ho are studied. The peculiarities of the second derivative V/dI a vs eV are found which correspond to the peculiarities of magnon spectra of these metals and are interpreted in terms of the energy dependence of the electron-magnon interaction function.
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The point-contact spectroscopy has recently been used successfully for investigation of electron-phonon interaction in metals.(1) In principle, the method also permits the interaction between electron and other excitations in metals to be studied. The paper presents the experimental data on small nonlinearities in current-voltage characteristics of point-contacts made of the rare-earth metals Gd, Tb and Ho.(2) The clear evidence of electron-magnon interaction in these metals is definitely found. In the experiments the pressure-type point-contacts of a "needle-anvil" geometry were used. The contact surfaces were treated only meoharzically because owing to a high chemical activity of these metals the etching or electropolishing produces a very hard oxide layer hindering the direct metal contact. In the course of experiments taken at the temperatures of 1.5 to 4.2 K the second harmonic of modulating signal, V2 , was recorded as a function of voltage, V, across the contact. This V2(V) dependences are proportional to the second derivative d~V/dI • and described as "point-contact spectra" (PC spectra). 'Z~e PC s p e c t r u m
o f Gd i s e h o w n i n F i gure la, while I m P i ~ A r e lb it is presented in a c o . r e s e e d V - e ~ l e . It is s e e n t h a t a t eV ~ 25 meV t h e r e a r e p e culiarities (-trked with ~rrows) superi m p o s e d on t h e m o n o t o n i c a l l y i n c r e a s i n g baok~ound. The p o s i t i o n s of these peculiarities c a n be o o m l ~ r e d w i t h t h e positions o f t h e d~O/dq . 0 s i n g u l a r p o i n t s ~u ~ne m a g n o n d l e p e r s i o n curves known f r o m t h e n e u t r o n d i f f r a c t i o n data.(3) The p h o n o n s p e c t r u m o f Gd t e r m i n a t e s at 13 meV. Hence, the part of VA(eV)-curve at s V > 13 meV can be only due to electron-magmon interaction. There are no peaks corresponding to 0378-4363/81/0000--0000/$02.50 © North-HollandPublishingCompany
phon0n density of states of Gd at eV< 13 meV either. Thus, one can assume that the whole Va(eV)-characteristic (Figure Is) is mainly due to electronmagnon interaction and is therefore proportional to the magnon density of states in Gd.
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E,mev Figure 1 It follows from the theory (4) that the initial part of the PC spectrum of Gd should be proportional to eV as observed experimentally at eV< 7 meV (Figure la). It is seen from Figure Ib that the intensity o f PC s p e c t r u m d r o p s down sharply at V > % . This singularity is due to heating the contact area by current up to the Curie temperature T¢. At V ~ Vc the ferromagnetic-paramagmetic transition of the metal in the contact region takes place. The observation of such singularity proves once more that the metal at the contact is in the magnetically ordered state at V < V c . 369
370 interaction are symmetric with respect to the I-V zero point and the linewidth is proportional to kT in accordance with the theory.(4) The nonlinearities observed correspond to a total change in the differential resistance by-~10%.
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Figure 2 The PC spectrum of Tb is shown in Figure 2a. It is compared with the magnon density of states (Figure 2b) known from the calculations based on the magnon dispersion curves. (5) The magnon and phonon spectra of Tb are within the same energy range e V < 13 meV but the PC spectrum observed is in better agreement with the magnon density of states. F o r e x a m p l e , t h e b r o a d p e a k a t 10 meV a n d s m a l l one a t 12 meV a r e s e e n b o t h i n t h e PC and n e u t r o n d a t a s p e c t r a . The p e a k s w h i c h a r e known t o be due t o t h e honon density of states (e.g. at eVN -7 meV as follows from Ref.(6) ) are not seen definitely in the PC spectrum, only some traces of them can be found.
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The point-contact spectrum of Ho shows a single maximum at e V ~ 4 . 3 meV. There is also an intensive maximum in the magnon density of states at eV=4-5 meV in the magnon spectrum of Ho.(7) Since for the above energy range the phonon density of states is low and have no maxima, the observed PC spectrum can be only due to electron-magnon inter action. The metals studied show also anomalous PC spectra. These are characterized by the value of V~(V) enhanced in the low energy region. The PC spectrum of a strongly deformed magnetic is considered to be observed in these oases. Typical PC spectra of the deformed Gd show three peculiar features: at 4 meV, 11 meV and 17 meV, and the spectrum terminates at eV,~20 - 25 meV. It should be noted that the intensity of peculiarities observed in spectra of different contacts can vary appreciably. All the spectra of electron-magnon
These facts along with the obvious correlations between positions of the V~(eV)-curve singularities at the energy axis and peculiar points in the magncn dispersion curves indicate convincingly that we succeded in observing the PC spectra of electron-magnon inter. action function in Gd, Tb, Ho. REFERENCES Yanson,I.K. and Kulik,I.O., Pointcontact spectroscopy of phonons in metals, J. de Phys., Coloque C6, Suppl. au n 88, 39 (1978) C6-1564C6-1567. L~ Akimenko,A.I. and Yanson,I.K., Point-contact spectroscopy of magnons in metals, Pisma v ZhETF 31
(1980) 209-213. E~ Koehler,W.C., Child,H.R., Nicklow, R.M., Smith,H.G., Moon R.M. and Cable,J.W., Spin-wave dispersion relations in gadolinium, Phys. Rev. Lett. 24 (1970) 16-18. ~41 Kulik,I.O. and Shekhter,R.l., Polnt-contact spectroscopy of ferro. magnetic metals, Fiz.Nizk.Temp.
2 (1980) 148-152. ~
Bjerrum,H., M~ller,H.B., Glyden Houmann,J.C. and Mackintosh,A.R., Magnetic interaction in Tb and Tb-IO% Ho from inelastic neutron scattering, J.Appl.Phys.39 (1968) 807-815. E~ Glyden Houmann,J.C. and Nicklow, R.M., Lattice dynamics of terbium, Ph~s.Rev. B1 (I~70) 3943-3952. [71 Stringfellow,M.W., Holden,T.M., Powell,B.M. and Woods,A.D.B., Spin waves in holmium, J.Phys.C! Metal Phys. Suppl. to No.2 (1970) 189200.
Physica 107B (1981) 369-370 North-Holland Publishing Company
POINT . CONTACT SPECTROSCOPY OF MAGNONS IN METALS A.I.Akimenko, A.B.Verkin, N.M.Ponomarenko and l.K.Yanson Physico-Technical Institute of Low Temperatures, UkrSSR Academy of Sciences, Kharkov, USSH The nonlinear current-voltage characteristics of point-contacts of Gd, and Ho are studied. The peculiarities of the second derivative V/dI a vs eV are found which correspond to the peculiarities of magnon spectra of these metals and are interpreted in terms of the energy dependence of the electron-magnon interaction function.
~
The point-contact spectroscopy has recently been used successfully for investigation of electron-phonon interaction in metals.(1) In principle, the method also permits the interaction between electron and other excitations in metals to be studied. The paper presents the experimental data on small nonlinearities in current-voltage characteristics of point-contacts made of the rare-earth metals Gd, Tb and Ho.(2) The clear evidence of electron-magnon interaction in these metals is definitely found. In the experiments the pressure-type point-contacts of a "needle-anvil" geometry were used. The contact surfaces were treated only meoharzically because owing to a high chemical activity of these metals the etching or electropolishing produces a very hard oxide layer hindering the direct metal contact. In the course of experiments taken at the temperatures of 1.5 to 4.2 K the second harmonic of modulating signal, V2 , was recorded as a function of voltage, V, across the contact. This V2(V) dependences are proportional to the second derivative d~V/dI • and described as "point-contact spectra" (PC spectra). 'Z~e PC s p e c t r u m
o f Gd i s e h o w n i n F i gure la, while I m P i ~ A r e lb it is presented in a c o . r e s e e d V - e ~ l e . It is s e e n t h a t a t eV ~ 25 meV t h e r e a r e p e culiarities (-trked with ~rrows) superi m p o s e d on t h e m o n o t o n i c a l l y i n c r e a s i n g baok~ound. The p o s i t i o n s of these peculiarities c a n be o o m l ~ r e d w i t h t h e positions o f t h e d~O/dq . 0 s i n g u l a r p o i n t s ~u ~ne m a g n o n d l e p e r s i o n curves known f r o m t h e n e u t r o n d i f f r a c t i o n data.(3) The p h o n o n s p e c t r u m o f Gd t e r m i n a t e s at 13 meV. Hence, the part of VA(eV)-curve at s V > 13 meV can be only due to electron-magmon interaction. There are no peaks corresponding to 0378-4363/81/0000--0000/$02.50 © North-HollandPublishingCompany
phon0n density of states of Gd at eV< 13 meV either. Thus, one can assume that the whole Va(eV)-characteristic (Figure Is) is mainly due to electronmagnon interaction and is therefore proportional to the magnon density of states in Gd.
0;7,
6_
•
'.
',
!
C-d
I
'.
E,mev Figure 1 It follows from the theory (4) that the initial part of the PC spectrum of Gd should be proportional to eV as observed experimentally at eV< 7 meV (Figure la). It is seen from Figure Ib that the intensity o f PC s p e c t r u m d r o p s down sharply at V > % . This singularity is due to heating the contact area by current up to the Curie temperature T¢. At V ~ Vc the ferromagnetic-paramagmetic transition of the metal in the contact region takes place. The observation of such singularity proves once more that the metal at the contact is in the magnetically ordered state at V < V c . 369
370 interaction are symmetric with respect to the I-V zero point and the linewidth is proportional to kT in accordance with the theory.(4) The nonlinearities observed correspond to a total change in the differential resistance by-~10%.
e,
o
5
4o
,!5 E rnev
Figure 2 The PC spectrum of Tb is shown in Figure 2a. It is compared with the magnon density of states (Figure 2b) known from the calculations based on the magnon dispersion curves. (5) The magnon and phonon spectra of Tb are within the same energy range e V < 13 meV but the PC spectrum observed is in better agreement with the magnon density of states. F o r e x a m p l e , t h e b r o a d p e a k a t 10 meV a n d s m a l l one a t 12 meV a r e s e e n b o t h i n t h e PC and n e u t r o n d a t a s p e c t r a . The p e a k s w h i c h a r e known t o be due t o t h e honon density of states (e.g. at eVN -7 meV as follows from Ref.(6) ) are not seen definitely in the PC spectrum, only some traces of them can be found.
~
The point-contact spectrum of Ho shows a single maximum at e V ~ 4 . 3 meV. There is also an intensive maximum in the magnon density of states at eV=4-5 meV in the magnon spectrum of Ho.(7) Since for the above energy range the phonon density of states is low and have no maxima, the observed PC spectrum can be only due to electron-magnon inter action. The metals studied show also anomalous PC spectra. These are characterized by the value of V~(V) enhanced in the low energy region. The PC spectrum of a strongly deformed magnetic is considered to be observed in these oases. Typical PC spectra of the deformed Gd show three peculiar features: at 4 meV, 11 meV and 17 meV, and the spectrum terminates at eV,~20 - 25 meV. It should be noted that the intensity of peculiarities observed in spectra of different contacts can vary appreciably. All the spectra of electron-magnon
These facts along with the obvious correlations between positions of the V~(eV)-curve singularities at the energy axis and peculiar points in the magncn dispersion curves indicate convincingly that we succeded in observing the PC spectra of electron-magnon inter. action function in Gd, Tb, Ho. REFERENCES Yanson,I.K. and Kulik,I.O., Pointcontact spectroscopy of phonons in metals, J. de Phys., Coloque C6, Suppl. au n 88, 39 (1978) C6-1564C6-1567. L~ Akimenko,A.I. and Yanson,I.K., Point-contact spectroscopy of magnons in metals, Pisma v ZhETF 31
(1980) 209-213. E~ Koehler,W.C., Child,H.R., Nicklow, R.M., Smith,H.G., Moon R.M. and Cable,J.W., Spin-wave dispersion relations in gadolinium, Phys. Rev. Lett. 24 (1970) 16-18. ~41 Kulik,I.O. and Shekhter,R.l., Polnt-contact spectroscopy of ferro. magnetic metals, Fiz.Nizk.Temp.
2 (1980) 148-152. ~
Bjerrum,H., M~ller,H.B., Glyden Houmann,J.C. and Mackintosh,A.R., Magnetic interaction in Tb and Tb-IO% Ho from inelastic neutron scattering, J.Appl.Phys.39 (1968) 807-815. E~ Glyden Houmann,J.C. and Nicklow, R.M., Lattice dynamics of terbium, Ph~s.Rev. B1 (I~70) 3943-3952. [71 Stringfellow,M.W., Holden,T.M., Powell,B.M. and Woods,A.D.B., Spin waves in holmium, J.Phys.C! Metal Phys. Suppl. to No.2 (1970) 189200.