Magnetic properties and domain-wall motion in single-crystal BaFe 10.2 Sn 0.74 Co 0.66 O 19 X. X. Zhang, J. M. Herna `ndez, and J. Tejada Departament de Fı ´sica Fonamental, Universitat de Barcelona, Diagonal 647, 08028 Barcelona, Spain R. Sole ´ and X. Ruiz Laboratori Fı ´sica Aplicada i Cristallografia. Universitat Rovira i Virgili. 43005 Tarragona, Spain Received 10 July 1995; revised manuscript received 26 October 1995 The magnetic properties of BaFe 12 O 19 and BaFe 10.2 Sn 0.74 Co 0.66 O 19 single crystals have been investigated in the temperature range 1.8 to 320 K with a varying field from -5 to +5 T applied parallel and perpendicular to the c axis. Low-temperature magnetic relaxation, which is ascribed to the domain-wall motion, was per- formed between 1.8 and 15 K. The relaxation of magnetization exhibits a linear dependence on logarithmic time. The magnetic viscosity extracted from the relaxation data, decreases linearly as temperature goes down, which may correspond to the thermal depinning of domain walls. Below 2.5 K, the viscosity begins to deviate from the linear dependence on temperature, tending to be temperature independent. The near temperature independence of viscosity suggests the existence of quantum tunneling of antiferromagnetic domain wall in this temperature range. INTRODUCTION The tunneling effect of magnetization was theoretically predicted by Chudnovsky and Gunther 1 in 1988. Since the pioneering theoretical studies, quantum tunneling of magne- tization QTM, has been a subject of great interests in condensed-matter physics. 2–11 Generally, tunneling in mag- nets involves two phenomena: 12 a tunneling of magnetiza- tion in single-domain particles or grains, in which some 1000 to 10 000 spins rotate together between two different orientations of magnetization, b tunneling of domain walls in a film or in bulk magnets; where walls containing 10 10 spins may tunnel from one pinning center to another. Most of the experimental studies on QTM are based on the first case, QTM in single-domain particles or grains, 2,3,5,7,8 mostly due to the difficulty in obtaining suit- able materials for observing the effect of quantum tunneling of domain walls QTDW. In our previous work, 13 QTDW was observed in an antiferromagnetic TbFeO 3 single crystal in magnetic relaxation measurements. The exponential mag- netic relaxation was found in the TbFeO 3 single crystal, which corresponds to the existence of a single barrier for the motion of DW. Our present intention is to study the domain- wall motion at low temperatures, using the relaxation mea- surements, in order to get deeper understanding of the mechanisms involved in domain-wall motion. Time-dependent effects of magnetization have long been known in magnetic materials: a collection of single-domain ferromagnetic particles, magnetic thin films, and bulk ferro- magnetic matters. 2–5,7,8,13 The dynamics of the effects has been assumed to be described by thermally activated pro- cesses. For a collection of identical noninteracting single- domain ferromagnetic particles frozen in a nonmagnetic ma- trix, by applying an external magnetic field, the magnetic moments of the particles can be aligned in one direction. After removing the external field, the magnetic moment de- cays exponentially with time 14,15 M  t  = M 0 e -t ,  = 0 exp  - U k B T  , 1 where M 0 is the remnant magnetic moment just after remov- ing the external field,  0 is the attempt frequency typically taken to be 10 9 –10 11 s -1 , k B is the Boltzmann constant, T is the absolute temperature, U =KV is the height of energy barrier associated with the switching process of magnetic moment of particles and V is the particle volume. The an- isotropy constant K is defined by the anisotropy field H K , and the saturation magnetization M S as H K =2 K / M S . The exponential time dependence of magnetization has been attributed to the single energy barrier height. But such a behavior has never been observed experimentally in particle systems, to our knowledge. Instead, a time dependence of, say, the magnetization follows a logarithmic decay over typi- cally 3–5 decades in time. 3–5,7,8 This nonexponential depen- dence has been linked to the distribution of energy barrier due to the distribution of size and shape of the particles. Thus, the relaxation of magnetization can be described by 4 M  t  = M 0  1 -S  T  ln t  , S  T  = k B T  U  , 2 instead of Eq. 1. Where S ( T ) is the magnetic viscosity,  U  is the average energy barrier over different shapes. The loga- rithmic time dependence of magnetization has also been ob- served experimentally in the magnetic thin films and bulk magnetic materials due to the magnetic metastable states in the materials which give a wide distribution of energy barrier heights. 2,4,5,7,8 Within the frame of a thermally activated process as tem- perature T decreasing to zero, both the exponential decay rate ( T ) and the magnetic viscosity S ( T ) goes to zero, that PHYSICAL REVIEW B 1 FEBRUARY 1996-II VOLUME 53, NUMBER 6 53 0163-1829/96/536/33365/$06.00 3336 © 1996 The American Physical Society