The Barnett effect refers to the magnetization induced by rotation of a demagnetized ferromagnet. We describe the location and stability of stationary states in rotating nanostructures using the Landau-Lifshitz-Gilbert equation. The conditions for an experimental observation of the Barnett effect in different materials and sample geometries are discussed. © 2009 American Institute of Physics. ͓doi:10.1063/1.3232221͔At the dawn of quantum mechanics, the Barnett 1,2 effect-magnetization induced by rotation-confirmed that magnetization is associated with angular momentum. Furthermore, Barnett measured the gyromagnetic ratio of electrons in ferromagnets and the anomalous g factor of the electron for the first time. The Barnett effect can be understood in terms of a rotating gyroscopic wheel, that aligns itself with the axis of rotation until a stationary state in the rotating frame of reference is achieved. Since angular momentum L is associated with magnetization M =−␥L, with ␥ = g B / ប = g͉e͉ / 2m being the gyromagnetic ratio, mechanical rotation induces a net magnetization antiparallel to the axis of rotation. The torque acting on the magnetization in the rotating frame of reference is equivalent to a torque due to the presence of a gauge magnetic fieldThere has recently been a renewed interest in the coupling of magnetization with mechanical motion, for example in mechanically detected ferromagnetic resonance spectroscopy measurements.3 A nanomagnetomechanical system consisting of a cantilever and a thin magnetic film shows coupled magnetovibrational modes. 4,5 Furthermore, the nanomechanical current-driven spin-flip torque at the normalmetal/ferromagnet interface of a suspended nanowire has been detected. 6 In Barnett's original experiments, rotation frequencies of Շ 500 Hz generated a change of the magnetic field of the order of 10 −4 G in macroscopic samples. Although in nanostructures detecting such small fields may become more challenging, a range of powerful techniques have recently been developed, which could be utilized for the purpose. To date, very small changes in the magnetization can be measured using the magneto-optical Kerr effect, Faraday spectroscopy, superconducting quantum interference devices or Hall micromagnetometry.7 Therefore, we present here a theoretical feasibility study of the Barnett effect in magnetic thin films and nanostructures. Our focus is the dynamics in magnetic thin films and nanoclusters, which we study by means of the Landau-Lifshitz-Gilbert ͑LLG͒ equation for the magnetization vector m,where H eff is the effective magnetic field, m is the unit vector of magnetization, and ␣ the dimensionless damping constant. We can separate the dynamics caused by the rotation of the system as a whole from the dynamics in the rotating frame of reference by the transformation m = R͑͒m R and H eff = R͑͒H eff R , where R͑͒ is a unitary matrix describing the rotation by a time-dependent angle ͑t͒ around the axis of rotation and m R ͑H eff R ͒ denote the magnetization ͑effective magnetic fiel...