Journal of Magnetism and Magnetic Materials 226 } 230 (2001) 337}338 Vortex-line-lattice torque in anisotropic superconductors I.G. de Oliveira*, W.A.M. Morgado, M.M. Doria, G. Carneiro Fac. de cie. Exatas e technologicas, Universidade Iguac 7 u-UNIG, Av. Abn & lio Augusto Ta & vora 2134, 26260-100, Nova Iguacu 7 , Rio de Janeiro, Brazil Universidade do Grande Rio, Rua Prof. Jose & de Souza Herdy 1160, Duque de Caxias, Rio de Janeiro, Brazil Instituto de Fn & sica, Universidade Federal do Rio de Janeiro, C.P. 21945-970, Rio de Janeiro, Brazil Abstract We calculate the magnetic torque "MH that an uniaxial superconductor feels in presence of an external magnetic "eld of magnitude H, oriented of an angle  with respect to its c-axis. Our simulated annealing numerical method minimize the Gibbs free energy in the London aproximation, and we assume straight vortex lines and a vortex-line lattice with only one vortex per unit cell. Here we report results near the lowest critical "eld region H  .  2001 Elsevier Science B.V. All rights reserved. Keywords: Superconductivity; Superconductors Below the critical temperature (¹  ) the superconduc- tor develops a magnetization not necessarily along the same direction of the external magnetic "eld. This mis- alignment yields a magnetic torque, whose measurement can bring important information about the magnetic properties of the superconductor. There are many factors that contribute to the superconducting torque, the two main reasons are the #ux pinning and the shape e!ect. However the intrinsic anisotropy also contributes to a magnetization not oriented along the external magnetic "eld, and this contribution is known as the intrinsic magnetic torque [1,2]. For temperatures close to ¹  and "elds HH  the pinning disappears and the torque  becomes highly reversible. In this region, it has been extensively measured [3] in samples of Y  Ba  Cu  O  and Bi  Sr  Cu  O  as a function of the angle  between the external "eld H and the axis of symmetry c of these samples. Shape e!ects were shown not to be the main source for the magnetic torque, according to Ref. [2], and so these torque measurements were probing the intrinsic torque, whose only source is the intrinsic anisotropy of * Correspondence address. Fac. de cie. Exatas e technologicas, Universidade Iguac 7 u-UNIG, Av. Abm H lio Augusto Ta H vora 2134, 26260-100, Nova Iguacu 7 , Rio de Janeiro, Brazil. E-mail address: isaias@unig.br (I.G. de Oliveira). the copper oxide materials. Anisotropy is known to produce vortex}vortex attraction that leads to a new vortex-line lattice (VLL) state, the so-called chain state that was observed experimentally few years ago [4]. Some of us (IGO and MMD) have proposed a procedure to observe vortex chain e!ects in low magnetic "eld torque measurements [5]. Recently angular- dependent torque magnetometry measurements on single- crystal HgBa  CuO  close to the critical temperature was analyzed within the framework of the three-dimen- sional X> critical behavior [6]. The magnetic torque is derived from a universal scaling function, where the scal- ing parameter z depends on temperature, "eld, and the angle between the external magnetic "eld and the c-axis of the sample. They were able to determine a universal scaling function by scaling the angular-dependent torque data. This shows that torque magnetometry remains a powerful and actual experimental tool to understand fundamental properties of the superconducting state. To obtain the VLL con"guration that results in an applied external magnetic "eld H at temperature ¹, we obtain the minimum of the Gibbs free-energy density with respect to all parameters other than the above ones: g(H, ¹,   )/   H  "0. Here we are only interested in the zero temperature torque produced by straight vortex lines parallel to each other, oriented of an angle  with respect to the c-axis. There is only one vortex per unit 0304-8853/01/$ - see front matter  2001 Elsevier Science B.V. All rights reserved. PII:S0304-8853(00)00814-3