VOLUME 81, NUMBER 26 P H Y S I C A L R E V I E W L E T T E R S 28 DECEMBER 1998 Quantum Phase Transition in Fe Cr Multilayers Tuned by a Magnetic Field F. G. Aliev,* V. V. Moshchalkov, and Y. Bruynseraede Laboratorium voor Vaste-Stoffysica en Magnetisme, Celestijnenlaan 200D, K.U. Leuven, B-3001, Leuven, Belgium (Received 16 March 1998) We report on the spin dependent electron transport near the transition from a ferromagnetic into an antiferromagnetic (AFM) state. We find that in the Fe Cr 10 multilayers the resistivity rS associated with the AFM scattering at 4 , T , 100 K varies as rS T rS 0 2 ATa with 0.5 , a H # 2. As T ! 0 K, rS saturates except for a magnetic field region near H H0S, which tunes the AFM transition down to 0 K. For temperatures upwards from 20 mK with H H0S a crossover between two linear in T dependences of rS is observed, indicating a possible transition from the critical quantum to the thermal spin fluctuations around 2­3 K. [S0031-9007(98)08049-1] PACS numbers: 72.15.­v, 75.50.Ee, 75.70.Cn A quantum phase transition (QPT) [1] occurs at 0 K in on the study of the Fe Cr system, we believe we have a quantum mechanical system due to variation of nonther- observed a general property of AFM coupled MML or mal control parameters which fundamentally change the other antiferromagnets with a well-defined characteristic ground state. The parameter used to tune QPT can be the field corresponding to the AFM/FM transition. chemical composition, pressure, or magnetic field [2­9]. By using isothermal magnetoresistance (MR) measure- Recently QPT's have attracted much interest because of ments, we reconstructed the magnetic phase diagram for their fascinating theoretical and experimental issues [7,10]. different orientations of the field with respect to the MML Since QPT cannot be studied at 0 K, its identification relies plane. The temperature dependence of the resistivity mea- on finding the specific finite temperature scaling behavior sured at different magnetic fields enables us to determine as a function of temperature itself, frequency, or ampli- the spin dependent contribution rS due to AFM coupling tude of various probes [7]. Quantum critical behavior may nearby and far away from the QPT point. We observe that be different from the classical one since the ground state over a wide temperature range above 4 K the spin depen- may be determined by quantum rather than thermal fluc- dent contribution varies as rS T rS 0 2 ATa, where tuations [7,10]. The important difference between QPT a is a function of the magnetic field. On the other side, and the finite temperature transition is that quantum fluc- for the temperatures below 2 K the spin dependent scat- tuations at QPT are present at all frequencies down to tering saturates: DrS T rS 0 2 rS T T2 except zero [7]. when the QPT is tuned exactly. In this case, rS varies Study of the temperature scaling, especially in elec- linearly as a function of temperature between 20 mK and tron transport, is shown to be particularly important to 120 K DrS T bT with b changing around 2­3 K. identify QPT in nearly antiferromagnetic (AFM) metals This change of the slope b may be explained by a transi- [2,4,11,12]. In all of these systems, the QPT into the tion from the quantum to the thermal critical spin fluctu- magnetically ordered phase occurs from the paramagnetic ating regime. state and, to our best knowledge, quantum critical behav- The epitaxial Fe 12 Å Cr 12 Å 10 multilayers are ior with AFM fluctuations developed from the ferromag- prepared in a molecular-beam epitaxy system on MgO netic state has not yet been reported. Moreover, so far (100) substrates held at 50 ±C and covered by a 12 Å no clear evidence for the quantum-thermal crossover has thick Cr seed layer. The thickness of Cr film in the been observed, probably because of the difficulty to sepa- multilayer corresponds to the first AFM peak in the rate magnetic interactions at high temperatures. interlayer exchange coupling producing a maximum GMR In this Letter, we present an experimental study of in this system [14]. In situ reflection high-energy electron the electron transport in a magnetic system in which diffraction and ex situ x-ray diffraction measurements are the transition between two magnetically different ground used to control the structural quality of the multilayers. A states is tuned by an external magnetic field. The system detailed description of sample preparation and structural we used is the antiferromagnetically coupled magnetic characterization has been reported elsewhere [15]. For multilayer (MML) Fe Cr 10 which demonstrates giant the transport measurements the films were patterned magnetoresistance effects (GMR) due to transition from by optical lithography. The electrical resistivity was AFM to ferromagnetic (FM) alignment of the Fe layers measured by a standard four-probe ac method. induced by a magnetic field [13]. Our important finding Figure 1a shows typical isothermal magnetoresistance is that at sufficiently low temperatures the AFM/FM curves measured in magnetic fields parallel Hk and per- transition in MML is strongly affected by quantum pendicular H to the multilayer plane. The largest fluctuations. Although our conclusions are based only part of parallel MR is linear: r 0 2 r H H; the 5884 0031-9007 98 81(26) 5884(4)$15.00 © 1998 The American Physical Society VOLUME 81, NUMBER 26 P H Y S I C A L R E V I E W L E T T E R S 28 DECEMBER 1998 parallel or perpendicular to the measurement current give almost identical results, indicating the domination of the spin scattering effects over the anisotropic MR. By linear extrapolation we find that TAFM 0 K when HSk H0Sk 0.75 T and HS H0S 2.7 T. At H 0, the studied system is most probably a non- collinear antiferromagnet with a finite Néel vector N 1. When temperature is decreased along the dashed lines indicated in Fig. 1b, a T 0 K phase transition from a FM to an AFM state may be approached resulting in a continuous enhancement of the effect of the AFM fluctuations. In our view, the FM state should be treated as "clean" ferromagnetism which could, however, have some degree of nonthermal disorder caused by the unavoidable presence of fluctuations of the Cr spacer layer thickness. On the other hand, the AFM state, which is approached along the above-mentioned line, is a noncollinear AFM with vanishing Néel vector. Figure 2 shows total and spin dependent parts in elec- trical resistivity for T . 4 K at different magnetic fields. Because of similarity, we present only the data obtained for the perpendicular field orientation. For H H0S . 1.2, the r T data (Fig. 2a) are almost field indepen- dent because in that field range the electron spins par- FIG. 1. (a) Isothermal magnetoresistance of Fe Cr allel to the Fe magnetic moment in the layers do not 10 in magnetic fields parallel Hk and perpendicular H to the MML plane at T 10 and 300 K. Also shown is the normalized by saturation value MS in-plane magnetization M, measured at 10 K for the magnetic field decreased between 2 and 0 T. (b) Magnetic phase diagram of Fe Cr 10 multilayers in parallel (squares) and perpendicular (circles) magnetic fields. The arrows show critical fields H0S which correspond to TAFM 0 K. When the temperature decreases along the dashed lines, a QPT is approached. perpendicular MR can be fitted by a parabolic field depen- dence r 0 2 r H H2. Similar r H dependences have been reported for Fe Cr MML [16]. The charac- teristic saturation field HSk HS is defined as the mag- netic field which corresponds to the disappearance of the Néel vector N M1 2 M2 2M0 (M1 and M2 are the magnetization vectors of the coupled Fe layers and M0 jM1,2j), i.e., as the field where the deviation from the linear (quadratic) decrease of MR starts (see Fig. 1a). We note that in the studied Fe Cr multilayers the hystere- sis effects in MR and magnetization are very small and do not affect the experimental data. Absence of low field saturation [17] of the in-plane magnetization (see Fig. 1a), which is characteristic for biquadratic exchange coupling (BC), proves that the bilinear antiferromagnetic coupling dominates over intrinsic BC or BC induced by spatial fluc- tuations of the Cr thickness [18]. Figure 1b shows the T-H phase diagrams clearly FIG. 2. (a) Temperature dependence of resistivity r T for indicating the transition between the AFM and FM states different perpendicular magnetic field values (in units H H0 as deduced from the curves shown in Fig. 1a. For S ). (b) Temperature dependences of the spin dependent contribu- the in-plane configuration, measurements with the field tion in resistivity rS T r T, H 2 r T, 2H0S . 5885 VOLUME 81, NUMBER 26 P H Y S I C A L R E V I E W L E T T E R S 28 DECEMBER 1998 suffer magnetic scattering [13]. For magnetic fields H , sistivity measurements down to 20 mK. Figure 4 shows 1.2H0S , one observes a low temperature upward shift the temperature variation of rS T for Hk and close to in rS T which at H H0S transforms into an addi- the point where fine-tuning of the QPT is obtained by ap- tional well-defined contribution. This MR was studied plying a magnetic field. For all magnetic fields, except so far only in the form of the difference between r in those corresponding to H H0Sk, the spin dependent con- the AFM (at H 0) and FM H . H0S states [19]. Fig- tribution to the resistivity saturates at T ! 0 K. Again, ure 2b shows the spin dependent part in electrical resistiv- as in the high temperature regime T . 4 K , the rS ity rS r T, H 2 r T, 2H0S at different magnetic varies linearly with temperature when QPT is approached: fields. We have found that for 0 , H H0S the observed rS T 2 rS 0 bT. The slope b at very low tem- variation of spin dependent contribution with temperature peratures is approximately half of the value observed at DrS T rS T 2 rS 0 may be fitted to a power law: T . 4 K. This observation, together with completely dif- DrS Ta in a wide temperature range below 100 K. ferent scaling of rS T with magnetic field near H H0S For H . H0S, the temperature interval, where the power when T is above (Figs. 2 and 3) or below (Fig. 4) 2­3 K, law may be obtained, is reduced. An important aspect indicates a possible fundamental change in the electron of these data is an apparent linear variation of DrS T scattering mechanism. For the perpendicular magnetic when temperature is varied by more than a decade in the fields, we observe similar behavior (see inset of Fig. 4) vicinity of H H0S, i.e., when tuning of the phase transi- which is, however, complicated by the presence of relaxa- tion with TAFM 0 K takes place. tion effects in the electron transport below 100 mK. Figure 3 shows the dependence of a on the normalized The influence of the temperature on r in the AFM and field H H0S for parallel and perpendicular field orientations FM states in Fe Cr MML has been attributed to the varia- for the field interval where rS T varies as DrS Ta tion of the mean free path [20], local spin excitations [21], within a temperature interval of more than one decade. magnons [19], and random exchange potentials [22]. In We can observe three different regimes: (i) for H H0 epitaxial Fe Cr trilayers, the MR saturates at low tem- S we find a 1; (ii) for H , 0.5H0 peratures and is linear as a function of T above 70 K S the exponent a 2; and (iii) a 1.7 for H 0. We note that for H . [23]. These data, however, involve normalization of rS 1.3H0 by the total resistivity r which itself is temperature depen- Sk 1.15H0S one cannot determine a H because the data cannot be fitted by the power law. We believe that dent. In sputtered Fe Cr superlattices below T 100 K, deviation from a 2 for H , 0.1H0S is mainly due to the electron interaction with the AFM domain walls. A peculiar character of the ground state realized at H H0S with a 1 is confirmed by the electrical re- FIG. 3. The dependence of a on the normalized magnetic field H H0S determined for parallel (open diamonds) and perpendicular (closed squares) field configurations. The dashed line corresponds to a 2, expected for the Fermi liquids. The vertical dotted line marks QPT. The vertical bars indicate the FIG. 4. Variation of the spin dependent contribution to re- deviation in a which could be induced by variation in r sistivity, r S S T 2 rS 0 , at temperatures between 20 mK and determined as r 1.3 K. This contribution is measured in the parallel magnetic S r T , H 2 r T , 80 kG and in parameter rS 0 , or when employing another HS definition (i.e., as a cross fields (in units H H0Sk) which provide fine-tuning of the quan- section between low field and high field asymptotics shown in tum magnetic phase transition. The inset shows the low tem- Fig. 1). perature part in rS T for H H0S . 5886 VOLUME 81, NUMBER 26 P H Y S I C A L R E V I E W L E T T E R S 28 DECEMBER 1998 rS T 2 rS 0 T2 [19]. We also note that critical be- sendonck, J. Barnas, and P. Coleman for useful discus- havior in divergent resistivity near TN in Dy was found to sions, and G. Verbanck for help with the experiment. be described by a power law with a 0.7 [24]. Although a non-Fermi liquid (NFL) variation of the electrical resistivity has been observed in some correlated electron systems, a satisfactory theoretical explanation is *Corresponding author. lacking [25]. The nearly antiferromagnetic Fermi-liquid New address: Dpto. Fisica Materia Condensada, C-III, model [26], which does not involve any quantum critical Universidad Autonoma de Madrid, 28049, Madrid, Spain. point, predicts a transition from linear to quadratic tem- [1] J. Hertz, Phys. Rev. B 14, 1165 (1976). perature dependence in the resistivity. Near T 0 K, [2] G. Aeppli et al., Science 278, 1432 (1997). magnetic phase transition spin-fluctuation theories [27­ [3] S. R. Julian et al., J. Phys. Condens. Matter 8, 9675 (1996). 29] predict r [4] H. von Lohneysen, Physica (Amsterdam) 206B­207B, S T 2 rS 0 T n with 4 3 , n , 5 3 determined by the type (ferro/antiferro) of paramagnons 101 (1995). and degree of disorder. Three-dimensional spin fluctua- [5] F. Steglich et al., J. Phys. Condens. Matter 8, 9909 (1996). tions in a heavy electron system near their AFM instabil- [6] K. Umeo et al., J. Phys. F 48, 9643 (1996). [7] S. L. Sondhi, S. M. Girvin, J. P. Carini, and D. 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