harmonically modulated structures
DESCRIPTION
HARMONICALLY MODULATED STRUCTURES. S. M. Dubiel * Faculty of Physics and Computer Science, AGH University of Science and Technology, PL-30-059 Krakow, Poland. * e-mail: [email protected]. INTRODUCTION. - PowerPoint PPT PresentationTRANSCRIPT
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“Gütlich, Bill, Trautwein: Mössbauer Spectroscopy and Transition Metal Chemistry@Springer-Verlag 2009”
HARMONICALLY HARMONICALLY MODULATED STRUCTURESMODULATED STRUCTURES
HARMONICALLY HARMONICALLY MODULATED STRUCTURESMODULATED STRUCTURES
S. M. Dubiel*
Faculty of Physics and Computer Science, AGH University of Science and Technology,
PL-30-059 Krakow, Poland
S. M. Dubiel*
Faculty of Physics and Computer Science, AGH University of Science and Technology,
PL-30-059 Krakow, Poland
*e-mail: [email protected]
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“Gütlich, Bill, Trautwein: Mössbauer Spectroscopy and Transition Metal Chemistry@Springer-Verlag 2009”
INTRODUCTIONINTRODUCTIONThere exist crystalline systems with harmonic modulation of their electronic structure in a real space. The modulation occurs below a critical temperature and is known as (a) charge-density waves (CDWs), in case only the density of charge is modulated, and as (b) spin-density waves (SDWs), in case the spin-density is modulated. If both densities are modulated we speak about the co-existence of CDWs and SDWs. One of the basic parameters pertinent to such structures is periodicity, . If n ·a, where a is the lattice constant and n is an integer, the modulation is commensurate with the lattice, if n ·a, the modulation is incommensurate. CDWs were found to exist in quasi-1D linear chain compounds like TaS3 and NbSe3 , 2D layered transition-metal dichalcogenides such as TaS2, VS2, or NbSe2, 3D metals like -Zr and Cr [1]. In the case of metallic Cr, which will be descussed here in more detail, SDWs originate from s- and d-like electrons and show a variety of interesting properties [2]. The most fundamental is their relationship to a density of electrons at the Fermi surface (FS). Between the Néel temperature of 313 K and the so-called spin-flip temperature, TSF of 123 K, SDWs in chromium are transversely polarized i.e. the wave vector, q , is perpendicular to the polarization vector, p. Below TSF they are longitudinally polarized.
There exist crystalline systems with harmonic modulation of their electronic structure in a real space. The modulation occurs below a critical temperature and is known as (a) charge-density waves (CDWs), in case only the density of charge is modulated, and as (b) spin-density waves (SDWs), in case the spin-density is modulated. If both densities are modulated we speak about the co-existence of CDWs and SDWs. One of the basic parameters pertinent to such structures is periodicity, . If n ·a, where a is the lattice constant and n is an integer, the modulation is commensurate with the lattice, if n ·a, the modulation is incommensurate. CDWs were found to exist in quasi-1D linear chain compounds like TaS3 and NbSe3 , 2D layered transition-metal dichalcogenides such as TaS2, VS2, or NbSe2, 3D metals like -Zr and Cr [1]. In the case of metallic Cr, which will be descussed here in more detail, SDWs originate from s- and d-like electrons and show a variety of interesting properties [2]. The most fundamental is their relationship to a density of electrons at the Fermi surface (FS). Between the Néel temperature of 313 K and the so-called spin-flip temperature, TSF of 123 K, SDWs in chromium are transversely polarized i.e. the wave vector, q , is perpendicular to the polarization vector, p. Below TSF they are longitudinally polarized.
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Another peculiarity of the SDWs in chromium is their incommensurability i.e. q 2/a. This feature can be measured by a parameter , such that q 2(1-)/a. The periodicity can thus be expressed as a/(1-), hence > a. In chromium depends on temperature and a a/ varies between ~60 nm at 4 K and 80 nm at RT.
[1] T. Butz in Nuclear Spectroscopy on Charge Density Waves Systems, 1992, Kluwer Academic Publ.
[2] E. Fawcett, Rev. Mod. Phys., 60 (1988) 209
Another peculiarity of the SDWs in chromium is their incommensurability i.e. q 2/a. This feature can be measured by a parameter , such that q 2(1-)/a. The periodicity can thus be expressed as a/(1-), hence > a. In chromium depends on temperature and a a/ varies between ~60 nm at 4 K and 80 nm at RT.
[1] T. Butz in Nuclear Spectroscopy on Charge Density Waves Systems, 1992, Kluwer Academic Publ.
[2] E. Fawcett, Rev. Mod. Phys., 60 (1988) 209
Fermi Surface of chromiumFermi Surface of chromium
3D3D3D
2D
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SIMULATED SPECTRASIMULATED SPECTRASDWs can be described by a sinusoidal function or a series of odd harmonics, SDWs can be described by a sinusoidal function or a series of odd harmonics,
1
12)12sin[(
ii
iSDW H
and CDWs can be described by a series of even harmonics, where q · r and is a phase shift. H2i-1 and I2i are amplitudes of SDWs and CDWs, respectively.
Investigation of SDWs and CDWs with Mössbauer Spectroscopy (MS) requires that one of the elements constituting a sample shows the Mössbauer effect. If not, one has to introduce such an element into the sample matrix. In the latter case, a question of the influence of the probe atoms on SDWs and CDWs arises. Theoretical calculations show that magnetic atoms have a destructive effect i.e. they pin SDWs and/or CDWs. Consequently, such atoms are not suitable as probes. Unfortunately, 57Fe atoms belong to this category of probe atoms. On the other hand, non-magnetic atoms hardly affect SDWs and/or CDWs, hence they can be used as good Mössbauer probe nuclei. Among the latter 119Sn has prooved to be useful. In the following, all spectra were simulated and/or recorded on 119Sn.
and CDWs can be described by a series of even harmonics, where q · r and is a phase shift. H2i-1 and I2i are amplitudes of SDWs and CDWs, respectively.
Investigation of SDWs and CDWs with Mössbauer Spectroscopy (MS) requires that one of the elements constituting a sample shows the Mössbauer effect. If not, one has to introduce such an element into the sample matrix. In the latter case, a question of the influence of the probe atoms on SDWs and CDWs arises. Theoretical calculations show that magnetic atoms have a destructive effect i.e. they pin SDWs and/or CDWs. Consequently, such atoms are not suitable as probes. Unfortunately, 57Fe atoms belong to this category of probe atoms. On the other hand, non-magnetic atoms hardly affect SDWs and/or CDWs, hence they can be used as good Mössbauer probe nuclei. Among the latter 119Sn has prooved to be useful. In the following, all spectra were simulated and/or recorded on 119Sn.
1
20)2sin(sin
ii
iCDW II
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INCOMMENSURTATE CDWs and SDWs
• CDW = I0· sin – effect of I0 • SDW = H1· sin – effect of H1
INCOMMENSURTATE CDWs and SDWs
• CDW = I0· sin – effect of I0 • SDW = H1· sin – effect of H1
J. Cieslak and S. M. Dubiel, Nucl. Instr. Meth. Phys. Res. B, 101 (1995) 295; Acta Phys. Pol. A, 88 (1995) 1143
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INCOMMENSURTATE CDWs
• CDW = I0 · sin + I2 · sin (2+) - Effect of I2>0 and
INCOMMENSURTATE CDWs
• CDW = I0 · sin + I2 · sin (2+) - Effect of I2>0 and
J. Cieslak and S. M. Dubiel, Nucl. Instr. Metyh. Phys. Res. B, 101 (1995) 295
• 119Sn simulated spectra and underlying distributions of the charge-density for I2 > 0 and = 0o, (a) and (b), respectively, and for = 90o (c) and (d). I0 = 0.5.
• 119Sn simulated spectra and underlying distributions of the charge-density for I2 > 0 and = 0o, (a) and (b), respectively, and for = 90o (c) and (d). I0 = 0.5.
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INCOMMENSURTATE SDWsINCOMMENSURTATE SDWs
• SDW = H1 · sin + H3 · sin 3 - Effect of H3 and its sign • SDW = H1 · sin + H3 · sin 3 - Effect of H3 and its sign
G. LeCaer and S. M. Dubiel, J. Magn. Magn. Mater., 92 (1990) 251; J. Cieslak and S. M. Dubiel, Acta Phys. Pol. A, 88 (1995) 1143
• Simulated spectra for (a) H3 > 0 and (b) H3 < 0 with various amplitudes of H3 shown, and underlying distributions of the spin-density. H1 = 60.
• Simulated spectra for (a) H3 > 0 and (b) H3 < 0 with various amplitudes of H3 shown, and underlying distributions of the spin-density. H1 = 60.
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SINGLE-CRYSTAL CHROMIUMSINGLE-CRYSTAL CHROMIUMSINGLE-CRYSTAL CHROMIUMSINGLE-CRYSTAL CHROMIUM
S. M. Dubiel and G. LeCaer, Europhys. Lett., 4 (1987) 487; S. M. Dubiel et al., Phys. Rev. B, 53 (1996) 268
• First ME determination of H3 and its sign • First ME determination of H3 and its sign
• (left) RT and LHT spectra and underlying shapes of SDW and CDW, and (right) corresponding distributions of the spin- and charge densities.• (left) RT and LHT spectra and underlying shapes of SDW and CDW, and (right) corresponding distributions of the spin- and charge densities.
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POLYCRYSTALLINE CHROMIUMPOLYCRYSTALLINE CHROMIUMPOLYCRYSTALLINE CHROMIUMPOLYCRYSTALLINE CHROMIUM
S. M. Dubiel and J. Cieslak, Phys. Rev. B, 51 (1995) 9341
• 119Sn spectra recorded at 295 K on: (a) single- and (b) – (d) polycrystalline chromium with various size of grains in a decreasing sequence (left) and underlying distributions of spin- and charge densities (right). Note an increase of the maximum hf. field and appearance of zero-field peak. Both effects can be largely explained in terms of H3 < 0.
• 119Sn spectra recorded at 295 K on: (a) single- and (b) – (d) polycrystalline chromium with various size of grains in a decreasing sequence (left) and underlying distributions of spin- and charge densities (right). Note an increase of the maximum hf. field and appearance of zero-field peak. Both effects can be largely explained in terms of H3 < 0.
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INFLUENCE OF VANADIUMINFLUENCE OF VANADIUMINFLUENCE OF VANADIUMINFLUENCE OF VANADIUM
S. M. Dubiel, J. Cieslak and F. E. Wagner, Phys. Rev. B, 53 (1996) 268
• Spectra recorded at 4.2 K (left) and 295 K (right) on single-crystal samples of CrVx with (a) x = 0, (b) x =0.5, (c) x =2.5 and (d) x =5. The quenching effect of V is clearly seen.
• Spectra recorded at 4.2 K (left) and 295 K (right) on single-crystal samples of CrVx with (a) x = 0, (b) x =0.5, (c) x =2.5 and (d) x =5. The quenching effect of V is clearly seen.
cm
4.2 K4.2 K 295 K
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IMPLANTED CHROMIUMIMPLANTED CHROMIUMIMPLANTED CHROMIUMIMPLANTED CHROMIUM
S. M. Dubiel et al., Phys. Rev., 63 (2001) 060406(R), J. Cieslak et al., J. Alloys Comp., 442 (2007) 235
0
5
10
15
20
25
10 15 20 25 30 35 40
<d> [nm]
Hf.
Fie
ld [
T]
• Right: (a) CEMS spectrum recorded at RT on a single-crystal chromium implanted with 119Sn ions of 55 keV energy together with the underlying distribution of the spin-density, and (b) a spectrum recorded in a transmission geometry on a similar sample doped with 119Sn ions by diffusion.
Left: Hyperfine field vs. average implantation depth, <d>; triangles stand for the maximum and circules for the average hf. field values in the implanted samples, while the solid straight lines indicate the same quantities for the bulk sample.
• Right: (a) CEMS spectrum recorded at RT on a single-crystal chromium implanted with 119Sn ions of 55 keV energy together with the underlying distribution of the spin-density, and (b) a spectrum recorded in a transmission geometry on a similar sample doped with 119Sn ions by diffusion.
Left: Hyperfine field vs. average implantation depth, <d>; triangles stand for the maximum and circules for the average hf. field values in the implanted samples, while the solid straight lines indicate the same quantities for the bulk sample.
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CONCLUSIONSCONCLUSIONSCONCLUSIONSCONCLUSIONSHarmonically modulated structures (SDWs and CDWs) can be studied in detail with 119Sn-site Mössbauer spectroscopy, because spectral parameters, hence a shape of spectra, are very sensitive to various parameters pertinent to SDWs and CDWs, and in particular to: • periodicity, < 17a (for commensurate SDWs) • amplitude and sign of higher-order harmonics • phase shift
Several real applications were demonstrated for metallic chromium, and, in particular, the following issues were addressed: • third-order harmonic in a single-crystal • interaction of SDWs with grain boundaries (polycrystalline Cr) • quenching effect of vanadium • enhancement of spin-density (implanted single-crystal)
Harmonically modulated structures (SDWs and CDWs) can be studied in detail with 119Sn-site Mössbauer spectroscopy, because spectral parameters, hence a shape of spectra, are very sensitive to various parameters pertinent to SDWs and CDWs, and in particular to: • periodicity, < 17a (for commensurate SDWs) • amplitude and sign of higher-order harmonics • phase shift
Several real applications were demonstrated for metallic chromium, and, in particular, the following issues were addressed: • third-order harmonic in a single-crystal • interaction of SDWs with grain boundaries (polycrystalline Cr) • quenching effect of vanadium • enhancement of spin-density (implanted single-crystal)
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MORE TO READMORE TO READMORE TO READMORE TO READ• E. Fawcett et al., Rev. Mod. Phys., 66 (1994) 25
• S. M. Dubiel, Phys. Rev. B, 29 (1984) 2816
• R. Street et al., J. Appl. Phys., 39 (1968) 1050
• S. M. Dubiel, J. Magn. Magn. Mater., 124 (1993) 31
• S. M. Dubiel in Recent Res. Devel. Physics, 4 (2003) 835, ed. S. G. Pandali, Transworld Res. Network
• S. M. Dubiel and J. Cieslak, Europhys. Lett., 53 (2001) 383
• J. Cieslak and S. M. Dubiel, Acta Phys. Pol. A, 91 (1997) 1131
• K. Mibu et al., Hyp. Inter.(c), 3 (1998) 405
• K. Mibu et al., J. Phys. Soc. Jpn., 67 (1998) 2633
• K. Mibu and T. Shinjo, J. Phys. D; Appl. Phys., 35 (2002) 2359
• K. Mibu et al., Phys. Rev. Lett., 89 (2002) 287202