an example of the advantages of the present invention will be described using an embodiment . a glass substrate marketed for magnetic disks is suitable as a non - magnetic magnetic disk substrate . in order to reflect the surface roughness of a substrate surface , a magnetic disk medium which surface roughness ( ra ) was approximately 0 . 8 nm , was prepared . [ 0029 ] fig1 is a simplified drawing of the layer structure of a magnetic disk according to embodiment 1 . after washing a glass substrate 1 , a disk sputtering device ( intevac corp .&# 39 ; s mdp - 250 ) is used to form a seed layer 2 , a base layer 3 , a lower magnetic layer 4 , a non - magnetic intermediate layer 5 , an upper magnetic layer 6 , and a protective layer 7 , as shown in the figure . the seed layer 2 is sputtered using a nita alloy target to form a layer that is approximately 30 nm thick . the thickness of the seed layer was measured using x - ray spectrometry . after it is formed , the seed layer is heated at approximately 260 degrees centigrade and exposed for approximately 3 . 5 seconds to an ar — o 2 gas . the crti alloy base layer 3 is formed over the seed layer 2 with a thickness of approximately 5 nm . the base magnetic layer is formed as a cocrpt alloy magnetic layer with a thickness of approximately 3 . 5 nm . the intermediate layer is formed ru layer with a thickness of approximately 0 . 5 nm . the upper magnetic layer 6 is formed as a cocrptb alloy layer with a thickness of approximately 15 nm . the protective layer 7 is formed with a thickness of approximately 3 . 5 nm over the upper magnetic layer 6 . an example of this protective layer 7 is a dlc ( diamond - like carbon ) layer formed using cvd ( chemical vapor deposition ) or ibd ( ion beam deposition ). the thickness of the protective layer 7 is measured using x - ray reflection . to improve accuracy in the thickness measurement , quantizing is done by forming a 5 nm cr layer over the protective layer 7 . the x - ray reflection quantization of layer thickness was performed using rigaku denki kogyo corp .&# 39 ; s slx2000tm with an [ cuk alpha1 ] x - ray . using sumitomo - 3m corp .&# 39 ; s hft7100 as a solvent , a lubricating agent solution as shown in chemical formula ( 1 ) was created . the magnetic disk was dipped into this lubricating agent solution to form the lubricating layer 8 . the perfluoro polyether backbone chain in the lubricating agent based on chemical formula ( 1 ) has a number - average molecular weight of approximately 2 , 000 . an ftir measurement of the lubricating layer showed a thickness of approximately 1 . 5 nm . a magnetic disk was created in a manner similar to that used in embodiment 1 . however , a lubricating agent as shown in chemical formula ( 2 ) was used . the perfluoro polyether backbone chain in the lubricating agent based on chemical formula ( 2 ) has a number - average molecular weight of approximately 2 , 000 . an ftir measurement of the lubricating layer showed a thickness of approximately 1 . 5 nm . a magnetic disk was created in a manner similar to that used in embodiment 1 . however , a lubricating agent as shown in chemical formula ( 3 ) was used . five types of lubricating agents were used , with number - average molecular weights of 1 , 000 , 2 , 000 , 3 , 000 , 4 , 000 , and 6 , 000 , as measured using nmr ( nuclear magnetic resonance ). ftir measurements of the lubricating layer thicknesses showed that each had a thickness of approximately 1 . 5 nm . h och 2 cf 2 ( oc 2 f 4 ) p ( ocf 2 ) q ocf 2 ch 2 oh ( where p = 0 or an integer of 1 or more and q = 0 or an integer of 1 or more .) the magnetic disks from embodiment 1 , embodiment 2 , and comparative example 1 were installed in a 3 . 5 inch hard disk drive ( magnetic disk device ). a simplified drawing of the hard disk drive is shown in fig2 . the disk device includes : a spindle motor 10 for spinning a magnetic disk 9 ; an arm 12 for supporting a magnetic head 11 used to record information to the magnetic disk 9 and / or to read information recorded on the magnetic disk 9 ; a voice coil motor 13 for aligning the arm 12 ; a circuit 14 for processing information recorded on the magnetic disk 9 and read by the magnetic head 11 and information to be written to the magnetic disk 9 ; a mechanism for supplying the lubricating agent to the device ( in this case , a dust filter 15 ); and the like . an approximately 1 . 0 mg drop of the lubricating agent indicated by chemical formula ( 3 ) and having a number - average molecular weight of 2 , 000 was applied to the dust filter 15 , which was placed at a predetermined position to supply the lubricating agent to the device . the magnetic disks from the embodiments and the comparative examples were installed . the hard disk drive was operated at a speed of approximately 10 , 000 rpm ( rotations per minute ), with a recording density of approximately 20 gbit / inch 2 , a head flying height of approximately 15 nm , and a test environment temperature of approximately 50 degrees centigrade . the heads of the hard disk drive was fixed at a radial position of 38 mm so that they continuously followed a fixed recording track . the number of secondary errors was monitored , and the results are shown in fig3 . as shown in fig3 there were no secondary errors in embodiment 1 and embodiment 2 . thus , secondary errors were reduced and reliability was improved by applying perfluoro polyether lubricating agents having the molecular structures shown in chemical formula ( 1 ) and ( 2 ) to magnetic disks and using a hard disk drive equipped with a mechanism for supplying a lubricating agent shown in chemical formula ( 3 ) with a number - average molecular weight of 2 , 000 . with comparative example 1 , however , the number of secondary errors increased over time . as a result , it was found that secondary errors took place and the number increased over time when the same lubricating agent as shown in chemical formula ( 3 ) was applied to a magnetic disk . this hard disk drive was taken apart after it was operated for 465 hours , and ftir measurements were made of the lubricating layer thicknesses on the installed magnetic disks . fig4 shows the changes in lubricating layer thickness before and after the test . for example , the lubricating layer thickness of the magnetic disk from embodiment 1 was initially approximately 1 . 5 nm but increased to approximately 1 . 8 nm after the test . this indicates that the lubricating agent indicated by chemical formula ( 3 ) that was applied to the dust filter 15 adhered to the magnetic disk and increased the thickness . from this result , it can be postulated that the lubricating layer on the magnetic disk consists of approximately 1 . 5 nm of the lubricating agent indicated by the chemical formula ( 1 ) and approximately 0 . 3 nm of the lubricating agent indicated by the chemical formula ( 3 ). in this case , the lubricating agent from the chemical formula ( 1 ) would make up approximately 83 % of the entire lubricating layer . the values shown in fig4 show the proportions of lubricating agents on the magnetic disks before the test . after the test , the lubricating agent proportion was approximately 70 - 90 % compared to before the test for embodiment 1 , embodiment 2 , and comparative example 1 . these results show that the frequency of secondary errors can be reduced by forming the lubricating layer on the magnetic disk ahead of time as a mixture of the lubricating agents shown in chemical formula ( 1 ) and ( 2 ) and the lubricating agent shown in chemical formula ( 3 ) with a number - average molecular weight of 2 , 000 , and by setting the proportion of the mixture to be the same as that of the lubricating layer after the test . a magnetic disk was produced in the same manner as embodiment 2 . an ftir measurement showed that the lubricating layer had a thickness of approximately 1 . 5 nm . a drop of approximately 1 . 0 mg of lubricating agent as shown in chemical formula ( 3 ) with a number - average molecular weight of 1 , 000 was applied to the dust filter 15 , which was placed at a predetermined position in a 3 . 5 inch hard disk drive . in another 3 . 5 inch hard disk drive , a drop of 1 . 0 mg of the lubricating agent with a number - average molecular weight of 1 , 000 was applied to the dust filter 15 placed at a predetermined position . the magnetic disk from embodiment 3 was installed in the hard disk drives . a test was conducted in a manner similar to those for embodiment 1 and 2 . a magnetic disk was created in a manner similar to that used in embodiment 3 . however , a lubricating agent as shown in chemical formula ( 3 ) was used . three types of lubricating agents were used , with number - average molecular weights of 3 , 000 , 4 , 000 , and 6 , 000 , and 1 . 0 mg drops were applied to the dust filters 15 placed at predetermined positions in three hard disk drives , and the disks from the comparative example 2 were installed in these devices . a test was conducted in a manner similar to those for embodiment 1 and 2 . [ 0043 ] fig5 shows test results for the embodiment 3 and the comparative example 2 . these test results show that the frequency of secondary errors increases significantly as the molecular weight of the lubricating agent increases . fig6 shows the results illustrated using the molecular weights of the lubricating agents as a parameter . as fig6 shows , secondary errors are less frequent with lower molecular weights . in particular , almost no secondary errors take place at molecular weights of 2 , 400 and less . since a molecular weight that is too low can impede the function of the lubricating agent , e . g ., because there is too much evaporation , so an average molecular weight of at least approximately 600 is preferable . based on the test results for embodiments 1 , 2 , 3 and comparative examples 1 , 2 , a highly reliable hard disk drive can be achieved by supplying the hard disk drive with a lubricating agent as shown in chemical formula ( 3 ) and with a number - average molecular weights of at least approximately 600 and no more than approximately 2 , 400 and by forming the lubricating layer on the magnetic disks with a lubricating agent as shown in chemical formula ( 1 ) or chemical formula ( 2 ). next , the lubricating layer thickness of the hard disk drives from the embodiment 3 was measured after the test . it was found that the magnetic disk installed in the hard disk drive with the lubricating agent having a number - average molecular weight of 1 , 000 had a layer thickness of approximately 1 . 75 nm . the magnetic disk installed in the hard disk drive with the number - average molecular weight of 2 , 000 had a layer thickness of approximately 1 . 86 nm . as a result , it was determined that the proportions of the lubricating agent shown in chemical formula ( 2 ) were approximately 86 % and 81 % respectively . thus , it is believed that few secondary errors take place in magnetic disks with lubricating layers formed by mixing a lubricating agent from chemical formula ( 1 ) or ( 2 ) with a lubricating agent from chemical formula ( 3 ) with a number - average molecular weight of approximately 600 - 2 , 400 . magnetic disks were made in a manner similar to that of embodiment 2 . however , the lubricating layer thicknesses were set to 1 . 0 , 1 . 2 , 1 . 5 , and 1 . 8 nm . magnetic disks were made in a manner similar to that of embodiment 2 . however , the lubricating layer thicknesses were set to 0 . 4 , 0 . 6 , and 0 . 8 nm . two types of 3 . 5 - type hard disk drives were prepared , one in which a 1 . 0 mg drop of lubricating agent as shown in chemical formula ( 3 ) with a number - average molecular weight of 1 , 000 was applied to the dust filter 15 placed at a predetermined position in the device , the other in which a 1 . 0 mg drop of lubricating agent as shown in chemical formula ( 3 ) with a number - average molecular weight of 2 , 000 was applied to the dust filter 15 placed at a predetermined position in the device . the magnetic disks from the embodiment 4 and the comparative example 3 were installed in these hard disk drives . the hard disk drive was operated at a speed of approximately 10 , 000 rpm , with a recording density of approximately 20 gbit / inch 2 , a head flying height of approximately 15 nm , and a test environment temperature of approximately 50 degrees centigrade . a test was performed 500 hours and the numbers of secondary errors were compared . also , the lubricating layer thicknesses before and after the test were compared . [ 0050 ] fig7 shows lubricating layer thickness comparisons from before and after the test . fig8 shows the relationship between the proportion of the lubricating agent shown in chemical formula ( 2 ) in the lubricating layer after the test and the number of secondary errors . [ 0051 ] fig7 shows that the lubricating layer thicknesses increased after the test . the thicknesses were not dependent on the initial lubricating layer thickness and were about 1 . 8 nm . the samples with lower initial layer thicknesses had smaller proportions of the lubricating agent from chemical formula ( 2 ). also , fig8 shows that there were no secondary errors when the proportion of the chemical formula ( 2 ) was approximately 50 % or less , i . e ., the proportion of the lubricating agent from the chemical formula ( 3 ) was approximately 50 % or more . in other words , it was found that there were no secondary errors if the proportion of the lubricating agent from the chemical formula ( 3 ) was less than the proportion of the lubricating agent from the chemical formula ( 2 ). based on these results , a highly reliable hard disk drive with no secondary errors can be achieved with a lubricating layer containing a lubricating agent shown in chemical formula ( 1 ) or chemical formula ( 2 ) and a lubricating agent shown in chemical formula ( 3 ), where the average molecular weight is at least approximately 600 and no more than approximately 2 , 400 and the proportion of the lubricating agent shown in chemical formula ( 3 ) is no more than approximately 50 %. looking at these points from another perspective , this means that secondary errors do not take place if the initial layer thickness is at least approximately 1 . 0 nm . the test results show that the thickness of the lubricating layer from chemical formula ( 3 ) together with the lubricating agent from chemical formula ( 1 ) or ( 2 ) tends to not go over approximately 1 . 8 nm . in other words , applying a lubricating agent from chemical formula ( 1 ) or ( 2 ) at a thickness of more than approximately 1 . 8 nm may prevent the lubricating agent from chemical formula ( 3 ) from being adhered . thus , it would be preferable for the lubricating agent from chemical formula ( 1 ) or ( 2 ) to be approximately 1 . 0 nm - 1 . 8 nm . a magnetic disk was made in a manner similar to that of embodiment 1 . however , a lubricating agent applied to the magnetic disk is formed approximately 70 % from a lubricating agent shown in chemical formula ( 2 ) and approximately 30 % from a lubricating agent shown in chemical formula ( 4 ) with an average molecular weight of 3 , 000 . the lubricating agent layer thickness was approximately 1 . 5 nm . this magnetic disk was installed in a magnetic disk with a mechanism for supplying a lubricating agent with an average molecular weight of 2 , 000 . a following test was performed and secondary errors were studied . [ as a result , after 500 hours of testing , there were 24 errors , thus showing decreased reliability compared to the magnetic disks from the embodiments . thus , it is believed that secondary errors do not take place when chemical formula ( 1 ) or ( 2 ) and chemical formula ( 3 ) with an average molecular weight of approximately 600 - 2 , 400 are combined in the lubricating agent and when the proportion of the lubricating agent from chemical formula ( 1 ) or ( 2 ) is at least approximately 50 %. in the lubricating agents applied to the magnetic disks in the embodiments , the molecular weight of the backbone chain of the lubricating agent shown in chemical formula ( 1 ) or ( 2 ) was 2 , 000 . however , the present invention is not restricted to this molecular weight , and similar advantages can be obtained if the lubricating agent has an average molecular weight in the range of 1 , 500 - 6 , 500 . in general , aggregation in the lubricating layer decreases with higher molecular weights in the lubricating agent , so a high molecular weight of about 3 , 500 - 5 , 500 is believed to be suitable for stable head flight . as indicated by the embodiments , a magnetic disk that uses a mixed lubricating layer combining a lubricating agent as shown in chemical formula ( 1 ) or ( 2 ) with a lubricating agent shown in chemical formula ( 3 ) with an average molecular weight of 600 - 2400 , with the proportion of the lubricating agent shown in chemical formula ( 3 ) being at least 50 %, works well with a hard disk drive with a mechanism for supplying a lubricating agent as shown in chemical formula ( 3 ) with an average molecular weight of 600 - 2 , 400 . the reliability of the resulting hard disk drive is significantly improved . a magnetic disk with an ultrathin - layer protecting layer with a layer thickness of 1 . 0 - 5 . 0 nm according to the present invention provides superior recording / reproducing performance , dust resistance , and wear resistance .