44 research outputs found
Electron Spin Resonance Of Gd3+ In Gdm Mn In3m+2n (m=rh,ir; N=0,1; M=1,2) Antiferromagnets
We report electron spin resonance experiments of Gd3+ in the Gdm Mn In3m+2n (M=Rh,Ir; n=0,1; m=1,2) intermetallic compounds. For T TN ∼45 K, all compounds present a single Dysonian resonance and show a Korringa-like temperature dependence of the linewidth, ΔH=a+bT. The residual linewidth a is strongly affected by the transition metal M=Rh or Ir and/or by the layering (m=1 or 2) or change in structure (n=0,1). The residual linewidth is associated with an unresolved crystalline electrical field (CEF) fine structure. Consequently, a systematic evolution of the CEF in the Gdm Mn In3m+2n compounds is inferred. A discussion to what extent our results can explain to the CEF effects observed in isostructural R-based compounds will be given. © 2008 American Institute of Physics.1037Hegger, H., (2000) Phys. Rev. Lett., 84, p. 4986Petrovic, C., (2001) Europhys. Lett., 53, p. 354Petrovic, C., (2001) J. Phys.: Condens. Matter, 13, p. 337Pagliuso, P.G., (2001) Phys. Rev. B, 63, p. 054426Pagliuso, P.G., (2000) Phys. Rev. B, 62, p. 12266Thompson, J.D., (2001) J. Magn. Magn. Mater., 226-230, p. 5Pagliuso, P.G., (2001) Phys. Rev. B, 64, p. 100503. , (R)Sidorov, V.A., (2002) Phys. Rev. Lett., 89, p. 157004Bianchi, A., (2003) Phys. Rev. Lett., 91, p. 257001Park, T., (2006) Nature (London), 440, p. 65Pham, L.D., (2006) Phys. Rev. Lett., 97, p. 056404Hering, E.N., (2006) Physica B, 378-380, p. 423Pagliuso, P.G., (2006) J. Appl. Phys., 99, pp. 08P703Granado, E., (2006) Phys. Rev. B, 74, p. 214428Granado, E., (2004) Phys. Rev. B, 69, p. 144411Lora-Serrano, R., (2006) Phys. Rev. B, 74, p. 214404Lora-Serrano, R., (2006) Physica B, 384, p. 326Amara, M., Amara, M., Amara, M., (1994) J. Magn. Magn. Mater., 130, p. 127. , 0304-8853 10.1016/0304-8853(94)90665-3, ();, J. Magn. Magn. Mater. 0304-8853 10.1016/0304-8853(94)90284-4 131, 402 (1994);, J. Magn. Magn. Mater. 140-144, 1157 (1994)Czopnik, A., (1991) Phys. Status Solidi A, 127, p. 243Abragam, Bleaney, B., (1670), Electron Paramagnetic Resonance of Transition Ions (Clarendon, Oxford)Korringa, J., (1950) Physica (Amsterdam), 10, p. 601Rettori, C., (1974) Phys. Rev. B, 10, p. 1826Davidov, D., (1973) Solid State Commun., 12, p. 62
Evolution From Insulator (x=0.003) To Metal (x=1) Of The Eu 2+ Local Environment In Ca 1-xeu Xb 6
The local environment of Eu2+ (4 f7, S=72) in Ca1-x Eux B6 (0.003≤x≤1.00) is studied by means of electron spin resonance (ESR). For x≲0.07 the resonances have Lorentzian line shape, indicating an insulating environment for the Eu2+ ions. For x≳0.07, the lines broaden and become Dysonian in shape, suggesting a change to metallic environment for the Eu2+ ions, anticipating the semimetallic character of EuB6. The broadening is attributed to a spin-flip scattering relaxation process due to the exchange interaction between conduction and Eu2+ 4f electrons. High field ESR measurements for x≳0.30 reveal narrower and anisotropic linewidths, which are attributed to magnetic polarons and Fermi surface effects, respectively. © 2005 American Institute of Physics.9710Young, D.P., (1999) Nature (London), 397, p. 412Zhitomirsky, M.E., (1999) Nature (London), 402, p. 251Tromp, H.J., (2000) Phys. Rev. Lett., 87, p. 016401Massidda, S., Continenza, A., De Pascale, T.M., Monnier, R., (1997) Z. Phys. B: Condens. Matter, 102, p. 83Urbano, R.R., (2002) Phys. Rev. B, 65, p. 180407Bennett, M.C., (2004) Phys. Rev. B, 69, p. 132407Urbano, R.R., Pagliuso, P.G., Rettori, C., Oseroff, S.B., Sarrao, J.L., Schlottmann, P., Fisk, Z., (2004) Phys. Rev. B, 70, p. 140401Pake, G.E., Purcell, E.M., (1948) Phys. Rev., 74, p. 1184Bloembergen, N., (1952) J. Appl. Phys., 23, p. 1383Feher, G., Kip, A.F., (1955) Phys. Rev., 98, p. 337Dyson, F.J., (1955) Phys. Rev., 98, p. 349Sperlich, G., Jansen, K., (1974) Solid State Commun., 15, p. 1105Essam, J.W., (1972) Phase Transitions and Critical Phenomena, 2, p. 197. , Academic, LondonSchlottmann, P., Hellberg, C.S., (1996) J. Appl. Phys., 79, p. 6414Fisk, Z., (1979) J. Appl. Phys., 50, p. 1911Goodrich, R.G., Harrison, N., Vuillemin, J.J., Tekul, A., Hall, D.W., Fisk, Z., Young, D., Sarrao, J., (1998) Phys. Rev. B, 58, p. 14896Rhyee, J.-S., Cho, B.K., Ri, H.-C., (2003) Phys. Rev. B, 67, p. 125102Wigger, G.A., Beeli, C., Felder, E., Ott, H.R., Bianchi, A.D., Fisk, Z., (2004) Phys. Rev. Lett., 93, p. 14720
Noncubic Symmetry In Ca 1-xeu Xb 6 (0.15≲x≤1.00): An Electron-spin-resonance Study
The Eu2+ (4 f7, S=72) g value in Ca1-x Eux B6 (0.15≲x≤1.00) was measured by means of electron spin resonance at two frequencies (fields), 9.4 (≈3.4 kOe) and 34.4 GHz (≈12.1 kOe). The g value was found to be anisotropic and magnetic-field dependent. The amplitude of the anisotropy increases at low temperatures. The observed angular and temperature dependences of the g value suggest tetragonal symmetry caused, presumably, by a distortion along a direction perpendicular to the largest crystal face, the [001] direction. Due to the platelet shape of the samples, part of the anisotropy of the g value can also be attributed to demagnetization effects. The g values decrease at higher fields, which is interpreted in terms of a two-band model involving an exchange interaction between the localized Eu2+ 4 f7 electrons with conduction Eu2+ 5d -like electrons and B 2p -like holes. © 2006 American Institute of Physics.998Etourneau, J., Hagenmuller, P., (1985) Philos. Mag. B, 52, p. 589Young, D.P., (1999) Nature (London), 397, p. 412Zhitomirsky, M.E., Rice, T.M., Anisimov, V.I., (1999) Nature (London), 402, p. 251Degiorgi, L., Felder, E., Ott, H.R., Sarrao, J.L., Fisk, Z., (1997) Phys. Rev. Lett., 79, p. 5134Massidda, S., Continenza, A., De Pascale, T.M., Monnier, R., (1997) Z. Phys. B: Condens. Matter, 102, p. 83Süllow, S., (1998) Phys. Rev. B, 57, p. 5860Booth, C.H., Sarrao, J.L., Hundley, M.F., Cornelius, A.L., Kwei, G.H., Bianchi, A., Fisk, Z., Lawrence, J.M., (2001) Phys. Rev. B, 63, p. 224302Paschen, S., Pushim, D., Schlatter, M., Vonlanthen, P., Ott, H.R., Young, D.P., Fisk, Z., (2000) Phys. Rev. B, 61, p. 4174Wigger, G.A., Walti, Ch., Ott, H.R., Bianchi, A.D., Fisk, Z., (2002) Phys. Rev. B, 66, p. 212410Wigger, G.A., Beeli, C., Felder, E., Ott, H.R., Bianchi, A.D., Fisk, Z., (2004) Phys. Rev. Lett., 93, p. 147203Uimin, G., (1997) Phys. Rev. B, 55, p. 8267Sturm, H., Elschner, B., Hock, K.-H., (1985) Phys. Rev. Lett., 54, p. 1291Altshuler, T.S., Bresler, M.S., (1999) J. Exp. Theor. Phys., 88, p. 1019Süllow, S., Prasad, I., Aronson, M.C., Bogdanovich, S., Sarrao, J.L., Fisk, Z., (2000) Phys. Rev. B, 62, p. 11626Urbano, R.R., Pagliuso, P.G., Rettori, C., Oseroff, S.B., Sarrao, J.L., Schlottmann, P., Fisk, Z., (2004) Phys. Rev. B, 70, p. 140401Urbano, R.R., (2005) Phys. Rev. B, 71, p. 184422Feher, G., Kip, A.F., (1955) Phys. Rev., 98, p. 337. , 0031-899X 10.1103/PhysRev.98.337Dyson, F.J., (1955) Phys. Rev., 98, p. 349. , 0031-899X 10.1103/PhysRev.98.349Pake, G.E., Purcell, E.M., (1948) Phys. Rev., 74, p. 1184Abragam, A., Bleaney, B., (1970) EPR of Transition Ions, , Clarendon, OxfordKunii, S., Uemura, T., Chiba, Y., Kasuya, T., Date, M., (1985) J. Magn. Magn. Mater., 52, p. 271. , 0304-8853 10.1016/0304-8853(85)90277-XKunii, S., (2000) J. Phys. Soc. Jpn., 69, p. 3789Bisch, P.M., Troper, A., Gomes, A.A., (1976) Phys. Rev. B, 13, p. 3902. , 0556-2805 10.1103/PhysRevB.13.3902Troper, A., De Menezes, O.L.T., Lederer, P., Gomes, A.A., (1978) Phys. Rev. B, 18, p. 3709. , 0556-2805 10.1103/PhysRevB.18.3709Barberis, G.E., Davidov, D., Donoso, J.P., Rettori, C., Suassuna, J.F., Dokter, H.D., (1979) Phys. Rev. B, 19, p. 5495. , 0163-1829 10.1103/PhysRevB.19.5495Pagliuso, P.G., Rettori, C., Sarrao, J.L., Cornelius, A., Hundley, M.F., Fisk, Z., Oseroff, S.B., (1999) Phys. Rev. B, 60, p. 13515Calderón, M.J., Wegener, L.G.L., Littlewood, P.B., (2004) Phys. Rev. B, 70, p. 092404Davidov, D., Maki, K., Orbach, R., Rettori, C., Chock, E.P., (1973) Solid State Commun., 12, p. 62
Probing The Electronic Structure Of Pure And Doped Cem In5 (m=co,rh,ir) Crystals With Nuclear Quadrupolar Resonance
We report calculations of the electric-field gradients (EFGs) in pure and doped CeM In5 (M=Co, Rh, and Ir) compounds and compare with experiment. The degree to which the Ce4f electron is localized is treated within various models: the local-density approximation, generalized gradient approximation (GGA), GGA+U, and 4f -core approaches. We find that there is a correlation between the observed EFG and whether the 4f electron participates in the band formation or not. We also find that the EFG evolves linearly with Sn doping in CeRhIn5, suggesting the electronic structure is modified by doping. In contrast, the observed EFG in CeCoIn5 doped with Cd changes little with doping. These results indicate that nuclear quadrupolar resonance is a sensitive probe of electronic structure. © 2008 The American Physical Society.7724Slichter, C.P., (1990) Principles of Magnetic Resonance, , 3rd ed. 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Role Of Oxygen Vacancies In The Magnetic And Dielectric Properties Of The High-dielectric-constant System Cacu3 Ti4 O12: An Electron-spin Resonance Study
We report experiments of electron spin resonance (ESR) of Cu2+ in polycrystalline samples of CaCu3 Ti4 O12 post-annealed in different atmospheres. After being synthesized by solid state reaction, pellets of CaCu3 Ti4 O12 were annealed for 24 h at 1000°C under air, Ar or O2. Our temperature dependent ESR data revealed for all samples nearly temperature independent g value (2.15(1)) and linewidth for T TN ≈25 K. However, the values of ESR linewidth are strongly affected by the oxygen content in the sample. For instance, argon post-annealed samples show a much larger linewidth than the O2 or air post-annealed samples. We attribute this broadening to an increase of the dipolar homogeneous broadening of the Cu2+ ESR lines due to the presence of oxygen vacancies which induce an S=1 2 spin inside the TiO6 octahedra. Correlation between a systematic dependence of the ESR linewidth on the oxygen content and the high dielectric constant of these materials is addressed. Also, ESR, magnetic susceptibility, and specific heat data for a single crystal of CaCu3 Ti4 O12 and for polycrystals of CdCu3 Ti4 O12 are reported. © 2006 The American Physical Society.7322Subramanian, M.A., Li, D., Duan, N., Reisner, B., Sleight, A.W., (2000) J. Solid State Chem., 151, p. 323. , JSSCBI 0022-4596 10.1006/jssc.2000.8703Ramirez, A.P., Subramanian, M.A., Gardel, M., Blumberg, G., Li, D., Vogt, T., Shapiro, S.M., (2000) Solid State Commun., 151, p. 217. , SSCOA4 0038-1098Homes, C.C., Vogt, T., Shapiro, S.M., Wakimoto, S., Ramirez, A.P., (2001) Science, 293, p. 673. , SCIEAS 0036-8075 10.1126/science.292.5517.673Lunkenheimer, P., Bobnar, V., Pronin, A.V., Ritus, A.I., Volkov, A.A., Loidl, A., (2002) Phys. Rev. B, 66, p. 052105. , PRBMDO 0163-1829 10.1103/PhysRevB.66.052105Homes, C.C., Vogt, T., Shapiro, S.M., Wakimoto, S., Subramanian, M.A., Ramirez, A.P., (2003) Phys. Rev. B, 67, p. 092106. , PRBMDO 0163-1829 10.1103/PhysRevB.67.092106Sinclair, D.C., Admas, T.B., Morrison, F.D., West, A.R., (2002) Appl. Phys. Lett., 80, p. 2153. , APPLAB 0003-6951 10.1063/1.1463211Giulloto, E., Mozzati, M.C., Azzoni, C.B., Massarotti, V., Bini, M., (2004) Ferroelectrics, 298, p. 61. , FEROA8 0015-0193Mozzati, M.C., Azzoni, C.B., Capsoni, D., Bini, M., Massarotti, V., (2003) J. Phys.: Condens. Matter, 15, p. 7365. , JCOMEL 0953-8984 10.1088/0953-8984/15/43/018Subramanian, M.A., Sleight, A.W., (2002) Solid State Sci., 4, p. 347. , SSSCFJ 1293-2558 10.1016/S1293-2558(01)01262-6Fang, L., Shen, M., Cao, W., (2004) J. Appl. Phys., 95, p. 6483. , JAPIAU 0021-8979 10.1063/1.1728308Koitzsch, A., Blumberg, G., Gozar, A., Dennis, B., Ramirez, A.P., Trebst, S., Wakimoto, S., (2002) Phys. Rev. B, 65, p. 052406. , PRBMDO 0163-1829 10.1103/PhysRevB.65.052406Bosman, A.J., Van Daal, H.J., (1970) Adv. Phys., 19, p. 1. , ADPHAH 0001-8732 10.1080/00018737000101071Lenjer, S., Schirmer, O.F., Hesse, H., Kool, T.W., (2002) Phys. Rev. B, 66, p. 165106. , PRBMDO 0163-1829 10.1103/PhysRevB.66.165106Bednorz, J.G., Mller, K.A., (1988) Rev. Mod. Phys., 60, p. 585. , RMPHAT 0034-6861 10.1103/RevModPhys.60.585Salamon, M.B., Jaime, M., (2001) Rev. Mod. Phys., 73, p. 583. , RMPHAT 0034-6861 10.1103/RevModPhys.73.583Scharfschwerdt, R., Mazur, A., Schirmer, O.F., Hesse, H., Mendricks, S., (1996) Phys. Rev. B, 54, p. 15284. , PRBMDO 0163-1829 10.1103/PhysRevB.54.15284Laguta, V.V., Slipenyuk, A.M., Bykov, I.P., Glinchuck, M.D., Maglione, M., Michau, D., Rosa, J., Jastrabik, L., (2005) Appl. Phys. Lett., 87, p. 022903. , APPLAB 0003-6951 10.1063/1.1954900Cohn, J.L., Peterca, M., Neumeier, J.J., (2005) J. Appl. Phys., 97, p. 034102. , JAPIAU 0021-8979 10.1063/1.1834976Abragam, A., Bleaney, B., (1670) Electron Paramagnetic Resonance of Transition Ions, , Clarendon, OxfordPoole, C.P., Farach, H.A., (1971) Relaxation in Magnetic Resonance, , Academic, New YorkVan Vleck, J.H., (1948) Phys. Rev., 74, p. 1168. , PHRVAO 0031-899X 10.1103/PhysRev.74.1168Anderson, P.W., Weiss, P.R., (1953) Rev. Mod. Phys., 25, p. 269. , RMPHAT 0034-6861 10.1103/RevModPhys.25.269Wu, L., Zhu, Y., Park, S., Shapiro, S., Shirane, G., Tafto, J., (1953) Rev. Mod. Phys., 25, p. 269. , RMPHAT 0034-6861 10.1103/RevModPhys.25.26
Charge dynamics and "ferromagnetism" of A1-xLaxB6 (A=Ca and Sr)
Ferromagnetism has been reported recently in La-doped alkaline-earth
hexaborides, A1-xLaxB6 (A=Ca, Sr, and Ba). We have performed the reflectivity,
Hall resistivity, and magnetization measurements of A1-xLaxB6. The results
indicate that A1-xLaxB6 can be regarded as a simple doped semimetal, with no
signature of an excitonic state as suggested by several theories. It is also
found that the surface of as-grown samples (10 micrometer in thickness) has a
different electronic structure from a bulk one, and a fairly large number of
paramagnetic moments are confined in this region. After eliminating these
paramagnetic moments at the surface, we could not find any evidence of an
intrinsic ferromagnetic moment in our samples, implying the possibility that
the ferromagnetism of A1-xLaxB6 reported so far is neither intrinsic.Comment: 7 pages, 8 figure
Esr Study Of The Eu2+ G -value In The Metallic Phase Of Cubic Hexaboride Ca1-x Eux B6 (0.15 X≤1.00)
The angular, magnetic field, and temperature dependence of the Eu2+ (4 f7, S=7/2) g -value in Ca1-x Eux B6 (0.15 x≤1.00) is measured by means of electron spin resonance at two microwave frequencies, 9.4 and 34.4 GHz. The g -value is found to be anisotropic and magnetic-field-dependent. The reduction with field of the positive g -shift is interpreted in terms of the exchange interaction between the localized Eu2+ 4 f7 electrons with the conduction Eu2+ 5d -like electrons and B 2p -like holes. The angular, temperature, and x dependence of the anisotropy of the g -value can be attributed to demagnetization effects due to the platelet-like shape of the samples. High-resolution synchrotron x-ray diffraction experiments show the absence of distortions larger than δa/a∼ 10-4. 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Crystal Structure And Physical Properties Of Gd3co 4sn13 Intermetallic Antiferromagnet
We have synthesized single crystalline samples of Gd3 Co4 Sn13 intermetallic compound using a Sn-flux method. This compound crystallizes with a cubic Yb3 Co4 Sn13 -type structure, space group Pm-3n, which has 40 atoms per unit cell. Measurements of the magnetic susceptibility, heat capacity, electrical resistivity, and electron spin resonance (ESR) revealed that Gd3 Co4 Sn13 is a metallic Curie-Weiss paramagnet at high temperature and presents an antiferromagnetic ordering below TN =14.5 K. In the paramagnetic state, a single Gd3+ ESR line with a nearly temperature independent g∼2.005 (2) is observed, and its linewidth follows a Korringa-like behavior as a function of temperature. From the Korringa rate (ΔHΔT∼4 OeK) and g -shift (Δg∼0.012) obtained from the ESR experiments combined with the magnetic susceptibility and specific heat data for Gd3 Co4 Sn13, we have extracted the exchange parameters between the Gd3+ local moments and the conduction-electrons (c-e) in this compound. This exchange parameter Jfs ≈10 meV was found to be c-e wave-vector independent and the electronic structure of Gd3 Co4 Sn13 has a single band character. © 2006 American Institute of Physics.998Remeika, J.P., (1980) Solid State Commun., 34, p. 923Remeika, J.P., (1982) Solid State Commun., 42, p. 97Sato, H., (1993) Physica B, 188, p. 630Hundley, M.F., (2002) Phys. Rev. B, 65, p. 024401Israel, C., (2005) Physica B, 359-361, p. 251Cornelius, A., Physica BPagliuso, P.G., (2001) Phys. Rev. B, 63, p. 054426Granado, E., (2004) Phys. Rev. B, 69, p. 144411Davidov, D., Maki, K., Orbach, R., Rettori, C., Chock, E.P., (1973) Solid State Commun., 12, p. 621Feher, G., Kip, A.F., (1955) Phys. Rev., 98, p. 337. , 0031-899X 10.1103/PhysRev.98.337Dyson, F.J., (1955) Phys. Rev., 98, p. 349Yosida, K., (1957) Phys. Rev., 106, p. 893Korringa, J., (1950) Physica (Amsterdam), 16, p. 601Rettori, C., Kim, H.M., Chock, E.P., Davidov, D., (1974) Phys. Rev. B, 10, p. 1826Abragam, A., Bleaney, B., (1970) EPR of Transition Ions, , Clarendon, OxfordMoriya, T., (1963) J. Phys. Soc. Jpn., 18, p. 516Narath, A., (1967) Phys. Rev., 163, p. 232Pagliuso, P.G., (1999) Phys. Rev. B, 60, p. 13515Bittar, E.M.
Quantum Oscillations In Eufe2 As2 Single Crystals
Quantum oscillation measurements provide relevant information about the Fermi surface (FS) properties of strongly correlated metals. Here, we report on the Shubnikov-de Haas effect via high-field resistivity measurements of EuFe2As2 (Eu122) and BaFe2As2 (Ba122) single crystals. Although both pnictide compounds are isovalent with similar effective masses and density of states, at the Fermi level, our results reveal subtle changes in their fermiology. Remarkably, although the spin-density-wave (SDW) ordering temperature is higher in the Eu-rich end, Eu122 displays a much more isotropic and three-dimensional-like FS when compared with Ba122, in agreement with band structure calculations. Our experimental results suggest an anisotropic contribution of the Fe 3d orbitals to the FS in Ba122. We speculate that this orbital differentiation may be responsible for the suppression of the SDW phase in the FeAs-based compounds.9019Kamihara, Y., Watanabe, T., Hirano, M., Hosono, H., (2008) J. Am. 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Anomalous Phonon Shifts In The Paramagnetic Phase Of Multiferroic R Mn2 O5 (r=bi, Eu, Dy): Possible Manifestations Of Unconventional Magnetic Correlations
A Raman spectroscopic study of the high-frequency optical phonons in single crystals of the multiferroic system R Mn2 O5 (R=Bi, Eu, Dy) was performed. All studied materials show anomalous phonon shifts, below a new characteristic temperature for these materials, T* ∼60-65 K. The sign and magnitude of such shifts appear to be correlated with the ionic radius of R, envolving from softenings for R=Bi to hardenings for R=Dy and showing an intermediary behavior for R=Eu. Additional phonon anomalies were identified below ∼ TN ∼40-43 K, reflecting the onset of long-range ferroelectric and/or magnetic order of the Mn sublattice. Complementary dc-magnetic susceptibility [χ (T)] measurements for Bi Mn2 O5 up to 800 K yield a Curie-Weiss temperature θCW =-253 (3) K, revealing a fairly large frustration ratio (θCW TN =6.3). Deviations of χ (T) from a Curie-Weiss paramagnetic behavior due to magnetic correlations were observed below temperatures of the order of θCW, with the inverse susceptibility showing inflection points at ∼160 K and ∼ T*. Supported by χ (T) data, the anomalous Raman phonon shifts below T* are interpreted in terms of the spin-phonon coupling, in a scenario of strong magnetic correlations. Overall, these results support significant magnetic frustration, introduce a new characteristic temperature (T*), and suggest a surprisingly rich behavior for the magnetic correlations in the paramagnetic phase of this system. © 2006 The American Physical Society.7310Hill, N.A., (2000) J. Phys. Chem. B, 104, p. 6694. , JPCBFK 1089-5647 10.1021/jp000114xCurie, P., (1894) J. Phys. (Paris), Colloq., 3, p. 393. , JPQCAK 0449-1947Dzyaloshinskii, I.E., (1960) Sov. Phys. JETP, 10, p. 628. , SPHJAR 0038-5646Astrov, D.N., (1960) Sov. Phys. 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