Abstract: This self-compensating spiral spring for a mechanical balance-spiral spring oscillator for a watch or clock movement or other precision instrument, made of an Nb—Hf paramagnetic alloy possessing a thermal coefficient of Young's modulus (TCE), such that it enables the following expression to be substantially equal to zero: 1 E ⁢ ⅆ E ⅆ T + 3 ⁢ α s - 2 ⁢ α b where: E: Young's modulus of the spiral spring of the oscillator; 1 E ⁢ ⅆ E ⅆ T = T ⁢   ⁢ C ⁢   ⁢ E