1. Nanosized magnetic clusters and their relation to magnetoresistance in FeCr 2 S 4 spinel Z. Klencsár 1, E. Kuzmann 1, Z. Homonnay 2, A. Vértes 1, A. Simopoulos 3, E. Devlin 3, G. Kallias 3 1 Laboratory of Nuclear Chemistry, Hungarian Academy of Sciences Chemical Research Center, Pázmány P. s. 1/A, Budapest, Hungary 2 Laboratory of Nuclear Chemistry, Institute of Chemistry Eötvös Loránd University, Pázmány P. s. 1/A, Budapest, Hungary 3 Institute of Materials Science, NCSR Demokritos Aghia Paraskevi 153 10, Athens, Greece E-mail: z.klencsar@somogy.hu

2. The discovery of colossal magnetoresistance (CMR) in manganese-based perovskites has stimulated intense research on the physical bases of the CMR effect [1,2,3]. The puzzling existence of a considerable intrinsic magnetoresistance reported [4] in FeCr 2 S 4 chalcogenide spinels - that do not possess manganese, oxygen, perovskite structure, or even a metal-to- insulator transition – indicates that phenomena other than the double exchange effect [2] should also be considered in the explanation of magnetoresistance observed in these materials. FeCr 2 S 4 has long been known as a ferrimagnet with semiconducting-like resistivity characteristics [5-15]. It has a crystal structure of a cubic normal spinel where Fe 2+ and Cr 3+ cations occupy tetrahedrally and octahedrally coordinated positions, respectively [16]. The paramagnetic to ferrimagnetic transition occurs in the range T C = 170..180 K [4,5]. Research motivation [4] A.P. Ramirez, R.J. Cava, J. Krajewski: Nature 386 (1997) 156. [5] G. Shirane, D.E. Cox, S.J. Pickart: J. Appl. Phys. 35 (1964) 954. [6] G. Haacke, L.C. Beegle: Phys. Rev. Lett. 17 (1966) 427. [7] M. Eibschutz, S. Shtrikman, Y. Tenenbaum: Physics Letters 24A (1967) 563. [8] G. Haacke, L.C. Beegle: J. Phys. Chem. Solids 28 (1967) 1699. [9] C.M. Yagnik, H.B. Mathur: Solid State. Comm. 5 (1967) 841. [10] G.R. Hoy, K.P. Singh: Phys. Rev. 172 (1968) 514. [11] F.K. Lotgering, R.P. Van Stapele, G. Van der Steen, J.S. Van Wieringen: J. Phys. Chem. Solids 30 (1969) 799. [12] P. Gibart, J.-L. Dormann, Y. Pellerin: Phys. Stat. Sol. 36 (1969) 187. [13] P. Gibart, L. Goldstein, L. Brossard: J. Magn. Magnet. Mat. 3 (1976) 109. [14] A.M. Van Diepen, F.K. Lotgering, J.F. Olijhoek: J. Magn. Magnet. Mat. 3 (1976) 117. [15] L. Brossard, J.L. Dormann, L. Goldstein, P. Gibart, P. Renaudin: Phys. Rev. B 20 (1979) 2933. [16] Anthony R. West, Basic Solid State Chemistry, 2 nd edn., John Wiley & Sons, New York, 1999, p. 60. [1] R. Helmolt, J. Wecker, B. Holzapfel, L. Schultz, K. Samwer: Phys. Rev. Lett. 71 (1993) 2331. [2] C. Zener: Phys. Rev. 82 (1951) 403. [3] A.J. Millis: Nature 392 (1998) 147. [4] A.P. Ramirez, R.J. Cava, J. Krajewski: Nature 386 (1997) 156. D.G. Wickham, J.B. Goodenough: Phys. Rev. 115 (1959) 1156. A.P. Ramirez, R.J. Cava, J. Krajewski: Nature 386 (1997) 156. The structure of FeCr 2 S 4 Magnetization of FeCr 2 S 4 measured in 0.1 T magnetic field T C range The red and blue arrows indicate the preferred orientation of magnetic moments in the magnetically ordered state.

3. Research motivation The recent observation of negative magneto- resistance in FeCr 2 S 4 [4] initiated a reinvestigation of this compound by means of various methods [17 24]. By the help of 57 Fe Mössbauer spectroscopy we investigated the local magnetic and electronic state of Fe 2+ in FeCr 2 S 4 as a function of temperature in the range 75 K..290 K. Here we focus our attention on the relation between the magnetic state of iron in FeCr 2 S 4 and the magnetoresistivity as well as the resistivity anomaly observed in this compound at temperatures in the vicinity of the Curie temperature [4]. B = 0 T Magnetoresistivity is defined as where (B) is the resistivity measured in magnetic field B. B = 3 T B = 5 T Z. Yang, S. Tan, Z. Chen, Y. Zhang: Phys. Rev. B 62 (2000) 13872. B = 3 T B = 5 T

4. What is happening around the Curie temperature? A comparison of the temperature dependence of magnetization, resistivity and magnetoresistivity of FeCr 2 S 4 reveals that it is plausible to suppose that the resistivity anomaly as well as the magnetoresistivity are connected to the break down of long-range magnetic order at around the Curie temperature. (Here we prefer to consider the evolution of the physical state as a function of increasing temperature.) In order to find out what is special about the break down of magnetic order in FeCr 2 S 4, we recorded 57 Fe Mössbauer spectra of this compound as a function of increasing temperature. T The FeCr 2 S 4 sample that we investigated is the same material as that for which macroscopic magnetization, thermopower, resistivity and CMR measurements have been reported by Ramirez et al. in ref. [4] which article may be consulted for details of the sample preparation. 57 Fe Mössbauer spectroscopy measurements were carried out on powdered samples in transmission geometry. During measurements the temperature of the sample was kept constant with a precision of T 0.5 K. The material was first cooled down to 75 K, then measurements were performed by raising the temperature by 5 K between subsequent measurements. [4] A.P. Ramirez, R.J. Cava, J. Krajewski: Nature 386 (1997) 156. 57 Fe Mössbauer spectra of FeCr 2 S 4 155 K T C range

5. What is happening below the Curie temperature? Although the Curie temperature, determined by magnetization measurements, was reported to be T C 170 K for this particular FeCr 2 S 4 sample [4], 57 Fe Mössbauer spectra indicate that long-range magnetic order starts to break down already at T R 155 K, and the Mössbauer spectrum taken at T = 160 K consists mainly of a singlet. The existence of a magnetically unsplit singlet component in the Mössbauer spectrum of FeCr 2 S 4 below the Curie temperature is due to the magnetic relaxation effect [26], and indicates that in FeCr 2 S 4 magnetic order breaks down by the gradual fragmentation of magnetic domains into nanosized, only weakly interacting magnetic clusters of atoms. T 57 Fe Mössbauer spectra of FeCr 2 S 4

6. Why does long-range magnetic order break down already below the Curie temperature? A hint to the answer to the above question may be found in the result of Yang et al., who found that the coercivity of FeCr 2 S 4 decreases with increasing temperature, and goes to zero at around T R. This indicates that magneto- crystalline anisotropy originating mainly from the tetrahedrally coordinated Fe 2+ ions goes to zero with increasing temperature just about when the break down of long-range magnetic order and the associated relaxation phenomenon starts. The spin-orbit coupling characteristic of the Fe 2+ ions 3d electrons being at the root of the magnetocrystalline anisotropy in this compound becomes revealed also by Mössbauer spectroscopy: in the magnetically ordered state it results in a nonvanishing electric field gradient at the iron nuclei, which in turn presents itself as a nonzero quadrupole splitting in the corresponding Mössbauer spectra. The quadrupole splitting, however, also vanishes at T T R and not at T T C. Z.R. Yang, S. Tan, Y.H. Zhang: Appl. Phys. Lett. 79 (2001) 3645. T C range TRTR TRTR

7. Conclusions On the basis of evidence presented so far, we can already gain a qualitative understanding of the resistivity anomaly and negative magnetoresistance displayed by FeCr 2 S 4 : With increasing temperature (1) at T R 155 K spin-orbit coupling at Fe 2+ ions becomes ineffective in maintaining strong magnetocrystalline anisotropy: the material enters a soft ferrimagnetic state with near zero coercivity; (2) this new magnetic state evolves under the influence of frustrated (e.g. AFM Cr-Cr and AFM Fe-Cr) magnetic exchange interactions, further magnetic anisotropies (e.g. shape anisotropy) and thermal agitation; (3) in the range T R … T C the minimum-energy state of FeCr 2 S 4 is achieved by a gradual break- down into nanometer-sized magnetic domains; (4) the relaxation frequency of the magnetic domains increases, and enters the frequency window of 57 Fe Mössbauer spectroscopy: in the Mössbauer spectra this results in a collapse of the sextet component and the appearance of superparamagnetic-like relaxation; (5) in the range T R … T C electrical resistivity increases due to increasing magnetic disorder and spin-disorder scattering; (6) an external magnetic field can achieve the coalescence of magnetic domains, thereby lowering spin-disorder scattering and electrical resistivity: a negative magnetoresistance is realized. On the basis of evidence presented so far, we can already gain a qualitative understanding of the resistivity anomaly and negative magnetoresistance displayed by FeCr 2 S 4 : With increasing temperature (1) at T R 155 K spin-orbit coupling at Fe 2+ ions becomes ineffective in maintaining strong magnetocrystalline anisotropy: the material enters a soft ferrimagnetic state with near zero coercivity; (2) this new magnetic state evolves under the influence of frustrated (e.g. AFM Cr-Cr and AFM Fe-Cr) magnetic exchange interactions, further magnetic anisotropies (e.g. shape anisotropy) and thermal agitation; (3) in the range T R … T C the minimum-energy state of FeCr 2 S 4 is achieved by a gradual break-down into nanometer-sized magnetic domains; (4) the relaxation frequency of the magnetic domains increases, and enters the frequency window of 57 Fe Mössbauer spectroscopy: in the Mössbauer spectra this results in a collapse of the sextet component and the appearance of superparamagnetic-like relaxation; (5) in the range T R … T C electrical resistivity increases due to increasing magnetic disorder and spin-disorder scattering; (6) an external magnetic field can achieve the coalescence of magnetic domains, thereby lowering spin-disorder scattering and electrical resistivity: a negative magnetoresistance is realized.

8. What is happening above the Curie temperature? 9.89(1) T In order to find out what becomes of the nanometer-sized magnetic clusters above the Curie temperature, we performed 57 Fe Mössbauer measurements at T = 186.5 K with and without an external magnetic field oriented perpendicular to the direction of the -radiation. 4.0(1) T Surprisingly, the 57 Fe Mössbauer spectrum measured at T = 186.5 K without external magnetic field displays apart from the majority singlet component a minor magnetic component characterized by 4.0(1)T hyperfine magnetic field. Even more striking is that the applied 6 T external magnetic field is able to recover long-range magnetic order, and to fully orient the samples magnetization, as reflected by the 3:4:1:1:4:3 relative intensities of the sextets peaks. Furthermore, the hyperfine magnetic fields reflected by the sextet components obtained with and without the external magnetic field differ by the magnitude of the externally applied field inside the experimental error. This indicates, that iron magnetic moments become aligned opposite to the externally applied field, thereby proving that at T = 186.5 K the Fe-Cr AFM interaction is still strong enough to bind Fe and Cr magnetic moments together. Obviously, the studied FeCr 2 S 4 sample is not in a paramagnetic state at T = 186.5 K, but it still contains magnetically ordered clusters of atoms.

9. References Z. Klencsár, E. Kuzmann, Z. Homonnay, A. Vértes, A. Simopoulos, E. Devlin, G. Kallias: Magnetic relaxation and its relation to magnetoresistance in FeCr 2 S 4 spinel Hyperfine Interactions 144/145 (2002) 261. Z. Klencsár, E. Kuzmann, Z. Homonnay, A. Vértes, A. Simopoulos, E. Devlin, G. Kallias: Interplay between magnetic order and the vibrational state of Fe in FeCr 2 S 4 Journal of Physics and Chemistry of Solids 64 (2003) 325. [17] Z. Chen, S. Tan, Z. Yang, Y. Zhang: Phys. Rev. B 59 (1999) 11172. [18] Z. Yang, S. Tan, Y. Zhang: Solid State. Comm. 115 (2000) 679. [19] Z. Yang, S. Tan, Z. Chen, Y. Zhang: Phys. Rev. B 62 (2000) 13872. [20] V. Tsurkan, M. Lohmann, H.-A. Krug von Nidda, A. Loidl, S. Horn, R. Tidecks: Phys. Rev. B 63 (2001) 125209-1. [21] M.S. Park, S.K. Kwon, S.J. Youn, B.I. Min: Phys. Rev. B 59 (1999) 10018. [22] Z.R. Yang, S. Tan, Y.H. Zhang: Appl. Phys. Lett. 79 (2001) 3645. [23] V. Tsurkan, J. Hemberger, M. Klemm, S. Klimm, A. Loidl, S. Horn, R. Tidecks: J. Appl. Phys. 90 (2001) 4639. [24] S. Wang, K. Li, Z. Chen, Y. Zhang: Phys. Rev. B 61 (2000) 575.