HARMONICALLY MODULATED STRUCTURES

“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]


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.


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


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


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


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.


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.


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.


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.


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


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.


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)


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

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HARMONICALLY MODULATED STRUCTURES