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Experimental measurements and theoretical analysis of giant magnetoresistive (GMR) thermal magnetization fluctuation noise are presented. A new form of tensor damping, characteristic of the anisotropic thin-film geometry, is utilized. Rationalization and experimental confirmation for this expanded form are given as well. In general, this noise is-inversely proportional to the sensor volume and, at frequencies less than the sensor ferromagnetic resonance (FMR), is proportional to the dynamic damping. Approximate crosstrack anisotropy and stabilization fields are determined from signal transfer curves and utilized to determine damping for each head sensor. Damping parameters do not vary appreciably, although variation is seen even within a given manufacturing batch.