Taking into account both the dc magnetic susceptibility and the magnetization measurements as well as the
high-temperature expansion of the magnetic susceptibility procedure the hopping integrals and superexchange
integrals for the first and second coordination sphere were evaluated. The two hopping integrals are positive
and many times greater than the superexchange ones. The obtained results testify to that in the stoichiometric
compounds under study the double-exchange magnetic interaction is the main mechanism responsible for very
strong, ferromagnetic coupling. Using the total hopping integral B the bandwidth of mixed valence band of
chromium ions was determined

Groń, Tadeusz

Heimann, Jan

Krok-Kowalski, Józef

Malicka, Ewa

Pacyna, A. W.

Pawełczyk, Marian

Władarz, Grzegorz

Acta Physica Polonica A

English

Repozytorium Uniwersytetu Śląskiego RE-BUŚ

             Title: Magnetic coupling in CuCr2X4 (X = S, Se) spinel compounds obtained via substitution of the chromium ions by nonmagnetic Sb or Al ions  Author: Józef Krok-Kowalski, Ewa Malicka, Grzegorz Władarz, Tadeusz Groń, Marian Pawełczyk, Jan Heimann, A.W. Pacyna  Citation style: Krok-Kowalski Józef, Malicka Ewa, Władarz Grzegorz, Groń Tadeusz, Pawełczyk Marian, Heimann Jan, Pacyna A.W. (2011). Magnetic coupling in CuCr2X4 (X = S, Se) spinel compounds obtained via substitution of the chromium ions by nonmagnetic Sb or Al ions. "Acta Physica Polonica A" (Vol. 119, nr 5 (2011), s. 705-707).  Vol. 119 (2011) ACTA PHYSICA POLONICA A No. 5XXXIX “Jaszowiec” International School and Conference on the Physics of Semiconductors, Krynica-Zdrój 2010Magnetic Coupling in CuCr2X4 (X = S, Se) SpinelCompounds Obtained via Substitution of the ChromiumIons by Nonmagnetic Sb or Al IonsJ. Krok-Kowalskia, E. Malickab, G. Władarza, T. Grońa, M. Pawełczyka,J. Heimanna and A.W. PacynacaInstitute of Physics, University of Silesia, Uniwersytecka 4, 40-007 Katowice, PolandbInstitute of Chemistry, University of Silesia, Szkolna 9, 40-006 Katowice, PolandcThe Henryk Niewodniczański Institute of Nuclear Physics, Polish Academy of SciencesE. Radzikowskiego 152, 31-342 Kraków, PolandTaking into account both the dc magnetic susceptibility and the magnetization measurements as well as thehigh-temperature expansion of the magnetic susceptibility procedure the hopping integrals and superexchangeintegrals for the first and second coordination sphere were evaluated. The two hopping integrals are positiveand many times greater than the superexchange ones. The obtained results testify to that in the stoichiometriccompounds under study the double-exchange magnetic interaction is the main mechanism responsible for verystrong, ferromagnetic coupling. Using the total hopping integral B the bandwidth of mixed valence band ofchromium ions was determined.PACS: 75.50.Pp, 75.30.Kz, 75.30.Et1. IntroductionAs it was related in [1], on the base of the spinelmatrices CuCr2S4 and CuCr2Se4, four spinel familieswere obtained via substitution in the B-sites of the mag-netic chromium ions by the nonmagnetic Sb or Al ions.Three of these families turned out to be stoichiometric:CuCr2−xSbxS4 (x = 0.3, 0.4, 0.5) [1], CuCr2−xSbxSe4(x = 0.1, 0.2, 0.5, 0.8, 1.0) [2], CuCr2−xAlxSe4 (x =0.1, 0.2, 0.3, 0.4, 0.5) whereas the fourth one, namely:Cu1+xCr1.5+ySb0.5+zSe4+t (where −0.02 ≤ x ≤ 0.01,0.03 ≤ y ≤ 0.35, −0.2 ≤ z ≤ −0.02, 0.01 ≤ t ≤ 0.08) [3]occurred to be nonstoichiometric. From the extendedmagnetic measurements of both the magnetization andthe magnetic susceptibility it follows that:i) the spin glass states appear in all the compounds inwhich magnetic chromium sublattice is diluted by non-magnetic antimony ions [2–4],ii) both the stoichiometric compounds with sulfur anionand the nonstoichiometric ones with the selenium anionmagnetize very hard. In spite of the external magneticfield applied up to 14 T the samples belonging to thesetwo spinel families are still far from magnetic saturation,iii) the lack of the magnetic saturation as well as thechange of the slope of the rectilinear segments in the mag-netization isotherms testify to that in all these samplesmagnetic spin-flop phase transitions take place,iv) in the stoichiometric antimony compounds with theselenium anions, only the sample containing the anti-mony concentration x equal to 0.1 reaches the magneticsaturation,v) with the increase of the Sb concentration x in thesecompounds the magnetization decreases very fast and themagnetization processes become more and more hard.Moreover, the magnetization isotherms exhibit the hys-teresis phenomena and very large paraprocesses [3],vi) all the samples containing Al magnetize very easilyand reach the magnetization saturation at very low mag-netic field.The aim of this paper is to discuss the mechanismswhich are responsible for magnetic coupling in the com-pounds under study as well as to determine the contri-butions to the whole exchange energy coming from thesemechanisms.2. ExperimentalFor the compounds under study both the dc and acmagnetic susceptibility were measured. The dc measure-ments were carried out with the aid of the Cahn mag-netic balance whereas the ac measurements were car-ried out with the use of the Lake Shore magnetometer.The examples of the dc magnetic susceptibility obtainedfor stoichiometric compounds are presented in Figs. 1and 2, whereas the most important magnetic parametersfor these compounds are presented in Table I.(705)706 J. Krok-Kowalski et al.Fig. 1. The magnetic susceptibility and its reciprocalas a function of temperature for CuCr1.9Al0.1Se4 (tri-angle) and CuCr1.5Al0.5Se4 (square).Fig. 2. The magnetic susceptibility and its reciprocalas a function of temperature for CuCr1.9Sb0.1Se4 [3].TABLE IThe most important magnetic parameters of the spinelsunder study.Compound µs[µB]µef[µB]Tc[K]Θc-w[K]CuCr2Se4 [5] 4.76 5.21 416 436CuCr1.9Al0.1Se4 5.98 4.09 428 454CuCr1.8Al0.2Se4 5.35 4.50 435 446CuCr1.7Al0.3Se4 5.28 4.00 411 439CuCr1.6Al0.4Se4 5.19 3.93 402 427CuCr1.5Al0.5Se4 4.61 3.75 399 423CuCr1.9Sb0.1Se4 5.71 5.47 357 3753. Results and discussionIn the compounds under study exchange couplings be-tween magnetic moments localized on the chromium ionscan be realized via three following types of magnetic in-teractions: (i) the superexchange with the interactionspaths: Cr3+–X2−–Cr3+, Cr3+–X2−–X2−–Cr3+, Cr3+–X2−–A2+–X2−–Cr3+, (ii) the Zener double-exchangebetween Cr3+–Cr4+ ion pairs, (iii) Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction caused by the ap-pearance in the matrices of the itinerant electrons comingfrom the existence in them of a few percent of the Cu2+ions [3]. Because the crystal field of the ligands splitsevery 3d level of the cations into the triplet t2g and thedoublet eg the different overlaps (so called: σ, pi and ∆)are possible of the wave functions 3d with the p orbitals ofanions. The octahedral coordination of Cr3+ ions causesthat their eg orbitals participating in the coupling viaσ-band are empty whereas their t2g orbitals participat-ing in the coupling via pi-band are half-filled. Accord-ing to the Goodenough–Kanamori rules the couplingsof the type σ–∆–σ and pi–∆–pi are antiferromagnetic,whereas σ–∆–pi coupling is ferromagnetic. As concernsthe double-exchange mechanism of interactions, it givesboth ferromagnetic and very strong coupling of magneticmoments.From the magnetic susceptibility measurements it fol-lows that for the compounds under study with micto-magnetic ordering the superexchange interaction appear-ing simultaneously with the double-exchange interactionsdominates. On the other hand, in the compounds con-taining Al, double-exchange interaction absolutely dom-inates, giving very high values of both Curie (TC) andCurie–Weiss (θCW) temperatures. This qualitative anal-ysis, which was made on the base of the results con-tained in [1] as well as in this paper indicates that inthe compound under study apart from the exchange in-teraction the double-exchange interaction appears. Sodouble-exchange interaction becomes responsible for thevery strong magnetic coupling of the magnetic momentsin these compounds. The quantitative contribution of thedouble-exchange in the total exchange integral was cal-culated on the ground of the high temperature expansionof the magnetic susceptibility [5].The results of the utilization of this method are theequations describing the contributions to the paramag-netic Curie–Weiss temperature coming from the separatemechanisms of the exchange interactions. Because in thespinels under study the essential role is played by boththe superexchange and the double-exchange interactions,the equation for the paramagnetic Curie–Weiss temper-ature has the following form:Θc-w = Θsex +Θdex , (1)whereΘc-w is the paramagnetic Curie–Weiss temperature(from experiment), Θsex is the contribution to the Θc-wcoming from superexchange, Θdex is the contribution tothe Θc-w coming from double-exchange. Moreover,Magnetic Coupling in CuCr2X4 (X = S, Se) Spinel Compounds . . . 707Θsex = (2/3)XΘ , (2)where Θ ≈ 150 K denotes here an average value of theparamagnetic Curie–Weiss temperature coming from thesuperexchange interaction in the spinel compounds andX = x3(3/2)(3/2 + 1) + x41(1 + 1) , (3)where x3 is the concentration of Cr3+ ions with the spinS = 3/2, x4 is the concentration of Cr4+ ions with thespin S = 1. Concentrations x3 and x4 were calculatedfrom the saturation magnetization M :M = 2(g4x4 + g3x33/2) , (4)taking into account that in the matrixes CuCr2S4 andCuCr2Se4 one half of the chromium ions is Cr3+ and an-other one is Cr4+, the values of the Landé factors areg4 = 1.86 and g3 = 2, respectively. The following nor-malization condition is valid:x3 + x4 = 1 ,Θdex = (1/6)Xx3(1− x3)B , (5)where B stands for the total hopping integral for thefirst and second coordination spheres. Substituting (2),(3) and (5) into (1) one obtains an equation with B beingunknownΘc-w = (2/3)XΘ + (1/6)Xx3(1− x3)B . (6)The total hopping integral B calculated from Eq. (6) canbe written down as follows:B = 6baa + 36bab , (7)where baa stands for the contribution from the 6 near-est neighbors (with the distance to a given ion equal to0.354a) and bab stands for the contribution from the 36second nearest neighbors (with the distance to a givenion equal to 0.704a); a is the lattice parameter. Onthe ground of the Lotgering considerations [6] one canfind that the ratio baa/bab is equal to 5. This made itpossible to calculate the values of hopping integrals perpair of ions Cr3+–Cr4+ for the first and second coordi-nation spheres. Using Eq. (2) and the results of Ref. [7]the superexchange integrals Jaa and Jab between the twoions from the first and second coordination spheres havebeen calculated. The obtained results are presented inTable II.As it follows from Table II the exchange integrals con-nected with the double-exchange are positive for the twocoordination spheres. One can easily see that all theseintegrals are many times greater than Jaa. Thus, thisquantitative analysis has proved that in stoichiometriccompounds under study the double-exchange interactionis the main mechanism responsible for the strong, fer-romagnetic coupling. Moreover, taking into account thetotal hopping integral B listed in Table II we can get thebandwidth of the 3d t2g band connected with the mixedvalence of Cr3+–Cr4+. For the compounds containing Althe bandwidth of the 3d t2g band due to Cr ions is thenWd = 2B = 5400± 500 K ∼= 0.49± 0.05 eV. On the otherhand, for the compound containing Sb such bandwidthis Wd = 2B = 3520 ± 100 = 0.32 ± 0.01 eV. For com-parison the chromium mixed valence bandwidth Wd inthe CuCr2Se4 matrix is equal to 0.63± 0.05 eV [5]. It isworthy to underline that this fundamental parameter ofelectronic structure has been found from an interpreta-tion scheme of our magnetic measurements.TABLE IIThe exchange integrals following from both the doubleexchange and superexchange magnetic interactions for thecompounds under study.Compound B[K]baa[K]bab[K]Jaa[K]Jab[K]CuCr2Se4 [5] 4391 969.3 27.3 16.9 −8.50CuCr1.9Al0.1Se4 3218 243.8 48.8 17.2 −1.43CuCr1.8Al0.2Se4 2601 197.0 39.4 16.1 −1.45CuCr1.7Al0.3Se4 2631 199.3 39.9 17.1 −0.44CuCr1.6Al0.4Se4 2667 202.0 40.0 16.5 −0.32CuCr1.5Al0.5Se4 2401 181.9 36.4 15.5 −0.21CuCr1.9Sb0.1Se4 1764 133.7 26.7 18.8 −0.60AcknowledgmentsThis work is partly founded from science grant No. NN204 145938.References[1] E. Malicka, J. Krok-Kowalski, J. Warczewski,T. Groń, H. Duda, T. Mydlarz, M. Pawełczyk,A.W. Pacyna, P. Rduch, G. Władarz, Acta Phys.Pol. A 116, 967 (2009).[2] J. Warczewski, J. Krok-Kowalski, L.I. Koroleva,T. Mydlarz, A. Gilewski, A.W. Pacyna, J. AlloysComp. 319, 7 (2001).[3] J. Krok-Kowalski, J. Warczewski, P. Gusin, T. Śli-wińska, G. Urban, E. Malicka, A.W. Pacyna, T. Myd-larz, P. Rduch, G. Władarz, J. Alloys Comp. 478, 14(2009).[4] J. Krok-Kowalski, J. Warczewski, K. Krajewski,H. Duda, P. Gusin, T. Śliwińska, A.W. Pacyna,T. Mydlarz, S. Matyjasik, E. Malicka, A. Kita, J. Al-loys Comp. 430, 39 (2007).[5] J. Krok, J. Spałek, S. Juszczyk, J. Warczewski, Phys.Rev. B 28, 6499 (1983).[6] F.K. Lotgering, Solid State Commun. 3, 347 (1965).[7] P.K. Baltzer, P.J. Wojtowicz, M. Robbins,E. Lopatin, Phys. Rev. 151, 367 (1966).

Magnetic coupling in CuCr2X4 (X = S, Se) spinel compounds obtained via substitution of the chromium ions by nonmagnetic Sb or Al ions

https://rebus.us.edu.pl/bitstream/20.500.12128/8200/1/Krok_Kowalski_Magnetic_coupling_in_CuCrX4.pdf

Magnetic coupling in CuCr2X4 (X = S, Se) spinel compounds obtained via substitution of the chromium ions by nonmagnetic Sb or Al ions

Abstract

Similar works

Full text

Available Versions

Repozytorium Uniwersytetu Śląskiego RE-BUŚ